UNITED STATES DEPARTMENT OF COMMERCE • MAURICE H. STANS, Secretary

0. S , NATIONAL. BUREAU OF STANDARDS, • Lewis M. Branscomb, Director

Precision Measurement and Calibration

Selected NBS Papers on

Heat

Defoe C. Ginnings, Editor

A compilation of previously published papers by the staff of the National Bureau of Standards, including selected abstracts by NBS and non-NBS authors. Issued in several volumes, see page IV.

t

NBS Special Publication 300 — Volume 6

CODEN NAT. BUR. STAND. (U.S.), SPEC. PUBL. 300. V. 6, 387 pages, February 1970

Issued February 1970

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. C 13.10: 300/v.6). Price $5.00
NATIONAL BUREAU OF STANDARDS

SEP 8 1970

11+8450

Qcioo

' ,V 5" 7

Abstract

This volume is one of an extended series which brings together

the previously published papers, monographs, abstracts, and bibli- ographies by NBS authors dealing with the precision measurement of

specific physical quantities and the calibration of the related metrology

equipment. The contents have been selected as being useful to the

standards laboratories of the United States in tracing to NBS standards the accuracies of measurement needed for research work, factory

production, or field evaluation.

Volume 6 contains reprints through 1968 covering the following

topics: General Calorimetry and Techniques, Low Temperature

Calorimetry, High Temperature Calorimetry, Reaction Calorimetry,

and Heat Transfer.

Key words: Heat measurements, calorimetric methods,

calorimetric design principles, calorimetric theory, cryoscopic studies, differential thermal analysis, low temperature calorimetry, high temperature calorimetry, reaction

calorimetry, bomb calorimetry, heat transfer.

Library of Congress Catalog Card Number : 68-60042

ii
Foreword

In the 1950's the tremendous increase in industrial activity, particularly

in the missile and satellite fields, led to an unprecedented demand for precision measurement, which, in turn, brought about the establishment of hundreds of new standards laboratories. To aid these laboratories in transmitting

the accuracies of the national standards to the shops of industry, NBS in

1959 gathered together and reprinted a number of technical papers by members of its staff describing methods of precision measurement and the design

and calibration of standards and instruments. These reprints, representing

papers written over a period of several decades, were published as NBS Handbook 77, Precision Measurement and Calibration, in three volumes: Electricity

and Electronics; Heat and Mechanics; Optics, Metrology, and Radiation.

Some of the papers in Handbook 77 are still useful, but new theoretical

knowledge, improved materials, and increasingly complex experimental techniques have so advanced the art and science of measurement that a new compilation has become necessary. The present volume is part of a new reprint collection, designated NBS Special Publication 300, which has been planned to fill this need. Besides previously published papers by the NBS staff, the collection

includes selected abstracts by both NBS and non-NBS authors. It is hoped that

SP 300 will serve both as a textbook and as a reference source for the many

scientists and engineers who fill responsible positions in standards laboratories.

Lewis M. Branscomb, Director.

in
Preface

The general plan for this compilation has been reviewed by the Information Committee

of the National Conference of Standards Laboratories. The plan calls for Special Publication

300 to be published in 12 vol nines having the following titles and editors:

Statistical Concepts and Procedures, H. H. Ku

Frequency and Time, A. H. Morgan

Electricity—Low Frequency, F. L. Hermach and R. F. Dziuba

Electricity—Radio Frequency, A. J. Estin

Heat, D. C. Ginnings

Temperature, J. F. Swindells

Mechanics, R. L. Bloss and Mary J. Orloski

Dimensional Metrology—Length and Angle, H. K. Hammond, III Radiometry and Photometry, H. K. Hammond, III Colorimetry and Image Optics, I. Nimeroff and C. S. McCamy

Spectroehemical Analysis, B. F. Scribner

Ionizing Radiation, E. H. Eisenhower

This division of subject matter has been chosen to assure knowledgeable selection of context rather than to attain uniform size. It is believed, however, that the larger volumes,

of approximately 500 pages, will still be small enough for convenient handling in the laboratory.

The compilation consists primarily of original papers by NBS authors which have been

reprinted by photoreproduction, with occasional updating of graphs or numerical data when

this has appeared desirable. In addition, some important publications by non-NBS authors

that are too long to be included, are represented by abstracts or references; the abstracts

are signed by the individuals who wrote them, unless written by the author.

Each volume has a subject index and author index, and within each volume, contents

are grouped by subtopics to facilitate browsing. Many entries follow the recent Bureau practice of assigning several key words or phrases to each document; these may be collated with

titles in the index. Pagination is continuous within the volume, the page numbers in the original publications also being retained and combined with the volume page numbers, for example

100-10. The index notation 6-133 refers to volume 6, page 133 of this volume. A convenient

list of SI (Systeme International) physical units and a conversion table are to be found inside

the back cover. The publications listed herein for which a price is indicated are available from the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (foreign

postage, one-fourth additional). Many documents in the various NBS nonperiodical series are

also available from the NBS Clearinghouse for Federal Scientific and Technical Information,

Springfield, Va. 22151. Reprints from the NBS Journal of Research or from non-NBS journals

may sometimes be obtained directly from an author.

Suggestions as to the selection of papers which should be included in future editions

will be welcome. Current developments in measurement technology at NBS are covered in

annual seminars held at either the Gaithersburg (Maryland) or the Boulder (Colorado) laboratories. These developments are summarized, along with a running list of publications by NBS

authors, in the monthly NBS Technical News Bulletin.

H. L. Mason,

Office of Measurement Services,

NBS Institute for Basic Standards.

IV
Editor's Note

This volume supplements the papers on calorimetry and heat transfer given

in NBS Handbook 77—Volume II, Heat and Mechanics, published in 1961.

Because of its importance, an earlier paper on bomb calorimetry is repeated in

this volume (5.1). Also, one abstract is given of a paper that is now in preparation (4.3). All the papers in this volume are entirely by NBS authors except two. The emphasis in this volume is on methods and techniques of heat measurements, primarily in calorimetry but also in heat transfer measurements. In the

field of calorimetry, there are discussed methods, design, and errors in calorimetry, and the application of calorimetry to the measurement of a variety of thermodynamic and other properties. A list of "SI" recommended units, and a

table of conversion factors are given inside the back cover.

D. C. Ginnings, Editor. v
Contents

Pago

Foreword hi

Preface iv

Editor's Note v

1. General Calorimetry and Techniques

Paper

1.1. Introduction, Calorimetry of non-reacting systems.

Ginnings, D. C, Chapter in Experimental Thermodynamics, Ed.

J. P. McCullough and D. W. Scott, Vol. 1, Calorimetry of Nonreacting Systems, Chapt. 1, 1-13 (Butterworth & Co., London,

England, 1968).

Key words: Definitions; heat units and constants; methods

of calorimetry; standard reference substances; symbols;

terminology 1

1.2. Principles of calorimetric design.

Ginnings, D. C, West, E. D., Chapter in Experimental Thermodynamics, Ed. J. P. McCullough and D. W. Scott, Vol. 1, Calorimetry of non-reacting systems, Chapt. 4, 85-131 (Butterworth

& Co., London, England, 1968).

Key words: Design principles; heat leak errors; heat transfer;

temperature gradients in calorimeters; tempering of leads 15

1.3. Calorimetry of saturated fluids including determination of enthalpies

of vaporization.

Ginnings, D. C, Stimson, H. F., Chapter in Experimental Thermodynamics, Ed. J. P. McCullough and D. W. Scott, Vol. 1, Calorimetry of Non-reacting Systems, Chapt. 11, 395-420 (Butterworth & Co., London, England, 1968).

Key words: Adiabatic calorimetry; heat capacity; heats of vaporization 62

1.4. Heat capacity of a two-phase system, with applications to vapor

corrections in calorimetry.

Hoge, H. J., J. Res. Nat. Bur. Stand. (U.S.) 36, No. 2, 111-118

(Feb. 1946).

Key words: Heat capacity corrections; heat of fusion cor- rections; two-phase calorimetry; vapor corrections 88

1.5. Heating rate as a test of adiabatic calorimeters and the heat capacity

of a-alumina.

West, E. D., Trans. Faraday Soc. 59, Part 9, 1-4 (Sep. 1963).

Key words: Errors in calorimetry; temperature gradients in

calorimeters 96

1.6. A two-body model for calorimeters with constant temperature

environment.

West, E. D., and Churney, K. L., J. Appl. Physics 39, 4206-4215

(1968).

Key words: Heat leak errors; isoperibol calorimeter, temperature gradients in calorimeters; theory of calorimetry 100

VI
Contents

Paper Page

1.7. Electrical resistances of wires of low temperature coefficient of resistance useful in calorimetry (10°-380°K).

Furukawa, G. T., Reilly, M. L., and Saba, W. G., Rev. Sci. Instr. 35, 113-114 (Jan. 1964).

Key words: Low temperature calorimetry; resistance wires

for low temperatures 110

1.8. Techniques in calorimetry.—I. A noble metal thermocouple for

differential use. West, E. D., Rev. Sci. Instr. 31, 896 (Aug. 1960).

Key words: Differential thermocouple; high temperature

calorimetry 111

1.9. Calorimetric determination of the half-life of polonium.

Ginnings, D. C, Ball, A. F., and Vier, D. T., J. Res. Nat. Bur.

Stand. (U.S.) 50, 75-79 (Feb. 1953).

Key words: Ice calorimeter; radioactive power measurements 112

1.10. Heats of transformation in bismuth oxide by differential thermal

analysis.

Levin, E. M., and McDonald, C. L., J. Res. Nat. Bur. Stand.

(U.S.) 69A (Phys. and Chem.) No. 6, 237-243 (May-June 1965).

Key words: Differential thermal analysis 117

2. Cryoscopic Measurements

2.1. Comparison of cryoscopic determinations of purity of benzene by

thermometric and calorimetric procedures.

Glasgow, A. R., Ross, G. S., Horton, A. T., Enagonio, D., Dixon,

H. D., Saylor, C. P., Furukawa, G. T., Reilly, M. L., and Henning,

J. M. Anal. Chim. Acta 17, 54 (1957).

Keywords: Purity by heat measurements 127

2.2. A cryoscopic study of the solubility of uranium in liquid sodium at 97.8° C.

Douglas, T. B., J. Res. Nat. Bur. Stand. (U.S.) 52, No. 5, 223-226

(May 1954).

Key words: Solubility measurements by calorimetry 153

3. Low Temperature Calorimetry

3.1. Continuously operating He3 refrigerator for producing temperatures

down to %° K.

Ambler, E., and Dove, R. B., Rev. Sci. Instr. 32, No. 6, 737-739

June 1961).

Key words: Low temperature calorimetry; He3 refrigerator 159

3.2. Apparatus for determination of pressure-density-temperature re- lations and specific heats of hydrogen to 350 atmospheres at temperatures above 14° K.

Goodwin, R. D., J. Res. Nat, Bur. Stand. (U.S.) 65C, (Eng.

and Inst.) No. 4, 231-243 (Oct.-Dec. 1961).

Key words: PVT measurements at low temperatures; gas heat

capacities; and densities 162

VII
Contents

Paper Page

3.3. Detection and damping of thermal-acoustic oscillations in lowtemperature measurements.

Ditmars, D. A., and Furukawa, G. T., J. Res. Nat. Bur. Stand.

(U.S.) 69C, (Eng. and Inst.) No. 1, 35-38 (Jan.-Mar. 1965).

Key words: Heat transfer by gas oscillations 175

4. High Temperature Calorimetry

4.1. High temperature drop calorimetry.

Douglas, T. B., and King, E. G., Chapter in Experimental Thermodynamics, Ed. J. P. McCullough and D. W. Scott, Vol. 1, Calorimetry of Non-reacting Systems, Chapt. 8, 293-331 (Butterworth & Co., London, England, 1968).

Key words: Enthalpy measurements at high temperatures;

ice calorimeter; isoperibol calorimeter; furnaces 181

4.2. A calorimetric determination of the enthalpy of graphite from

1200 to 2600° K.

West, E. D., and Ishihara, S., Advances in Thermophysical Properties at Extreme Temperatures and Pressures, Am. Soc. Mech.

Engineers (1965).

Key words: Drop calorimetry; high temperature calorimetry. _ 220

4.3. Dynamic measurements of heat capacity and other thermal

properties of electrical conductors at high temperatures.

Cezairliyan, A., and Beckett, C. W. (Abstract).

Key words: Radiation emittance; electrical resistivity;

heat capacities, pulse calorimetry 226

4.4. The vapor pressure, vapor dimerization, and heat of sublimation of aluminum fluoride, using the entrainment method.

Krause, R. F. Jr., and Douglas, T. B., J. Phys. Chem. 72, No. 2, 475-481 (Feb. 1968).

Key words: Heat of sublimation, vapor pressures at high

temperatures 227

5. Reaction Calorimetry

5.1 . Precise measurement of heat of combustion with a bomb calorimeter.

Jessup, R. S., Nat. Bur. Stand. (U.S.) Monograph 7 (Feb. 1960).

Key words: Techniques in bomb calorimetry 237

5.2. Heat of isomerization of the two butadienes.

Prosen, E. J., Maron, F. W., and Rossini, F. D., J. Res. Nat,

Bur. Stand. (U.S.) 42, No. 3, 269-277 (Mar. 1949).

Key words: Bomb calorimetry 262

5.3. Heats of formation of diborane and pentaborane.

Prosen, E. J., Johnson, W. H., and Pergiel, F. Y., J. Res. Nat,

Bur. Stand. (U.S.) 61, No. 1, 247-250 (Oct, 1958).

Key words: Heats of formation 271

VIII
Contents

Paper Page 5.4. Studies in bomb calorimetry. A new determination of the energy.

of combustion of benzoic acid in terms of electrical units.

Churney, K. L. and Armstrong, G. T., J. Res. Nat. Bur. Stand.

(U.S.) 72A (Phys. and Chem.), No. 5, 453-465 (Sep.-Oct. 1968).

Key words: Errors in bomb calorimetry; techniques in bomb

calorimetry; benzoic acid standard 275

5.5. Constant pressure flame calorimetry with fluorine. II. The heat of formation of oxygen difluoride.

King, R. C, and Armstrong, G. T., J. Res. Nat. Bur. Stand.

(U.S.) 72A (Phys. and Chem.), No. 2, 113-131 (Mar-Apr. 1968).

Key words: Flame calorimetry; flow combustion calorimetry;

fluorine calorimetry 288

6. Heat Transfer

6.1. Heat conduction through insulating supports in very low temperature

equipment.

Mikesell, R. P., and Scott, R. B., J. Res. Nat, Bur. Stand. (U.S.)

57, No. 6, 371-378 (Dec, 1956).

Key words: Low temperature insulation 309

6.2. Thermal conductivity of gases, I. The coaxial cylinder cell. Guildner, L. A., J. Res. Nat, Bur. Stand. (U.S.) 66A, No. 4, 333-340 (Jul -Aug. 1962).

Key words: Gas thermal conductivity 317

6.3. A radial-flow apparatus for determining the thermal conductivity of

loose-fill insulations to high temperatures.

Flynn, D. R., J. Res. Nat, Bur. Stand. (U.S.) 67C (Eng. and

Instr.), No. 2, 129-137 (Apr.-June 1963).

Key words: High temperature thermal conductivities 325

6.4. Measurements of the thermal conductivity and electrical resistivity of platinum from 100 to 900 °C.

Flynn D. R., and O'Hagan, M. E., J. Res. Nat, Bur. Stand. (U.S.)

71C, (Engr. and Instr.) No. 4, 255-278 (Oct.-Dec. 1968).

Key words: High temperature thermal conductivity and electrical resistivity 334

6.5. Emissivities of metallic surfaces at 76 °K.

Fulk, M. M., and Reynolds, M. M., J. Appl. Phys. 28, No. 12,

1464-1467 (Dec. 1957).

Key words: Radiation emissivity measurements.. 358

6.6. An apparatus for measurement of thermal conductivities for solids at low temperatures.

Powell, R. L., Rogers, W. M. and Coffin, D. O., J. Res. Nat, Bur.

Stand. (U.S.) 59, No. 5, 349-355 (Nov. 1957).

Key words: Low temperature thermal conductivities 362

Author index 372

Subject index 369

SI physical units (inside the back cover).

IX

1. General Calorimetry and

Techniques

Paper Page

1.1. Introduction, Calorimetry of non-reacting systems.

Ginnings, D. C, Chapter in Experimental Thermodynamics, Ed.

J. P. McCullough and D. W. Scott, Vol. 1, Calorimetry of Nonreacting Systems, Chapt. 1, 1-13 (Butterworth & Co., London,

England, 1968).

Key words: Definitions; heat units and constants; methods

of calorimetry; standard reference substances; symbols;

terminology 1

1.2. Principles of calorimetric design.

Ginnings, D. C, West, E. D., Chapter in Experimental Thermodynamics, Ed. J. P. McCullough and D. W. Scott, Vol. 1, Calorimetry of non-reacting systems, Chapt. 4, 85-131 (Butterworth

& Co., London, England, 1968).

Key words: Design principles; heat leak errors; heat transfer;

temperature gradients in calorimeters; tempering of leads 15

1.3. Calorimetry of saturated fluids including determination of enthalpies

of vaporization.

Ginnings, D. C, Stimson, H. F., Chapter in Experimental Thermodynamics, Ed. J. P. McCullough and D. W. Scott, Vol. 1, Calorimetry of Non-reacting Systems, Chapt. 11, 395-420 (Butterworth & Co., London, England, 1968).

Key words: Adiabatic calorimetry; heat capacity; heats of vaporization 62

1.4. Heat capacity of a two-phase system, with applications to vapor

corrections in calorimetry.

Hoge, H. J., J. Kes. Nat. Bur. Stand. (U.S. 36, No. 2, 111-118

(Feb. 1946).

Key words: Heat capacity corrections; heat of fusion corrections; two-phase calorimetry; vapor corrections 88

1.5. Heating rate as a test of adiabatic calorimeters and the heat capacity

of a-alumina.

West, E. D., Trans. Faraday Soc. 59, Part 9, 1-4 (Sep. 1963).

Key words: Errors in calorimetry; temperature gradients in

calorimeters 96

1.6. A two-body model for calorimeters with constant temperature en- vironment.

West, E. D., and Churney, K. L., J. Appl. Physics 39, 4206-4215

(1968).

Key words: Heat leak errors; isoperibol calorimeter; temperature gradients in calorimeters; theory of calorimetry 100

XL
1. General Calorimetry and

Techniques—Continued

Paper Page

1.7. Electrical resistances of wires of low temperature coefficient of re- sistance useful in calorimetry (10°-380°K).

Furukawa, G. T., Reilly, M. L., and Saba, W. G., Rev. Sci. Instr. 35, 113-114 (Jan. 1964).

Key words: Low temperature calorimetry; resistance wires

for low temperatures 110

1.8. Techniques in calorimetry. I. A noble metal thermocouple for dif- ferential use. West, E. D., Rev. Sci. Instr. 31, 896 (Aug. 1960).

Key words: Differential thermocouple; high temperature

calorimetry 111

1.9. Calorimetric determination of the half-life of polonium.

Ginnings, D. C, Ball, A. F., and Vier, D. T., J. Res. Nat, Bur.

Stand. (U.S.) 50, 75-79 (Feb. 1953).

Key words: Ice calorimeter; radioactive power measurements. 112

1.10. Heats of transformation in bismuth oxide by differential thermal

analysis.

Levin, E. M., and McDonald, C. L., J. Res. Nat, Bur. Stand.

(U.S.) 69A (Phys. and Chem.) No. 6, 237-243 (May-June 1965).

Key words: Differential thermal analysis 117

XII
Reprinted from

Experimental Thermodynamics

Volume I

Calorimetry of Non-reacting Systems

Editors: John P. McCullough and Donald W. Scott

Chapter 1. Introduction

Defoe C. Ginning

s

National Bureau of Standards

INTERNATIONAL UNION OF PURE AND APPLIED

CHEMISTRY

1968

BUTTERWORTHS

LONDON

l-I
CHAPTER 1

Introduction

Defoe C. Ginnings

National Bureau of Standards, Washington, D.C., U.S.A.

Contents

I. General Principles and Terminology 1 II. Definitions and Symbols .. 4

III. Heat Units and Constants ..7

IV. Standard Reference Substances .. 8

V. Choice of Calorimetric Method .. 9

VI. Summary ..13

VII. Bibliography and References ..13

I. General Principles and Terminology

The word calorimeter is derived from the Latin word for heat and the Greek

word for measure. A calorimeter is accepted today to mean an instrument

to measure the heat involved in a known change in state of a material.

This can involve a change in phase, temperature, pressure, volume, chemical composition, or any other property of the material which is associated

with the change in heat. Thus, it is possible that a calorimeter may really

be used to measure several quantities besides heat. Ordinarily, however,

in non-reacting systems, only one or two other quantities are significant.

For example, in measuring the heat capacity of a solid at moderate temperatures and pressures, the temperature change in the solid is usually the

only significant quantity, although the volume of the solid and the pressure on it have some slight effect. A calorimeter can measure the heat involved either directly by comparison

with a known electrical energy or indirectly by comparison with materials

with known properties. Direct measurement usually involves the addition

of a known amount of electrical energy in the form of heat, because with

modern techniques, electrical energy can be measured more accurately

and conveniently than other forms of energy. Frequently, one can avoid

the use of electrical energy measurements by utilizing some thermal property

which has already been measured electrically. An example of this is the

"calibration" of a calorimeter, with a "standard" material such as aluminum

oxide (sapphire), in heat capacity measurements. Whether direct or in- direct measurements of heat are used, the heat involved in the change in

state usually includes some heat (called heat leak) which is due to the nonideality of the calorimeter and its application. This heat leak is usually

significant for accurate heat measurements. The importance of heat leak

2-1
in accurate calorimetry was pointed out in 1928 by W. P. White in his book The Modern Calorimeter2®. He says "There is a difference of opinion

as to whether thermal leakage is necessarily the chief source of error in calorimetry, but it is undoubtedly responsible for most of the experimental

features and devices in accurate work". With increased emphasis on accuracy

this is more true today than it was in 1928!

The term calorimeter is commonly used with two different meanings. In the

broad sense, it is used to describe an entire calorimetric apparatus. Although

this meaning is very useful in a general description, it is more useful in much of this book to limit it to a particular part of the calorimetric apparatus. Specifically, when the word calorimeter is used in this limited sense,

it is defined as that part of the apparatus in which the change in energy is accounted for. Sometimes, such terms as calorimeter proper and calorimeter

vessel have been used to have the above meaning.

The calorimeter as defined above in the limited sense can consist of either

few or many parts, depending on the type of calorimeter, accuracy desired,

and many other factors. The exact geometric location of the boundary

between the calorimeter (used in this limited sense) and its surroundings

usually has little significance because of the method of using the calorimeter,

as described later in this book.

Calorimeters may be classified in several ways. One method of classification

is according to which physical variables are kept constant. Thus isothermal

calorimeters, as the name implies, are those in which there is ideally no

temperature change during the experiment. The general usage of the term

isothermal here implies constancy of temperature with time of any part of

the calorimeter, rather than the uniformity of temperature over the calori- meter at any one time. Many isothermal calorimeters utilize a phase change

to maintain constancy of temperature. The solid-liquid phase change is used in the ice calorimeter5

, the resulting volume change being used as a measure of either the heat added or removed. The liquid-vapor phase

change also has been used7 ' 18 . Other methods that have been used to keep

constancy of temperature during the experiment include use of electric heating to balance removal of heat and electric cooling (Peltier effect) to balance the addition of heat9 > 14 . Sometimes a heat flow is provided to balance out a heat source. Such a calorimeter may be called a heat flow

isothermal calorimeter or simply a heat flow calorimeter. In a heat flow calori- meter, the heat may be removed either by fluid flow, such as in a flow

calorimeter, or by using heat leak by radiation21

, convection or conduction.

Twin "

conduction''' calorimeters have been used by Calvet in the microcalorimetric study of slow thermal processes. A second class of calorimeters are referred to as adiabatic. An adiabatic

calorimeter is one which ideally has no heat transfer across its boundary.

Strictly speaking, the term adiabatic is used in a vague sense because no

practical calorimeter is truly adiabatic. A calorimeter can be made more

adiabatic by reducing the heat exchange between the calorimeter and its surroundings. This can be done by (i) minimizing the temperature difference

between calorimeter and surroundings, (it) minimizing the heat transfer

coefficient (sometimes called leakage modulus), or (Hi) minimizing the time

for the heat exchange. It is true that common usage implies mainly the

3-2
minimizing of temperature difference when describing an adiabatic calori- meter, even though the other factors may be just as important. There is also a tendency in modern calorimetry to restrict the term adiabatic calorimeter

to one which both changes in temperature and minimizes heat leak

by control of the temperature of the surrounding surface of the shield to the same temperature as the calorimeter. The term adiabatic shield (or jacket)

is used to describe the above shield. Such a restricted definition of adiabatic

calorimeter would not include an ice calorimeter, even though its shield temperature is the same as that of the calorimeter. Possibly the greatest use of the term adiabatic calorimeter is to differentiate it from the calori- meter whose surrounding shield is kept at a constant temperature, rather

than at the calorimeter temperature (See Chapter 6). The latter calori- meter could be named appropriately an isothermal shield calorimeter or iso- thermal jacket calorimeter. Since these names are somewhat cumbersome to use,

this calorimeter has sometimes loosely and erroneously been called iso- thermal calorimeter. As an alternative name for this calorimeter, the term

isoperibol has been suggested by Kubaschewski and Hultgren15 . The use of the term adiabatic calorimeter has been questioned when

electric energy passes through the calorimeter boundary. In this regard,

it should be noted that the basic definition of adiabatic refers to heat, not any other form of energy. The accepted meaning of an adiabatic calori- meter permits measured electric energy to enter the calorimeter and be

transformed to heat, as in a calorimeter heater. By carrying this principle even further, it would be possible in an adiabatic calorimeter to absorb

y-radiation from the surroundings, the resulting temperature change being

a measure of the radiation energy13

. Perhaps the dividing line in the case of

radiation would depend on its frequency; that is, the radiation frequency

must not be in the range produced by the temperatures involved in the

calorimeter and shield. Sometimes, a type of calorimeter is named after the scientist who first used it extensively. Examples are the Bunsen ice calorimeter (Chapter 8), which

is an isothermal calorimeter using the ice-water phase change, the Nernst

calorimeter (Chapter 6), which is the isothermal shield type (isoperibol) used

frequently in combustion calorimetry and in low-temperature calorimetry,

and the Joule twin calorimeter system, which uses two calorimeters differentially to minimize errors due to heat leak. Frequently, the latter calorimeters are called simply twin calorimeters or differential calorimeters. Of historical interest is the Dewar low-temperature calorimeter using evacuation and surfaces with low radiation emittance for insulation. The Calvet calorimeter3 is a twin microcalorimeter characterized by use of a metal block for isothermal surroundings, with evaluation of heat in one

twin either by compensation (Peltier cooling or Joule heating) or by time

integration of the temperature difference between the twins. The Callendar

radiation balance2

, sometimes called Callendar radio balance, consists of twin

microcalorimeters used to measure heats of radioactivity or solar radiation.

Peltier cooling in a thermocouple is used to balance out the unknown heat. The names of several calorimeters describe a characteristic property or function of the calorimeter. A microcalorimeter refers to a calorimeter used to measure small amounts of heat. It is not necessarily small in size 17 although

4-3
in modern microcalorimetry it usually is. Aflow calorimeter is one used with

fluid samples flowing through the calorimeter. Ofhistoric value are the names

continuous or continuous electric calorimeters used to describe early flow calori- meters1

. Flow calorimeters have been used both to measure the thermal

properties of a fluid in terms of electric energy {See Chapter 10) and to measure a steady heat source, by using the known thermal properties of

the fluid. An aneroid calorimeter is usually interpreted as one which depends on

solid conduction rather than liquids for distributing heat. Thus the usual

combustion bomb calorimeter, with its reaction vessel immersed in a stirred liquid bath, is not an aneroid calorimeter. One aneroid calorimeter is the

copper block calorimeter which has been used frequently in the drop method

for measuring enthalpies at high temperatures. Sometimes, a calorimeter

which is used in the drop method is called a receiving calorimeter. The term

radiation calorimeter has sometimes been used to describe an isothermal

calorimeter in which heat radiated to the surroundings is used to balance a

heat evolution in the calorimeter plus a measured electric heat. In the field of chemical reactions such names as combustion, bomb, reaction, flame, and

solution calorimeters are used to describe the various types of reactions

studied15 . The method of mixtures uses a mixing process to measure th thermal

properties of one material in terms of the known thermal properties of another

material. For example, when a known mass of sample at a known temperature is "mixed" with a known mass of water at another known temperature,

the mixture will come to thermal equilibrium at a third known temperature.

By using the known heat capacity of water, the average heat capacity of the

sample over its change in temperature can be calculated. Sometimes the

method of mixtures is considered perhaps loosely to include the case of the

"standard" material changing in phase, rather than temperature, such as

in the ice calorimeter. In this case, the amount of the phase change, and its corresponding heat change, must be known.

As pointed out earlier, a large part of the effort in accurate calorimetry

is usually devoted to either minimizing and/or measuring the heat transfer between the calorimeter and its surroundings. The terminology for the

immediate surroundings varies considerably among different laboratories.

Among the various names for the surroundings are shield, jacket, guard, envelope, thermostat, etc. The reader must depend upon the author of a particular

chapter to define his terms for the calorimeter surroundings. The term shield will be used in this introduction to describe the calorimeter surroundings.

II. Definitions and Symbols

In calorimetry there are a few thermodynamic properties which relate directly to the experimentally measured heat. The simplest property is the internal energy, E, of a system, which depends only on the state of the

system. Thus, the difference in internal energy, AE, between two states

is independent of the "path" the system follows in going from one state to the other. An example of a direct calorimetric measurement of E as a function of

temperature is that of a gas at a constant volume. In this case, because no

5-4
work is done by the gas on its surroundings, the heat input, q, corresponds

directly to the change in internal energy, E, of the gas, so that q = (E2 — E\)

.

Most calorimetry, however, is not carried out with the sample at constant volume. This is especially true with solids and liquid-, f r which this pro- cedure would be very difficult. Most calorimetry is carried out at approximately constant pressure so that the sample does work on the surroundings

and the heat input does not correspond to the change in internal energy E. In this case, the heat measured, q, corresponds to the change in the thermodynamic quantity enthalpy, H, which is defined by H = E + PV, in which

P and V represent the pressure and volume of the sample. In other words, at constant pressure P, q = H2 — H = AH = (E2 — Ei) + P(V2 — V{). The

quantity enthalpy was called heat content (or total heat) in earlier calorimetry.

These older names are sometimes misleading because they describe a quantity

whose change does not always correspond to the heat input. Such a case is the heat input, q, to a system in which the pressure changes so that q =fc AH.

A system with changing pressure is frequently encountered in calorimetric

measurements on liquids having significant vapor pressure (see Chapter 11). If the liquid sample is in equilibrium with its vapor in a calorimeter, the

pressure in the calorimeter will vary with temperature.

The previous discussion covers measurements of heats corresponding

to the three "paths", (i) constant volume, (ii) constant pressure, and (ro) "saturation" pressure (defined as equilibrium vapor pressure). In all these measurements if no transition or phase change is involved, a heat

input q results in a temperature change A J". The ratio qjAT defines the term

average heat capacity of the system over the temperature interval A T. The limit of this ratio as q is made indefinitely small is called the heat capacity,

C, (sometimes true heat capacity or thermal capacity). Thus the dimensions of

heat capacity are (energy) (temperature) -1 and it is an extensive property.

The three types of heat capacity defined by the three "paths" previously

given areCV[= (8E/dT)v], heat capacity at constant volume, Cp[= (d/HdT)p\

heat capacity at constant pressure, and Cs, heat capacity at saturation pressure. The term molal heat capacity (or molar heat capacity) refers to the heat

capacity of one gram-formula-weight of a material, and is an intensive

property.

The term specific (heat or specific heat capacity) is frequently used interchangeably

with heat capacity. Specific heat is generally interpreted as the heat capacity per

unit mass ofthe sample, so that it is an intensive property. From these definitions,

it is seen that the term heat capacity applies to any system, such as a calori- meter with many separate components. When the system is restricted to one mole of a compound, the term molal (or molar) heat capacity is used. In a

strict sense, molal heat capacity is a specific heat, but the term specific heat

is usually limited to other units of mass than one mole, such as one gram,

etc. Although the distinction between the quantities heat capacity and specific

heat is not always sharply defined, there should be no confusion if the authors

give the units of the quantity. In most general discussions, they can be used

interchangeably. In the case of solutions involving two or more components, the terms

partial molal heat capacity and apparent molal heat capacity are used to describe

the behaviour of single components (See Chapter 12). In a similar way,

6-5
partial molal, apparent molal, and relative molal are applied to other thermodynamic properties of solutions. The term water equivalent has been used as the heat capacity of the calori- meter (sometimes called energy equivalent). In modern calorimetry, use of the

term water equivalent has little meaning because heat units are not defined

in terms of the heat capacity of water. The terms heat of vaporization and latent heat of vaporization are both used to describe the heat required to transform unit mass of liquid to vapor, so they have dimensions of (energy) (mass) _1

. The older term latent heat is used

very rarely in modern calorimetry. While in principle the term heat ofvaporization can be applied to any process in which liquid is vaporized, it is generally interpreted to be limited to vaporization at a constant temperature and

pressure. In this case, the term heat of vaporization, &HV, is synonymous

with enthalpy of vaporization. Since most heat of vaporization experiments

correspond to enthalpies of vaporization, it is recommended that the term

enthalpy of vaporization be used if it applies.

The terms heat of fusion and latent heat of fusion are analogous to the case ofvaporization except they apply to the solid-liquid instead of the liquidvapor phase change. Here again, the term latent heat is used rarely in modern calorimetry. The term enthalpy offusion is synonymous with heat of

fusion for a constant-pressure melting. Similarly, the term enthalpy of subli- mation applies to a heat of sublimation at constant pressure. The term entropy, S, applied to calorimetric experiments, is defined simply

by the relation dS = 8qjT, in which dS is the change in entropy in a reversible process and 8q the heat involved at the temperature T. The term free

energy has been used for many years to include the Gibbs energy, defined as H — TS or Helmholtz energy, defined as E — TS. Of these two quantities, the

Gibbs energy has been used more frequently. There has not been international

agreement on symbols for these two quantities. European textbooks have

used the symbol F and the name free energy or Helmholtz energy for the function, E — TS. These books also use the symbol G and names such as Gibbs

function, Gibbs energy, or free enthalpy for the function, H — TS. On the other

hand, in America, the quantity, H — TS, has been represented by the symbol F, and the quantity, E — TS, by the symbol A. As a result of the inter- national confusion on these symbols, I.U.P.A.G. has recommended that the

function, H — TS, be named the Gibbs energy, represented by the symbol G,

and the function E — TS be named the Helmholtz energy, represented by the

symbol A. This notation will be used throughout in this book. A summary

of notation used is given in the Appendix.

It seems appropriate to mention here the terms precision and accuracy

for those who may not realize their difference in usage in modern science. The term precision is used to measure the reproducibility of experiments and

may not be a measure of the accuracy of experiments. The precision may

be so good that this source of error is negligible in comparison with the

systematic error. On the other hand, the term accuracy is used to describe

how close the experimental quantities are to the true quantities. In other

words, systematic errors as well as random errors should be considered in estimating accuracy. In most calorimetric measurements it is believed that

high precision is necessary in order to obtain high accuracy. In giving

7-6
either precision or accuracy, the number given is necessarily statistical, so that it is imperative that the statistical basis be given in order that

the number be meaningful. In early calorimetry, the term average deviation from the mean was used frequently as a measure of precision of a set of experi- ments. This term, defined as the average of differences between each measure- ment and the average for the set, is not nearly so useful and meaningful as the term standard deviation of the mean, which is commonly used now14 as an

indication of the precision of a set of experiments. Standard deviation of the

mean, s, is defined:

s=

/Z(xt - xj*

\J n (n — 1) in which x is the average of the observations, X{, and n is the number of observations. The term standard deviation of the mean should not be confused with

the term standard deviation of an individual experiment, which is defined as \/n times the standard deviation of the mean. Since there has been some

question as to which of the above two meanings the term standard deviation applies to, the term standard error has been suggested to be synonymous with

standard deviation of the mean. Most of the literature uses a as the symbol

for the standard deviation. However, statisticians use the symbol 5 when

derived from a finite number of experiments, so that j—> u when ra—>oo. Probable error has also been used as a measure of precision. Representing an

error which has a 50 per cent chance of being exceeded, the probable error, P, is related to the standard deviation of the mean by P — 0-6745 s, if there are a large number of observations. Another term is the variance which is the square of the standard deviation. This term is rarely used because it is not convenient to compare with the original measurements. The term confidence

limit is used sometimes as a measure of the reproducibility of results. If an infinite number of observations have been made, the relation between

confidence limits and standard deviation of the mean is fixed by the normal

distribution curve. For 50 per cent confidence limit, error = 0-6745 s; for 90 per cent confidence limit, error = 1-64 s; for 95 per cent confidence limit, error = 1-96 s; for 99 per cent confidence limit, error = 2-58 s. A more

complete discussion of assignment of calorimetric uncertainties has been given

previously W.

III. Heat Units and Constants

In early work in calorimetry in which most measurements were made near room temperature, it was convenient to both measure and express the heat

in terms of a unit called the calorie which was defined as the heat required

to raise the temperature of one gram of liquid water one degree C. As

calorimetric measurements became more accurate, it was realized that the

magnitude of the calorie so defined depends on the temperature of the water. Consequently, a variety of "calories" originated, such as the 4°-calorie, the

15°-calorie, the 20°-calorie, the mean (0-100°) calorie, etc. Although the comparative heat measurements could be made with relative

ease, it was recognized very early that it was necessary to determine the

quantity of energy corresponding to a given calorie. The energy corresponding to a specific calorie was called J, the mechanical equivalent of heat10.

8-7
Investigations of this quantity were carried out over most of a century with

either mechanical or electrical sources of energy. With the development of accurate electrical standards and instrumentation, it became possible to measure electrical energy more precisely than heat

could be measured in terms of the heat capacity of water. After this time, the

calorie and the mechanical equivalent of heat had little significance except

as measurements of the heat capacity of water. Out of habit, however, the

calorie continued to be used as a heat unit, so that it became desirable in accurate calorimetry to separate the definition of calorie from the heat capacity of water. As a result, there are two "dry" or defined calories used today11 . In engineering steam tables, the I.T. calorie (International Table calorie)

is used and defined as 4-1868 joules. In the field of calorimetry as applied by

physicists and chemists, if the term calorie is used, it usually refers to the

thermochemical calorie, which is defined as 4*1840 joules. The joule referred to here is by international agreement the absolute joule which was accepted in 1948 and is discussed in Chapter 3. The name mechanical equivalent of heat is now obsolete, because it refers merely to a conversion factor to change from one to another unit of heat. Although the term calorie has lost its original utility, its use has persisted in many fields. No doubt it will be used for a long time, but logically it is destined ultimately for obsolescence along with many other superfluous units.

It should be noted that in a Resolution which was adopted in 1948 by the 9th International General Conference on Weights and Measures16

, the

recommendation on the unit of heat was the joule, and that it was requested

that the results of calorimetric experiments be expressed in joules when

possible. If the calorimetric results are expressed in units other than joules, the unit should be defined in terms of the joule.

IV. Standard Reference Substances

In evaluating the results of calorimetric research, uncertainties in the final results may arise from two sources, namely from errors in the calorimetry

itself (energy, temperature, mass, etc.), or from uncertainties in the purity

and state of the material whose properties are measured. In order to minimize the errors in the calorimetry, it may sometimes be a considerable advantage to check the reliability of the calorimetric measurements with a

"reference" material whose state is reproducible and known. If the thermal

properties of this reference material are known, this check yields evidence on the reliability of the calorimetric measurements. Of course, this requires

that someone must have made accurate measurements on this reference

material. When moderate calorimetric accuracy is adequate, it may not be

difficult to find a reference material whose thermal properties have been

measured with higher accuracy. When high calorimetric accuracy is re- quired, this becomes more difficult because the accuracy of other calorimetric

measurements may not be significantly better. However, even in this case, a

reference material is useful. By having samples of any one material taken from

one source of high purity, one has a means of comparing calorimetric measure- ments made in different laboratories under different experimental conditions. It was with this in mind that in 1949 the Fourth Calorimetry Confer- ence4 recommended three substances to be used as "standard" reference 9-8
materials for heat capacity measurements. These three substances were

benzoic acid, n-heptane, and aluminum oxide (corundum). Benzoic acid

and n-heptane were intended for the moderate to low temperature range, whereas aluminum oxide was intended primarily for the high temperature

range, although it is also useful at lower temperatures.

For calorimetric measurements near room temperature, water has always

been used as a reference material, partly because of its universal availability in a pure state, and partly because of the numerous measurements on its heat capacity. In the range 0-100°C, the specific heat of liquid water is believed to be known to within 0-0 1-0*02 per cent12 . When using standard reference materials, some experimenters regard

their use as a "calibration" of their calorimeters, with the conclusion that when using their calorimeters as a comparison device, the accuracy on the

unknown sample is comparable to the accuracy of the standard reference

materials. The experimenter should be warned against this conclusion.

Although it is true that a comparison method does reduce certain errors, the

degree of reduction depends upon the experimental conditions. The comparison method is no "cure-all" for experimental defects! The comparison

method is most effective in reducing errors when the physical properties

and amount of the material being investigated are identical with those of

the standard reference material. Departure from this ideal results in errors whose magnitudes depend upon the particular calorimetric apparatus. Even

when the material has identical physical properties, there is always the possibility of the variation of the performance of a calorimetric apparatus from

day-to-day.

V. Choice of Calorimetric Method

The first question raised after embarking on a calorimetric project is the

choice of method. There are numerous factors which should be considered

in choosing a calorimetric method. Some of these factors will be discussed now.One of the most important factors to be considered is the accuracy re- quired. The effort required increases exponentially as higher accuracy

is desired. Many calorimetric measurements near room temperature can be

made with 1 per cent accuracy with an ordinary household Dewar flask and very simple instrumentation15 . Measurements to 0-1 per cent accuracy,

if possible, usually require at least one and possibly two or three orders

of magnitude increased effort, depending upon circumstances. Measurements accurate to 0-01 per cent are usually impractical with most calori- meters, although there are special examples near room temperature in which

this accuracy has been approached with great effort12 . At extreme temperatures or other conditions, the difficulties in attaining 1 per cent may be as great as attaining 0-01 per cent near room temperature.

Another important factor related to the accuracy required is whether

to make absolute or relative calorimetric measurements. If the accuracy

required is not as high as the accuracy obtained in published calorimetric

measurements on a certain material, then it may be advantageous to use

this reference material to "calibrate" a less complicated calorimeter. In

this regard, one must keep in mind that this "calibration" usually only

10-9
partially compensates for calorimeter errors, depending upon a number of

factors. If possible, a reference material should be chosen which has thermal

properties similar to those of the material being investigated.

The physical properties of the sample and its thermal property to be

measured usually have considerable influence on the choice of method and

calorimetric design. A flow method may be used with advantage to measure

the heat capacity of a gas which requires large volumes to give the desired mass. The temperature and pressure range involved in the measurements are important, as well as the amount of sample available. If only a few milliliters of solid or liquid sample are available and if a large number of samples are

to be measured, the use of the drop method offers simplicity in changing

samples. The drop method is most useful for deriving heat capacity values if the heat capacity is not changing rapidly with temperature.

If the measurements involve very small heats, it may be advantageous

to use twin calorimeters to minimize errors introduced by uncertainties in heat leak. In microcalorimetry, twin calorimeters are usually used for this reason. In measurements for which the time of experiment is necessarily

very long, it may be necessary to choose a method having small heat leak

(power) uncertainty.

As a practical matter, the choice of method is frequently determined by

available apparatus and personnel. If a minimum of electrical measuring

equipment is available, an isothermal calorimeter (such as the Bunsen ice calorimeter) might be considered because it does not require electrical instrumentation. Choice of a method using a platinum resistance thermometer for temperature measurement might not be possible if an expensive

resistance bridge (or potentiometer) is not available. As a general rule, an adiabatic calorimeter would require more instrumentation (or personnel)

than either an isothermal calorimeter or an isothermal shield calorimeter.

The quality of personnel available may be a determining factor in choice of a method and apparatus. It is of little value to use a very elaborate and complicated apparatus if qualified personnel are not available for its operation.

It seems appropriate here to consider some of the advantages and dis- advantages of various calorimetric methods. There is no "best" method

for a general calorimetric problem. Even for a very specific problem,

there may be no significant over-all advantage of one method over another.

Consider first the isothermal shield calorimeter [isoperibol calorimeter) which has

been used so extensively. Here, the calorimeter may change temperature

(such as in heat capacity experiments) while the shield is kept at a constant temperature. One obvious advantage of this method is the simplicity of the

operation of the shield, controlled either manually or automatically. Another

advantage may be the relative independence from variable thermal contact

in the shield, since it is at constant temperature. On the other side of the

ledger, the corrections for "heat leak" from the calorimeter may be relatively

large in some experiments, with the requirement that the heat leak coefficient (leakage modulus) be both constant and accurately known. In this regard,

it should be pointed out that it is only the uncertainty in the heat leak

correction which affects the results, not the magnitude of the correction.

This is no doubt why in combustion bomb calorimetry, the isothermal shield 11-10
has been used almost universally. The rapid change in the calorimeter

immediately following the combustion has made it very difficult to control

the shield temperature to that of the calorimeter. Even though the actual

heat leak corrections could no doubt be reduced by changing the temperature

of the jacket, the uncertainties in the heat leak might be larger than if the

jacket is kept at a constant temperature. With modern instrumentation

and advanced jacket design this situation may not be the same ! Isothermal

shield calorimeters for measuring heat capacities are still used for accurate measurements in low temperature calorimetry for which heat leak becomes

less important owing to the decrease in radiative heat transfer. The use of

isothermal shield calorimeters at higher temperatures depends upon successfully keeping heat leaks down to a reasonable value. In a very special type

of calorimetric experiment, it is possible to use an isothermal shield at room

temperature and still measure heat capacities at high temperatures with

little heat leak error 19 . However, this is accomplished by making the time of

the experiment so short that the total energy transferred from the sample

(wire) is still small compared to the energy used to heat the wire.

The adiabatic calorimeter has increased in use along with the availability

of modern electronic instrumentation for temperature control and recording.

However, the design of the calorimeter and its auxiliary parts is at least as important as the external instrumentation in obtaining good temperature

control. For example, large thermal "lags" in parts of the apparatus can make it difficult if not impossible to control an adiabatic calorimeter

properly. Also, the calorimeter becomes more difficult to use in going to higher temperatures, because of increased heat leak coefficients. At 500 °C,

it is very difficult to obtain 0-1 per cent accuracy and at higher temperatures

difficulties are much greater. Consequently, most of the heat capacity

measurements in the range above 500 °C have been made by using the "drop'*

method which keeps the heat leak small by allowing unwanted heat transfer

for only a very short time during the drop.

The drop method is an example of the method of mixtures in which the

receiving calorimeter measures the change in heat in the sample between

its initial and final temperatures. The principal application of the drop

method has been in measuring enthalpies at high temperatures. With the

drop method, the initial temperature of the sample (in a furnace) is varied,

but the final temperature is kept essentially constant, usually near room

temperature. This restriction of varying only one temperature places an

important limitation on the application of the drop method. For this method

to be valid requires that the sample be at a thermodynamically reproducible

state at both temperatures. If the sample (or its container) has a solid-solid

transition, it is possible that the transition will not be complete in the time

of drop so that some energy of transition will be "frozen in"6 . Consequently,

whenever the drop method is used with materials having such transitions,

the experimenter must be aware of this possibility of error. Another dis- advantage of the drop method is that it obtains values of heat from differences

in heats which may be quite large by comparison. For example, it may be

necessary to measure over-all heats (relative enthalpies) to 0-01 per cent to obtain 0-1 per cent accuracy on the enthalpy derivative, heat capacity, if this heat capacity changes significantly with temperature. This disadvantage

12-11
is partly overcome in the drop method because the calorimeter is usually

operated in a favorable temperature range (room temperature) so that measurements can be made very precisely. The drop method has an important advantage in its ease of changing from one sample to another.

Sometimes, the drop method has been applied to enthalpy measurements at lower temperatures than the "receiving" calorimeter8

. The principal value

of this is its use when a receiving calorimeter already exists for measure- ments at higher temperatures. The drop method usually finds little application at low temperatures because (z) the heat capacity frequently changes more rapidly than at high temperatures, and (zz) the quantities of heat

are smaller. The isothermal calorimeter has an advantage that its heat capacity does not

affect the results since its temperature does not change. Also the problem

of minimizing uncertainty in heat leak is frequently made easier. In the ice calorimeter, for example, the heat in the inside ideally goes to melting ice and the outer part of the calorimeter is unaffected. In the history of calori- metry, this advantage has been considerable ; however, with modern instru- mentation, it is not so great. Even today, however, the isothermal calorimeter

offers excellent heat leak control without elaborate instrumentation. With

experiments of long duration, this control may be necessary. The isothermal

calorimeter using vaporization (liquid-vapor equilibrium) may provide high

sensitivity. If liquid hydrogen or helium is used, for example, a very small

quantity of heat results in the evolution ofa large volume ofgas to be measured.

This is partly because the heats of vaporization of hydrogen and helium are

relatively low whereas the specific volumes of gas are large.

Recent developments in thermoelectricity have provided calorimetry

with a useful tool with the availability of semi-conductor materials for refrigeration. With available thermocouples, it is now possible to make an

isothermal calorimeter to measure heat quantities without using a change in phase of a material. The heat in a calorimeter can be balanced out with

thermoelectric cooling to provide isothermal conditions, and the thermoelectric device can be calibrated in place with an electric heater. Even before

semi-conductor thermocouples were available, metallic thermocouples were

used in microcalorimetry for heat compensation9 - 14. The use of twin calorimeters may be a real advantage if the necessary control

of heat leak is difficult. In microcalorimetry, in which only very small heats are measured, the use of twin calorimeters minimizes the effect of changes in temperature of the environment. To be effective, the twin calorimeters

should be as nearly alike as possible and located so that they are affected the same by their environment. One disadvantage of the twin calorimeters is the

effort required to build an extra calorimeter and in many cases to prove that the two calorimeters have identical thermal characteristics. Another advantage of twin calorimeters is that differential thermo-elements can be used

to best advantage for measuring the temperature difference between twin

calorimeters. In most calorimetry involving large amounts of heat, twin

calorimeters are not used. Flow calorimeters have been used with both gases and liquids. When used

to measure heat capacities, the flow calorimeter offers an advantage that the heat capacity of the calorimeter is not involved since ideally the

13-12
calorimeter does not change temperature during an experiment. Although the

flow calorimeter was used in early calorimetry on liquids, its principal use

in accurate calorimetry today is with gases. Here, the flow method provides a relatively large volume of sample per experiment, which would be impractical with non-flow calorimeters.

VI. Summary

The principal fundamental physical quantities measured in calorimetry are temperature, energy, and mass. Whereas the first two are covered in Chapters 2 and 3, the techniques for measuring mass are so generally known

or available, that no treatment is given here. In calorimetry it is frequently necessary to measure other quantities such as pressure and volume. Since

measurements of these two quantities are usually secondary in calorimetric

measurements, a discussion of them will be deferred to Volume II, which will cover P-V-T and transport properties.

For the student in calorimetry, a brief bibliography is given. The field of reacting systems has recently been covered14 ' 15 and some of the tech- niques are applicable to non-reacting systems. The specialized field ofmicrocalorimetry is covered in two books in the following bibliography.

VII. Bibliography and References

Bibliography

White, W. P., The Modern Calorimeter, Chemical Catalog Co., New York (1928). Swietoslawski, W., Microcalorimetry, Reinhold, New York (1964). Calvet, E., and H. Prat, Microcalorimetrie, Masson et Cie, Paris (1956). Roth, W. A., and F. Becker, Kalorimetrische Methoden zur Bestimmung chemischer Reaktionswdr- men, F. Vieweg, Braunschweig (1956).

Rossini, F. D. (Ed.), Experimental Thermochemistry, Vol. I, Interscience, New York (1956). Weissberger, A. (Ed.), "Calorimetry" in. Technique of Organic Chemistry—Vol. I. Physical Methods of Organic Chemistry, Chap. X, Interscience, New York (1959). Skinner, H. A. (Ed.), Experimental Thermochemistry, Vol. II, Interscience, London (1962).

References

1 Callendar, H. L., Phil. Trans. Roy. Soc. {London), A199, 55 (1902).

2 Callendar, H. L., Proc. Phys. Soc. {London), 23, 1 (1911).

3 Calvet, E., and H. Prat, Microcalorimetrie, Masson et Cie, Paris (1956).

4 Chem. Eng. News, 27, 2772 (1949).

5 Ginnings, D. C, T. B. Douglas, and A. F. Ball, /. Research Natl. Bur. Standards, 45, 23 (1950).

« Ginnings, D. C, /. Phys. Chem., 67, 1917 (1963).

7 Kraus, C. A., and J. A. Ridderhof, /. Am. Chem. Soc, 56, 79 (1934).

8 Lucks, C. F. and H. W. Deem, Special Publication No. 227, Am. Soc. Testing Materials (1958).

9 Mann, W. B., /. Research Natl. Bir. Standards, 52, 177 (1954).

10 Mueller, E. F., Mech. Eng., 52, 139 (1930). " Mueller, E. F., and F. D. Rossini, Am. J. Phys., 12, 1 (1944).

12 Osborne, N. S., H. F. Stimson, and D. C. Ginnings, J. Research Natl. Bur. Standards, 23, 197 (1939).

1 3 Pruitt, J. S., and S. R. Domen, /. Research Natl. Bur. Standards, 60A, 371 (1962). "Rossini, F. D. (Ed.), Experimental Thermochemistry, Vol. I, pp. 239, 297, Interscience, New

York, (1956).

15 Skinner, H. A. (Ed.), Experimental Thermochemistry, Vol. II, pp. 343, 189, Interscience, London (1962).

i« Stimson, H. F., Am. J. Phys., 2, 617 (1955).

17 Swietoslawski, W., Microcalorimetry, Reinhold, New York (1946).

i» Tong, L. K. J., and W. O. Kenyon, /. Am. Chem. Soc, 67, 1278 (1945).

19 Wallace, D. C, P. H. Sidles, and G. C. Danielson, /. Appl. Phys., 31, 168 (1960).

20 White, W. P., The Modern Calorimeter, p. 17, Chemical Catalog Co., New York (1928).

2 1 Wittig, V. F. E., and W. Schilling, Z. Elektrochem., 65, 70 (1961). 14-13
Experimental Thermodynamics

Volume I

CHAPTER 4

Principles of Galorimetric Design

D. C. Ginnings and E. D. West

National Bureau of Standards, Washington, D.C., U.S.A.

Contents

I. Introduction

II. Chemical, Mechanical, and Electrical Considerations

1 . Chemical

2. Mechanical

3. Electrical A. Thermocouples

B. Calorimeter Heater

C. Heaters for Temperature Control D. Galvanometers and Electronic Amplifiers

III. Heat Flow Considerations

1 . General

2. Heat Transfer by Radiation

3. Heat Transfer by Convection

4. Heat Transfer by Thermal Acoustical Oscillation

5. Heat Transfer by Mechanical Vibration

6. Heat Transfer by Conduction .

.

A. Steady-State Heat Flow

(1) Rod

(2) Wire Carrying Current. . (3) Cylindrical Shell

(4) Radial Heat Flow in a Hollow

(5) Thin Disk with Uniform Heating and Cooling

(6) Tempering of Electrical Leads and Other Conductors

(7) Continuous Tempering

(8) Tempering of Wires Carrying Current

(9) Step Tempering

(10) Tempering of Fluid in a Tube

B. Unsteady-State Heat Flow . . . . .

.

(1) The Principle of Superposition

(2) Transients in One-Dimensional Heat Conduction

IV. Applications to Calorimeter Design

1 . Temperature in a Calorimeter Wall at Constant Heating Rate

2. Uncertainty in Heat Leak Due to Temperature Gradients

3. Methods of Minimizing Heat Leak Due to Temperat

Gradients

4. The Calorimeter Heater Lead Problem

V. References

Cylinder and Sphere

8586

86

87

919194

97

9799

99

100

103

108 108

108

111

111

111 112

112 113

113

113

115

115

116

117 119

121 122

122

124

124

127 130

I. Introduction

The design of calorimetric apparatus involves consideration of many

factors. The first factor is obviously the choice of the calorimetric method, as discussed in Chapter 1. This choice depends upon temperature range, accuracy desired, properties of the sample, amount of heat involved, duration of experiment, available apparatus and personnel, cost of the apparatus,

and many other factors. After the choice of method comes the detailed

* ——

See complete ref. on page 1-1.

15-85
design of the calorimetric apparatus needed. If the scientific literature describes calorimeters suitable for the investigation, it sometimes is possible to obtain constructional details either from the published papers or directly

from the authors. More often, however, either this is impractical or certain

variations in design are needed for the particular investigation. In any case, the construction and operation of a calorimetric apparatus is probably

facilitated if certain fundamentals of design are known. It is the purpose of

this chapter to review some general principles which underlie the design

and operation of accurate calorimeters. For details of design and construction, the reader is referred to the various chapters describing apparatus. To

illustrate some of the principles, simple examples will be given together

with corresponding calculations of significant quantities. In the references at the end of this Chapter are listed some of the handbooks and other sources of values of properties of materials useful in calori- metric design. Such information may be found also in Mechanical Engineers

Handbook, McGraw-Hill Book Co., Inc., New York, 1958 and Handbook of

Chemistry and Physics, Chemical Rubber Publishing Co., Cleveland, Ohio,

published annually.

The specific design of calorimetric apparatus involves mechanical,

chemical, electrical, thermal, and perhaps other properties of construction

materials. Usually, the actual design is a compromise with at least some

of these properties. For example, it may be necessary to sacrifice mechanical

rigidity to obtain low thermal conductance in certain parts, or in selecting the size of the calorimeter heater current leads, it is necessary to compromise

between electrical heat developed in the leads and thermal conductance

of the leads. Some discussion will be given of the mechanical, chemical, and

electrical design factors, but the major part of this chapter will be devoted to consideration of heat flow because it is believed that lack of understanding

of heat flow is the source of most errors in accurate calorimetry.

II. Chemical, Mechanical, and Electrical Considerations

1. Chemical

For most calorimetry at moderate and low temperatures, the problem of

chemical properties of materials is not difficult to solve. In this temperature

range, it is usually possible to select inexpensive metals or alloys which are

sufficiently unreactive either to the sample material or to the environment.

Sometimes the use of noble metals such as platinum and gold is warranted.

Glass is usually considered to be unreactive to most materials in this temperature range, and in earlier calorimetry it was frequently used. However,

its use in modern calorimetry is limited because of its other properties. If good thermal conductance is desired, glass is undesirable because of its low

thermal conductivity. If poor thermal conductance is desired, it frequently

turns out that for mechanical reasons it is necessary to use a greater cross sectional area than would be required with metal, so there may be no

significant gain. For example, in a glass tube, it might be necessary to use a

wall thickness many times that required for a metal tube. Although the use of metals for most calorimetry is most convenient, at higher temperatures

16-86
they become more reactive, both with the sample and with air when they

are in contact with it. Although there has been some progress in the development of materials inert at high temperatures, the chemical problem here

still may be the major one. Further discussion of the chemical problem will not be given here, partly because it is not difficult in most calorimetry, and

partly because any problems involved are usually characteristic of the particular experiment.

2. Mechanical

In all calorimetric apparatus, it is necessary to contain the sample, and

to position and support the various parts. The mechanical design is necessarily a compromise between mechanical and other considerations, such as thermal and chemical. First of all, in order to contain the sample, the calorimeter must be strong enough to withstand any pressure and temperature encountered. The term "strong" here means not only avoiding rupture,

but also keeping down to a reasonable tolerance any change in dimension

due to pressure In accurate calorimetry, for example, if there is any signi- ficant change in dimension due to either pressure or temperature, the

dimensions should be a reproducible function of these variables. An example

of irreproducibility is exceeding the mechanical elastic limit of the material.

The elastic limit (which has values essentially the same as the proportional

limit) of a material may be defined as the greatest stress to which a material

may be subjected without developing a permanent set. The calculation of

the pressure effect will be given for simple cases. If the mechanical properties of the calorimeter are likely to be a serious

limitation, the shape of the calorimeter should be designed to minimize

strain. In this respect, a spherical shape might be ideal mechanically and

also offers the smallest area for heat transfer to the outside. Since a sphere

is not always convenient to fabricate, a cylindrical section having hemispherical ends frequently is used. In both cases the use of supporting internal

struts gives added strength with relatively little additional material. The

internal struts can serve also to distribute heat to reduce temperature

gradients. In considering the strengths of calorimeter sample containers, one must

consider the effect of both external and internal pressure. Usually, the external pressure is limited to atmospheric pressure so that the sample

container does not have to withstand more than one atmosphere differential pressure. Therefore, a small amount ofmetal can be used in order to minimize

the heat capacity of the empty calorimeter. This is especially important at low temperatures where the heat capacity of the metal sample container

may be a large fraction of the total. The reader is referred to Chapters 5, 6,

7, and 13 for details of low-temperature sample containers, including those

designed for one atmosphere external pressure. For sample containers with internal pressure, calculations are now given

for the sphere and cylinder, which approximate most cases. Assume that the calorimeter is a spherical shell having a diameter D and thickness w, and containing an internal pressure P. The force operating to stretch the wall is P(ttD2 /4) and is exerted on a wall cross-sectional area (vDw), so

17-87
that the stress on the material (force/area) is PD/4w. If P = 100 lb/in2

, D = 4 in, and w — 0-02 in, the stress is then 5000 lb/in2 . If the material

is cold-worked copper, we find in tables of mechanical propertiesf that the

"proportional limit" of this copper at room temperature is about 15 000

lb/in2

. This means that there is a safety factor on pressure of about three

before the pressure will cause permanent set. In actual design, this safety

factor seems too small, so that either the material or some other factor probably would be changed. Now calculate the change in the diameter D

due to the pressure P. The material property which determines this change

is called modulus of elasticity. The fractional increase in length of a specimen

under tension is the ratio of stress to modulus of elasticity. For the copper, with a modulus of elasticity of about 16 x 106 lb/in2

, the pressure of 100

lb/in2

, which results in a stress of 5000 lb/in2

, increases the diameter D by

[(5 x 10*)/(16 X 106

)] D = 0-00125 in. Using a length (/) of the same material in a cylinder of the same thickness

(w) gives a force (PDl) operating on an area of 2wl, so that the stress is PDl\2wl = PD\2w = 10 000 lb/in2 . The increase in diameter is then

[104/(16 x 106

)] 4 = 0-0025 in. There is another way in which modulus of elasticity enters into calori- metric design, namely in calculating stress in a material caused by increase

in temperature in the material which is not allowed to expand significantly in one dimension. Assume in a simplified example that a specimen disk is held flat between two parallel fixed plates so that there is perfect contact

at temperature T±. Now heat the specimen to a temperature T%. If the disk were free to expand, its thickness would increase by the factor a{T^ — T\)

in which a is the coefficient of linear thermal expansion. Since we keep the

disk from expanding axially, a stress is developed which can be calculated

from the modulus of elasticity by using the relation, stress = [a(T2 — 7*i)] X [Modulus of Elas.]. Consider as an example a silver disk heated from 0*

to 200°C. Taking an average value of a = 18 x 10~6 and modulus of

elasticity = 107 lb/in2

, one obtains stress = 36 000 lb/in2

. However, this figure is considerably greater than the elastic limit of silver which is about

1000 lb/in2

, so that actually the silver would flow radially. When the specimen

is cooled to room temperature, it will have a permanent set, its thickness

being less than its original thickness. If the specimen is steel with an average

coefficient of expansion of 10_5/°C, a modulus of elasticity of 3 x 107 lb/in2

, and an elastic limit of 40 000 lb/in2

, then the calculated stress is 60 000 lb/in 2

, which is also above the elastic limit, so that there would be some permanent

set.One application of the above principles to calorimetry is in the use of

gasket materials for sealing two parts together, as in a "union". The above

examples indicate that if a union is to be used over a wide temperature

range, two precautions should be considered. First, the union body material

might be made of a material having about the same coefficient of expansion,

thereby minimizing the change in stress due to differential expansion.

Second, the union might be designed to provide some flexure, so that large

t English units are used here because of their general use in engineering tables of properties of materials. 18-88
changes in stress in the gasket are avoided. This spring quality could be

obtained either in a separate spring, or possibly in the configuration of the

union body, if a material with high elastic limit is used. The effect of thermal expansion in calorimetry over a wide temperature

range is important also in choosing materials which are in contact, such as in soldered joints. As a general rule, the materials should be chosen so that

the change in termperature results in a force tending to tighten the joint

(compression) rather than loosen it (tension). For example, in a low temperature calorimeter, if there is a differential thermal expansion in a joint,

the outer part preferably should have the higher coefficient of thermal

expansion in the low temperature range. A universal mechanical problem in calorimetry is the use of soldered

joints, both in giving a "tight" joint and in providing strength. A variety of

available solders17 provides a melting temperature over a wide range of

temperature. This is frequently useful in assembly of various calorimetric

components. However, the lower melting solders are not generally as strong

as the higher melting solders, especially at temperatures approaching

melting. For example, in the design and preliminary testing of the 0-100°

calorimeter described in Chapter 11, it was found that a lead-tin soldered

joint holding the two hemispherical shells together failed at 100°C. When

the lead-tin solder was replaced with a tin-antimony solder having both

higher melting point and better mechanical properties at 100°C, the

soldered joint was successful. Soldered joints should be subjected to the least possible stress and should depend as little as possible on the strength of the

solder, which is usually considerably less than the strength of the metals

being joined. In practice this means avoiding thick layers. The design of

soldered joints is especially important in calorimeters used over large

temperature ranges where differential expansion may cause large stresses in the joints. In calorimeters operating over a large temperature range, account should

be taken of the change in mechanical properties with temperature. Most

materials are weaker at high temperatures so that their properties at the

highest operational temperature must be used in the design. In the discussion

earlier on modulus of elasticity, the modulus under tension or compression was

used. Under special circumstances, the modulus in shear might be more

appropriate.

A warning should be given on the use of certain "cast" metals or alloys

if vacuum tightness is required. As an extreme example, when silver is cast in an air atmosphere, considerable oxygen in solution is expelled on solidi- fication, thereby giving a porous structure. In this case a vacuum casting

should be used to give a non-porous solid. The presence of oxygen in copper

may lead to less desirable mechanical properties. For example, ordinary

copper work hardens much faster than oxygen-free copper, which is now

available commercially.

The design of the calorimeter supports, together with the choice of

materials, is always a compromise among various requirements, which

include mechanical, chemical, and heat flow. Discussion of the heat flow

problems will be given later in this chapter. The shape of the mechanical

support is a large factor in obtaining maximum support strength for a given

19-89
thermal conductance. The optimum shape is determined partly by the

direction in which strength is needed. For example, with certain calorimeters

which have no connecting tubes to the outside, vertical strength may be

needed primarily for suspending the calorimeter, with little strength

needed horizontally. In this circumstance it might be possible to use one

or more small wires or "threads" under tension. If more horizontal strength

is needed, the mechanical supports may consist of thin "struts" which may

be tubes. For a given cross section of material (given thermal conductance)

a tube gives greater mechanical rigidity than a rod. In one apparatus

described in Chapter 1 1 the shield was suspended by three short thin mica

strips spaced 120° apart so that they could be considered as narrow sections of a large "mica tube". This arrangement gave considerable strength

horizontally, as well as vertically with the mica under tension. In general,

if a minimum of material is desired, it is more stable under tension than

compression. Also, because the deflection of "beams" is usually directly

proportional to the cube of the length of the beam, it is better to use a short

support piece, and keep to a minimum its dimension in a direction perpendicular to the force. In choosing materials for mechanical supports, the thermal diffusivity

of the material, together with dimensions, determines the time lag in the material as its ends are heated. Because ceramic materials usually have

lower thermal diffusivities than metals, their time lags should be considered

before using them in calorimeter design.

The above brief consideration of mechanical design is intended only to point out a few of the simple problems encountered in calorimetry. For

detailed computations, the reader is referred to texts and handbooks cover- ing the strength of materials16 and to the various chapters in this book for

specific calorimetric applications.

A question which arises repeatedly in calorimetric design is the thermal

conduction between two surfaces in mechanical contact. The mechanism of

heat transfer is by gas conduction, radiation, and by direct conduction at

solid-solid contacts. Under pressure, the solid-solid contacts increase in number and in area and it is possible to gain considerably over gas conduction and radiation. The small amount of information available is for metallic

surfaces. For rather rough laminated steel surfaces at temperatures slightly above room temperature, aluminiun foil placed between surfaces increases the

thermal contact conductance in air by a factor of about two with moderate

contact pressures. An organic material in the space usually improves con- duction considerably. For solid steel blocks, the largest contact conduction is for lapped surfaces. They show only slight dependence on contact pressure

in air. Rougher surfaces show increased conduction by about a factor of

two for pressures of 300 lb/in2 (ref. 3). Data for smooth aluminum alloys, steel, and bronze show considerable

variation for different assemblies20. The conduction of aluminum joints is considerably better than steel at each pressure measured. Furthermore,

copper plating one of the surfaces improves the conduction of the joints.

Oil in the joint increases conduction, especially at low pressure, owing to the higher conductivity of oil compared to that of air.

20-90
For polished gold, silver and copper surfaces in vacuum at 25 °C, the conduction of a metallic joint is negligible at zero contact pressure and

increases linearly for copper to 0-3 W cm-2 deg-1 at 4 kg/cm2

. For gold and

silver, the conductance is 0'22 W cm"2 deg -1 at a constant pressure of 1 kg/cm2

, increasing to 0-4 at 4 kg/cm2 (ref. 11). Qualitatively, conductance through metallic contact is increased by using

softer metallic surfaces, smoother surfaces, and higher pressure. If such joints

must be used, a large number of bolts or screws should be used to obtain a high pressure. If thermal conductance is needed in a contact in a vacuum,

precaution should be taken either to apply sufficient force or to use a softer material at the contact. Some measurements of thermal contact resistance

in vacuum at low temperatures have been made2 on a few metals and nonmetals.

Most of the factors involving the electrical system in the calorimetric

apparatus also involve heat flow, so that both must be considered in the

design. Consider first the sizes of electrical leads of thermocouples. Of

course, the minimum size is that which can be handled safely during assembly

and disassembly. In deciding how much larger to make the leads, one must

compromise between electrical resistance and thermal conductance. If heat

flow is important, one uses the smallest thermocouple wire compatible with

the two requirements of strength for convenient handling and of tolerable

resistance of the thermocouple circuit. This point depends upon the electrical resistance of the circuit external to the thermocouple, which frequently

consists of a galvanometer and potentiometer. Consider the schematic circuit in Figure 1, in which E\ and R\ represent the e.m.f. and resistance of the

thermocouple and E2 and R2 represent the potentiometer bucking e.m.f. and the total resistance of the external circuit, considered to be a potentiometer and a galvanometer, G, for the simple case. At ideal balance, the

current, /, is zero and E2 — Ei- The actual balance occurs at some finite current, Ii, representing the smallest current which the galvanometer can

detect. In this actual case, this error signal is (E2 — E\) = h {R\ + ^2)-

If R2 ^> Ri> then an increase in Ri, the thermocouple resistance, does not

3. Electrical

A. Thermocouples

Internal External

circuit circuit

Figure 1 . Thermocouple measuring circuit.

21-91
change significantly the error signal I\ (Ri + R2). However, if Ri > R2, this error signal increases in proportion to the resistance R\. With a given

measuring circuit, the resistance of the thermocouples may determine the

practical limit of the number of thermocouples which can be used in series (thermopile) to increase the sensitivity. If R\ |> R2 , then increasing the

number of thermocouples increases the resistance (Ri + ^2) in proportion

to the increase in E\ so that the relative value of the error signal (precision of

measurement) to the total e.m.f. (£1) remains the same. A typical resistance of a galvanometer-potentiometer circuit is perhaps

50 Q., so that as a practical matter the resistance of any combination of

thermocouples used should not be much larger than this resistance. Although

higher resistance galvanometers can be used with thermocouple circuits having higher resistances, it is usually more practical to use electronic

amplifiers because of their flexibility of input impedance. Even with lowresistance circuits, the use of electronic amplifiers has increased greatly in recent years. A comparison of the galvanometer with the electronic amplifier

will be given later in this section (II-3-D). In designing a temperature measuring system involving thermocouples,

it is necessary to decide on thermocouple materials. Since this decision

depends greatly upon the temperature range involved, only a brief discussion

will be given here. In Chapter 2, the general subject of thermocouples has

already been covered. In most accurate calorimetry, thermocouples have

their main utility in measuring temperature differences in different parts

of the apparatus. For this purpose, frequently it is convenient to use thermocouple materials having high thermoelectric powers, low thermal conductivities, and good mechanical properties. Reference should be made to the

various chapters for the authors' choices of materials. In the use of thermocouples in accurate calorimetry, it is necessary that the

thermocouple e.m.f. be a true measure of difference in temperature between

the components to which the principal and reference junctions of the thermocouple are attached. In order that this be true, several precautions should

be taken. First, the thermocouple should be used under conditions which

do not invalidate its calibration. The calibration of the thermocouple

cannot be expected to apply to a thermocouple which has been contaminated

after its calibration. For example, it is possible that a platinum-rhodium

thermocouple becomes contaminated in use at high temperatures if it is in contact with certain materials in a chemically reducing atmosphere. Sometimes it is possible to calibrate thermocouples under the exact conditions of

the experiment in which they are used. For example, in the calorimeters

described in Chapter 11, thermocouples are used to measure the temperature

difference between the calorimeter and a "reference block" containing

platinum resistance thermometers. The thermoelectric coefficients of these thermocouples can be determined in place at any time during the experiments

by comparing with the platinum resistance thermometer. This "in place"

calibration also has the advantage that certain thermocouple errors are

also accounted for. Another example of "in place" calibration of thermocouples is with differential thermocouples between the calorimeter and the

surrounding shield. In this use, the calibration of the e.m.f. in terms of

temperature difference is unnecessary. Instead, the e.m.f. is calibrated

22-92
directly in terms of heat flow by observing the resultant change in temperature ofthe calorimeter whose heat capacity is known with adequate accuracy. A second precaution in the use of thermocouples concerns spurious

e.m.f.s due, for example, to inhomogeneities in the thermocouple material.

If an inhomogeneity is located in a region of temperature gradient in the

thermocouple wire, there may be a spurious e.m.f. which will be measured

along with the "true" e.m.f. of the thermocouple. Frequently, the thermocouple wires are tested for inhomogeneities before their use by moving a

sharp temperature gradient along the wire and observing any resulting

e.m.f. If the thermocouples are used only to measure small temperature

differences, most of the effect of the inhomogeneities can be avoided by

keeping the thermocouple material in relatively isothermal regions and using

pure metal electrical leads which are relatively free from inhomogeneities.

An example of this technique is described in Chapter 1 1 where many thermocouples measure temperatures relative to a "reference block" whose temperature is very close to that of the calorimeter.

A third precaution in using thermocouples is to make certain that their junctions are really at the temperatures of the components whose temperatures they measure. This problem usually is not serious if the thermojunction

is soldered or welded to the component. However, it is not always possible or convenient to make this attachment. Frequently, it is necessary to insulate electrically the thermojunction from the component, so that thermocouples can be connected in series either for differential measurements, for increasing sensitivity, or for integration of temperature gradients.

Electrical insulation of the thermoj unction usually incurs some thermal

insulation, so that if there is a heat flow from the thermojunction, its temperature necessarily will be different from the temperature of the component to which it is attached. Much of the heat flow from the thermojunction is along wires connected to it. It may be necessary, therefore, in accurate calorimetry to make sure that there is no significant heat flow along

these wires. This can be accomplished by a technique sometimes called "tempering" of the thermocouple wires. Tempering of these wires may be

defined as the process of bringing them to the temperature of the component

before the wires reach the thermojunction. The tempering of wires will be

discussed later in this chapter. A common method of tempering wires at moderate to low temperatures is to fasten the insulated wires in thermal

contact with the component by using an organic cementing material to attach them, thereby providing both thermal contact and electrical insulation. At somewhat higher temperatures5 in the presence of gas, bare wires

may be placed in ceramic tubes or between strips of mica to be held in contact with the component.

Sometimes the choice of thermocouple material depends not only on

temperature range but also on the environment. For example, at high

temperatures, some materials should not be used in oxidizing atmospheres

whereas other materials should not be used in reducing atmospheres. For an appropriate discussion of thermocouples, the readers are referred to books4 covering the subject. In addition to the requirement in accurate calorimetry that the thermocouple e.m.f. be a true measure of temperature difference, there is the prob23-93
lem of proper location of the junctions to evaluate properly the effective temperatures so that proper accounting can be made for both heat leak and

temperature change, even if temperature gradients exist. Further discussion

will be given later in this chapter on the problem of location of thermocouples.

B. Calorimeter Heater

The design of the calorimeter heater and its leads is important to accurate

calorimetry in two different ways. The first way relates to the location of

the potential leads in order to evaluate that part of the electrical heat in the leads which belongs to the calorimeter. Although this problem is dis- cussed later in Section IV, it may be mentioned here that the calorimeter

heater resistance should be large compared to its lead resistance, and that

the thermal contacts between the ends of the heater current lead segment and

the calorimeter and shield should be either good or equal and preferably

both.

The second way design is important as it relates to changes in resistance

in the heater and leads due to their temperature change. These changes in resistance make the accurate measurement of power more difficult. In the

calorimeter heater, the change in temperature may be considered in two

parts, the first due to the initial thermal transient as the heater wire attains

its normal temperature excess, and the second due to the slower change in temperature as the calorimeter temperature increases f. When the current is first switched to the heater, its temperature is very near that of the calori- meter. Before it can deliver power to the calorimeter, its temperature must

rise to provide a thermal head for heat flow. Since the heater itself has some heat capacity, usually an appreciable time is required for the initial rise to take place. In general, the resistance of the heater wire will increase

during this time and the effect on the d.c. power measurements must be

considered.

The thermal transient may be considered a simple exponential with time

constant (time for 63 per cent of change) equal to the product of the heat

capacity of the heater and the thermal resistance to the calorimeter. Since

the total effect is small, only the order of magnitude is important and this "lumped constant" approximation is adequate. For small heater wires

varnished to the calorimeter surface, the time constant is probably so small

that the effect is negligible. More massive heaters and poor thermal contact depending on gas conduction or radiation across a mechanical space make

the time constant larger and warrant considering it. A typical case is a heater with heat capacity of 2 J/deg and thermal

resistance to the calorimeter of 10 deg/W. This heater has a time constant of 20 sec, so that the effect would not be accounted for by "conventional"

measurements of current and potential for which the first measurement is usually after 20 sec. A plot of resistance against time after turning on the

heater is given in Figure 2 for a linear resistance-temperature dependence

f The electrical transients in a calorimeter heater circuit are always over in such a short time that it is usually not necessary to consider them.

24-94
and constant heating rate. This heater resistance curve approaches exponentially the straight line which would be obtained by extrapolating from the current and potential measurements made later during the experiment. If a constant voltage is imposed on the heater, the electrical power is P = E2 \R,

and there is a small error because the extrapolated resistance (dashed line)

i

Time - *

Figure 2. Change of heater resistance during experiment.

between start of the heating and the first measurement is different from the

actual resistance. If the eventual excess temperature of the heater is A T,

and R is a linear function of the temperature, the resistance at any time t can be written

R = R0 {1 + a [A 7X1 - e-"T) + fit]}, (1)

in which a is the temperature coefficient of resistance, /S is the heating rate of the calorimeter, r the heater time constant, and Ro is the resistance at the

beginning of the experiment. The difference between the extrapolated

resistance and the true resistance is due to the exponential term in Equation

(1). The difference AR between the true average value and observed average

value is obtained by integrating over the heating period of length /f. The

fractional error when tt |> r is then given approximately by the equation

AR

Ro

a AT (2)

For our typical case a = 4 X 10~4 deg, AT — 30 deg for 3 watts of heater

power, so that (AR/Ro) = (024//f). In a 600 sec experiment, the fractional error is four parts in 10 000. If the heating rate is doubled, AT" is doubled

and ti is halved so that the fractional error is 4 times as great. If the calori- metric measurements have sufficient sensitivity, the error may be detected by

changing the heating rate. In addition to the starting transient the slower

change of resistance must be considered, but usually this is not bothersome

except in very accurate calorimetry (see Chapter 5). Several schemes have been developed to maintain constant power input

when the calorimeter heater resistance changes owing either to the starting

transient in the heater or to the gradual change of heater resistance with

25-95
the temperature of the calorimeter. In one scheme, approximately constant power with a moderate change in heater resistance can be obtained from a

constant current source supplying the calorimeter heater shunted by an external

resistance which is equal to the average calorimeter heater resistance18. In

another scheme using a constant voltage source, the equal resistance is placed

in series with the calorimeter heater10

. Sometimes (see Chapter 5) the

calorimeter heater leads are important in that they also change resistance during an experiment. This case is illustrated by Figure 3 in which Rs

is

Figure 3. Calorimeter heater equivalent circuit.

constant whereas Ri and Rh are functions of the temperature of the calori- meter. For this circuit the power in the calorimeter is given by the equation

p = £2 ^5 . (3) (RB + Ri + Rb)*

1 ;

To find the condition for no change in the power with a change in the heater

and lead resistance we take the total differential of Equation (3) and set the

result equal to zero. The condition for constant power is then given by the

equation

Rs + Ri- Rb dRb =

2d^i

Ri Rh Ri

If the fractional changes in the heater and lead resistance are related by some proportionality constant m, (mdRhlRb) = (di?i//?i), then the choice of

Rs is determined from the following equation

Rs -Rh = (2m - 1) Rh (5) A more convenient method is to make the change in the lead resistance dRi

negligible so that the condition for constant power is simply Rs + Ri = RhThe obvious solution to the problems resulting from change in resistance of the calorimeter heater and its leads is (i) to minimize the starting transient

by keeping the heater in good thermal contact with the calorimeter, (it) to construct the heater with a material having a small temperature coefficient of resistance, and (Hi) to either make the heater leads of low electrical resis- tance or use a material with small temperature coefficient. Although the use of such a material is not always practical, it is available for calorimetry at low to moderate temperatures, as described in Chapter 5.

26-96
C. Heaters for Temperature Control

In the design of other heaters in calorimetric apparatus, it is usually also advantageous to have good thermal contact and low heat capacity in

order to avoid lags. In addition, there are two other important factors.

First, the resistance of a heater should be made to be compatible with an

available power supply. With the extensive use of automatic controls in the past, the use of moderately high resistance heaters facilitated the use of

electron tubes as power sources when the power required was not excessive. With the recent development of the transistor which has a lower impedance

output than the electron tube, it may be more advantageous to use lowresistance heaters because of the high current available with the transistor. The availability of low-cost transistors controlling over 100 watts of power

ensures their increasing use in calorimetric measurements.

In apparatus requiring larger power, it is frequently convenient to use magnetic amplifiers (saturable reactors) for control. The magnetic amplifier

is usually used with a 60 c/s power supply and has a time constant longer

than that of a transistor. In addition the output of the magnetic amplifier

is either a.c. or d.c. with an a.c. component. As pointed out in the next

section, this a.c. may cause trouble with pickup in other circuits if high

sensitivity electronic amplifiers are used. Of course the rectified output of

the magnetic amplifier can be filtered to eliminate the a.c. component at the expense of lengthening the time constant to perhaps a second. It should

be pointed out that most magnetic amplifiers have the disadvantage in many

control applications that their output powers cannot be reduced to zero. Two other devices used for control of a.c. power are the thyratron and

its modern solid-state equivalent, the SCR (silicon controlled rectifier) whose cost is decreasing steadily. The output of the SCR is pulsed so that it has a large a.c. component.

D. Galvanometers and Electronic Amplifiers

The use of d.c. electronic amplifiers in place of galvanometers has in- creased in recent years, so that it is believed appropriate here to compare

their application to calorimetric measurements. The galvanometer has two

fundamental disadvantages due to its mechanical nature. Most sensitive galvanometers are affected by mechanical vibration, so that considerable

effort may be necessary to avoid motion of the moving coil due to this vibration. In addition, if a relatively large voltage is impressed on the

galvanometer, the moving coil system may be damaged, possibly so that a new suspension wire is required. The electronic amplifier is essentially free from mechanical difficulties. The electronic amplifier also has the advantage

of flexibility of power output and input impedance. The flexibility in the magnitude and impedance of the output of the electronic amplifier facili- tates its use in recording and automatic control. In most calorimetric

measurements the signal source is less than 100 ohms, so that a typical

measuring circuit using a sensitive galvanometer is reasonably matched to the signal source ; in other words, the power developed in the galvanometer

approaches the maximum possible from the signal source. If the signal

27-97
source has a high resistance, a low-resistance galvanometer would be relatively insensitive to a voltage source. The electronic amplifier can easily be

made with either high or low impedance input.

Most modern electronic d.c. amplifiers "chop" the d.c. signal before

amplifying, so that an a.c. amplifier can be used. The purpose of this is two-fold. First, by chopping, any drift with time of the amplifier characteristics only changes its sensitivity so that its use as a null device is satisfactory f. Second, by use of a step-up transformer after the chopper, the signal voltage

from a low-impedance source can be amplified before the first electron tube

(or transistor). The practical limit of this transformer gain is determined by

the ratio of impedances of the signal circuit to that of the grid circuit of the

first amplifier tube. By using a phase detector (synchronized chopper on the amplifier signal), the amplifier gives a d.c. output.

Although the electronic amplifier can be designed for use with signal sources having high impedances, the reader should be aware of possible

difficulties resulting from the high impedance. When using any detector,

the theoretical minimum of the electrical noise in the input circuit is that

due to "thermal" noise, which in a resistive circuit is directly proportional

to the square root of the resistance. With circuits having resistance of

about 100 Q and with detectors having time constants about one second,

the thermal noise equivalent (root mean square voltage) in the signal source at room temperature is about 0-001 [xV. More often, the high impedance signal source gives trouble because of increased "pickup" of both

transients and power line frequency (60 c/s). Consequently, when it is necessary to have very high sensitivity, high impedance signal sources should be avoided if possible.

When a typical galvanometer is used with a low-impedance signal source, not only is the "pickup" relatively small, but the inertia of the

galvanometer serves as a high frequency filter which attenuates 60 c/s pickup. In most sensitive electronic amplifiers (d.c), the effects of 60 c/s pickup are attenuated by an electrical filter in the early stages of the amplifier. To be completely free from first stage amplifier "saturation", the filter should precede the amplifier. However, this location of the filter requires it to have a low impedance when used with a low impedance signal source in order to avoid increased 60 c/s pickup in the signal circuit. Most commercial

electronic amplifiers do not have this low-impedance input filter so that they

are most susceptible to large 60 c/s pickup than galvanometers having the same time constant.

It follows from the previous discussion that electronic d.c. amplifiers have

several advantages over galvanometers in many calorimetric measurements.

For many applications, galvanometers are frequently less expensive. When

very sensitive electronic amplifiers are used with signal sources susceptible

to power line frequency pickup, a low-impedance signal source should be

used and suitable steps should be taken to avoid using a.c. (60 c/s) close to any component leading to the input to the amplifier and to follow the usual

precautions of shielding, twisted leads, etc.

t Negative feed-back is used sometimes to minimize change in sensitivity, to obtain a

constant gain, and to make the amplifier have a high input impedance.

28-93
III. Heat Flow Considerations

1. General

For accurate calorimetry, the essential quantities to be measured are mass, temperature, and energy. Sometimes, additional quantities are measured, such as pressure and volume. Except in extreme ranges, it is possible to measure most of these quantities with all the accuracy that is needed. In most experiments, the major part of the energy is either derived

from or compared with electric power which, with precautions, can be

measured very accurately. However, the energy also includes heat from

other sources, such as that resulting from heat leak. It is believed that the

uncertainty in the evaluation of this heat leak is the principal source of error

in a large fraction of measurements for accurate calorimetry. Of historical

interest is the comment of W. P. White23 on the first page of his book The

Modern Calorimeter [1928]. He says "There is a difference of opinion as to whether thermal leakage is necessarily the chief source of error in calori- metry, but it is undoubtedly responsible for most of the experimental

features and devices in accurate work." This is more true today than it was

in 1928!

It should be pointed out that in calorimetric measurements, the absolute

uncertainty in the evaluation of heat leak is not necessarily proportional

to the value of the heat leak. For example, in Chapter 1, it has been pointed

out that in calorimeters using an isothermal shield (surroundings), the

absolute heat leak is usually considerably larger than with calorimeters

with adiabatic shields. However, it must be emphasized that it is the absolute

uncertainty in the heat leak that results in error, rather than the magnitude

of the heat leak. The problem of reducing heat leak is usually much more difficult than the problem of reducing electrical leakage. This is more obvious when one compares heat and electrical transport properties at room temperature. In electrical measurements, there are solid insulating materials available which have

electrical resistivities about a factor of 1025 greater than the best electrical conductors. This means usually that it is not difficult, at least at moderate

temperatures, to reduce electrical leakage to a very small amount. However,

the best solid thermal insulators at room temperatures have thermal resistivities only a factor of about 104 greater than the best thermal conductor.

Therefore, one cannot expect to minimize heat leakage to the extent that one

can usually minimize electric current leakage. Furthermore, in thermal

measurements, even when all material connections are removed, heat

transfer by radiation may still persist. As shown later, at low temperatures,

the radiative heat transfer may be relatively unimportant because radiation

is proportional to T4. On the other hand, at very high temperatures, radiation may be the predominant means of heat transfer. In the ideal adiabatic calorimeter, for example, there is no heat transfer between the calorimeter and its surroundings. This ideal condition can be

approximated if the heat transfer coefficient and the temperature difference

between the calorimeter and surroundings are both very small. In the real adiabatic calorimeter, there are five principal steps which can be taken to reduce errors due to heat leak: (z) design the calorimeter to have a large

29-99
thermal resistance to its surrounding shield; (ii) design both calorimeter and

shield to minimize temperature gradients in them; (Hi) design the calori- meter and shield to have adequate temperature sensing devices at suitable

locations to measure the effective temperature differences between the

calorimeter and its surroundings, even with temperature gradients; (iv) design the calorimeter so that the experimental method or procedure can be

made to compensate for at least some of the unknown heat leaks, such as by

making two series of experiments ; (v) make corrections for any measurable

heat leak in an effort to account for it. Of the above five steps, all but the

last involve calorimetric design requiring heat flow calculations. Many of

these calculations can be made easily by assuming simple boundary conditions which are adequate for design purposes. It seems desirable to review

briefly the fundamentals of heat flow before applying them to calorimeter

design.

Heat flow is by radiation, convection, and conduction in most calori- metric operations. Although the separation of these three modes of heat

flow is not always sharply defined, in most calorimetry at moderate temperatures, these modes can be treated independently for design purposes.

2. Heat transfer by radiation

In calorimetry we are concerned with heat radiated from one body at temperature T± to a cooler body at temperature T2

. The rate of heat (Pi) transferred to body (2) from unit area of body (1) is given by the relation

Pi = oA2F12 [TV* - T24] (6)

in which P is in watts cm-2

, a is the Stefan-Boltzman constant (5-67 X 10-12 watts cm-2 degK-4

), T\ and T2 are absolute temperatures (°K), A2

is the area on body 2, and Fi2

is a dimensionless factor determined by the radiation

emittances and geometric configuration of the surfaces. If Ti and T2 are nearly the same at about temperature T, the differential form of Equation

(6) applies, i.e.,

<^f

=AoA2Fl2 T*. (7)

The degree of approximation of Equation (7) can be shown by taking the

case of T = 300°K and AT/2 = 5 deg K. In this case the use of the value of

dPjdT at 300 °K for the temperature difference between 295 to 305 °K

gives the same average heat transfer coefficient within less than 1 part in 5000

as that calculated from Equation (6) . Nevertheless, the experimenter must be aware that the radiative heat transfer coefficient is greatly dependent upon

absolute temperature, so that it cannot be considered constant over as large a

temperature interval as heat transfer by conduction or convection. Between

295 and 305 °K the increase in the radiative heat transfer coefficient due to temperature increase is about 7 per cent. Any experiment which depends on

constancy of this coefficient should be examined to determine how great an

error will result.

30-100
A discussion of the evaluation of the emissivry factor F\2 is given in various books13 . For the simplest case of a completely enclosed body,

small compared to the enclosing body, the factor is given by F\% = ei in which ei is the emittance of the enclosed body. For a completely enclosed

body comparable in size and shape to the enclosure, the case becomes

essentially the same as two infinite parallel planes for which

*12 =

J \~ (8) - + - - 1

in which ei and €2 are the emittances of the two surfaces. In using these or

other approximations, it is usually relatively easy to calculate radiative

heat transfer to the accuracy needed in most design calculations, if values of

e are known. The difference in the usage of terms emissivity, effective emissivity, and emittance should be pointed out here. As used in this chapter,

the above relation F12 = ei really defines ei as either the effective emissivity or the emittance of the small enclosed body, such as a sphere. The outer

surface Ai of the sphere is considered in this case to be the ideal surface area Attt2

, even though the actual surface is rough and several times this area. If this surface is actually perfectly smooth such as with a highly polished

metal, the value of its emittance is the same as what is called emissivity. In

other words, the emissivity of a metal is for a smooth polished surface (no concave surfaces) but its emittance is for any surface. In most cases we do

not have very smooth surfaces, so that the term emittance is more appropriate. As used in this chapter the term emittance is dimensionless, so that it should not be confused with a second meaning of emittance (radiant

emittance) which has the dimensions of power.

In considering the effect of radiation on calorimetric design, simple

calculations show how radiative heat transfer usually becomes relatively

small at low temperatures. On the other hand, at room temperature with

two infinite parallel planes each having an emittance of 0-6, and with

a 1-cm still air space between them, the radiative heat transfer is about

the same as the gaseous heat transfer (see Figure 4) . At higher temperatures,

the radiative heat transfer soon becomes the predominant heat transfer. In

calorimetric design for accurate work, radiation shields can be quite useful even below room temperature, and at high temperatures extreme pre- cautions may have to be taken. Radiative heat transfer between two surfaces can be decreased by inserting one or more "floating" shields between them. One type of shield is a thin

metallic surface completely surrounding the calorimeter. As soon as the

steady state of heat flow has been established to a shield, the same amount

of power, Pt, flows across each space. (The transient effect for a single shield is discussed in the next section.) This power can be written for the ith space as Pt = oAi+1 Fu I+i (7?- 7W)

A series of equations can be written for n spaces and summed

oA\Fi2

31-101
Pt -tV = r24 - 7Y

a

A

2r 23

1

* O'^n-^n, n+1

p'(2^^) =ri4 - r" i=l whence Pt can be found by

7Y* - rn+14 Pt = i = n

i aAyFi, i+i i= 1 The overall heat flow is still proportional to the difference in the fourth

powers of the temperature, but is smaller than in the unshielded case. If the shields have equal areas and emittances, as is approximately true in many calorimeters the ^iFjj factors are equal and the heat flow is inversely

proportional to m + 1, in which m is the number of "floating" shields. A

simple case shows the advantage of the radiation shield. If a bright shield (such as one gold plated and polished to give an emittance of 0-02) is inserted between two black (e = 1) parallel planes, the radiative heat

transfer is reduced by a factor of 100. Even a black shield would reduce the

radiative heat transfer by a factor of 2. Figure 4 given under Section III—3, illustrates the effectiveness of shields, both for radiation and convection. In shielding a calorimeter or furnace, the area of the shield increases

with the distance from the center and the effectiveness of successive shields decreases proportionately. It follows that the spacing of multiple shields should be the smallest compatible with mechanical and gas conduction

considerations. At high temperatures the shields may be in the form of a

fine powder which effectively inserts many shields in a narrow space. Because of surface roughness and higher intrinsic emissivities, a single

powder surface is less effective than a metallic surface by perhaps a factor of

10, but ten particles of 1000 mesh powders at ~50 per cent bulk density

occupy only 0-25 mm. Powder used for radiation shielding in vacuum should

be placed in hot parts of the apparatus where it will outgas readily. Another

consideration in selecting a powder is that a particle should not be trans- parent to the radiation at the highest temperature of operation.

A combination of this sort of radiation shielding with spaces shorter than the mean free path has resulted in an air-filled silica gel insulator being

better than still air14 . Although a powder is a useful insulating material,

especially in furnaces, it is not generally used directly next to the calorimeter

where energy must be accounted for. This is because of the heat capacity

of the powder and the uncertainty of the calorimeter boundary, within which

energy must be accounted for.

32-102
In making computations of heat transfer by radiation, it is sometimes

difficult to select the proper value of the emittance for a particular problem.

This is not so much because the data lack precision but because they may

not apply to the particular surfaces under consideration. For example, the

emittance of an aluminum surface changes by a factor of about 12 as the

oxide layer increases from 0-25 \i to 7 fx. Another uncertainty in radiation

computations is in the geometry of the calorimeter. The effective emittances

of indentations and corners can be quite different from the emittances of the

plane surface. The best approach is perhaps to choose the most unfavorable

value of the emittance to make the calculation. More detailed treatment of

radiant heat transfer is given by Jakob13.

3. Heat transfer by convection

Heat transfer by convection is the result of mass transfer of a fluid (gas or

liquid) from one region to another at another temperature. Convection is classified into two general types, (I) forced convection and (2) free convection. In forced convection the fluid is forced to move, such as by a stirrer in a

liquid bath. In free convection the motion of the fluid is due to gravitational

forces acting because of different densities of the fluid at different temperatures. The laws governing the behavior of convective heat transfer are the same for both liquids and gases, although values of their physical properties

vary greatly. If these physical properties are known, calculations of both

forced and free convection can be made by using engineering formulae12 . Consideration will be given first to free convection.

Where the calorimeter is surrounded by a gas such as air, heat transfer by

free convection (as well as by conduction) must be considered in designing and

using the calorimeter. In precise calorimetry at room temperature and

below, evacuation can be used advantageously to eliminate both gaseous

convection and conduction between calorimeter and shield. At higher

temperatures, at which radiation becomes more important, the use of

evacuation depends on the particular design, which must weigh the advantages against the disadvantages of evacuation. Sometimes, partial evacuation

is used to avoid convection while leaving gaseous conduction. In some

apparatus, the gaseous conduction may be desirable to provide thermal

contact between two components in poor mechanical contact. As a general

rule, atmospheric gas pressure can be reduced by several orders of magnitude

without much change in thermal conductivity while the effect of convection

is made negligible. In the case of convection with a gas between two parallel vertical surfaces

at different temperatures, the denser gas near the cold surface moves down to displace the gas near the bottom of the warm surface which has

been warmed by conduction. Warm gas at the top of the space is moved

into contact with the top part of the cold surface, where it is cooled. Heat is thus transported by motion of the air as well as by direct gas conduction

across the space. For horizontal surfaces with the hot surface above the cold surface, the low density gas is in stable equilibrium and ideally no

convection occurs. When the hot surface is below, convection takes place

as a local phenomenon, with upward and downward streams close to one

another, sometimes resulting in considerable turbulence.

33-103
Early workers in calorimetry, recognizing the requirements for the linear

relationship between heat transfer and temperature difference, performed

experiments on the gaseous heat transfer in their apparatus. As long as heat transfer is only by gaseous conduction, this heat transfer is nearly

proportional to the temperature difference (AT") because the thermal conductivity of a gas does not change very much with temperature. Of his- torical note, when this proportionality is valid, Newton's Law of Cooling is said to apply, i.e. the rate of cooling of a hot body is directly proportional

to the temperature difference from its surroundings. As the temperature

difference is made larger, convection begins to be significant. Since gas convection is not proportional to AT", the total heat transfer is no longer

proportional to A T when the convection is significant. In the calculation of the magnitude of free convection, the dimensionless

quantity Grashof Number (Nqt) is needed. This quantity is NGT = %-/3(r! - T2 ) (9)

in which (8 is the cubical expansion coefficient (deg K_1

), g is the acceleration due to gravity (cm sec

-2

), p is the density (g/cm3

), / is the width of the gas space (cm), -q is the dynamic viscosity (poise), and T is temperature

(°K). Jakob12 gives dimensionless plots of the equivalent conductivity

(defined as conduction plus convection) against the Grashof Number, for cases of air layers bounded by horizontal planes, by vertical planes, and by

coaxial cylinders. As a general rule, the convection is almost negligible

for Grashof Numbers less than 1000. For horizontal planes and a Grashof

Number of about two thousand, the ratio of equivalent to true conductivity

is about 1 -05 ; in other words, for this case the contribution of the convection

is about 5 per cent of the thermal conductivity. The other cases yield similar

results. For air near room temperature and one atmosphere pressure one can

write that lz {T\ — T%) must be less than 11 cm3 deg K to be reasonably

sure that heat transfer is directly proportional to temperature difference. This is in reasonable agreement with the work of White24 and Barry1

. From the formula for the Grashof Number it is evident that the most

useful experimental ways of decreasing this number are to work with small

temperature differences, to reduce the spacing (at the expense of increasing

the gas conduction) or to reduce the density. Of course, the ultimate step

in reducing the effect of convection is to remove all of the gas, reducing the

density to zero. In cases for which it is desirable to reduce convection but to retain gas conduction in order to maintain the thermal contact of heaters or temperature measuring devices with the calorimeter, it is possible to reduce

the density of the gas substantially without impairing the thermal conduction

of the gas. Until the pressure is reduced to the point at which the mean free path of the gas molecule is comparable to the dimensions of the gas space, the thermal conductivity of a gas is substantially independent of its pressure. At 0-1 atmosphere, the Grashof number is reduced by a factor of 100, but

the mean free path in air is about 9 x 10-4 cm, so that gas conduction in spaces around thermometers and heaters is only slightly less than at 1 atm. When calorimeters are used with gas at atmospheric pressure surrounding

34-104
the shield (and perhaps the calorimeter also), the problems of radiation

and convection frequently can be solved simultaneously by the use of thin

metal heaterless shields which act both to reduce radiative heat transfer

(as noted in Section 1 1 1-2) and to reduce convective heat transfer by

reducing the thickness of the gas gap. Figure 4 illustrates the effectiveness of

0-05

Number of shields

Figure 4. Effect of number of shields on heat transfer.

these radiation-convection shields in reducing the heat transfer coefficient between two parallel horizontal planes, spaced 5 cm apart with the lower

plane at 400°K and the upper at 300°K with air between them. The

emittance ( e) of both plane and shield surfaces is assumed to be 0-5. The

figure shows that even with the large temperature difference of 100°, the use of shields 1 cm apart reduces the convection to a relatively small value. The

figure also illustrates that the shields reduce the radiative heat transfer by

the factor l/(m + 1) in which m is the number of shields, if all surfaces are assumed to have the same emittance. In using convection shields, precautions

should be taken to avoid "chimney" type convection which might occur if the shields allow gas to leak through.

One or more heaterless or "floating" shields can appreciably reduce both

convection and radiation between the calorimeter and its surroundings,

but only at the expense of introducing an additional time lag in the calori- meter temperature whenever either the calorimeter or surrounding temperature is changed. This lag may be calculated if the geometric and heat

transfer data are known. The calculation will be illustrated for one floating

shield between a calorimeter and its constant temperature surroundings, a

water jacket, for example. Usually, the surfaces involved are of comparable

areas, and it is an adequate approximation to treat them as parallel planes

with heat flow perpendicular to the planes. Let p be the power (heat flow)

per unit area, h the heat transfer coefficient, C the heat capacity per unit area of the floating shield, T the temperature, t the time, and the subscripts

c, s and j refer to calorimeter, floating shield and jacket, respectively. For

35-105
small temperature differences, heat flow is proportional to the temperature

difference

pes = ^cs ( Tc — Ta ) (9a)

psi =hi (Ts - T-). (9b)

The change of temperature of the shield is equal to the heat absorbed

divided by the heat capacity

dTs = (pcs -ps}) d//C8 . (9c)

These equations can be solved by substituting from Equations (9a) and (9b)

.

The time constant t is computed for the case in which the calorimeter,

floating shield and jacket are at 7~j initially and the calorimeter temperature

is increased suddenly to a constant Tc

. The time constant will be the same

for any time-temperature relation for the calorimeter, and the amplitude

factor will generally be less, so that we are considering a "worse" case. When Acs = ^sj = h, the heat flow from the calorimeter is given by the

equation

h t 2ht\ Pes = 2 (Tc - Tt) 1 + exp I-

—J.

(9d)

To reduce the time constant, Cs /2h, the only practical step is to reduce the

heat capacity of the shield, because increasing the heat transfer coefficient increases the uncertainty in heat loss from the calorimeter.

It is instructive to consider a particular case. For an aluminum shield spaced 1 cm from aluminum-surfaced calorimeter and shield in air at room

temperature, the heat transfer coefficient is about 2-5 x 10 -4 W cm-2 deg-1. The heat capacity is 2-4 J cm-3 deg -1 and the time constant as a function of

the thickness d of the shield is

t = 4-8 x 103 d

in which t is in sec if d is in cm. For ordinary aluminum foil, d = 2-5 X 10~3 cm, and t = 12 sec. For pcs to reach within 1/1000 of its ultimate value, 6-9 t or 83 sec are required. If aluminum sheet having d = 0-025 cm is used

for its greater mechanical strength, 6-9 t = 830. If the aluminum floating shield is used in an evacuated space, the time constants for the 0-0025-cm

and 0-025-cm thick shields are about 200 and 2000 sec, respectively, so that the total times for the power to reach within 1/1000 of its ultimate value are 1380 and 13 800 sec respectively. These figures show that in calorimetry

using floating shields in evacuated spaces near room temperature, serious consideration should be given to errors resulting from the time lags. In experiments using furnaces, frequently we need to know the power

required to keep the inner core of the furnace at some given temperature

and the corresponding temperature of the outside surface of the furnace. The calculation of the power required to maintain a given temperature

difference in the furnace can be made simply by methods described later.

36-106
However, the temperature on the outside of the furnace depends upon the

coefficient of heat transfer away from the outside surfaces. In this case, it is usually considered desirable to have a large enough heat transfer coefficient

to hold the outside to a reasonable temperature. Radiative heat loss can be

calculated as described earlier. The heat loss by free convection may be

calculated with sufficient accuracy for furnace design, using methods

described by Jakob12 . If the heat flow is written proportional to the temperature difference (P = hAT), the constant of proportionality, h, which we

term the heat transfer coefficient, is a function of A T and may be calculated

approximately for typical conditions by the following relations

horizontal surface — heat lost up

h = 2-2 x 10-4 (AT)i (10)

horizontal surface — heat lost down

h = 1-1 X 10-4 (AT)* (11)

vertical surface — (height > 30 cm)

h — 1-5 x lO-4 (AT)1 (12)

in which A T is the difference between room temperature and the surface temperature in °K (or °C) and h is in W cm-2 deg-1

. For vertical surfaces

less than 30 cm high, h may be somewhat larger, perhaps by as much as a

factor of 2 or 3. In addition to free convection which may or may not be desired in calorimetry, we sometimes use forced convection to obtain good thermal

contact between a fluid and its surrounding tube. In forced convection,

there are two distinct types of heat transfer, depending upon whether the

fluid flow is laminar (streamline) or turbulent. For fluid flow in smooth tubes,

the transition between laminar and turbulent flow occurs at a value of the

dimensionless Reynolds Number (vDplrj) of approximately 2000. In this expression, v is the average velocity of the fluid (cm/sec), D is the diameter

of the tube (cm), p is the density of the fluid (g/cm3

), and 77 is the dynamic

viscosity of the fluid (poise). Turbulent flow is sometimes used to obtain a maximum heat transfer between the fluid and a solid surface. For laminar

flow in a tube, the flow of gas at pressures for which the molecular mean

free path is much less than the diameter of the tube may be calculated from

Poiseuille's equation

128?? L

K '

in which v is the rate of volume flow (cm3 /sec), AP the pressure drop between

the ends of the tube (in dynes/cm2

; note that 1 atm ~106 dynes/cm2

), L and D the length and diameter of the tube (cm), and 77 the dynamic

viscosity of the fluid (poise). For laminar flow, for calculating the heat

transfer coefficient between a tube and a fluid inside it, it is convenient for

37-107
design purposes to use a simple approximation to estimate a value of heat

transfer coefficient which will be slightly less than the true value. This

approximation is that the heat transfer coefficient (h) per unit length of tube

per unit temperature difference is 577 A in which A is the thermal conductivity

of the fluid in the tube. If A is in W cm-1 deg-1

, then h will be in watts per

cm length of tube per degree C difference in temperature between tube and

the fluid. For turbulent flow in a tube, the relation

will be adequate for most design purposes. In this relation, h is the heat

transfer coefficient (W cm-1 deg-1

) for unit length of tube and unit temperature difference, A is thermal conductivity (W cm-1 deg-1

), F the rate of mass flow of fluid (g/sec), Cthe heat capacity (J g

-1 deg-1

), and D the inner

diameter of the tube (cm).

In apparatuses which have gas contained in a tube having a temperature

gradient, there may be another mechanism of heat transfer which is unknown

in most calorimetry. This mechanism, which may be called "thermal

acoustical oscillation" may be important in low temperature calorimetry,

especially in the liquid helium range. Under certain conditions depending on the tube dimensions, gas present, temperature gradient, etc., this gaseous

oscillation may result in large pressure variations, together with a relatively

large heat transfer which may make calorimetric measurements difficult or

impossible. While a change in design of the apparatus may avoid this oscillation, a recent study8 has developed a method to minimize the oscilla- tion by using a "damping" device attached externally to the apparatus. With

this device, consisting basically of a Helmholtz resonator, it is not necessary

to redesign the apparatus.

Another mechanism of energy transfer which may result in heat developed

in a calorimeter is by mechanical vibration. This is a problem which sometimes arises where measurements are made of very small heats. In localities with large mechanical vibrations, detectable mechanical power has sometimes been transmitted to the calorimeter where it has been transformed into heat. This "anomalous" heat has been a problem in some calorimeters

operating at liquid helium temperatures where a small amount of heat can

be detected. One solution here is to mount the apparatus on a solid pier

which is free from vibration. In case this is not practical, a mounting can be

designed to attenuate the vibration before it reaches the calorimeter.

In design calculation in most calorimetry except at high temperatures,

heat transfer by solid conduction is probably more important than other

modes of heat transfer. Frequently, conduction plays the predominant role in

determining temperature gradients in the calorimeter and on its surface.

(14)

4. Heat transfer by thermal acoustical oscillation

5. Heat transfer by mechanical vibration

6. Heat transfer by conduction

38-108
At low to moderate temperatures, solid conduction usually is the main

source of heat transfer between calorimeter and shield. In many cases, dependence on thermal conduction is necessary in the evaluation of temperature, etc. As a consequence of the variety of calorimetric design problems

in which conduction is important, this heat transfer mode will be considered

in more detail, and some examples of calculations involving conduction

will be given. In most calorimetric work, thermal conductivity changes more slowly

as a function of temperature than coefficients for heat transfer by radiation

and convection. With most materials the changes with temperature of their thermal conductivities are sufficiently small over 10°C so that for design

purposes, the heat conduction-heat transfer coefficient can be considered

constant in an average experiment. One noteworthy exception is where a phase change takes place in the material. Consequently, materials of

construction preferably should have no phase transitions in the temperature

range of calorimeter operation. In all the following examples of heat flow

calculations, it will be assumed that the thermal conductivity is constant and that there are no transitions in the material.

Heat flow calculations are usually classed into two types, steady-state and

unsteady-state. In steady-state heat flow, the temperature at any point in the

material does not change with time, whereas in unsteady-state heat flow,

the temperature is a function of time.

The quantity thermal conductivity (A) is the proportionality constant

defined by the steady-state relation Px — —XA (BT/dx) in which Px is the

power (rate of heat flow at x) in the x direction through an isotropic material

having a cross sectional area A, and BTjBx is the temperature gradient at x

in the x direction. The minus sign in the defining equation is used to indicate

that heat flow (power) is positive in the direction of increasing x if the temperature decreases with increasing x (BTjdx is negative). Let us consider now a case in which [BTjBx) is a function of x. If at x the power is —XA(BT/Bx), then at x -f- dx the power is B I BT \ BT w S -

2 r , XA ¥X {

T +Tx ix

) =

-XA TX "*

Thus, the difference in power at x and at (x + dx) is

Px -P(x+dx) —

B*T , (15)

The magnitude of this difference in power is determined by the boundary

conditions for the particular heat flow problem. In solving any heat flow

problem, the starting point is to set up the "heat balance" equation expressing the conditions of the particular problem. In principle, the solution of

any such equation can be obtained if the boundary conditions are all known. The heat balance differential equation for a homogeneous isotropic

solid has been derived for the general three-dimensional case in which tem- perature is changing with time and there is a power source (or sink) in the

material. This general equation can be written as [8*T B

2 T B*T~\ BT

39-109
in which p and c are density and specific heat of the material, dTjdt is the

rate of change of temperature at a point (x,y, z) with time, t, and F(x,y, z, t)

is the power source per unit volume. The above equation is written conventionally as

/ oc\ dT —F(x,y,z,t) - (a) ¥ - a

1

< 17> V2 r

in which (A/pc) is a quantity known usually as thermal diffusivity, a. In the

case of steady-state heat flow, [dTjdt) = 0, so that we have Poisson's

equation

-F(x,y, z, t) v2 r = (18)

If no heat is supplied to the body, this equation reduces to Laplace's equation V2 T= 0. If instead of rectangular coordinates, cylindrical coordinates are used, the

heat balance differential equation for the case of no heat generated in the cylinder is

8

2 T 1 dT 1

"or2 + r "dr + r2

8

2 T d2 T

8~¥ +

dz*

pc dT

ct (19)

in which r is the radial distance from the cylindrical axis, 8 the azimuth

around the axis and z the distance along the axis. Many cylindrical heat

flow problems of interest in calorimetry can be approximated by assuming

T to be independent both of 9 (symmetrical heat flow around axis) and of z

(effectively infinitely long cylinders). In this case the cylindrical heat flow

equation reduces to

or

a

2 r

IP"

1 dT

r dr

pc dT

~dt

d

2 T 1 dT _ 1 dT

dr2 r dr a dt (20)

in which r is the radial distance from the axis of the cylinder.

There is a corresponding general heat flow differential equation for spherical polar coordinates6 . Most applications in calorimetric design use the

approximation that isothermal surfaces are concentric spheres. In this case the general equation reduces to

S2T

+

2 dT _ 1 dT

dr2 r dr a dt

in which r is the radial distance from the center of the sphere.

Steady-state heat flow will now be discussed because it is usually simpler

and more frequently encountered in calorimetric design.

40-110
A. Steady-State Heat Flow

(1) Rod. The simplest steady-state heat flow case is for linear (unidirectional) heat flow in a rod having constant cross sectional area A in the direction of heat flow. We have linear heat flow if there is no lateral heat transfer. Here, the defining equation of thermal conductivity (A) applies,

so the power P = —XAdTjdx and dTydx = —Pj(XA). Integrating this equation between x\ and x2 , corresponding to temperatures 7~i and T2 , gives

(T2 - 7i) = — V". d*

XA XA

{X1 ~ *2) - (22)

In calorimetry, this simple equation may be used to calculate heat flow

along a conductor (such as a wire or tube) corresponding to a known or estimated temperature difference across a known length.

The linear temperature-distance relation is common, but by no means

general. For example, if the cross sectional area is not constant, as in a cone for which A — Mx2

, integration gives

(T2 - Ti) XAdx

-P

XM

dx P_

XM

1 x2 (23)

A more practical example is the heat flow along a tube of constant cross section for which the thermal conductivity changes drastically over the temperature variation on the tube. For example, take a stainless steel tube

with constant cross section A, length /, and variable thermal conductivity A. If this tube is used between a calorimeter at 4°K and a liquid nitrogen bath

at 90 °K, its thermal conductivity changes by about a factor of thirty over

the temperature range. As a first approximation, adequate for most calori- metric design, A = 0-0009 T in this temperature range, with A in watt cm-1 deg-1 and T in deg K. Integrating, we get (0-00045) T2 = — (PjA) x + C. From the boundary condition that T — 4° when x = 0, the integration constant is 0-0072. Using the boundary condition that T = 90° when

x = 10 cm, and with A = 0-05 cm2

, we get P — 0-018 watt. The temperature

distribution along this tube is T = \f(808*4 x + 16).

(2) Wire Carrying Current. An important example of a non-linear temperature-distance relationship arises when power is developed in the body, as in a heater lead. In calorimetry it is important that the heater lead wire not be

excessively hot. A heater lead can be treated as a small rod of length /, cross sectional area A, and thermal conductivity A, with power p developed per

unit length of the wire. To simplify the problem, both ends of the wire are taken to be at temperature 7~o and losses from the surface of the wire by

radiation and conduction are assumed negligible. The power developed in a

differential length d# of the wire is simply pdx. As shown earlier in Equation

(15), this power can also be expressed in terms of the second differential

41-111
d

2 Tjdx2

, so that the heat balance equation is

and by integrating,

8

2 T

T =

2XA

X* + ClX + C2 (24)

in which Ci and C2 are integration constants to be determined by the

boundary conditions. Then

C2 = Tq and C\ =

2XA'

so that

(25)

The above equation shows that the maximum temperature for this case is at x — //2. As an example, take a 5 cm length of AWG#26 copper wire with

a current of 0-5 amp. The excess temperature at the middle of the wire

is calculated to be about 0-6°C.

(3) Cylindrical Shell. Consider the gradient in the axial (z) direction in a

thin cylindrical shell (length /) due to constant power supplied per unit

length of cylinder and removed at one end of the cylindrical shell (z = /). The heat balance equation is

so that

(4) Radial Heat Flow in a Hollow Cylinder and Sphere. A frequent problem

in calorimetric design is steady-state radial heat flow in a cylinder for which the temperature is a function only of the radius r. Applying the

defining equation for thermal conductivity (A) to plane polar coordinates,

and assuming a constant power P flowing radially for unit length of the cylinder,

then one finds at any radius r, P = —A(27rr) dTjdr. Integrating this between

ri and r2 gives the corresponding temperature difference

(27)

42-112
A similar treatment for steady-state heat flow in a sphere gives a heat

balance equation P = —A(4tjt2

) dTjdr in which P is the total power flow. Integrating this between r\ and r2 gives

(T2 - 7i) =

-P /l

4ttA (28)

(5) Thin Disk with Uniform Heating and Cooling. A simple heat conduction

case involving radial heat flow (such as in the top or bottom of a calorimeter

sample container) is the calculation of the temperature in a thin disk in which there is introduced a constant power p per unit area which is dissi- pated at its circumference. The power crossing the cylindrical surface of

radius r is p(irr2

) so that p(irr2) = —X{2irrw) dTjdr in which w and A are the

thickness and thermal conductivity respectively. The solution here for the

temperature ( Tr) at radius r is

If we impose the boundary conditions that T = To at the circumference

(r = a, with a the radius of the disk), then

This solution also holds (except for sign) for the reverse case for which

a constant power p per unit area is removed from the disk.

(6) Tempering of Electrical Leads and Other Conductors. Consider now a

slightly more complicated case which is basic to most calorimetry. This is the problem of "tempering" of electrical leads, defined as bringing the

temperature of leads to the temperature of the body by thermal contact. This problem is exceedingly important in accurate calorimetry if the true temperature of lead wires must be known in order to minimize and measure

heat leak. Tempering of wires may be accomplished either continuously over a

length of wire or in steps. These two methods will be considered separately.

(7) Continuous Tempering. For continuous tempering, consider a small wire

having a thermal conductivity A and cross sectional area A. Let the temperature of a wire be T\ at x = 0, where the wire first comes in thermal contact with a body at a temperature To. Let h represent the constant heat transfer (power) from wire to body per unit length of the wire and per unit temperature difference. The heat transfer (power) from dx length of wire to the

and

(

fl 2 _ ,2) + ro. (29)

43-113
body is therefore h(T — To) dx in which T is the temperature of the wire.

From previous consideration Equation (15), this power must be

XA

d*T

dU2

d*.

Hence the heat balance equation is

A/1 02 T

dx = h ( T — To) dx (30)

or

(31)

The general solution to this linear differential equation is

( T — To) = C\ exp [- x y'(hjXA)] + C2 exp [x y/WXA)]. (32)

Imposing the boundary conditions that T = Ti at x = 0 and T = To at x = oo we get C2 = 0 and Ci = ( Ti — To; , so that

The physical meaning of this equation is that when x\Z{h\\A) = 1, the

excess temperature of the wire has been reduced from T\ — To to ( T\ — To) \e. Solving for this distance xe , we get xe = \Z(XA/h). To reduce the temperature excess of the wire to ( Ti — To)/ 10 requires *io = (2-303 xe ) = 2-303

y/iXAjh) length of wire. If it is desired to bring the temperature of the

wire to (Ti — To)/ 1000, we must have *i 0 oo = 3(2-303) ^{XAjh) length

of wire. This type of tempering problem has application in calorimetry

in a number of problems in which the heat flow can be approximated in the above manner. The heat transfer coefficient h (W cm-1 deg-1

) must be

evaluated for the particular problem. In the case of a wire insulated from a

tube, the cylindrical heat flow formula (Equation 27) is used to evaluate it. In the case of radiative heat transfer frequently it is sufficiently constant

for design purposes so that a "radiative" h can be calculated. In case the

calorimeter is used over a temperature range, sometimes the "worst case"

is assumed.

There is a similar example for afinite length (/) of wire with the boundary

conditions that T = T\ at both x — 0 and x = I. In this case, the values of

Ci and G<i satisfying the boundary conditions are

in which m - y/(h(\A).

A problem that sometimes arises is to estimate the extent of tempering

of a wire which cannot be treated as having an infinite length in contact

(T - To) = (Ti - To) exp [- x y/(h/XA)]. (33)

Ci =

(Tx - T0) [exp(wQ - 1] [exp(— ml) — exp(m/)]

and Ci =

(Ti - To) [exp(- ml) - 1] [exp(— ml) — exp(w/)]

44-114
with the body. Such a case arises when a lead is brought through a body

at a temperature between that of the surroundings (e.g., room temperature)

and the temperature of the calorimeter. This body will supply some of the heat flowing along the wire and reduce the amount which must be supplied

from the direction of the calorimeter. Equation (32) still applies, but with

different boundary conditions. Neglecting heat flow from the direction of

the calorimeter (a less favorable case) gives dT/dx = 0 at x — 0. The

other boundary condition is obtained by equating heat flow along the

external part of the wire to the total heat flow from the body to the wire,

with the result that

r =r =

(Ts -T0) V(hlXA)

1 2 [1 - L VWM)] {exp [ly/fflAA)] - exp [- l^/(hjAA)]}

in which Ts

is the temperature of the surroundings, To is the temperature

of the body, and L is the length of the wire between the body and the

surroundings.

(8) Tempering of Wires Carrying Current. The problem of tempering a wire

carrying current is similar to the problem of a wire with no current. If p is the power developed per unit length of wire, the heat balance equation is

d

2 T

XA dx + pdx — h(T — Tq)&x

or 82 T

dx2 = (^)<r - r»>-(xi)- < 34 >

Solving this linear differential equation gives

[T - To) = Ci exp [- x VWXA)] + C2 exp [x y/(hjXA)] + (p/h)

for the same boundary conditions that T = T\ at x = 0 and x = /, and

with

c

[Ti-T0 -(plh)][txp(ml)-l]

1 [exp (ml)] — [exp (— ml)]

and

c =

[Ti -To- (pjh)] [1 - exp (- ml)]

2 [exp (ml)] — [exp (— ml)] '

in which m = ^/(h\XA).

(9) Step Tempering. Another method of tempering leads is by steps in contrast to continuous tempering. This is done by "thermal tiedowns", as used extensively in calorimeters described in Figure 2 in Chapter 11. A

thermal tiedown, as used here, is defined as a thermal connection between

45-115
a point on the wire and a small region on the body whose temperature is to be approached. For a given electrical insulation between wire and the

body, this method may have an advantage in that it can give better tempering by effectively increasing the length of path of heat flow along the wire.

This method may also have certain other advantages, such as ease of

disassembly, etc. The principle of this step tempering is shown in Figure 5. In this figure, T\, T2, and 7*3 represent the temperatures along a wire

(referred to the temperature To of the body) in the tempering network, R±

represents the thermal resistance of a chosen length of the wire, whereas R%

represents the thermal resistance of the thermal tiedown. If R\ — 100 Rz,

then (T2 - To) 0-01 (7*i - T0 ) and (7s - To) £ 0-01 (7*2 - T0), so that (7*3 — To) = 0-0001 (7i — 7b). In one calorimeter described in Chapter 11, the thermal resistance R± was that of about 10 cm of small

wire whereas R2 (thermal tiedown) was equivalent in thermal resistance to about 0* 1 cm length of the same wire, thus giving an attenuation factor of

0-01 for each tiedown. Details of the thermal tiedown which has proved

effective even in vacuum are given in Chapter 1 1

.

(10) Tempering of Fluid in a Tube. In some calorimetry, such as flow

calorimetry, a fluid (liquid or gas) is brought close to the temperature ( To)

of a bath by flowing through a "tempering" tube in the bath. In designing

this tempering tube, it may be advantageous to know the minimum length

required to bring the temperature of the fluid sufficiently close to the bath

temperature If F is the mass rate of flow of fluid (g/sec), c is the specific heat

of the fluid (J g

_1deg _1

), T\ is the temperature of the fluid at x = 0, and h

is the heat transfer coefficient (Wcm_1deg -1

) between tube and fluid12 per

cm length of tube, then the heat balance equation is

Figure 5. Principle of thermal tiedowns.

h(T-T0) = -cF^ (35)

or

(36)

which is a linear differential equation whose solution is T = To + (7i - To) exp - {hjcF)x. (37)

46-116
The above solution assumes that the radial gradient in the fluid is small

by comparison with the difference in temperature between fluid and tube. This type of approximation is usually adequate for design purposes. The

length of tube necessary for the fluid to come to the fraction l/e(63 per cent)

of its starting temperature difference ( 7i — To) is cF/h. These examples of steady-state heat flow are only a few of the many

calorimetric problems that may arise. Solutions to many more complicated

problems are given in Carslaw and Jaeger6

. In most calorimetric problems,

the heat balance differential equation is a linear differential equation so

that its solution can be treated as the combination of several solutions. This

is known as the Principle of Superposition, which is discussed in the following

section (B).

B. Unsteady-State Heat Flow

An unsteady-state heat flow problem is one in which temperature changes

with time. Although perhaps the majority of calorimetric design problems can be solved using steady-state heat flow, there are some important unsteady-state problems which arise. In general, the complete solution of a heat

flow problem, in which temperature is a function of both distance and time,

is considerably more difficult than that for the steady state. The complete

solution usually consists of a "transient" term, which may be short-lived, and

a "steady" term, which changes only owing to either change in the material

physical properties or time variable boundary conditions. If the transient terms decay before the final temperature is observed, West21 has shown

that in an adiabatic calorimeter heated intermittently, heat leaks due to

initial and final transients are equal and opposite in sign. It is usually

advantageous, therefore, to design the calorimeter and shield with fast transients, i.e. with small "time constants". In unsteady state heat flow, in which the transient may be approximated by a single exponential term, the

term "time constant" frequently is used in a manner similar to the electrical time constant RC. If a capacitor is charged to some potential difference

(£1 — Eo), and then connected to the resistance, the potential difference

across the capacitor will decay exponentially through the relation AE —

(£1 - E0) exp [- (tIRC)]. When t = RC, AE = (£1 - E0)je, so that RC

is called the electrical time constant (t) defined as that time in a single ex- ponential decay for the potential difference to come to Ije of its initial value. In the analogous heat case, the capacitor corresponds to a body with a heat

capacity c, which is heated to an initial temperature T\ and then put in thermal contact through thermal resistance R with another body held at temperature T = To- This is mathematically similar to the discussion of

tempering a wire in which there is a distance to bring the wire to 1 je of its initial temperature difference. In both cases we are considering a decay

through a single exponential term. The time required to come to 1/10 the

initial temperature difference is simply 2-303 (t), the time to come to 1/100

is 2 (2-303 t), etc. Sometimes it is desired to estimate this time constant t from cooling experiments. In principle, this can be done from any two

measurements of temperature at different times. As a simple short cut, it is sometimes convenient to measure the initial cooling rate and divide the

initial temperature difference by this initial cooling rate to get the time

47-U7
constant (t). For example, if a body with a heat capacity of 1000 joules/deg

C, has an initial cooling rate of 10 deg C/sec, for an initial temperature

difference of 1000 deg C, then the time constant (t) = 100 sec. If the thermal

resistance is known, the time constant is merely the product of the heat

capacity and thermal resistance. For example, the above case corresponds

to a thermal resistance of 0*1 deg C/watt.

Although in some calorimetric design the use of a single exponential may

be adequate for design purposes, the actual transient is usually not so simple. Fortunately, a variety of unsteady state heat problems have already

been solved6

, and in some important cases the solution is shown graphically

to facilitate its use. Consider the case of a thin cylindrical shell similar to that treated earlier in a steady-state case. Suppose this shell has a specific heat c, thermal conductivity A, density p, and length /, and the cylinder is initially at tempera

ture T = To- Assume also that the thermal properties are independent oi temperature. Now at time / = 0, start to heat one end (z = 0) at a constant

rate B, so that T"2 =o = Bt. Putting the initial and boundary conditions into the general heat balance differential equation gives

(38,

8z2 H8t

K '

The complete solution is given as

Bz2

( T - To) + + [transient term] (39)

2a

in which a is thermal diffusivity (A/pc). If the transient term is short-lived

as it is frequently in good calorimetric design, the "steady" temperature

gradient on the cylindrical shell is of primary interest. This temperature

difference (after transient has died out) over the length / is Bl2 /2a. Note that the average temperature is not at z = //2. Consider now a case of radial instead of linear heat flow. In terms of

cylindrical coordinates, the general differential heat balance equation for a cylinder infinitely long for which the temperature is dependent only on

radius r and time /, is Equation (20)

8

2 T 1 8T /1\ 8T

Now suppose that we have a circular disk of radius a which initially is at temperature T = To, but at time t = 0, the circumferential area of the

disk is heated at a constant rate B so that TT=a, = To + fit- Upon assuming

that there is no heat transfer at the plane surfaces of the disk, this problem

becomes the same as for a cylinder of infinite length, whose solution is T-To = B

(a2 — r

2 4a~~

+ [transient]. (41)

48-118
Although the transient in Equation (41) can be calculated6

, it is usually

short-lived so that the "steady" temperature difference between r = 0 and

r — a is most important. This temperature difference is simply /3a 2 /4a.

(1) The Principle ofSuperposition. Before consideration of thermal transients in calorimetry, the Principle of Superposition should be mentioned. This

principle, which can be applied to linear differential equations, states that

solutions to linear differential equations with linear boundary conditions

may be summed to give other solutions; a complex solution can be obtained

by adding the solutions to simpler problems. This method not only makes

numerical solutions easier but also provides physical insight into the heat

flow process in calorimetry. A concise statement of superposition theorems

is given by Korn and Korn15

. In brief, the temperature for some particular

problem may be considered as a sum of terms all satisfying the heat flow

equation, but separately taking account of (i) heat generated in the calori- meter, (it) heat exchange between calorimeter and surroundings, and (Hi) an initial temperature distribution in the calorimeter.

A problem involving two thermocouple errors will be used to illustrate the use of the principle of superposition. Suppose that the shield control in an adiabatic calorimeter is subject to errors due (i) to an inhomogeneity in a segment of thermocouple wire between the calorimeter and the shield and

(it) to a constant zero bias, which might be caused by an inhomogeneity in a

region outside of the shield or simply to a zero offset in an electronic control

device. Since the shield temperature is not matched to the calorimeter

temperature because of these two spurious e.m.f.s, there will be a temperature gradient in the segment of thermocouple wire and an additional offset due to the effect of this gradient on the inhomogeneityf. When the calori- meter is heated, the heat flowing into the wire segment from the calorimeter

and shield will have an additional effect on the inhomogeneity. The problem is to account for the two effects in the measurement process. To set up the equations, the segment of wire is taken to be of length I, the constant heating rate dT/dt = /3 deg/sec, and the constant control offset A7"c . Assuming negligible current in the thermocouple, the heat balance

equation is d*T 8T

a = — (42

8z2 3t

V

which is just Equation (17) with the power term zero. Since the solution

for constant heating rate is desired, the substitution dT/dt = /? can be

made at once. Equation (42) is linear either before or after the substitution, since the temperature and its derivatives appear only in the first power.

(Linear equations also cannot have cross products such as T (8T/8z)).

The boundary condition at the calorimeter end of the wire is that the temperature is rising at a constant rate and that its temperature would have

been To at t = 0

T = T0 + j8f at z = 0.

f In adiabatic calorimetry, this secondary effect is probably negligible; however, similar reasoning applies in isothermal shield calorimetry for which the effect on the spurious e.m.f. of the temperature difference between calorimeter and shield may be appreciable.

49-119
The temperature at the shield end of the wire differs from that on the

calorimeter by the constant offset A Tc and the effect of the inhomogeneity

T = TQ + pt + ATC + b (7i - T2) at z = /

in which T± and 7*2 represent the temperatures at the ends of the inhomogeneity and b is the ratio of the thermoelectric power of the inhomogeneity

to that of the thermocouple.

The problem can be written in terms of T — 7*o = U + V [noting

dTjdt = d (T - T0)ldt] in which

dHJ _ §

dz2 a U = 0/ at z = 0

Z7 = - t/a) + j8< at z = I (43)

and

V = 0 at z = 0

F = ATC + b(Vi - V2 ) at z = /. (44)

Evidently summing Equations (43) and (44) for U and F will result in the equation for T — Tq. Inspection of these two sets of equations for U and V

shows that the contribution V to the temperature due to the control offset has been separated from the effect of heating the calorimeter, even with

respect to the spurious e.m.f. This effect is constant and independent of the

heating rate, so that it can be evaluated in separate experiments, as in fore and after rating periods, assuming only that A Tc is the same in both cases. The effect on U of a change in the heating rate is now easily deduced. If the rate is changed by a constant ratio to kfi, then it is easily verified by

substitution that kU satisfies the equations for U, including the effect of the

spurious e.m.f. Any error associated with U, such as the effect of the spurious

e.m.f., is directly proportional to the heating rate. It does not follow that heat leak due to U or similar functions can be detected by measuring the

heat capacity of a calorimeter at various heating rates. The time required

to heat through the temperature rise for which comparison is made is inversely proportional to the heating rate. Heat transfer between the calorimeter and its surroundings is proportional to the product of the time

and functions like U, but the heating rate constant cancels from the product.

The more general problem of the effect of heating rates on heat exchange

in adiabatic calorimeters is discussed in Chapter 9, based on detailed mathematical arguments given in the literature21 . By contrast, the inclusion of a simple variation of the thermal conductivity

50-120
with temperature, such as A = Ao (1 + aT), results in the following nonlinear equation

X0 l{\ + aT)~ = ^c, ox 8x

(45)

and the substitution T = U + V results in cross terms in U, V, and their derivatives. Mathematical tractability is gone, but more important is the

loss of validity of the correction for the control offset. In general, of course, the thermal properties of materials are functions of temperature, so that the

linear equations are approximations. The designer must keep in mind that temperature differences in the experiment should be small enough that the

linear differential equation provide an adequate description. The tolerable temperature differences are greater when the temperature variations of

thermal properties are small and when the total heat transfer between the

calorimeter and its surroundings is small. Obviously, if the heat leak is zero,

it cannot produce a temperature distribution to interact with that due to heating. In testing an apparatus after assembly, it seems worth while to investigate

the linearity by deliberately exaggerating the magnitudes of the various

contributions to the temperature distribution. In the simple case of the terms U and V discussed above, different rates of rapid heating and different

offset of controls might set an upper limit on permissible rates and offsets. Variable heating rates commonly used in adiabatic heat capacity calori- meters rarely reveal a corresponding variation in the observed heat capacity.

One obvious interpretation is that it is not very difficult to obtain an apparatus which is adequately described by linear partial differential equations.

(2) Transients in One-Dimensional Heat Conduction. Transients may be

important to the design of calorimeters. Calorimeters must come to equilibrium in a reasonable time so that the uncertainty in the heat leak correction

remains tolerable. Transient problems are difficult, but most cases of

interest for the approximate design calculations in calorimetry have been

worked out6 . A transient problem will be illustrated with a calculation of

the flow in one direction (one-dimensional) with no lateral losses. This problem treats approximately the temperature distribution in a lead wire, with one end fastened to the constant temperature bath and the other heated at the rate /J, with the initial temperature that of the bath. Although the problem

seems restricted in scope, by the principle of superposition we can apply it also to the case for which both ends are heated and the wire has an initial temperature distribution which might be the steady state between a calori- meter at one temperature and a bath at another temperature.

The solution to this problem is given by Churchill7

00 T-T0 = P

xt 2 (- l)n-l

i n - 1 exp [(- XnWtjpel2

)] [sin {nrrxll)} . (46)

51-121
The exponential series does not converge rapidly for small values of the

argument, but for Xtjpcl2 greater than 0-1 only the term for n — 1 is signi- ficant in the time required for the calorimeter to come to equilibrium.

Qualitatively, in order to get rapid equilibrium in the calorimeter, we

would like to have the thermal conductivity large and the length, which

appears to the second power, small. For a copper wire 10 cm long at room

temperature, the time constant for the first term is equal to 10 sec (time to decrease to ( 1 je) of the initial value) . For an insulated copper wire we can

use the approximation that heat is conducted along the copper to the insulating material which contributes to the heat capacity but not to conduction. For a copper wire of 0-02 cm diam and 0-0025 cm thickness of insula- tion of approximately the same heat capacity per unit volume, the time

constant is increased to 14 sec. Doubling the length increases the time constant for the insulated wire to 56 sec. The time constant is greatly increased

for alloy wires. If we consider a constantan wire instead of the insulated

copper wire above, the time constant is about 20 times longer or 220 sec. If such a wire has a spurious e.m.f. or sufficiently large heat capacity so

that we must wait until it is within one per cent of its final value then the

time required is about 2(2-3) times the time constant or 1000 seconds. If it

is necessary to install long wires in the apparatus, their temperatures should

be kept constant during an experiment.

If supports for a calorimeter are chosen only on the basis of low thermal

conductivity, harmful lags may be introduced. A calorimeter supported on

glass rods provides an example. Equation (46) applies with the thermal

diffusivity Xjpc ~ 5-7 X 10~3 for a glass near room temperature, and the

time constant for the first term is 176 sec for a 1 cm length, and 704 sec for a 2 cm length. Of course, if the calorimeter merely rests on the glass rods,

the additional thermal resistance of the contact will give a still longer time

constant. Although Equation (46) applies to the case of turning on power in a

calorimeter, the same arguments apply when the power is turned off. To

obtain the solution for this case we merely subtract the right hand side of

Equation (46) in which we have substituted (t — if) for t, in which £f is the

time at which the power is turned off. In the general case there will be two

sets of decaying exponentials, but those in t — tf will be predominant and

the equilibrium time depends on these. When some portion of the apparatus is subjected to automatic control

it is important that the transient response be rapid. The thermal conductivity should be as large as possible, the distances between heaters should

be kept small and heat capacities should be kept small. These problems are

discussed in detail in other chapters. The previous example of transients is for a linear heat flow. Many other problems, including transients in radial

heat flow, are solved in Carslaw and Jaeger's book6 .

IV. Applications to Calorimeter Design

1. Temperature in a calorimeter wall at constant heating rate

One of the most important problems in accurate calorimetry results from

temperature gradients in the calorimeter. In most calorimeters the heater

52-122
is not distributed in such a manner as to avoid gradients, and even if it were

for one amount of filling in the calorimeter, the same condition probably

would not hold for another filling. Consider as a simple example the temperature difference in a cylindrical

calorimeter wall which receives heat only at one end (z = 0). Assume that the wall has a length /, thickness w, radius r, thermal conductivity A, density

p, and heat capacity c, and that all these quantities are constant during an

experiment so that each part is heating at a constant rate /3. The heat

balance differential equation here is X{2-rrrw) dT/dz = p(l — z) in which

p is the power per unit length of cylinder necessary to heat it at a rate /?. The power p is simply p — (2-n-rw) pcf$, so that

O rri X{2imv) — = (2irrw) PcP (I - z) (47)

dz

or

fz = fi (I - «) =ld- z) (48)

in which a is thermal diffusivity, X/pc.

Integrating between z = 0 and z = I gives

(Tz -To) = -f

2 (49)

la

in which Ti and To are both increasing at the rate /}. This relation is the same as that given by Equation (39) after the transient. It is apparent that the largest temperature gradient occurs near the heat source, so that the assumption of linear temperature change on the surface is invalid. The

average temperature (relative to To) over the surface can be calculated

from the equation

J [( Z 2/2) - Iz] dz

(r-r0)av =

^° - = ^

(50) a ' a 6

J dz

o

However, — To) = — £/a(3/8)/2

, so that the difference between

the average temperature and 7// 2

is about (0-042 /3/a I 2

). The example given above is for a cylindrical calorimeter wall heated at one end. In a similar manner there may be obtained the temperatures in a

shell heated equally from both ends. The solution here using boundary

conditions that T — To at z = 0 and z — / is

(Tm -T0) = -£-(lz-z2) (51)

la

53-123
The minimum temperature is at z — //2, and its value is (T1/2 — To) =

— (/3/2 /8a), so that the use of two heaters reduces the maximum gradient by

a factor of four. To avoid temperature differences on the surface, various techniques are

used. Stirred liquids are used to distribute the heat in many calorimeters

and in others metal vanes run from the heat source to the surface. In large

calorimeters, the stirred liquid technique is usually preferable. Conduction is less attractive for large dimensions because the temperature difference

increases rapidly with the distance. In the simple case described by Equation

(49), the temperature increases with the square of the distance. In small

calorimeters, good metallic conductors serve well and avoid the heat and

mechanical problems of stirring.

2. Uncertainty in heat leak due to temperature gradients

It has been illustrated that for the different methods of heating the

calorimeter wall the temperature gradients in the wall may be different. When the heater is located at one end of the cylindrical wall, the average temperature of the cylindrical surface occurs at a distance of about (0-43/) in which / is the length of cylinder. If the heat leak is entirely by radiation

from the wall surface (assume constant emittance), then a single thermocouple should be located at 043/ from the end for proper accounting of

radiation heat leak. If the thermocouple had been located at the middle

of the cylindrical wall (at //2), then the thermocouple temperature would

differ from the average surface temperature. Let us examine an actual case

to see the magnitude of this difference. As an unfavorable case, take a

calorimeter wall of steel having length / = 10 cm, thermal diffusivity a = 0-1, and heated at a rate of 0-01 deg/sec. The temperature at its middle

(112) referred to the heated end is less by j8/a [(3/8 I2

)] = 3-75 deg.

However, the average temperature of the surface is j3/a (/2/3) = 3-33 deg.

Therefore, the location of the thermocouple at //2 gives a heat leak error corresponding to 0-42 °C over the surface. If copper were used instead of

steel, the temperature difference would be about 0-04 deg.

3. Methods of minimizing heat leak due to temperature gradients

The previous example indicates that temperature gradients in a calori- meter or shield wall can result in errors in heat leak measurement if the

thermocouple (or couples) used are not located properly to account for the

temperature gradients. Where possible, one obvious solution to the problem

is to design the calorimeter and shield to minimize temperature gradients.

This may be done by stirring or by use of materials with high conductivity

or proper distribution of heater so that heat has to flow only a short distance.

This latter solution may be complicated by different relative power requirements at different times. For example, in heating experiments with most

of the power going to changing the temperature, the power distribution

needed in the shield will be approximately according to mass. However, at steady temperatures with the power going only to heat leak, the power

distribution needed probably will be entirely different. One partial solution

to this problem has been to use two separate heaters, one distributed according to mass and one according to heat leak.

54-124
Another method of minimizing temperature gradients in a shield is to minimize the power required to keep it at a given temperature. This may

be accomplished with better insulation from its cooler surroundings. Generally, it is better to provide insulation with a minimum of heat capacity

because of effects of time lag in the insulation. One such insulation with a minimum of lag is a number of concentric thin shells, such as discussed

later in this chapter. Another method of reducing the power required in a

shield, thereby reducing temperature gradients, is to provide external

concentric shells, with the temperature of each independently controlled. In this manner, the power in the shield (inner shell) at a constant temperature can be negligible. An example of this is given in Chapter 11. However,

use of such a system does not avoid temperature gradients on the shield

while heating.

Another solution of the temperature gradient problem is to use a sufficient number of thermocouples to provide adequate information on the temperature distribution. One calorimeter (Chapter 11) used eight thermocouples on both the calorimeter and shield wall surfaces to evaluate average temperatures. In the case of heat capacity experiments, it is possible in principle

to reduce errors in heat leak due to temperature gradients by using two

series of experiments, a tare and a gross series. If the gradients on both

calorimeter and shield are the same (considering each separately) in both

series, then ideally the absolute heat leak errors are the same. They then

cancel out when taking the difference between the tare and gross series. The

effectiveness of this method for reducing heat leak errors depends upon the extent that the temperature gradients are the same. The shield gradients

do not have to be the same as the calorimeter gradients. This method is used

commonly with the assumption that the gradients are nearly the same in the two series. The fallacy in this assumption is that the temperature gradients

in the calorimeter are necessarily changed by the change in the amount of

sample, the magnitude of the change being a function of the design.

The obvious solution to this problem is to provide a calorimeter surface whose temperature is independent of the presence of the sample. This ideal condition can be approached in many calorimeters by a technique applied

in Chapters 9 and 11. The principle of this technique is illustrated simply

in Figure 6 which shows a portion of a sample container with a heaterless

Figure 6. Method of reducing heat leak errors due to temperature gradients on sample

container. 55-125
thin metal shell S thermally attached only at the zone Z. In heating experiments, in which it is assumed for simplicity that the calorimeter is solid metal, the heater produces a temperature gradient. After the starting

transient has diminished, all of the calorimeter, including the ring at Z and

the heaterless shell, will be heating at the rate jS. This, of course, assumes

constancy of A, p, c, and no heat transfer except by solid conduction at zone

Z. Under this condition, the heaterless shell will also have gradients. Since

the gradients will be independent of the gradients on the calorimeter, any

heat leak will also be independent of the gradients in the calorimeter. In

this case, in principle, the use of the tare and gross series of experiments

avoids heat leak errors if the temperature at the zone Z follows the same

time-temperature function in the two series of experiments \. The success of

this technique depends on the extent of thermal isolation of the heaterless

shield S from the sample container G over the cylindrical surface. In one

adiabatic calorimeter near room temperature with a single heaterless shell on the sample container, the thermal isolation was obtained by evacuation

and use of polished gold surfaces. The effectiveness of this single shell can be

demonstrated by considering the effect of the vertical gradient in the sample

container [Figure 6) on the temperature of the shell. The principle of superposition can be used to separate the vertical gradient in the shell into two

components, one due to heat flow through the zone Z to heat the shell at the rate /3, and the other due to heat flow from the sample container directly across to the shell by radiation. For simplicity, consider only the cylindrical

portions. Let h = heat transfer coefficient between the two surfaces, A, w, r, and / the thermal conductivity, thickness, radius, and length of the heaterless cylindrical shell. Also assume there is a gradient on the sample container

so that its surface temperature (referred to zone Z) is Mz2 in which z = 0 at the zone Z. Also as a first approximation, assume that the resulting gradient

in the shell is much smaller than the gradient on the sample container. The

heat balance equation here is

A(2tt7w) ~dz = - h (Zttt&z) (Mz2

) (52)

dz2

in which h is the heat transfer coefficient between sample container and the

shell, so that d

2 T\dz2 — — (hMjXw) z

2

. Integrating this equation

between the limits z — 0 and z = I gives

hM /I* AT — (Ti — To) = — — + C\ly (53,

Using the boundary condition that dT/dz = 0 at z = I, gives Ci — — hMl3/3\w so that hM 11* \ Ar =-3to(4-'4

) =

hMl4 4Xw (54)

t In general, the transient effects for the gross differ from those for the tare. The statement

is valid, but depends on a more sophisticated argument which does not even require the same heating rate21 . 56-126
For an example, use 1 = 5 cm, w = 0-025 cm, A = 1-0 W cm-1 deg-1

, and M — 1, giving a 25 deg temperature difference on the sample container. If the space is evacuated and the surfaces are polished gold plated,

the radiative heat transfer coefficient is about 10~5 W cm_2deg _1

. Substituting these values gives AT" = 0-0625 deg C. This contrasts with the 25 °C

temperature difference on the sample container. The conclusion is that in

this case, one heaterless shell has attenuated the effect of the sample container gradient by a factor of approximately 400. It is interesting to note

the magnitude of the temperature difference in this shell due to heating

the shell at a constant rate /3. This temperature difference after the transient

has vanished can be calculated using Equation (49), giving (Tj — To) = —

/?/2 /2a. Using / = 5 cm, a heating rate of 0-01 deg/sec, and a = 1 cm2 /sec

(for copper) we get AT = 0-125 deg C. With this technique of providing a calorimeter surface whose temperature

is independent of temperature differences in the calorimeter, it is no longer

necessary to position thermocouples on the surface of the shell in order to obtain an average surface temperature. The tare and gross experiment will have the same heat loss, independent of the location of the thermocouple.

It usually is convenient to locate one or more thermocouples at the zone 22 . The use of the heaterless shell is equally valuable in experiments such as heat of vaporization for which the calorimeter temperature is not changing

with time. In this case, the shell attached to the calorimeter at one zone is isothermal in spite of temperature gradients in the calorimeter due to vaporization. A similar shell attached to the inside of the shield at one zone

also is isothermal, in spite of temperature gradients in the shield due to heat

loss to the surroundings.

It is not always possible to obtain as low a heat transfer coefficient as there was in the evacuated space bounded by polished gold surfaces. In a high-temperature adiabatic calorimeter22 in which the space was not

evacuated, the effectiveness of an unheated shield was not so great, so that

it was necessary to use several shells.

4. The calorimetric heater lead problem

A more complicated case in steady-state heat flow is the problem of the calorimeter heater leads between calorimeter and shield. This problem has

been considered in great detail in a recent publication9

, so that it will be

discussed here only briefly.

The calorimeter heater current leads must be considered differently than

the other calorimeter leads because the electric current in them develops

heat which must be properly accounted for and apportioned to calorimeter

and shield. The other leads merely serve as heat conductors to contribute

to heat leak coefficients. The calorimetric error resulting from any uncertainty in the apportionment of the heat in the current lead segment between

calorimeter and shield may be made small by using current lead segments

of low electrical resistance relative to the calorimeter heater resistance. The

problem here is that electrical and thermal resistances are usually proportional under ordinary conditions with metal wires, so that the smaller

electrical resistance gives smaller thermal resistance. In turn, this results in

57-127
a larger heat transfer coefficient which increases the heat leak uncertainty.

The optimum size of lead depends on the particular calorimeter.

There is, however, a method by which any error in current lead power

apportionment can be made smaller without this increased heat leak

uncertainty. This method is simply to increase the relative resistance of the

calorimeter heater. Accordingly, in most calorimeters at moderate temperatures, a calorimeter heater resistance of at least 100 D is considered

desirable if accuracies approaching 0-01 per cent are desired. Sometimes at low temperatures, heaters are used which have resistances of thousands of

ohms.

In accounting for the power in the current lead segments, the convention assumes that the heat developed in a current lead segment divides equally

between calorimeter and shield, so that the potential lead is attached to the center of the current lead segment. It has been pointed out earlier (Equation

25) that this assumption is strictly true only when the ends of a current lead

segment are at the same temperature. This condition for validity is satisfied

if the calorimeter and shield are at the same temperatures and the thermal

connections to the calorimeter and shield at the ends of a current lead are

also the same. It has also been pointed out that even if these thermal connections are the same, the use of potential leads at mid points is valid with

the calorimeter and shield at different temperatures only if a. heat leak correction is made for the "apparent" heat flow along the current lead segments

assuming their ends are at the temperatures of calorimeter and shield. This

procedure is approximated in accurate calorimetry by merely measuring an

overall heat transfer coefficient between calorimeter and shield when there is no current in the calorimeter heater and using this coefficient to calculate h ;at leak corrections, including periods when there is current through the heater

lead. The general problem of calorimeter current leads is when (i) the calori- meter and shield are at different temperatures (Tc and Ts), and (ii) the thermal connections at the ends of the current lead segments are different. Consider calorimeter current leads, each having cross section A and

length / between calorimeter and shield, and having a thermal conductivity

A. Now suppose that there is electric heat developed at a time rate p for unit length of the wire, and that all heat lost from the current lead segment

is by solid conduction along the wire. Also suppose that each current lead is thermally and electrically insulated from the calorimeter or shield and that

these thermal resistances per unit length between the wire and the calori- meter or shield are Rc and Rs , respectively. With these conditions a solution9 of the heat balance equations gives the rate of heat flow Pc into the calori- meter by conduction along the current lead segment.

P - P-

/2 + 2lV(MRs) + 2\A(RB - Rc)

I + ^/{XARB) + V(MRc) +

XA(TB - Tc)

I + y/{XARa) + V(A^c)

(55)

]

The solution is shown in the two terms to demonstrate its physical signi- ficance. The second term in the solution is independent of power developed

in the wire and is the heat flow due to the temperature difference ( Ta — Tc ) 58-128
between shield and calorimeter. It is important to note that this second

term (involving Ts — Tc) is usually accounted for by conventional calori- metric techniques, which experimentally measure and correct for the

overall heat transfer coefficient between shield and calorimeter when there is no current in the leads. The first term in Equation (55) is proportional to the power developed in the current lead so that it accounts for that part of

the heat flow caused by the current in the lead. The resulting overall calorimetric error resulting from this first term has been calculated9 to be

Calorimetric Error (%) = 100 r 2(L82 - Lc2) + (L8 - Lc

1 + Ls + Lc (56)

in which r is the ratio of electrical resistance of length / of the current lead

segment to the total electrical resistance of the calorimeter heater, including

leads out to the potential terminal, and

, and Lc =

I

The relation between these dimensionless quantities Lc and Ls and [(1/r). Calorimetric error] is illustrated in Figure 7.

0-5 10 1-5 20

Lc

Figure 7. Calorimeter error relation.

2-5

In order to judge the practical importance of the error described above,

it is necessary to calculate values of Ls and Lc and r for specific examples.

Suppose that the current lead is circular, that the length / of the current

lead segment is 3 cm, and that the lead is copper with o.d. = 0-02 cm

Also suppose for thermal contact in the calorimeter this lead is electrically

insulated by a cylindrical solid surrounding the wire to an o.d. of 0-2 cm

and having a thermal conductivity of 0-002 W cm-1 deg-1 corresponding

to a typical organic material. In this case, Rc — 184 degW-1 cm-1 and

Lc = 0-166. Now suppose that in the shield there is an air gap of 0-005 cm

59-129
between the wire and the insulation (o.d. of 0*2 cm). The resulting value of

RB = 411 deg W"1 cm"1 so that Ls = 0-238 and [(1/r) • (calorimetric

error)] is 9-3 per cent. If the calorimeter heater has a resistance of 10 Q,

r = 0*0016 so that the calorimetric error in the power measurements due

to using a potential lead at the mid point of the current lead is 0-0016 (9-3) =0-015 per cent. This error is only significant in the most accurate calorimetry.

On the other hand, it is possible to have considerably larger error in a poor

design. Take a case in which Rc is reasonably small but Rs is perhaps 2000

degW-1 cm"1 due, for example, to an evacuated powder insulation. In this case, the calorimeteric error is 0-083 per cent. In the previous discussion of calorimeter heater leads, it has been assumed

that the potential leads were attached to the current lead segments at their mid points and that heat flow along these leads is negligible. If this heat flow

is not negligible, consideration should be given to the location of their attachments. The mid point attachment has the disadvantage that the

temperature of the mid point is a function of the current in the calorimeter

heater, but the resulting heat conduction along the potential lead is not accounted for in the first term in Equation (55). Although probably an

analysis for the heat flow could be obtained, since the effect is usually a

small one, it is easier to change the design to avoid the error. One method

which has been used22 is to attach thermal tiedowns on the current leads

close to the calorimeter and shield mechanical boundaries. If the two current

leads and their thermal tiedowns are symmetrical, it is convenient to attach one potential lead at the calorimeter tiedown of one current lead and the other potential lead at the shield tiedown of the other current lead. In this way, the energy apportionment is effectively at the mid points of the current

leads without having the problem of heat transfer along the potential leads being a function of the heater current.

V. References

1 Barry, F., J. Am. Chem. Soc, 44, 927 (1922).

2 Berman, R., /. Appl. Phys., 27, 318 (1956) ; Berman, R., and C. F. Mate, Nature, 182, 1661

(1958).

3 Brunot, A. S., and F. F. Buckland, Trans. Am. Soc. Mech. Engrs., 71, 253 (1949).

4 Caldwell, F., Thermocouple Materials, Natl. Bur. Standards Monograph 40, U.S. Govt.

Printing Office, Washington, D.C., 1962; Temperature, Its Measurement and Control in Science and Industry, Vol. I, American Institute of Physics, Reinhold, New York, 1941; Vol. Ill, C. M. Herzfeld, editor-in-chief, Part 1, F. G. Brickwedde, ed., Part 2, A. I. Dahl, ed., Reinhold, New York, 1962.

5 Campbell, I. E., High-Temperature Technology, John Wiley and Sons, Inc., New York, 1956.

6 Carslaw, H. S., and J. C. Jaeger, Conduction of Heat in Solids, Oxford University Press, London, 1959.

7 Churchill, R. V., Operational Mathematics, McGraw-Hill Book Co., Inc., New York, 1958.

8 Ditmars, D. A., and G. T. Furakawa, /. Res. Natl. Bur. Std., 69C, 35 (1964).

9 Ginnings, D. O, and E. D. West, Rev. Sci. Instr., 35, 965 (1964).

10 Hoge, H. J., Rev. Sci. Instr., 20, 59 (1949).

11 Jacobs, R. B., and C. Starr, Rev. Sci. Instr., 10, 140 (1939).

1 2 Jakob, M., Heat Transfer, Vol. I, John Wiley and Sons, Inc., New York, 1949.

1 3 Jakob, M., Heat Transfer, Vol. II, John Wiley and Sons, Inc., New York, 1957.

1 4 Kistler, S. S., and A. G. Caldwell, Ind. Eng. Chem., 26, 658 (1934).

15 Korn, G. A., and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGrawHill Book Co., Inc., New York, 1961.

1 6 Lyman, T., ed., Metals Handbook, 8th ed., American Society for Metals, Novelty, Ohio,

1961 ; American Institute of Physics Handbook, McGraw-Hill Book Co., Inc., New York, 1957;

International Critical Tables, McGraw-Hill Book Co., Inc., New York, 1928. 60-130
17 Mebs, R. W., and W. F. Roeser, Solders and Soldering, Natl. Bur. Standards Circular 492, U.S. Govt. Printing Office, Washington, D.C., 1950.

18 Petree, B., and G. Ward, Natl. Bur. Standards Technical Note 163 (1962), U.S. Govt. Printing

Office, Washington, D.C.

19 Scott, R. B., Cryogenic Engineering, D. Van Nostrand and Co., Inc., New York (1959).

20 Weills, N. D., and E. A. Rider, Trans. Am. Soc. Mech. Engrs., 71, 259 (1949).

21 West, E. D., /. Res. Natl. Bur. Std., 67A, 331 (1963).

22 West, E. D., and D. C. Ginnings, /. Res. Natl. Bur. Std., 60, 309 (1958).

23 White, W. P., The Modern Calorimeter, The Chemical Catalog Co., Inc., New York, 1928.

24 White, W. P., J. Am. Chem. Soc, 40, 382 (1918).

61-131
Reprinted from*

Experimental Thermodynamics

Volume I

CHAPTER 11

Calorimetry of Saturated Fluids Including

Determination of Enthalpies of Vaporization

D. C. GlNNINGS

National Bureau of Standards, Washington, D.C., U.S.A. H. F. Stimson

National Bureau of Standards, Washington, D.C., U.S.A. (retired)

Contents

I. Introduction . . . . . . . . . . . . . . 395

II. Theory of the Method 396

III. General Galorimetric Design and Procedures . . . . . . 399

IV. Calorimeters for Measuring Properties of Water . . . . 403

1. Calorimeter for 0-270 °C 403

2. Calorimeter for 1 00-374 °C 404

3. Calorimeter for 0-100°C 407

A. Accounting for Mass of Sample .. .. .. ..411

B. Accounting for Energy . . . . . . . . ..411

( 1

) Electrical Energy .. .. .. .. ..411

(2) Pump Energy . . . . 412

(3) Heat Leaks 412

C. Accounting for Change in State .. .. .. ..412

4. Comparison of Results with the Three Calorimeters . . 413

V. Calorimeter for Hydrocarbons .. .. .. .. ..413

VI. Other Calorimetric Methods for Measuring Enthalpy of Vaporization . . . . . . . . . . . . . . 418

VII. Summary .. .. .. .. .. .. ..419

VIII. References 419

I. Introduction

Calorimetry of saturated fluids is the measurement of the heat required

for changes of state in them (liquids and vapors). The term "saturated",

as used in this chapter, restricts the states of the fluid to those for which

the liquid and the vapor phases are both present in equilibrium within the

calorimeter. The relative amounts of the two phases, however, may differ by large factors; i.e., the calorimeter may be nearly full of liquid in a highfilling experiment or may have only a little liquid in a low-filling experiment. In heat capacity determinations both high and low fillings can be used. Sometimes such experiments are called gross and tare experiments. The

method of saturation calorimetry described in this chapter differs from

calorimetric methods in some other chapters of this book in which tare ex- periments are made with an empty calorimeter. In 1917 Osborne5 described

his experiments on the specific and latent heats of ammonia in which he

made tare experiments with an empty calorimeter. These required him to make some troublesome corrections about whose accuracy he felt somewhat

*See complete ref. on page 1-1.

62-395
uncertain. In 1924 he developed6 the method described here, to be used for determining the thermal properties of water and steam. This method of

saturation calorimetry not only simplifies the computations but also, in

principle, eliminates certain errors. In saturation calorimetry the temperatures depend only on the pressures along the vapor pressure line; thus, at any instant, the temperature at all liquid-vapor interfaces in the calorimeter is essentially uniform and

depends only on the pressure of the vapor there. Enthalpy of vaporization

experiments, therefore, can be performed at a constant temperature, by

adding heat and withdrawing fluid from the calorimeter while controlling

the flow rate to keep the pressure constant. In heat capacity experiments, the power input can be chosen so that the temperature may be raised at essentially the same rate in both the high and

the low fillings, thus making the pressure changes occur in the same way in both. This procedure has the advantage that, by taking differences, one can

eliminate the correction for fluids in the filling tubes and the correction for work done by strain of the calorimeter as the pressure is raised. By Osborne's method the enthalpy values of both the saturated liquid

and the vapor can be obtained directly from three types of experiments

made in one apparatus without precise knowledge of the volume in the

calorimeter or other thermal properties of the fluid. This calorimetric method

was first applied to water and steam7 - 9. 10 and later to hydrocarbons12 . A

review of the theory of this method will be given, together with experimental

applications to determine some thermal properties of water in the temperature range from 0-374 °C. In addition, there will be some discussion of

other methods of measuring enthalpies of vaporization.

II. Theory of the Method

The method makes use of a single calorimetric apparatus. A sample (both

liquid and vapor) is so isolated (in the calorimeter) that its quantity,

state and energy can be accounted for. With this apparatus, a system of

measurements can be made at progressively higher temperatures to deter- mine values of enthalpy of both the liquid and the vapor, referred to values

at some reference temperature such as 0°C.

The calorimeter is provided with two outlet tubes, one at the bottom

for introducing or withdrawing liquid and the other at the top for withdrawing vapor. Valves on these tubes either shut the fluid in the calorimeter

or control the rate at which fluids are withdrawn. Provisions are made for observing the mass of fluid put into the calorimeter, the heat added, and the temperature of the calorimeter with its contents. The calorimeter is sur- rounded by a shield whose temperature is controlled so as to minimize

net exchange of heat between them. All experiments are made with both

the liquid and vapor phases present in the calorimeter.

The essential equations involved in the method follow; for more detail on the derivations of these equations the reader is referred to Osborne's

original papers6 . First consider two heat capacity experiments with the

calorimeter, (a) one with a large volume of liquid and some vapor, and (b)

the other with a small volume of liquid and the rest vapor. In these two

experiments the calorimeter contains the sample masses m& and m-^, 63-396
respectively. The corresponding quantities of energy, qA and qB, which are necessary to heat the calorimeter and its contents from an initial temperature,

Tx, to a higher final temperature, Ti, are found. From these experiments

it is concluded that the difference of the energies, q& — qB, is used to heat

the difference of the masses of the sample, mA — %, from T\ to T<i. The quotient of these differences would represent the change of the enthalpy, H, of the saturated liquid, were it not for the larger volume of vapor in experiment (it). This requires a "vapor correction", AHv [Vj(V — V)\ in which AHV

is the

enthalpy of vaporization and V and V are the specific volumes of the saturated liquid and vapor respectively. The equations are

AqjAm = (qA — qB)l(mA — mB) = H-AHv [Vj(V - V)]

- [a]£ (1) The quantity in brackets, [H — AHv [Vj(V — V)]], is a specific thermodynamic property of the sample itself and is not dependent on the calorimeter.

This property, which Osborne called a, has the dimensions of enthalpy.

Equation ( 1

) shows that this property, a, is less than H by a vapor correction term AHv [Vj(V ' — V)] which Osborne called ft and which is also a

specific thermodynamic property of the sample. Hence

a = H-AHv [Vj(V - V)] =H-p. (2) Now cftnsider a second type of experiment which can be used for measuring

the enthalpy of vaporization AHV . Let heat be supplied to evaporate liquid

while withdrawing vapor. A throttle valve is operated to control the rate of withdrawal so as to keep the pressure, and consequently the temperature

of evaporation, constant throughout the experiment. The vapor thus

removed is essentially saturated at the temperature of the experiment. The

theory shows that the heat added, Aq, divided by the mass withdrawn, Am,

is equal to the enthalpy of vaporization AHV plus the same vapor correction ft described above in the a experiments. The quantity AqjAm used for this vaporization experiment, and called y by Osborne, is also a specific ther- modynamic property of the sample so that

y = AqjAm = AHV + AHV [V(V - V)] = AHV + ft. (3) Now consider a third type of experiment in which liquid is withdrawn

through the lower tube as heat is added. Here it is obvious that all energy

goes to producing vapor to fill the space whence liquid is removed. For unit mass of liquid withdrawn, there is [Vj(V — V)], of unit mass of liquid

vaporized in the calorimeter, so that

AqjAm = AHV [V(V - V)] = ft. (4) Here then is an experiment which directly evaluates the vapor correction

ft used to obtain H and AHV from the a and y experiments.

The relations between Osborne's measured a, ft, and y, and conventional

enthalpy (at saturation) are summarized by the equations 5 to 7. 64-397
// a + P

y-fi

(5) AHVX (6) H' H + AHVX = a + y (7)

in which H' is the enthalpy of the saturated vapor. So far these derivations have involved only the first law of thermodynamics. If the Clapeyron relation is used, which involves the second law

of thermodynamics, the following equations result

y = AHv + AHV [VI(V - V)] = AHV [V'I(V - V)] = V'T(dP/dT) (9)

in which T is the absolute thermodynamic temperature and P is the vapor

pressure. The ratio of these equations reduces to

at any temperature. From this it is seen that calorimetric measurements

can lead directly to the ratio of the specific volumes of the saturated fluids. From equations (8) and (9) it is also seen that the calorimetric measurements

can lead to values of the specific volumes if the vapor pressure derivative,

dP/dT, is known.

In order to visualize the relative magnitudes of these specific thermal

properties (a, j8, y, and H), Figure 1 shows the formulated results of the

experiments which were performed to obtain values of the thermodynamic

properties of saturated water and water vapor. The a is shown starting from

zero at 0°C and increasing almost linearly up to the critical point (~374°C).

The y is greatest at 0°C and decreases with increasing rapidity until its slope becomes — oo at the critical point. The j8, on the other hand, is very

small at 0°C, but its slope increases with temperature. Above 300 °C the

slope increases faster than exponentially and /S meets y at the critical point

where the slope is oo. The enthalpy of the saturated liquid, H, is the sum of

a and /J. The enthalpy of the saturated vapor, H', is the sum of a and y

and it meets H at the critical point. At any temperature the difference

H' — H, which is the same as the corresponding y — /?, is the enthalpy

of vaporization AHV. The mean diameter is defined as (y + /3)/2. Figure 1 shows that for water, /? is relatively small except at the higher

temperatures and pressures. At 100°C, the normal boiling point of water, /?

is only about y/1600 and about a/300. For liquids below their normal boiling

points it is usually more accurate to calculate the values of /3, by using the

equation = VT(dP/dT), than to measure them calorimetrically.

The saturation enthalpy is H = a + j8, so that

For most liquids near their normal boiling points dj3/dTis as much as 1 per

cent of da/dTso some care must be taken there when using the Clapeyron

relation for calculating and dfijdT accurately.

)8 =AHV [V/(V' - V)} = VT[dP/dT) (8)

(dHldT)s = da/dT+ dp/dT. (11)

65-398
800

100 200 300 Temperature, °C

Figure 1. Thermodynamic properties of water.

Values of the specific heats, Cs = (8q/dT) s and Cp = (dqjdT)?, are

often needed. The value of Cs can be obtained from the relation

Cs = (dH/8T)s - V{8P/8T)S = da/dT + d^S/dT - p/T. (12)

Cp may be obtained from Cs using the relation

CP = Cs + T(8VldT)?(dPldT)s. (13)

As a general rule (8H/8T)s, Cs, and Cp differ from each other by less than

0-1 per cent at temperatures below the normal boiling points.

III. General Calorimetric Design and Procedures

The design of apparatus for the calorimetry of saturated fluids depends

upon such factors as the amount of the sample available, the temperature

and pressure range, the accuracy desired, the thermal properties of the

sample, and the state of calorimeter design at the time. In the calorimetry

of Osborne and his collaborators, several general principles were adopted at the start. Some of these will now be discussed. Early in the program it was accepted that heat leak uncertainties could

be the largest item of error in accurate calorimetry and that it was necessary

to minimize and evaluate the heat leaks. The solution to this problem

involved three different procedures, (z) minimization of the heat transfer

coefficient between calorimeter and surroundings, (zz) minimization of the temperature differences between calorimeter and surroundings, and (tit) measurement of all unavoidable temperature differences in order to correct

for the resulting heat leak. The application of these three procedures

follows. In three of the calorimeters described in this chapter the space surrounding

66-399
the calorimeter was evacuated in order to eliminate heat leak by gaseous conduction and convection. However, in one calorimeter operating at higher temperatures at which heat leak by radiation is large, it was not convenient to evacuate, but the heat transfer was minimized by using a series of progressively larger shields, appropriately spaced. The coefficients of

heat transfer by radiation were minimized also by using polished reflecting surfaces of gold or silver, which had low emittances. Minimizing the

coefficient of heat transfer by solid conduction was more difficult because some metallic connections were necessary. The metal connecting tubes

at the top and bottom of the calorimeter were made of alloys chosen for their low thermal conductivity, chemical inertness and mechanical strength.

The dimensions of these tubes were chosen to give adequate strength and

fluid conductance without excessive cross section. There was also a heat

leak from the calorimeter along some of the thermocouple wires. The sizes and materials of these were chosen by giving consideration to the combination of sturdiness, thermal and electrical conductance, and thermoelectric

power.

It is more difficult to make the temperature differences between the calorimeter and its surroundings small when there are temperature gradients on the surface of the calorimeter and the shield. The first step, therefore, was to minimize temperature gradients. This was accomplished in several

different ways, depending upon the particular calorimeter. In two calori- meters, mechanical stirring was used to distribute heat and thus reduce

the temperature differences over the surface of the calorimeter. In the

calorimeter designed for higher pressures and temperatures, for which

mechanical stirring would have been difficult, bubbles of vapor mixed the

fluid as in a coffee percolator and heat was distributed further by conduction

in a system of silver vanes. In a fourth small calorimeter, many copper vanes

distributed the heat by conduction.

It is not only important to consider the temperature gradients in the calorimeter but also the gradients in its surroundings. Although it is true

that calorimetric procedures usually reduce the effect of errors which are due to temperature gradients in a shield, this reduction of errors is more

effective if the gradients are small and essentially independent of the

environment. One calorimeter used a stirred liquid bath to distribute

heat over a shield (shell) surrounding the calorimeter. In another calorimeter

at higher temperatures, for which it was impractical to use a stirred liquid bath, a heavy silver shield was used to distribute heat from a heater wound on it. In still another designed for the maximum accuracy at moderate temperatures, a novel heat distribution system using a saturated vapor bath was very

effective over a large surface. In addition to minimizing heat transfer coefficients and temperature

gradients, the remaining unavoidable temperature differences were recorded

and summed algebraically so corrections could be made for the net amount of heat transfer. The evaluation of the overall heat leak in an

experiment was performed by dividing the heat leak into four parts, (i) the heat leak to the shield from most of the surface area of the calorimeter,

usually measured by means of a combination of thermocouples, (ii) the heat

leak along the upper tube connecting to the calorimeter, (Hi) the heat leak 67-400
along the lower tube and (iv) a heat leak called the "residual" heat leak,

which is that heat leak occurring when there is no indicated temperature

difference between the calorimeter and its surroundings. In order to eyaluate

the various heat leaks adequately, it was necessary to give systematic

attention to experiments designed for this purpose. For example, the

residual heat leak was usually evaluated before and after each experiment.

Experiments to evaluate the various heat transfer coefficients at different temperatures were made daily by deliberately exaggerating the temperature

difference and measuring the change of temperature produced in the calorimeter.

The most difficult problem in measuring and evaluating heat leak is the measurement of the effective temperature differences along the various

paths for heat flow between the calorimeter and its surroundings, especially

when the calorimeter is not at thermal equilibrium. One obvious solution

of this problem would be to use a great many thermocouples located at representative places. In one calorimeter9

, 38 thermocouples were used to obtain information on temperature distribution. Of these, 31 had measuring

junctions located on the calorimeter and its immediate surroundings.

Experience had shown that the design of the attachment of a thermocouple

junction to a calorimeter was vital to the validity of the temperature measurement. When the thermojunction could be soldered directly to metal, it was assumed to be in good thermal contact. In this case, if the wires were

small and made of material having low thermal conductivity, the temperature

of the junction would represent the temperature of the metal to which

it was attached. In most cases, however, the thermocouple junctions needed

to be electrically insulated from the metal so that they could be connected

in series for averaging temperatures or be used for measuring temperature

differences. Since most good electrical insulators are also good thermal

insulators, a special type of thermocouple attachment was developed. This

type of attachment, called a "thermal tie-down" and shown in Figure 2, was

used extensively in all calorimeters developed by Osborne and his colleagues.

It has been used subsequently in a calorimeter described in Chapter 9. Basically, this thermojunction tie-down consists of a gold terminal, T,

insulated by thin mica, M, all pressed firmly against the metal part by a nut on a threaded stud. Two or more gold terminals were used together

to connect thermocouples with each other. If the thermocouples were to be

used in a region where there would be large temperature gradients and heat

flow along the thermocouple wires which would affect the temperature of

the thermojunctions, thermal tie-downs were used on the lead wires before

they reached the thermojunction. In some calorimeters, second tie-downs were used for this purpose. This type of thermal tie-down was found to be

effective even in an evacuated space. The general theory of heat tempering

along wires is discussed in Chapter 4. An alternative method of minimizing heat leak uncertainties, which

avoided the use of a multitude of thermocouples, was developed for one

calorimeter12 . The principle of this method seems so important to calori- metry that some discussion will now be given. In accurate calorimetry, it is desirable to utilize the comparison method as much as possible for minimizing

errors. In heat capacity calorimetry, the comparison method is used by

68-401
Figure 2. Details of thermal tie-downs.

making two series of experiments, one gross series with the calorimeter

nearly full and one tare series with the calorimeter nearly or completely

empty. If the two series of experiments are made in the same manner,

the gradients on the shield (immediate surroundings) should be very

nearly identical in the two series of experiments. If the gradients on the

calorimeter are also the same in the two series, the heat leak will be the same. Even though its magnitude is not known, the heat leak should be balanced

out by differences when the tare measurements are subtracted from the

gross measurements. The difficulty with this assumption is that different amounts of the sample in the calorimeter practically always give rise to different temperature gradients in the calorimeter, so that the above

assumption is not usually valid. It is possible, however, to design a calori- meter which validates this assumption reasonably. The principle of the

design is to add an outer calorimeter surface whose temperature-time

function is essentially independent of the contents of the calorimeter, so that temperature gradients on it are the same in the gross and tare series. This can be accomplished by providing an outer calorimeter surface which is thermally separated from the sample container except in one chosen zone whose temperature is measured. Examples of this type of construction have

been given in Chapter 9. and further examples are given later in this chapter.

Another characteristic of all four of the calorimeters used by Osborne and

his collaborators in the study of water and hydrocarbons was the use of a

"reference block" to contain the platinum resistance thermometers which

determine the temperature on the international scale. Many experimenters

using a resistance thermometer place it inside the calorimeter and use its temperature at equilibrium to represent the temperature of the calorimeter. In the calorimeters used by Osborne and his collaborators, the resistance thermometers were placed in a reference block separate from the calorimeter.

The block temperature was kept at about the same temperature as the calori- meter, and all temperatures on the calorimeter and its surroundings were 69-402
referred to the reference block temperature by means of thermocouples.

The use of a reference block has several advantages, (i) The heat capacity

of the empty calorimeter can be less, (ii) It facilitates the use of two or more

resistance thermometers instead of one, so that a failure of one resistance

thermometer may be detected before it invalidates the experimental results.

(Hi) By the use of a silver or copper block of appropriate dimensions, the

reference block can conveniently provide an isothermal region for both the

resistance thermometers and the reference junctions of thermocouples. By

using thermocouples differentially so that the thermocouple wires do not

pass through large temperature gradients, most of the effects of thermocouple

inhomogeneities are avoided. While the use of a reference block has the above

advantages, it adds two complications which may have prevented its general

use. These are (2) that it may require a more complex design and also (ii) that the temperature of the reference block may have to be controlled separately,

depending on the design.

IV. Calorimeters for Measuring Properties of Water

1. Calorimeter for 0-270 °C

The first calorimeter described here was used to measure values of the

thermodynamic properties a, |3, and y of water up to 270°C. Figure 3

shows a diagram of the calorimeter and its accessory parts. In the bottom

of the calorimeter there was a double centrifugal pump which served two

functions, (i) to circulate liquid over almost the entire inner wall of the

calorimeter and (ii) to flow water in a thin stream over the heater, located near the top of the calorimeter. The pump capacity was sufficient to circulate

the entire contents of the calorimeter in about 5 sec, so that temperature

gradients on the calorimeter surface were minimized. Furthermore, in the

vaporization experiment, the use of a thin flowing layer of water over the

heater, H, permitted quiet evaporation, thus producing essentially saturated vapor. The calorimeter was held in place by the upper and lower tubes,

ST, inside a shell, E, whose temperature was controlled by a circulating

oil bath. In the upper part of this bath was located the reference block, R,

containing three resistance thermometers, T, and various reference junctions

of thermocouples, J. The upper and lower tubes, connecting to the calori- meter, led to throttle valves used for controlling the flow of vapor or liquid,

respectively. In the vaporization (y) experiments, vapor flow was diverted

from one receiving container to another by valves actuated by time signals. In the /? experiments (withdrawal of liquid), however, only one receiving

container was used, so that the flow of liquid was started and stopped during an experiment. In this calorimeter, a experiments were made over the entire range

0-270 °C, but j8 and y experiments were made only over the range 1 00-270 °C.

The values of a from these experiments were converted to H, enthalpy at saturation pressure referred to 0°C, by using measured values of above

100°C. Below 100°C, the values of /? are so small that values calculated

from the relation = TVdP/dT were better. The values of AHV were

obtained directly from the observed values of and y between 100 and

270°C. The accuracy of the derived values of H, C, and AHV was usually

70-403
Figure 3. Calorimeter for 0-270 °G

c, Calorimeter shell CL, Current lead E, Envelope shell (shield) PL, Potential lead B, Threaded band R, Reference block

G, Gold gaskets M, Mantle ST, Support tubes Ji, Ji, etc., Measuring junctions of

I, Pump impeller thermocouples

F, Pump casing RJ, Reference junctions of

o, Ball bearings thermocouples

P, Water port TL, Thermocouple leads H, Calorimeter heater T, Platinum resistance thermometer WA, Gauze apron AH, Auxiliary heater MH, Main heater RC, Refrigerating coil

better than 0-1 per cent, as confirmed by experiments with two later calorimeters.

2. Calorimeter for 100-374° C

This calorimeter was designed for measurements on water up to the critical temperature (about 374-1 °C) and pressure (about 218 atm). Because of

the higher pressure and temperature, the design required more mechanical

strength and corrosion resistance. Although in the earlier calorimeter (0—

270 °C) a copper-nickel alloy had sufficient strength for the calorimeter

71-404
shell, it was necessary in the 1 00-374 °C calorimeter to use a special noncorrosive alloy steel to avoid mechanical creep at the higher temperatures.

Figure 4 shows a diagram of this calorimeter, together with some of its

K

Figure 4. Calorimeter for 1 00-374 °C

c, Calorimeter shell Hz, Shield heater Hi, Calorimeter heater Ha, Guard heater D, Heat diffusion system Hs, Lower tube heater

R, Reference block CW, Cooling water H3 Reference block heater s, Aluminum radiation T, Platinum resistance shields thermometers VT, Vapor throttle valve

Ji, J%, etc. Measuring junctions of He, Heater for valve thermocouples AS, Adjusting screw for valve

E, Shield K, Outer casing

72-405
accessory parts. The calorimeter heater, Hi, was located in the bottom of the

calorimeter, C, and was concentrated so as to produce bubbles of vapor for convective mixing by use of the principle of the coffee percolator. A system

of radial silver vanes, D, was placed inside the calorimeter to speed thermal

equilibrium and minimize temperature gradients. As in the previous

example, the calorimeter was held in place by the upper and lower tubes, in a space surrounded by a shield, E, made of £ in. thick silver. The reference

block, R, also located in this space above the calorimeter, held two platinum

resistance thermometers, T, and the reference junctions of the thermocouples. In this apparatus there were 38 thermocouples, 13 located on the outer surface of the calorimeter, 12 on the inner surface of the shield (J in.), 2 on the upper tube, 1 on the vapor throttle valve, VT, 3 on the lower tube

and 7 on the inner surface of another silver shell (f in.) which served as a guard surrounding the shield. One purpose of the guard was to supply

most of the heat required at a steady state, so that essentially no heat was

needed in the shield when accurate temperature measurements were made

at thermal equilibrium. This procedure helped make the temperatures on

various parts of the shield independent of changes in outside temperatures.

The heaters, and H\, on both the shield and guard were distributed

approximately proportional to area. The guard was thermally insulated by

successive thin aluminum shells, S, surrounding it to impede the loss of

heat both by radiation and convection. The use of thin aluminum also minimizes thermal lag in the insulation, thereby enabling the control of

guard temperature to be fast. One feature of this calorimeter, which was believed to be important in vaporization experiments at temperatures approaching the critical temperature, was the baffle system, B, located in the vapor flow path at the exit from

the calorimeter. This baffle system, made of silver gauze, was designed to catch small water drops so that they would not be carried out of the calori- meter. Evidence of the effectiveness of the baffle system was obtained by

measurements at different rates of vaporization on the assumption that, if drops were formed, the amount of liquid so entrained and carried out with

the vapor would vary with the rate and show differences in the results. Additional evidence on the effectiveness of the baffle system was obtained

from special measurements of the specific volume of vapor, described later. In this calorimeter, vaporization experiments were successfully made up to within about one degree of the critical temperature before any evidence of

entrained water droplets was found.

The apparatus was also provided with means for observing the pressure

in the calorimeter, using a diaphragm-type pressure-transmitting cell in the liquid line to confine the liquid while transmitting the pressure to a

pressure gauge. The use of this calorimeter for accurate measurement of

the vapor pressure of water is described in a separate publication8

. In the

calorimetric experiments for /S and y, this provision for pressure measurement

proved very useful. At thermal equilibrium before starting an experiment,

the pressure in an outside container was made equal to that inside the

calorimeter, as indicated by the null position of the diaphragm in the

pressure transmitting cell. During the y experiment, the fluid withdrawal

rate was controlled so that the pressure in the calorimeter was the same as

73-406
before the experiment. In this way, the surface of the liquid in the calorimeter was maintained essentially at the starting temperature, even though most

of the liquid became somewhat warmer during evaporation. The throttle valves used to control the fluid withdrawal rate were specially designed to provide continuous adjustment without back-lash. Since this calorimeter was used for accurate pressure measurements, it was possible to provide an independent check on fi and y at high temperatures

where the possibility of mixing of liquid and vapor phases might exist, even though there had been no evidence for it in the experiments changing the

rate of flow. As stated earlier in section II of this chapter using the Clapeyron

relation we have

y = TV'dP/dT

and fi = TVdP/dT.

If V and V are known, values of y and fi can be calculated from the vapor

pressure data. Although it was not convenient to use the calorimeter as a volume-measuring device for extensive measurements on the specific

volumes of saturated liquid and vapor, a method was devised to make such

measurements at 370 °C in order to check the calorimetrically measured

y and fi. For these measurements it was possible to establish a reasonably

sharp boundary for the volume of the calorimeter, by means of the thermocouples and heater on the lower tube from the calorimeter. From a calibration

of this volume it was possible to measure the specific volumes of both the saturated liquid and vapor at 370 °C, and to calculate values of y and fi by

using the vapor pressure data. These calculated values -of y and fi agreed

with the calorimetrically measured values of y and fi to within about 0-3 per

cent, which could be attributed to the error of these specific volume measurements.

3. Calorimeter for 0-100° C

Measurements of the heat capacity of water in the range 0-100°C have

special significance because water has been used for a heat capacity standard

in this range. The calorimeter described here was designed to obtain as high an accuracy as possible, using the techniques available in 1938, on both

heat capacity and enthalpy of vaporization. Following Osborne's method,

this meant measurements of a, fi, and y. However, at temperatures below

100°C, fi is so small that values calculated by using the Clapeyron relation were more accurate than values measured calorimetrically. At 100°G, fi is less than 0*1 per cent of y, and at lower temperatures it is a still smaller

fraction. Therefore, no measurements of fi were made with this calorimeter. In order to strive for accuracies of 0-01 per cent for heat capacities, it was

decided to use a calorimeter with a capacity larger than the earlier ones, namely almost 1200 cm3

. It was thought that a large sample would be more

favorable for higher accuracies for several reasons, (i) The mass accounting

should be more reliable, (n) The volume of a calorimeter of a given shape

increases as the cube of the linear dimension, whereas .the surface increases

only as the square and hence the area subject to heat leak is proportionately

less. (Hi) A sphere has the least surface for its volume and the spherical

74-407
shape deforms less under pressure. At temperatures seldom exceeding 100°C

the pressure would be moderate so the calorimeter could be thin-walled.

It was recognized that the larger surfaces of the calorimeter would cause

larger temperature differences which would be less favorable for heat leak accounting, so it was decided to stir the liquid contents by using a synchronous motor for its constant speed. By these means it was possible to keep the

effective heat capacity in the low-filling experiments down to less than

5 per cent of the effective sample size, which is the difference between masses

of samples in high and low fillings. (With many calorimeters the empty

calorimeter heat capacity is more than 20 per cent of the sample heat

capacity.)

A study was made of the method of the stirring to provide the maximum

amount of mixing with a minimum of pump power. The system chosen is shown in Figure 5. The circulating system consisted of two screw propellers on one shaft, and a system of guides to direct the water flow. The larger

(upper) propeller, P\ did most of the circulating, and the smaller (lower)

propeller, Pi, was used to avoid stagnation in the extreme bottom of the

calorimeter. The liquid went downward next to the wall of the calorimeter

shell and was directed by radial guides, PG, at the bottom so that the liquid

flowed without swirl past the heater, Hi, into the propeller. The water from

the propellers was guided axially upward by a circulator pump casing,

PC, and curved guide vanes served to remove the swirl imparted to the water by the propellers. A synchronous motor kept the pump speed very constant

at 70 rev/min which gave adequate circulation while dissipating only about

0-004 W in the calorimeter. Such low pump power was possible in this design because the water level was not raised as it had been in the 0-270 °C

calorimeter. It was found, however, that even with this low power, there was

a random variation in the dissipated pump power which may have been a major contribution to the variation in the experimental results. The calorimeter shell, C, was made of copper, all surfaces of it and parts

inside were gold-plated, and the outer calorimeter surface was polished to minimize heat transfer by radiation. A baffle, B, was installed near the vapor

outlet tube to prevent passage of liquid drops during the vapor withdrawal

experiments.

For accurate evaluation of electric power in the calorimeter, particular

attention was given to the design of the calorimeter heater. The earlier calorimeter heaters had resistances of about 10 O with the usual four

electrical leads, i.e., two current leads and two potential leads attached

to the current leads at points midway between the calorimeter and its surrounding shield. This selection of points for attaching the potential

terminals seemed reasonable for measuring the power to the calorimeter.

The choice of size and resistance of the current leads between the calori- meter and shield was a compromise between the amount of heat developed

in the leads and the heat transferred along these leads. With calorimeter

heaters having 10 D. resistance, this compromise was difficult to make when

accuracies of 0-01 per cent were sought. If, however, the heater resistance was

increased from 10 Q. to 100 Q, the relative heat developed in the leads compared to that in the calorimeter heater was reduced by a factor of 10. A discussion of this problem is given in Chapter 4. The resistance of this

75-408
VAC

Figure 5. Calorimeter for 0-100°C

C, Calorimeter shell Hi,

Hi, Calorimeter heater R,

Pi. P2, Pump propellers Hz, PC, Pump casing T, PC, Flow guides B, Gauze baffle Wu

JT, Ji, etc., Measuring junctions TV,

of thermocouples H4,

S, Saturated steam bath VAC,

Steam bath heater Reference block Heater for block Platinum resistance thermometers Condenser

Throttle valve Heater for valve Vacuum line

calorimeter heater was made about 107 Q. so that the problem of accounting

for heat developed in the leads was considerably simplified. Actually the

entire heat developed in both current leads between calorimeter shell and

shield amounted to only about 0-03 per cent of the heat developed in the calorimeter heater. In this calorimeter a different method of attaching potential leads was

used. The mid-points of the current leads between the calorimeter and

shield became hot, so that it seemed preferable to avoid attaching potential

leads to the mid-points if possible. One potential lead was attached to one

current lead where it entered the calorimeter shell and the other potential

76-409
lead was attached to the other current lead where it entered the shield. If the two leads are tied down thermally to the calorimeter and the shield

symmetrically, the method accounts better for the heat developed in the leads. The shield for this calorimeter was double-walled so as to contain a

saturated steam bath, S, to control its temperature. This type of temperature

control has considerable advantage for large areas such as in this calorimeter.

The principle of the saturated steam bath is simply that, for a metal surface covered with a thin film ofliquid, the metal surface temperature is determined

essentially by the pressure of the saturated vapor. If the surface is cooler than

the saturation temperature, some vapor will condense to warm the surface.

If, on the other hand, the surface is warmer than the saturation temperature

of the vapor but is wet, some liquid will evaporate until the surface cools to the saturation temperature. This system is very effective when the surface can be kept wet with a thin film of liquid. In this apparatus, the surface of the

saturated steam bath was kept wet by condensing liquid at the top and

directing the condensate down over the inner wall of the shield. The outer

wall of the shield was kept wet automatically because its surroundings 'were always kept slightly cooler. The pressure of the saturated vapor was controlled by a heater located in the liquid water at the bottom of the bath. The liquid necessary to wet the shield surface (inner saturated steam bath

surface) was supplied by two condensers, one at the top of the shield and

the other in the top of a part of the saturated steam bath which contained

the reference block, R. In this way, the reference block temperature was

maintained essentially at the shield temperature which in turn was controlled

to a temperature very close to that of the calorimeter. The reference block

accommodated several resistance thermometers, T, and also the reference

junctions for the thermocouples.

There were eight thermocouples, JT, JB, with measuring junctions

distributed in azimuth and height on the surface of the calorimeter, in an

attempt to give them equal weighting for heat leak accounting. Individual

leads to these thermocouples were brought out either for check of the

temperature uniformity, when used individually, or for connection in series for evaluation of the average temperature. All eight were used in series to measure the temperature difference between calorimeter and reference

block, or the group of eight could be opposed to eight corresponding thermocouples distributed over the inside area of the shield for maintaining adiabatic

conditions. In addition to these, there were three thermocouples, J$, J7, on the upper tube and two thermocouples, Jg, J9, on the lower tube. The

thermocouple, J$, located at the mid-point of the upper tube, furnished

data for calculation of the temperature of the vapor leaving the calorimeter

during the vaporization experiments. The thermocouples used in all the

calorimeters described here were made of Ghromel P versus Constantan (or their equivalent) because these materials give a high thermoelectromotive

force (~60 ^V/°C near room temperature) and have reasonable thermal

and electrical resistivities. Since this calorimeter was intended to give results consistent with the

best techniques available in 1938, some discussion will now be given of the

precautions taken to insure highest accuracy. This discussion will be in three parts as follows. 77-410
A. Accounting for Mass of Sample

Precautions were taken to insure pure samples of water and proper

accounting for the masses. In the heat capacity measurements, the difference

in masses of water in the calorimeter in the high and low fillings was

approximately 1 kg. In all experiments, the amount initially put into the

calorimeter was compared with the amount finally taken out. Usually these amounts agreed to 0-02 g, which corresponded to about 1 part in 50000 in the heat capacity experiments. When the mass accounting was not this accurate, the experimental results were discarded. In preparing the sample,

precautions were taken to reduce the impurities (including dissolved gases) to a negligible amount. For transferring samples, the connecting tubes were

evacuated before the transfer. In the vaporization experiments, the mass

taken ouf in a typical experiment was about 20 g. Systematic precautions were taken to insure reproducible weighing conditions for the sample

container. It is believed, therefore, that the accounting for mass was not

the principal limitation on the overall accuracy of the results.

B. Accounting for Energy

The energy supplied to the calorimeter can be considered in three principal

parts (i) the electrical energy supplied, (ii) the energy supplied by the

circulating pump, and (Hi) the heat leak from the calorimeter. These three parts will now be considered, with emphasis on their effects on the overall accuracies of the experiments.

(1) Electrical Energy. With modern techniques the measurement of electrical energy does not seem to be a limitation on the accuracy of calorimetric

experiments. For standards of e.m.f., a group of saturated standard cells was maintained in a specially insulated aluminum box whose temperature was controlled constant within 0-01 °C4 . These standard cells and also the

resistance standards were calibrated periodically. The temperatures of both

the standard cells and the standard resistors were usually checked at both

the beginning and the end of the day. Two specially constructed volt boxes were used in combination so that if any part of either volt box changed resist- ance between calibrations, the daily check on them would detect it. A check was made at least twice a day for any change in the potentiometer factor. This check consisted essentially of comparing a given potentiometer reading

(which is effectively a ratio) with the ratio of two standard resistors. The accounting for heat developed in the current leads to the calorimeter

heater has already been discussed. Another small effect which was considered was the "starting effect" of the change in calorimeter heater resistance immediately after the current was started. With the high resistance of the calorimeter heater which required a high voltage storage battery, it was

not convenient to use an external resistor having the same resistance in order

to minimize the effect on power of change in resistance of the heater3. Consequently, because of a significant change in resistance of the heater

during the first 30 sec before the first power reading, the calorimeter heater

power could not be extrapolated perfectly from regular periodic observations

starting at 30 sec. A study was made of this starting correction, observing

the change in power during the first 30 sec. The result was that a correction

78-411
was made which amounted to only 0-01 per cent of the whole energy input, even for the extreme case of a short experiment. In addition to measurements of power, measurements of time intervals were necessary in order to calculate energies. These time interval measure- ments were perhaps the easiest of all measurements because they were

determined by using accurate standard time signals (seconds). The time

signals were used to trip a switch in the heater circuit. The time for operation

of this switch was determined to be negligible.

(J?) Pump Energy. As mentioned previously, the pump power in the heat

capacity experiments was approximately 0-004 W which, with the pump

running continuously, amounted to about 0-015 per cent of the energy put

into the sample during a typical 10° heat capacity experiment. Although

this is small, separate measurements of this power were made near the time of the experiment in order to estimate the correction. Even though the pump speed was very constant, the mechanical power dissipated was found

to vary at random by amounts larger than couid be accounted for by the uncertainty in temperature measurement. This variation, however, was

usually not more than would correspond to about 0-005 per cent for the

value of a. (3) Heat Leaks. The accurate control and measurement of heat leak is vital in accurate calorimetry. Heat leaks in this calorimeter are classified, like those in earlier calorimeters, into shield heat leak, upper tube heat leak,

lower tube heat leak, and residual heat leak. Measurements of these heat

leaks were made daily throughout the experiments, and calibration experiments were made for determinations of the various heat transfer coefficients. In spite of the large calorimeter surface it was possible to keep the shield heat leak down to a very low value by use of the evacuated space and

polished gold-plated surfaces. The use of numerous thermocouples on this surface, in addition to the effective use of the circulating pump to reduce

temperature gradients, made it possible to reduce the actual shield heat

leak to a small value. The residual heat leaks, such as could have resulted from imperfect weighting of the controlling thermocouples, were almost

negligible and were automatically included with the pump energies in the

experiments. The upper and lower tube heat leaks were small and were

accurately evaluated by the thermocouples located on them. In the heat

capacity experiments, the net corrections applied for all measured heat

leaks averaged less than 0-001 per cent of the energy put into the sample.

C. Accounting for Change in State

The temperature of the calorimeter was determined by measurements

with platinum resistance thermometers, calibrated on the International

Temperature Scale, combined with thermocouple measurements. The temperature of the calorimeter was observed at essentially thermal equilibrium

at the beginning and end of each experiment. For this temperature measure- ment, the temperature of the reference block containing the resistance thermometers was brought very close to the temperature of the calorimeter,

as indicated by the eight thermocouples (in series) having measuring junctions on the calorimeter and reference junctions on the reference block. Thus, the

temperature measured by the resistance thermometers was essentially the

79-412
average temperature of the calorimeter, except for a small difference which was calculated from the thermocouple readings. For this calculation, the

sensitivity of the thermocouples was determined in place directly against

the resistance thermometers.

In all the experiments, the change in proportion of liquid and vapor

in the calorimeter is accounted for in the theory of the method as described

earlier. In the vaporization experiments, the calorimeter was usually about

half-full. Under this condition, the temperature of the vapor leaving the calorimeter was determined by means of the group of four thermocouples on the upper part of the calorimeter, representing its average temperature,

in conjunction with the three thermocouples giving temperatures along the upper tube. During the actual vaporization and withdrawal of vapor through

the upper tube, this tube was tempered by the outgoing vapor so there was no correction for upper tube heat leak during this period. In the vaporization

experiments, the shield heat leak accounting was slightly less accurate than

in the heat capacity experiments because of the larger temperature gradients on the calorimeter. These gradients were larger on account of the sharp

temperature gradient in the liquid next to the surface where evaporation was

taking place. These gradients were large even when the circulating pump

speed was increased to 106 rev/min. A small correction, sometimes amounting to as much as 0-002 per cent and depending on the location of the liquid

level in the calorimeter, was applied to account for the change in liquid level.

4. Comparison of results -with the three calorimeters

Of the three calorimeters described, the 0-100°C calorimeter was designed

to have the highest accuracy, probably about 0-01 per cent. It is interesting

to compare the results from this calorimeter with the results from the others where measurements were made at the same temperatures. In all three

calorimeters, the measurements were made of the enthalpy of vaporization

at 100°C. If the vaporization results with the 0-100°C calorimeter are used

as a basis for comparison at 100°C, the 0-270 °C calorimeter gave a value

0-06 per cent high whereas the 1 00-374 °C one gave a value 0-02 per cent

high. Measurements of enthalpy of vaporization at 50°, 70°, and 90°C

with the 0-270 °C calorimeter2 gave values averaging less than 0-02 per cent higher than the one used for 0-100°C. Heat capacities from measurements

made with the 0-270 °C calorimeter could also be compared with those

from the one used for 0-100°C over its entire range. These values were

found to be about 0-07 per cent higher.

V. Calorimeter for Hydrocarbons

As part of a program for the investigation of the properties of hydrocarbons, accurate measurements of enthalpies of vaporization at 25 °C of a

large number of pure samples were needed. The calorimeter described here was designed particularly for measuring these although it was used for a few

times at other temperatures above and below 25°, both for vaporization

and heat capacity experiments. In designing this calorimeter, there were three principal aims, [i) The

calorimeter shell should be made small because some of the pure hydrocarbons were available in relatively small amounts, (u) The measurements

80-413
(especially vaporization) should be accurate to at least 0-1 per cent. (Hi) The

apparatus should permit relatively rapid measurements of vaporization

so that a large number of materials could be investigated. Making the

calorimeter small has certain other advantages besides favoring the use of

small samples. In a small calorimeter, it is possible to distribute heat by

conduction with a system of many copper vanes and dispense with mechanical

stirring. These vanes minimized the time required for thermal equilibrium

and contributed both to accuracy and ease of operation. Mechanical

stirring was purposely avoided after having found in the 0-100°C calori- meter that there were unpredictable variations in the dissipated pump power.

Another advantage of a small calorimeter is that it is possible to use effectively

unheated metal shields for the control and evaluation of heat leak, and thus

practically eliminate one common source of error in adiabatic heat capacity

calorimetry. This important feature will be discussed while describing

details of the apparatus. Because measurements on most of the materials were at temperatures

considerably below the normal boiling point, values of the quantity [3 were

negligible in some cases, and in other cases small enough so that they could

be calculated adequately from known thermal properties of the material.

Therefore, this calorimeter was not provided with a lower tube for experi- ments. All samples were vaporized into and out of the calorimeter. A

schematic drawing of the apparatus is shown in Figure 6, and a scale drawing

of essential features is shown in Figure 7. The calorimeter, holding approximately 100 ml of sample, had the heat distributing system shown in Figure 8.

Figure 6. Schematic diagram of calorimeter for hydrocarbons

C, Calorimeter shell E, Adiabatic shield FC, Fluid container H, Calorimeter heater

V, Valve

R, Reference block

T, Resistance thermometer TV, Throttle valve U, Union

VAC, Vacuum line 81-414
I 1 1 1 1 1 I I I

I I 0 5 10cm

Figure 7. Scale drawing of calorimeter for hydrocarbons

A, Attachment of calorimeter shell to its shield

C, Calorimeter shell and shield D, Attachment of adiabatic shield to its shield E, Adiabatic shield with its shield

F, G, K, L, Zones of thermal attachment of thermocouples

Hi, Calorimeter heater Hi, Adiabatic shield heater H3, Reference block heater Hi, Heater

H5, Throttle valve heater

Ji> Jzt etc., Measuring junctions of thermocouples

M, Receptacles for platinum resistance thermometers

.V, Deck of adiabatic shield P, Lead wire and vacuum duct

R, Reference block

S, Gauze baffle TV, Throttle valve seat

The tinned copper vanes were arranged so that no point in the liquid sample was more than 3 mm from a conducting metal part. The heater, Hi, (100 Q) was located on the bottom part of the calorimeter shell, as shown in Figure 7. The heater was covered with a copper sheath soldered to the calorimeter

shell. Thermocouple measuring junctions, J, were located as shown, with

reference junctions on the reference block. The calorimeter shell was pro- vided with a thin copper 'heaterless' shell surrounding it and attached to it

82-415
1 I I I

I I 0 5cm

Figure 8. Heat distribution system in a calorimeter for hydrocarbons.

at one zone. Thus, so far as calorimetric experiments were concerned, this thin shell was part of the calorimeter where energy must be accounted for. The calorimeter was surrounded with an adiabatic shield, E, provided with

heaters. This adiabatic shield, similar to the calorimeter shell, was also provided with a thin heaterless copper shell which was attached inside the

shield at a zone at the same height as that on the calorimeter. Thus the outer calorimeter surface was one heaterless thin copper shell and the inner

shield surface another. The calorimeter shell, the adiabatic shield, the

heaterless copper shells and the reference block, R, were all gold plated and

polished to minimize radiation emittance. The spaces between and around

these parts were evacuated to eliminate gaseous conduction and convection.

There were therefore two paths for heat leak from the calorimeter, one by

radiation from the polished gold surface of the calorimeter heaterless thin

shell, and the other by solid conduction along the upper tube and electrical leads from the calorimeter which were thermally attached to the tube. The

heat leak along the upper tube was controlled and measured by means of

the thermocouples (J7—J5) and {Ji-—J$>) attached to it. The heat leak from

the calorimeter was controlled and measured using the thermocouples

(J10-J9) and Uw-Jv ). In the vaporization experiments, even though there was a significant

temperature gradient on the calorimeter shell, the heaterless copper shell attached to the calorimeter shell was nearly isothermal owing primarily to the very low heat transfer coefficient to the calorimeter at all points except

83-416
at the chosen attachment zone. The thermocouples and Jq. measured

effectively the temperature of the calorimeter surface relative to the temperature of the reference block. Similarly, in the vaporization experiments, yio and yio- measured the temperatures of the surrounding surface. During the heat capacity experiments, however, there were necessarily

temperature gradients on both of these heaterless shells. Although the two

thermocouples were located so as to represent approximately the average

temperature of these two surfaces when heating, it is not necessary that they

do so. When using the method of two series of heat capacity experiments, a gross series and a tare series, the only requirement is that both surfaces have the same temperature distributions at corresponding times in both

series of experiments. This means that to have a valid heat leak accounting,

any change in temperature gradients on the surface of the calorimeter

shell itself must not affect the temperature distribution on its heaterless

shell. With the design shown, the temperature distribution on this heaterless shell was essentially independent of any temperature gradients on the calorimeter shell due to either the presence of the sample or the type of ex- periment conducted.

Similarly, the temperatures on the heaterless shell which was attached

to the adiabatic shield were independent of the temperature gradients on the adiabatic shield. Thus with this design in the heat capacity experiments,

the thermocouples {Jio~J§) were not required to measure the true heat leak

in any experiment, although these thermocouples probably did so. It is believed that the above principle of design is vital to all calorimetry

and that many of the differences in results in accurate calorimetry can be

attributed to the effects on heat leak caused by temperature gradients in the calorimeter and by changes in these gradients between the gross and tare

series in heat capacity experiments. A much more comprehensive discussion

of this and related questions is given in Chapter 9. Since further details of the apparatus can be obtained from the original

publication, further discussion will be limited to significant points in its use and the accuracies obtained. The effectiveness of the overall heat accounting was remarkable. It was proved possible to use this calorimeter for accurate

vaporization experiments with samples of less than 3g in the calorimeter. In various vaporization experiments, temperature differences on the calori- meter varied by about 1 °, depending upon liquid level and rate of vaporization. In spite of this there was no evidence of change in measured enthalpy

of vaporization due either to liquid level or to rate of vaporization. This

latter independence is also evidence of the withdrawal of essentially saturated vapor, rather than of either superheated vapor or vapor containing liquid

droplets. The independence of the measured enthalpies of vaporization upon

temperature differences in the calorimeter shell was evidence of the effective- ness of the method using unheated shields. Possibly the most convincing evidence of the accuracy of this calorimeter

is the comparison of results on the same material used both in this calori- meter and the earlier 0-100°C calorimeter. For this purpose, vaporization

measurements at 25°C were made on water before, during, and after the

series of experiments on 59 hydrocarbons. The average of the measurements,

with the present calorimeter, for enthalpy of vaporization at 25 °C differed 84-417
by about 0-001 per cent from the tabulated value in the previous work11

, and the average deviation of values from individual experiments from this tabulated value was about 0-01 per cent.

It is interesting to note that this calorimeter was used also on materials

having relatively low vapor pressures, such as w-octane. With this material,

the mass rate of withdrawal was limited to about 0-15 g/min. In spite of these unfavorable conditions, it is believed that the results justify the estimate of

accuracy of 0-1 p^r cent in the vaporization experiments, which was made

when the calorimeter was designed.

Although the heat capacity experiments with this calorimeter were inci- dental to the vaporization experiments, it is interesting to examine the heat

capacity results for evidence of their accuracy. Here again, possibly the best evidence lies in a comparison of results on water used to check the perfor- mance of the calorimeter. Heat capacity measurements with water were made at the beginning and near the end of this series of experiments. It was

found that the 30 experiments with water gave results about 0-025 per cent

different from the previous results in the 0-100°C calorimeter. Additional

evidence was also available in the measurements on rc-heptane, because some

experiments were made on a sample of heptane in the 0-100°C calorimeter. In spite of the use of a sample from a different source, heat capacity measure- ments in the range 10-35°C gave an average deviation of 0-037 per cent from a least-square formulation of the results with the 0— 100°C calorimeter.

It is of interest that these earlier experimental measurements gave an average

deviation of 0-028 per cent from the same formulation. The evidence from

the results seems to indicate that the hydrocarbon calorimeter, although

intended for vaporization experiments, is capable of an accuracy better than 0-1 per cent for heat capacity experiments in its temperature range.

VI. Other Calorimetric Methods for Measuring Enthalpy of Vaporization

The calorimeters described have been used in vaporization measurements

in the range 0-374 °G and at pressures up to 218 atm. No attempt will be made to describe other vaporization calorimeters which use similar

methods in this temperature range. At temperatures below 0°C heat capacity

calorimeters have also been used for vaporization measurements. Some of

these are described in Chapters 5 and 6. At high temperatures at which

accurate direct measurements of enthalpy of vaporization are very difficult or impossible, indirect measurements can be made by using the Glapeyron

relation AHV = T(dPjdT) (V — V). For this evaluation the determination

of dPjdT is probably the most difficult. In the direct methods described, the heat required to vaporize the liquid

has usually been supplied by electrical heaters because of the convenience

and accuracy of the electrical measurements. Some measurements, mostly

of historic value, have measured the heat of condensation, rather than that of vaporization.

Another direct method which has proved useful in certain vaporization

measurements is the transpiration method, sometimes known as the carrier gas method. In this method, which has application mostly below the normal

boiling temperatures of liquids, vapor is removed from the calorimeter

85-418
with an inert carrier gas. Measured electric power is usually used to evaporate the liquid. An advantage of this method is the relative ease in controlling the rate of vaporization by controlling the rate of flow of the

carrier gas; no elaborate throttle valve is required for this control. A recent example of the application of this method at 25 °C is the work of Wadso13

, who measured enthalpies of vaporization of samples as small as 0-15 g to an accuracy better than 0-5 per cent. His calorimeter was designed for samples

having vapor pressures at 25 °C in the range 1-100 mm Hg.

In the transpiration method there are several precautions that should

be considered in addition to the usual heat leak measurement. As in the method used by Osborne and colleagues it is necessary, in principle, to make a /? vaporization correction, that is, to correct for the vaporization

into the space occupied by the liquid evaporated. As pointed out earlier,

this vaporization correction is small and sometimes negligible at temperatures

below the normal boiling point. Another possible correction, which is usually small, allows for departures from the ideal process of evaporation at saturation pressure, such as might occur at large rates of gas flow. Another interesting vaporization calorimeter using the transpiration

method is that of Coon and Daniels 1. They made measurements on small

samples of carbon tetrachloride incidental to its use as a refrigerating material

in microcalorimetry. By using twin calorimeters and compensating unknown

heat with the vaporization of carbon tetrachloride they were able to measure

exothermic reactions at room temperature which gave heat rates of about

4J/h.

VII. Summary

Discussion has been mainly of calorimetry of saturated fluids, as carried out at the National Bureau of Standards over the period 1928 -1942. From

these experimental measurements values of enthalpy of vaporization, heat

capacities and derived thermodynamic quantities were obtained. Four

calorimeters have been described, three for water to pressures of 218 atm

in the temperature range 0-374 °C, and one for hydrocarbons near 25 °C. An effort has been made to discuss the advantages and disadvantages both

of method and various experimental features. Although in general this calorimetry was carried out with as high an accuracy as the "state of the art" permitted at the time, it must be remembered that the calorimeters were developed about three decades ago. With advances in technology

since that time, and with the benefit of the experience with these calori- meters, it seems certain that improvements could now be made in both

design and operation.

VIII. References

1 Coon, E. D., and F. Daniels, /. Phys. Chen. 37, 1 (1933).

2 Fiock, E. F., and D. C. Ginnings, /. Rss. Natl. Bur. Std. 8, 321 (1932).

3 Hog:, H. J., /. Res. Natl. Bur. Std., 36, 111 (1946).

t Mueller, E. F., and H. F. Stimson, /. R;s. Natl. Bur. Std., 13, 699 (1934).

a Osborne, N. S., Bu. Stds. Bull., 14, Scientific Papers 301, 313, and 315 (1917).

6 Osborne, N. S., /. Opt. Soc. Am., 8, 519 (1924); /. Res. Natl. Bur. Std. 4, 609 (1930);

Trans. Am. Soc. Meek. Engrs., 52, 221 (1930).

7 Osborne, N. S., H. F. Stimson, and E. F. Fiock, /. Res. Natl. Bur. Std. 5, 411 (1930);

Trans. Am. Soc. Meek. Engrs., 52, 191 (1930). 86-419
8 Osborne, N. S., H. F. Stimson, and D. C. Ginnings, /. Res. Natl. Bur. Std., 10, 155 (1933)

;

Mech. Eng., 54, 118 (1932).

9 Osborne, N. S., H. F. Stimson, and D. G. Ginnings, /. Res. Natl. Bur. Std., 18, 389 (1937).

10 Osborne, N. S., H. F. Stimson, and D. G. Ginnings, /. Res. Natl. Bur. Std., 23, 197 (1939).

11 Osborne, N. S., H. F. Stimson, and D. G. Ginnings, /. Res. Natl. Bur. Std., 23, 261 (1939).

12 Osborne, N. S., and D. G. Ginnings, /. Res. Natl. Bur. Std., 39, 453 (1947).

13 Wadso, L, Acta Chem. Scand., 14, 566 (1960).

87-420
U. S. Department of Commerce National Bureau of Standards

RESEARCH PAPER RP1693

Part of Journal of Research of the Rational Bureau of Standards, Volume 36,

February 1946

HEAT CAPACITY OF A TWO-PHASE SYSTEM, WITH APPLICATIONS TO VAPOR CORRECTIONS IN CALORIMETRY

By Harold J. Hoge

abstract

A formula is derived that gives the heat capacity of a system composed of solid or liquid in equilibrium with saturated vapor in terms of the specific heat of the condensed phase and certain auxiliary data. This formula is valid throughout the

entire range from 0 to 100 percent of vapor, and at the latter extreme reduces to a well-known relation between the specific heats of saturated liquid and saturated

vapor. The formula is applied to the calculation of vapor corrections in calorimetry.

Its advantage lies in the fact that the correction is expressed as a single term that may be readily transformed with Clapeyron's equation, .yielding two alternative

correction formulas. Vapor corrections to the beat capacity and to the heat of fusion are summarized

and tabulated for four different experimental procedures in calorimetry.

CONTENTS

Page

1. Introduction ]11

II. Heat capacity of a two-phase system 112

III. Vapor correction to the heat of fusion 114

IV. Application to calorimetry 115

V. Summary of formulas and required data 116

VI. Definitions and symbols 117

VII. References . 118

I. INTRODUCTION

A solid or liquid having an appreciable vapor pressure will partially

vaporize when placed in a closed calorimeter. The presence of vapor,

which changes both in volume and density as the temperature is changed, makes it necessary in such cases to apply a vapor correction

to heat-capacity data. The size of the correction varies with the

degree of filling of the calorimeter. In practice it seldom exceeds 3 or 4 percent of the heat capacity of the solid or liquid, but under

unusual conditions has been reported to be as large as 20 percent [1].* Osborne and Van Dusen [2 J appear .to have been the first to give a

detailed mathematical treatment of the problem of vapor corrections.

Their equations are given in the Handbuch der Experimentalphysik

[3J and seem to have been widely adopted. In 1924 Osborne [4, 5] gave a new treatment of the problem of vapor corrections based on

the practice of making duplicate calorimetric runs, one with a large

and the other with a small amount of material in the calorimeter.

He appears to have been the first to use this method, which has

• Figures in brackets indicate the literature references at the end of this paper. 88-111
Journal of Research of the National Bureau of Standards

several advantages, among which are the elimination both of the

effect of material in the filling tube and the effect of strain on the heat

capacity of the calorimeter. Others who have discussed vapor corrections, either incidentally or in detail include Babcock [6], Awbery

and Griffiths [7], and Bennewitz and Splittgerber [8]. All the correction formulas given by these authors are mathematically and physically correct, but some are unnecessarily complicated. Nowhere has it been clearly brought out that the correction can

always be expressed in two alternative forms, one of which is in terms

of latent heats, the other in terms of vapor pressures. The present

paper is an attempt to clarify the situation, and to present in their

simplest form the equations needed for making the vapor correction

in any ordinary calorimetric experiment. It is thought that these

correction formulas may help to eliminate the unnecessary work that

is sometimes done when vapor pressure data are first used to compute

latent heats, the latent heats then being used in a vapor correction

formula. In such a calculation the specific volume of the vapor

appears twice, once in Clapeyron's equation, and again in computing

x, the fraction of the material in the vapor phase. If incorrect vapor

volumes are used, incorrect latent heats are obtained, but this error

is exactly compensated by the error in x, so that the vapor correction

is independent of the assumed vapor volume. It seems unlikely that

investigators have been generally aware of this fact. The starting point in the derivation given below is an equation for the entropy of a two-phase system. This considerably shortens the

derivation as compared with the conventional approach of accounting

for all the energy supplied, and yields the results directly in the desired

form without the necessity of combining terms. The suggestion that

the problem be treated from the entropy standpoint was made

by Harold W. Woolley, and it was this point of view that led to equation 5.

II. HEAT CAPACITY OF A TWO-PHASE SYSTEM

Consider a mass M1 of material confined in a volume, V, and partially vaporized, so that there are Mg grams of gas in equilibrium

with Mc grams of condensed phase, which may be either solid or liquid.

This system has a definite heat capacity, provided the volume, V,

is a definite function of temperature, for if this is the case, the state

of the system is completely defined by the temperature. The pres- sure in the system is always the vapor pressure of the material.

We wish to find an expression for the heat capacity of this system.

This is most easily done by finding an expression for the total entropy

of the system, and finally converting this expression by differentiation

into an equation giving the desired heat capacity.

Let sg and s c be the entropies per unit mass of saturated vapor and

saturated condensed phase, respectively. Then the total entropy of

the system is S=Mcse +MgSg =Mse+Me{se—sc). (1)

1 Symbols are defined as they appear, and a table of symbols used is given at the end oi this paper. 89-112
Vapor Corrections m Galorimetry

Since sg —

s

c is the entropy of vaporization per unit mass it is equal

to Ij T, where I is the heat of vaporization per unit mass, so that

S=Msc +Mgl/T. (2)

The quantity MJ/T may be considered an "excess" entropy, since

it represents the difference between the entropy of the actual system

and that of the corresponding system with no vapor phase. Putting

S'=Msl/Twc have

S=Ms0 +S' (3)

and differentiating with respect to T

Now for any reversible absorption of heat dS= 8QjT=CdT/T. Hence we may substitute dS/dT—CJT and dsc/dT=cJT, where C is the heat

capacity of the two-phase system and cc is the heat capacity of unit mass of saturated condensed phase. This gives

C=Mcc +T~, (5)

which is the basic formula for the heat capacity of a two-phase system.

The next problem is to evaluate S' =Mgl/T. The mass of vapor, Mg , can be expressed in terms of the total mass, M, the total volume,

V, and the specific volumes of vapor and condensed phase, vg and ve> as

follows:

V=Mcve +Mgvg =Mv0 +Mg (vg -vD ), whence

V—Mv

' vg —ve The excess entropy is therefore

o,_Mgl_l V-Mvc

. 8 =-f—f Vg _Ve

• (7a)

The quantity l/[T(vg—vc )] is by Clapeyron's equation equal to dp/dT,

the slope of the vapor-pressure curve. This substitution gives an

alternative expression for excess entropy.2 S'=%{V-Mv0 ). (7b)

Equations 5, 7a, and 7b, permit c0 , the specific heat of saturated

condensed phase to be calculated from 0, the heat capacity of the

two-phase system, and certain auxiliary data, which may be either

V, vg , and vc ; or dp/dT, V, and vc

. When these formulas are used to make vapor corrections they will ordinarily be applied to systems

whose vapor fraction, or dryness (=MJM) is between 0 and 10 per2 A shorter but less obvious method of getting equations 7a and 7b is to note that S' is the change in entropy when the volume occupied by the material is increased from Mve to V at constant temperature, so that S'=(dS/d V) r( V—Mvc ). Since, by Maxwell's relation (£>S/d V) T=dpldT, we have 7b at once and 7a may

be obtained from 7b by use of Clapeyron's equation. 90-113
Jowrnal of Research of the National Bureau of Standards

cent. They are valid, however, throughout the whole range from 0 to 100 percent dryness. For the limiting case of 100 percent dryness,

5 and 7a yield a well-known relation between the heat capacities of

saturated vapor and saturated liquid. For this particular case, V=Mvg , so that S' is simply Ml/T, and 5 is C=Mcg =Mcc + T^(~\

where cg is the heat capacity per gram of saturated vapor. Since Mis independent of T, this reduces to the usual form

III. VAPOR CORRECTION TO THE HEAT OF FUSION

When a melting point or other first-order transition is encountered

in a two-phase system, special formulas are needed for making the

vapor correction. The simplest way to obtain these is to start with

equation 3, the equation for the entropy of the two-phase system,

S=Msc -\-S' . Let the subscript "a" refer to the system just before

the transition starts (solid-gas) and let the subscript "b" characterize

it at the end of the transition (liquid-gas). The change in entropy

during melting is, by equation 3, Sb -S& =M{scb -sc&)+S'b -S'a . (23)

If Q is the measured quantity of heat supplied during the process, then Q/T=Sb —S!l . Likewise, s cb —s ca, the difference in specific

entropies of the two condensed phases, is l t /T, where l t is the heat of

fusion per gram. Making these substitutions and multiplying by T

gives

Q=Mlt +nSb -S'a). (24)

The excess entropies may be evaluated with the formulas previously

developed. If 7a is used,s;_s;= r <z=M$r, (25)

while if 7b is used,

S'b -S:=[%(V-Mve )J& (26)

When evaluating these expressions it should be remembered that the

only quantities having the same value at both limits are V, M, T,

and ve

. The vapor correction to the heat of fusion may be considered to be

made up of two parts. One part is due to the fact that Me is not zero, and hence not all of the total mass M takes part in the process of melting. The other is due to the fact that Mg generally changes a little one way or the other owing to a difference between vca and vcb . This

causes the absorption or liberation of the heat of vaDorization of a small amount of material.

91-114
Vapor Corrections in Cdlorimetry

IV. APPLICATION TO CALORIMETRY

Use of the formulas derived above in making vapor corrections is a straightforward procedure that need not be discussed in detail. The

vapor correction is not made until after the calculation of the gross,

tare, and net heat capacities. In calculating both the gross and the

tare heat capacities it may be necessary to apply a curvature correction

[reference 9, p. 79]. After this correction has been applied it is con- venient to tabulate the gross and tare heat capacities at 5-degree

intervals and to subtract one table from the other to obtain the net

heat capacity. The vapor correction is then applied to the net heat

capacity.

The working formulas for this purpose depend on the type of ex- periment. Four different types of experiment may be considered,

characterized by the presence or absence of a filling tube that contains

a small part of the calorimetric charge, and by whether the tare charge

is zero or a mass of material M2 , which is small compared to the gross charge Mi but sufficient to fill the system with saturated vapor at all temperatures.

In the next section the appropriate formulas for each of the four

types of experiment are tabulated. The quantities which must be

known in order to evaluate the formulas are also listed. These are divided into two groups: the basic data, which are required regardless

of the vapor correction; and the auxiliary data, which are needed only

to evaluate the vapor correction. For one type of experiment, for- mulas are given which contain Mu the mass of material in the filling

tube. These formulas may be derived by treating the vapor in the

tube as an ideal gas. The problem is essentially the same as that of

correcting for the gas in the capillary of a gas thermometer [10]. In order that the filling tube shall contain only vapor, it is of course necessary that no part of it shall have a temperature lower than that

of the calorimeter proper.3

' In calculating the vapor correction, the derivative dE/dT must

always be calculated, and in many cases the derivative dp/dT also. A procedure which has been found satisfactory for this purpose is to tabulate (or p) at 5-degree intervals and to calculate Acf/AT for each interval. The values of A'Sf/AT are ordinarily sufficiently good

approximations to the values of (hEfdT at the midpoints of the intervals. Where greater accuracy is desired, formulas such as that of

Rutledge [11], which are based on polynomial approximations of

higher degree may be used.

The author acknowledges valuable discussions with M. S. Van

Dusen, of the Bureau's Pyrometry Section.

» Osborne and his coworkers have for certain experiments used a filling tube that is at all times filled with

liquid. This requires the opposite condition— that no part of the tube shall have a temperature higher than

that of the calorimeter proper.

92-115
Journal of Research of the National Bureau of Standards

V. SUMMARY OF FORMULAS AND REQUIRED DATA

For definitions of terms and symbols, see section VI.

Type 1. Gross charge: M

Tare charge: 0

Fining tube: No

CDet -TdS'/dT

M

lt ~ M

.Basic data: Caet , M, T, Q

S,= L V—Mve

or

T vg —ve

Auxiliary data: la , lb , V, vc& , vcb , ve S'=%(V-Mve)

Auxihary data: (dp/dT)^ (dp/dT) b , V, vc& , vc Type 2. Gross charge: Mx Tare charge: M2 Filling tube: No

CDet-Td(Sj-S;)/dT

or

Mx —

M

2

7 p. rp [(Sl —S2)b— (Si —S2)q] il-Vnet L Ml -M2 Basic data: Cnet, Mx —

M

2 , T, QDet ,

[ Q» c

, I (M1 -M2 )vc

\ Sl~S* T Vg -Vo [Auxihary data: la , lb , vca , vcb , ve

.

[Auxiliary data: (dp/dT)^ (dp/dT) b , vc& , vcb .

Type 3. Gross charge: Mx Tare charge: 2 Filling tube: Yes

The temperature distribution in the tube must be the same in the

tare run as in the gross run. With this precaution, the quantities Mt and dMt /dT drop out of the working equations, which become

identical with those for an experiment of type 2.

93-116
Vapor Corrections in Galorimetry

or

also

Type 4. Gross charge: M

Tare charge: 0

Filling tube: Yes

( _q,et - TdS'/dT-ldMJdT

P M-Mt <i_ Q-T(S'b -S:)

lt ~ M—Mt .Basic data: Cnet , M, T, Q.

L, I V-(M-Mt)vc

I T vg —ve [Auxiliary data: la , lb , V, veA, vcb . ve

S'=fT[V-{M-MM

Auxiliary data: (dp/dT) u (dp/dT) b , V, vta , vcb

Mi==pR L:t>

dMt _wrdp\\Vi , ^-LvZlI

dT ~ R IdTZjiTx^dTZjiTd

.Auxiliary data: p, Vu Tu dp/dT.

VI. DEFINITIONS AND SYMBOLS

Calorimeter.—That part of the apparatus which contains the material

and participates in absorbing the measured power input.

Charge.—Mass of material in the calorimeter and filling tube.

Filling tube.—Tube extending from the calorimeter to outside the

apparatus. Contains a small part of the total charge during

measurements.

Gross heat capacity.—Heat capacity of calorimeter plus a large charge

Ml

Tare heat capacity.—Pleat capacity of calorimeter with no charge, or with a small charge M2 . Net heat capacity.—Gross heat capacity minus tare heat capacity.

C=heat capacity

c=specific heat (heat capacity per unit mass)

£=heat of sublimation, vaporization or fusion per unit mass M=mass of charge contained in calorimeter and filling tube

2»=pressure, equal to vapor pressure of material at temperature T

Q=heat absorbed during a transition such as melting

R=gas constant

S=entropy

<S"= excess entropy of a system, as compared with the same mass

of saturated condensed phase

s= entropy per unit mass T=absolute temperature of calorimeter and contents

V=volume of the calorimeter

94-117
Journal of Research of the National Bureau of Standards

v=volume per unit mass W=molecular weight of the material

x=fraction of the material in the vapor phase, sometimes called

dryness.

SUBSCEIPTS

a=pertaining to the form stable below a transition

b=pertaining to the form stable above a transition

c= condensed phase, solid or liquid

f =pertaining to fusion

g=gaseous phase

i=pertaining to the iih element of volume of the filling tube

t=pertaining to the filling tube

1 =corresponding to the gross charge Mi

2 =corresponding to the tare charge M2 .

VII. REFERENCES

[1] A. Eucken and E. Schroder, Low temperature caloric measurements on a few

fluorides (BF3 , CF4 , SF6 ), Z. physik. Chem. [B] 41, 307-319 (1938).

[2] Nathan S. Osborne and Milton S. Van Dusen, Specific heat of liquid ammonia, Bui. BS 14, 397-432 (1918) S313.

[3] A. Eucken, Hand. Experimentalphysik 8, part 1, p. 291-294 (1929).

[4] Nathan S. Osborne, Calorimefry of saturated fluids, J. Out. Soc. Am. & Rev.

Sci. Instr. 8, 519-540 (1924).

[5] Nathan S. Osborne, Calorimetrv of a fluid, BS J. Research 4, 609-629 (1930)

RP168.

[6] Henry A. Babcock, The specific heat of ammonia, Proc. Am. Acad. Arts Sci. 55, 323-409 (1920).

[7] J. H. Awberv and Ezer Griffiths, The specific heat of liquid CH3 C1, Proc. Phys. Soc. "52, 770-776 (1940).

[8] K. Bennewitz and E. Splittgerber, Investigations in the critical region.

I. Specific heat of C02 near the critical point, Z. physik. Chem. 124, 49-65

(1926).

[9] N. S. Osborne, H. F. Stimson, T. S. Sligh, Jr., and C. S. Cragoe, Specific heat of superheated NH3 vapor, BS Sci. Pap. 20, 65-110 (1925) S501.

[10] Harold J. Hoge and Ferdinand G. Brickwedde, Establishment of a temperature scale for the calibration of thermometers between 14° and 83° K,

J. Research NBS 22, 351-373 (1939) RP1188.

[11] George Rutledge,. A reliable method of obtaining the derivative function from smoothed data of observation, Phys. Rev. 40, 262-8 (1932). Washington, October 24, 1945.

95-H8
Offprinted from the Transactions of The Faraday Society, No. 489, Vol. 59, Part 9, September, 1963

Heating Rate as a Test of Adiabatic Calorimeters and the

Heat Capacity of a-Alumina*

By E. D. West

Heat Division, National Bureau of Standards, Washington, D.G.

Received \Ath January, 1963

The constancy of heat capacities measured in an adiabatic calorimeter at different heating rates does not demonstrate the absence of heat leak errors due to departures of the surface temperature

from the " isothermal " condition. On the contrary, the total heat exchange between the calori- meter and its shield is virtually independent of the heating rate. The tests tend to obscure a real source of error due to the variation in the total heat exchange between experiments with the empty

and the full calorimeter.

Edwards and Kington 1 have recently described a low-temperature adiabatic

calorimeter together with measurements of the heat capacity of a-alumina. Their

data, in common with other sets of data discussed in their paper, were generally

higher than the results of Furukawa et al., 2 and of West and Ginnings. 3 As a

possible explanation, Edwards and Kington considered heat loss : " One possible

explanation might be offered in terms of a non-isothermal surface on the calorimeter or radiation shield. This effect has been investigated by using different calorimeter

heating rates. At slower rates of heating there is a greater chance of attaining a

near-isothermal surface on the calorimeter and shield." Their experiments at

different heating rates revealed no significant effect and they concluded, " Thus no

explanation can be found from this source for the difference between the present

results and those of Furukawa et al." The variation of heating rate is commonly used to test calorimeters, although

the effects to be revealed by the variation usually are not specified. It will be shown

below that the variation should not be expected to detect the heat exchange due to non-isothermal surfaces on the calorimeter and adiabatic shield. In an adiabatic calorimetric apparatus, the calorimeter is surrounded by an

adiabatic shield. Usually the temperatures of the outer surface of the calorimeter

and the inner surface of the shield are sensed by a thermocouple (or a thermopile)

and the two temperatures (or average temperatures) are controlled to be equal.

During the heating period, the heat flow (energy per unit time) from the respective heaters sets up temperature gradients with the result that the effective temperatures

of the surfaces of the calorimeter and shield differ from the temperatures at the

thermocouple junctions. The result is, in general, a net heat flow to or from the

calorimeter.

Edwards and Kington argue that, at lower heating rates, the calorimeter and

shield surfaces will be more nearly isothermal. There can be no disagreement

with this statement, nor with the implication that the rate at which heat flows

between the calorimeter and shield will be smaller at lower heating rates. In fact, in most adiabatic calorimeters, temperature differences on either of the surfaces and

the corresponding heat flow between them are, to a good approximation, directly

proportional to the heating rate except for transients.

* with special reference to Trans. Faraday Soc, 1962, 58, 1313. 96-1
The continuous heating method for adiabatic calonmetry minimizes transient

effects in the heat exchange between calorimeter and shield. After the calorimeter

heater has been on for a sufficient time, the temperature distribution in an adiabatic

calorimeter reaches a quasi-steady state in which the temperature at all points in the calorimeter and shield is rising at the same rate and the temperature difference

between any two points is constant and proportional to the heating rate. If one

of the points is that at which the temperature for shield control is taken, it is apparent

that the average temperature difference of the other points on the calorimeter is proportional to the heating rate. A similar argument applies to the shield relative to the control point on it. The heat flow resulting from these deviations from

isothermal surfaces is therefore proportional to the heating rate. For calorimeters using alternate heating and equilibration periods, the transients due to turning the power on and off confuse the problem of heat flow. With the approximation implicit in most calorimetry that the heat flow equations are linear,

the principle of superposition can be used to express the temperature as a sum of

terms satisfying various boundary and initial conditions.* The temperature differ- ence between the control point and an arbitrary point on the surface of the calori- meter or on the surface of the shield can be expressed as a sum of three terms

(i) the quasi-steady state distribution, satisfying exactly the same equations as in continuous heating, but taken to be zero outside the heating period ; (ii) a transient

at the beginning of the heating period to allow for the fact that the quasi-steady

state is not set up instantaneously ; and (iii) a final transient after the end of the

heating period to allow for the gradual decay of the quasi-steady state after the heater

is turned off. Assuming no geometrical changes during the heating period, as from

melting or mechanical motion, the same heat flow equations and boundary conditions apply to both the beginning and final transient terms. At the beginning of

the heating period, the temperature gradient due to heating is zero, but the quasisteady state term used to describe heat flow during the heating period is independent

of time as in continuous heating calorimetry. The " initial " condition is therefore imposed on the beginning transient term that it must be equal and opposite to the

quasi-steady state term. When the calorimeter is turned off, the quasi-steady state term is set to zero and its decay is described by the final transient. The " initial

condition on the final transient is therefore imposed that it be equal to the quasisteady state term. The transients are therefore equal and opposite for equal incre- ments of time (see footnote). If the final temperature of the calorimeter is taken

after the transients become negligible, the sum of the time integrals of the heat flow

due to the transients is also negligible. The heat exchange between the calorimeter

* There are two sources of heat in the apparatus : the calorimeter heater and the shield heater. Some of the shield heater power flows to the surroundings, assumed to be at some constant temperature, and some goes to raise the temperature of the shield during the heating period. The effect of the first part of the shield proper is to set up a gradient in the shield which causes a temperature

mismatch and an exchange of heat between the calorimeter and the shield throughout the experi- ment. Heat leak observations at equilibrium can be used to correct for this heat leak. The re- maining shield power and the calorimeter power are present only during the heating period, so that no observations of heat leak can be made independent of heat capacity measurements. However,

by putting the shield-to-environment temperature difference in the boundary conditions for the heat

leak at equilibrium, we obtain homogeneous boundary conditions on the terms describing the

gradients in the calorimeter and shield during heating. From the equal and opposite magnitude

of the initial conditions on the transients, it follows that they are equal and opposite for equal incre- ments of time. (If y is a solution to a homogeneous differential equation, with homogeneous

boundary conditions, then ky is also a solution, where k is any constant, including k = — 1 as required by our initial condition.) The mathematics have been worked out in detail for an ac- curately denned physical model.4 97-2
and the shield due to heating the calorimeter can now be treated as due to the same

quasi-steady state gradients in the calorimeter and shield as in continuous heating;

that is, an adiabatic calorimeter should give the same observed heat capacities by

either method. For intermittent as well as continuous heating, it follows that the average temperature of the calorimeter or shield surface differs from the temperature

at the control point and that this difference and the corresponding heat flow are proportional to the heating rate.

It does not follow that the rate of heating affects the observed heat capacity.

The effect of heat flow between calorimeter and shield on the observed heat capacity

is due to the total heat exchanged, not to the rate at which the exchange takes place

;

i.e., the length of the heating period must be taken into account. The effect of the

heat exchanged is apparent from the following argument

If the power P generated in the calorimeter is subject to no other appreciable

effect than the one under consideration (or has been corrected), then, from conservation of energy, one obtains the relation CAT = (P + PL

)At,

where C is the heat capacity, Pl is the small quasi-steady state heat flow between

the calorimeter and the shield, At is the time interval, and AT is the temperature

interval for an experiment. It was shown above that Pl — kP, where k may be a

positive or negative constant depending on the apparatus. Substituting in the equation above and rearranging gives the result, PAt/AT = C/(l + k). Although various combinations of P and At may be taken to give the temperature

increase over which comparison is made, the observed heat capacity based on these

quantities is wrong by the constant ratio 1/(1 +k). Evidently, the observed heat

capacity, in this somewhat simplified view, could not be expected to vary with the heating rate. This conclusion is bolstered by observations with a high-temperature

adiabatic calorimeter. 3 For heating rates different by a factor of two, the observed

heat capacities agree to about one part in 10,000, although the calorimeter surface temperature varies up to 0-1° from the temperature at the location of the control

thermopile. The heat loss from the calorimeter corresponding to this temperature

gradient is about 36 times the reproducibility of the measurements.

Since the heat capacity experiments at different heating rate do not reveal the

effects of the heat exchange during heating, it must be admitted as a possibly significant

quantity in the work of Edwards and Kington, as well as in the work of other groups.

It is suggested here that the differences in heat capacity obtained by various groups

are due in part to differences in the unknown heat exchange in experiments with

the full and empty calorimeter.

Edwards and Kington remark that three independent sets of authors report

positive deviations from the work of Furukawa et al. Two other sets of data may

be considered. Martin 5 reports heat capacities at room temperature 0-2 to 0-3 %

higher than those of Furukawa et al, but 0-4 to 0-5 % below those of Edwards and

Kington. West and Ginnings report agreement with the room temperature data

of Furukawa et al. to +0-02 %. In the design of the calorimeter used in the latter measurements considerable care was taken to make the surface temperature dis- tributions the same for the empty and the full calorimeter. The analysis presented

here does not, however, explain the predominantly positive deviations from the work of Furukawa et ah, and of West and Ginnings. As Edwards and Kington

point out, the cause of such generally positive systematic deviations is worth further

investigation.

98-3
The question of which calorimeter gives the best data for the heat capacity of

AI2O3 cannot be answered unequivocally. To analyze heat flow in each apparatus

completely is not possible from information given in publications. Too many

additional details of construction are required. Even with these details, probably

only rough estimates are possible. A major problem in accurate adiabatic calori- metry is to develop methods to demonstrate experimentally that no changes are made in the surface temperature distribution and in the thermal contact of the control

thermocouple when the sample is introduced. Evidently, data for the heat capacity

of AI2O3 of more generally accepted accuracy would be of value.

It may be pointed out that the systematic error due to the unknown heat exchange

will, in general, differ from one sample to another, depending on thermal properties.

Even if exact values \vere available for the heat capacity of AI2O3, it would not

necessarily follow that a calorimeter which reproduced those values would give

comparable data for other materials.

1 Edwards and Kington, Trans. Faraday Soc, 1962, 58, 1313.

2 Furukawa, Douglas, McCoskey and Ginnings, /. Res. Nat. Bur. Stand., 1956, 57, 67.

3 West and Ginnings, /. Res. Nat. Bur. Stand., 1958, 60, 309.

4 West, /. Res. Nat. Bur. Stand., 1963, 67A, 331.

5 Martin, Can. J. Physics, 1962, 40, 1166.

99-4
A Two-Body Model for Calorimeters with Constant-Temperature Environment

Estal D. West and Kenneth L. Churney

National Bureau of Standards, Washington, D. C.

(Received 18 March 1968)

Equations are derived describing a model of an isoperibol calorimeter in which the calorimeter proper

consists of two parts thermally connected, one surrounding the other and exchanging heat with the constant- temperature environment. These solutions provide insights into the behavior of real calorimeters. Inferences

are drawn relative to the effect of the locations of the thermometer and heat source on the energy equivalent

of the calorimeter and some possible errors are pointed out. Macleod's application of the two-body theory

of King and Grover to high-temperature enthalpy measurements is discussed and weaknesses in theory and experiment are pointed out. Procedures having a better theoretical basis are outlined.

INTRODUCTION

Isoperibol calorimeters1—those in which the temperature of the calorimeter varies and the temperature

of the surroundings is constant—are in common use for solution calorimetry, for combustion calorimetry, for heat-capacity measurements, and for the determination

of enthalpy changes between high temperatures and

standard temperatures. They are of both stirred water and aneroid types. The theory of operation of these calorimeters has not been worked out in detail from the laws of thermodynamics and heat transfer, probably

because of the difficulty of describing the apparatus in mathematical terms. Instead, only very simple theoretical models have been discussed for which rigorous

mathematical solutions can be obtained.

The simplest theoretical model of an isoperibol

calorimeter represents the calorimeter by a single body

having a geometrically uniform but time-dependent

temperature, and exchanging heat with an environment at a uniform, constant temperature. This singlebody model fails for accurate calorimetry because it neglects the temperature gradient and the changes in the gradient with time in both the calorimeter and its environment.

White2 considers isoperibol calorimeters in a more

comprehensive way. He summarizes the effect of temperature gradients in what he terms "the general law

of lag." This "law" is frequently expressed by the quotation from White: "When the calorimeter is cali- brated, it is calibrated, lag effects and all." He restricts this statement to "constant" lags. In another part of

his book (p. 36) he notes that a systematic error may

occur if the location of a heat source is different from

the location of the calibrating heater. White's treat- ment is inadequate because he does not state clearly

what assumptions he makes about the calorimeter

which lead to "the general law of lag." For this reason,

it is difficult to judge whether a calorimeter satisfies

1 0. Kubaschewski and R. Hultgren, in Experimenlal Thermochemistry, H. A. Skinner, Ed. (Interscience Publishers, Inc., London, 1962), Vol. 2, p. 351.

* W. P. White, The Modern Calorimeter (Reinhold Publishing

Corp., New York, 1928), p. 88. 100

the conditions under which White's conclusions about

lags are valid. A two-body model of an isoperibol calorimeter, consisting of two bodies, each having a geometrically uni- form, but time-dependent temperature, is the simplest

model in which effects of temperature differences in the calorimeter can be considered in explicit mathematical

terms. Equations derived for this model illustrate some

of the deficiencies of the one-body model and some of the conditions under which "the general law of lag" is valid. A two-body model is especially attractive for treating the problems encountered in measuring relative enthalpies at high temperatures. This experiment requires that a hot body be placed in the calorimeter where the heat given up on cooling is compared to a known energy. The thermal resistance between the hot body and the calorimeter is large compared to the thermal resistances between other parts of the calorimeter, so that it is logical to treat the calorimeter during the rating periods

as consisting of two heat capacities with a thermal

resistance between them. This approximation is similar

to the lumped constant treatment of an electrical net- work of two capacitors and a resistance connected by

wires of negligible resistance and capacitance.

The two-body model is treated by King and Grover,3 but they do not explore the general implications and

reach some wrong conclusions. Jessup4 extends the treatment, criticizing the results of King and Grover,

pointing out the errors, especially as they relate to bomb calorimetry.

King and Grover3 use the two-body model to develop

a method for treating data from high-temperature

enthalpy experiments. This method represents a radical departure from established methods because it assumes

a particular form for the heat flow between the hot

body and the calorimeter. Macleod5 applies the method

to actual calorimetric data, with the claim that it is more accurate than other methods. Such a claim affects a great deal of thermodynamic data obtained by iso3 A. King and H. Grover, J. Appl. Phys. 12, 557 (1941).

4 R. S. Jessup, J. Appl. Phys. 13, 128 (1942).

s A. C. Macleod, Trans. Faraday Soc. 63, 289 (1967). 4206
peribol calorimetry and therefore warrants careful ex- amination of its bases. THE TWO-BODY HEAT-FLOW PROBLEM

The two-body model for an isoperibol calorimeter is represented schematically in Fig. 1. The calorimeter

consists of two bodies—an inner body having a uniform

temperature 6 and heat capacity K2 completely en- closed by an outer body with a uniform temperature

6 and heat capacity Ki.6 The calorimeter is completely

enclosed by surroundings having a uniform constant temperature dj. The fundamental relationship for the

calorimeter is obtained by application of the first law of thermodynamics. For an infinitesimal time interval dt, we equate the increase in enthalpy to the net heat to

(or work done on) the calorimeter:

Ki{dB/dt) +K2 (dQ/dt) = (dQi/dt) + (dQ2 /dl)

-rki(8-0j)+P.. (1)

In (1), Q\ and Q2 are heats developed in the outer and

inner bodies, respectively; Ps is the stirring power7 in the outer body; and ki is the constant coefficient for heat transfer between the outer body and the sur- roundings. In the usual manner, we consider a calorimetric

experiment consisting of three time intervals—an

initial rating period, a main period, and a final rating

period. The main period includes the time during which

heat is generated in the calorimeter; the rating periods

are chosen before and after the main period when

dQi/dt and dQ2/dt have been zero long enough to have

negligible effects on 6 and 0. Experimentally, this

SURROUNDINGS

CALORIMETER OUTER B00Y

CALORIMETER

INNER BODY © ,

K

2 ,Q 2

h 2

8, K,,Q|

Fig. 1. Schematic cross section showing the inner body at temperature O enclosed by an outer body at temperature 0 and

both bodies of the calorimeter enclosed by the surroundings at the constant temperature 8j.

6 Where possible, the notation of King and Grover3 and Jessup4 have been retained to facilitate inlercomparisons.

7 If the stirring work is done on the inner body, the convergence

temperature will be different for the two bodies. We do not consider this case.

criterion means that the observed temperature is a

single exponential function of time. We now define the convergence temperature 8k of the calorimeter in the usual way: 8k = 8j-\-P„/h\. Substituting in Eq. (1) and integrating between a state

(do, Go, to) in the initial rating period and a state

Qi, h) in the final rating period, assuming K\, K2 , and hi are independent of temperature, we obtain the

following equation:

K1 (eL-do)+K2 (ei-e0 ) = Qi+Q2 -Jhf'

i (e-ek )di. (2)

J to

Physically, Eq. (2) equates the increase in enthalpy of the calorimeter to the net heat added to the calorimeter

for the time interval ti—t0 . 8 In an actual calorimeter,

K\, K2 , and hi change slowly with temperature, so that the temperature range is restricted for real calorimeters. Only one temperature is measured in actual experi- ments. To impose this condition in (2), we need an

additional relationship which will let us write the entire equation in terms of either 6 or 6 alone. If the temperature is measured in the outer body, then we need only

express Gi and Go in terms of di and d0, respectively,

during the rating periods in order to make comparisons

of different Q's—electrical energy and a heat of combustion, for example.

During the rating periods G — 6 will be small and

the heat flow between the two bodies can be described

by Newton's Law of Cooling. Applying the first law of thermodynamics to the inner body alone, we obtain

K2dQ/dt=-h2 (e-6). (3)

In Eq. (3) h2 is the heat-transfer coefficient between

the inner and outer bodies. Subtracting (3) from (1) for the rating period when Qi = Q2 —0, we obtain

K1d8/dt=h2 (Q-8)-fa(8-8k ). (4)

It is important, especially if the inner body is a hot

capsule as in high-temperature enthalpy measurements,

that no restriction has yet been made on the heat transfer between the inner and outer bodies during the main

period. Solution of the simultaneous Eqs. (3) and (4) gives the results of Jessup4

: d-dk =Ae-tt +B exp[- (2p-e)Q, (5) Q-8k =[_a/ (a-e)~]Ae-lt +laB/(a-2p+e)~]exp[,-(2p-e)f\> (6)

where a, p, q, and t are defined in Table I, and A and

8 In an electrical calibration, Qi or Qz will represent electrical work done on the system calorimeter plus contents, and the

integral term is the heat transferred to the system from the surroundings. In a combustion experiment, for example, Qi or Q2 represents the heat of combustion, so the net increase in enthalpy

of the system is the left-hand side of (2) less Qi or Q2 . Equation

(2) permits determination of an unknown heat effect in terms of

electrical units; it remains to translate the unknown heat effect into thermodynamic quantities.

101-4207
Table I. Symbols.

0 temperature of inner body d = dB/dt 9 temperature of outer body

Oj temperature of surroundings

6k =9j+Pa/h, the convergence temperature

P, constant power sources—stirring, thermometer, etc., in outer body

/ time

A'i heat capacity of outer body

A"2 heat capacity of inner body

Qx heat generated in a finite time in outer body

Qi heat generated in a finite time in inner body

hi coefficient for heat transfer between outer body and sur- roundings

Ih coefficient for heat transfer between inner and outer bodies a =h<i/Ki, b = Ih/K\, c = hi/K\

2p = VA'i+VA', +h1 /K1 = a+b+c

q =hihilK\Ki — ac

e =p-(p>-q)"> = h/lKi+aKi/ (a -e) ]

B are constants to be determined from values of 0 and

0 at a particular time in the appropriate rating period.

These equations are derived from two first-order equations, so there can be only two undetermined constants. From the definition of p and q, it may be shown that

p

2 >q and p>(p2 -q) U2»0. Thus, e and 2p-e are always real and positive. In good design, h\/K\ should

be small compared to h2/K2 ; that is, equilibrium within

the calorimeter is attained more rapidly than equilibrium with the environment. In this case (2p—e)^Z>e

and the second exponential terms in (5) and (6) decay

relatively rapidly. After the second exponentials become

negligible, the following relationships, valid only during

rating periods, are easily derived9

; de/dt=-e(e-ek), dQ/dt=-t(e-6k ), e-0*=[a/(a-€)](0-0*).

(7)

(8)

(9) The relations (7) or (8) are statements of the usual

exponential behavior of the observed temperature of an isoperibol calorimeter during the rating periods.

THERMOMETER ON OUTER BODY

If the thermometer is located on the outer body, 0

is the measured temperature and 9 in (2) must be

expressed in terms of 0 using (9) and the definitions of

e, p, and q, in Table I. On rearranging, we obtain the equation in the form commonly used in isoperibol

calorimetry:

[tfi+atfaAa-e)] 0i-0o+^" (0-0*)^] = Qi+Qt

(10)

In (10), K\-\-aKi/{a— e) is an energy equivalent,

•In our derivation, we take Eqs. (1) and (3) to describe the calorimeter and derive (4) and (7) -(10). The argument can be made in another way. Equation (7) states a commonly observed phenomenon and can be used with (1) to derive the other

equations.

multiplying a corrected temperature rise. Several sig- nificant points are contained in (10). The energy

equivalent is independent of the form of the timetemperature curve, in agreement with the "general

law of lag." The energy equivalent has the dimensions of heat capacity, but it is not the sum of the heat capacities.

To calculate the energy equivalent even for this simple

model would require knowing hi, h2 , K\, and K2 separately. This illustrates a reason for preferring the experimental determination of energy equivalents to calculation. Equation (10) does not discriminate between Q\ and

Q2 . That is, when the temperature is measured on the outer body, an electrical calibration with the heater on

either body determines the proper energy equivalent

for measurements of some unknown heat developed in either body (but see the next section)

.

According to (7) and (8), c- can be determined by

measurements on either body. We emphasize, in agree- ment with Jessup,4 that the cooling constant t =

hi/[_Kr +aKi/ {a— t)] is exactly the one desired, and

not the ratio hi/K\ as recommended by King and

Grover.3 This point is discussed in detail below.

There is no restriction in (10) on the rate at which

heat is developed nor on the duration of heating, so that different heating rates in electrical calibrations must give the same energy equivalent, a result deduced

earlier for adiabatic calorimeters.10 THERMOMETER ON INNER BODY

If the thermometer is located on the inner body, 0

is the temperature measured and 0 in (2) must be

expressed in terms of 0. To obtain the desired relation, we again substitute

into (2) from (9), but we must also substitute for 0

in the integrand. Since the integral must be taken over

the heating period, the expression for 0 must be valid during the heating period. We again assume, as in (3)

,

that the heat transfer is proportional to the temperature

difference, which restricts our description to experiments in which 0—0 is small. Applying the first law

of thermodynamics to the inner body, we obtain

K2 {dQ/dl) = - /z2 (©-0) + (dQ2/dt)

,

(11)

Dividing by h2 and adding (0—0*) to both sides, we

obtain

B-ek = (K2/h2 ) {dQ/dt)-(l/h2 ) (dQ2/dt)+Q-dk . (12)

Substituting (12) into the integral in (2) and using

(9) to express 0i and 0O in terms of 0i and 0o, we obtain

after rearrangement

(kx + —) Oi-Oo+e/"

1 (0-0*

\ a— e/l J t0 Q.+ ^Q2 -

(13)

10 E. D. West, J. Res. Natl. Bur. Std. 67, 337 (1963).

102-4208
This equation states that the energy equivalent deter- mined by supplying a known amount of heat Q\ to the outer body is not applicable to determinations of heat

generated in the inner body Q2 when the temperature

is measured on the inner body. This result illustrates a

limitation of the general law of lag and emphasizes

White's warning that electric heat produced in a part

of the calorimeter different from the part where other

heat is produced, may cause a systematic error. For a thermometer on the inner body, as in the preceding section, e is exactly the cooling constant

required.

THE TWO-BODY ANALYSIS OF KING

AND GROVER

Since the results of the two preceding sections are in conflict with statements of King and Grover,3 and

since, despite Jessup's4 treatment, some confusion about

the problem apparently remains, it appears worthwhile

to consider in detail just where their analysis3 is at

fault. They state that "The heating period has been

considered to end when the time-temperature curve

begins to obey... a pure exponential relation. Our

analysis of this problem indicates that this assumption

is not valid." This statement is contrary to our Eqs.

(10) and (13), which are exact, providing that the end

of the experiment is taken when the time-temperature

curve does obey a single exponential relation. We consider their analysis in some detail to point out the

errors which lead to their statement. The first difficulty with King and Grover's analysis

is in connection with their Eq. (6)

dO/dt=F(t)-c(0-6k ), (KG6)

where c=hi/Ki and F{() is the "heating function,"

representing the heat flowing from the inner body

divided by the heat capacity of the outer body. This

equation is an alternate, but less specific version of our Eq. (1). They integrate this equation with the restric- tion that F(l) — 0 during rating periods. Comparing

(KG6) with Eq. (1), which is just the application of the first law in a two-body calorimeter, we identify

F(t) = (Ki/KO (dQ/dl). (14)

Since Qi and Q2 are zero in rating periods, their restric- tion that F(t)=0 in rating periods means that either dQ/dt=0 or K2 =0. If dO/dt=0, then 6 = 0=0* and we

have the trivial case of zero temperature rise. If K2 =0,

there is no inner body. Hence, (KG6) and related equations [their (7)— (26) ] apply to a calorimeter

consisting of a single body at uniform temperature. In

this case, of course, c would be the cooling constant. The same type of error occurs in connection with

their Eq. (27), which is the same as (KG6) with the

additional restriction that F(l) is, . .a constant over

a limited time (the heating period) and zero otherwise."

This equation was intended to apply to electrical calibrations. It suffers from the same defect as (KG6)

and an additional defect during the heating period. This

additional defect can be seen from the following. Again

comparing with (1), but for the heating period, then the heating rate d(Qi+Q2 ) /dt must be adjusted to compensate for the change in dQ/dt, which is a practical

absurdity, or K2 must again be zero. The burden of this criticism is that their concept of a "limited heating period" with F(t)=0 in rating

periods is not compatible with a meaningful two-body

problem. In the resulting one-body problem, no time

is needed for equilibration. This rough approximation is used in their Eq. (29) which takes the final temperature

reading at the end of the heating period.

A practical objection can be made to this identifica- tion of the end of the experiment with the end of the heating period [e.g., their Eqs. (9) and (29)]. This

identification follows from their disguised one-body

problem; it is wrong for the next more-subtle model,

the two-body problem, and certainly goes contrary to experience with actual calorimeters. Their further treatment of the two-body problem

beginning with their Eq. (33) does treat the case where K2 is finite, but Qi=Q2 =0. However, they still identify the constant c=hi/K\ as the cooling constant

(p. 563). To illustrate the fallacy of this identification by a physical example, we consider a large block as the

inner body, so that K2 is very large, surrounded by a a thin shield, so that K\ is very small. If the temperature

of the shield is measured and the heat is generated by

a source located on the shield, then, when the heat

supplied by the source is stopped, e~

ct goes to zero almost instantaneously. If c were really the cooling

constant, the temperature of the shield would have to revert to 0* very soon after the supply of heat is stopped.

Actually, of course the heat flow to the shield from the

inner body would maintain the temperature of the shield above the temperature of the surroundings.

One further precaution is necessary if their Eq. (4)

is used for experimental data. It is derived from their (39) which follows directly from the equation of mixtures (see their footnote 20). We rewrite their (39),

using the identity b{a+b) =K2/(K1 +K2 )

(Kt+Kt) (dJ-60 )=K2 (Go-e0 ). (15)

The right-hand side is the total energy given up by the

inner body in cooling from 80 to 0O . The energy equivalent appropriate to the corrected temperature rise defined in this way is therefore Ki+K2 . A basic flaw

of this definition and the associated procedure is that no isoperibol method will determine Ki-\-K2 because

different parts of the calorimeter undergo different temperature rises. (In fact, Ki+K2 is an energy equivalent only for a two-body adiabatic calorimeter, as the

definition implies.)

103-4209
TIME Fig. 2. Illustration of Dickinson's method for the case that

the final temperature 6e is above the convergence temperature 8k. The time tx is chosen so that A-\-D = B-\-C.

DICKINSON'S GRAPHICAL METHOD

Dickinson's graphical method11 for evaluating the temperature-time integral in isoperibol calorimetry was

based on the experimental fact that the rate of change

of the calorimeter temperature during rating periods is proportional to the thermal head as in (7) and (8). For the two-body model, as well as for real calorimeters, the rating periods must, therefore, begin some time

after the end of the heating period to permit decay of other exponentials. The discussion of Dickinson's

method by King and Grover is wrong because they

take the final temperature at the end of the heating

period. Macleod5 selects the maximum temperature for use in Dickinson's method.

Because of this evidence of improper use and because

the method is sometimes poorly described, it is instructive to derive the method in connection with the two- body problem. It should be pointed out that, for real calorimeters, Dickinson's method requires only that

heat transfer between calorimeter surface and sur- roundings be proportional to the observed temperature

difference and that (7) and (8) hold during rating

periods. We treat the case where 6i>dk , because that seems to cause the most trouble. In Fig. 2 a hypothetical temperature-time curve is represented for which the integral in (1) must be

evaluated. This is done by finding two rectangles of equal area. From the figure, the integral is expressed in terms of two rectangles and the areas A, B, C, and D:

f' (ek -e)dt= (ek -d0 ) (tx -t0)-A+B

J to -l{6e -ek ){t-tx )-C+Dl. (16)

If tx is found so that A-\-D=C-\-B, and substitution is made from (7) and (8) , the form given by Coops et a/. 12

11 H. C. Dickinson, Bull. Bur. Std. 11, 189 (1915).

12 J. Coops, R. S. Jessup, and K. Van Ness in Experimental

Thermochemistry, F. D. Rossini, Ed. (Interscience Publishers,

Inc., New York, 1956), Vol. 1.

is obtained in terms of experimental quantities:

For either the one- or the two-body model, Dickinson's

method is a theoretically exact evaluation of the integral. Any approximations occur in the application to experimental data. Roth and Becker13 present an alternative method

for evaluating the time-temperature integral. The two

methods give exactly the same corrected temperature

rise but the values of obtained by one method must

not be used with the other method. Jessup4 has used

the Roth and Becker method, but has erroneously

ascribed it to Dickinson.

ISOPERIBOL CALORIMETRY FOR HIGHTEMPERATURE ENTHALPY

MEASUREMENTS

An isoperibol aneroid "receiving" calorimeter for use

in high-temperature enthalpy measurements presents

problems of data reduction which can be analyzed by

means of a two-body model of the calorimeter. In these measurements, a hot body at a high temperature is dropped into the calorimeter at the end of the initial rating period and allowed to cool. The final rating

period is taken with the added body still in the calorimeter. Since the calorimeter has a different energy equivalent and therefore a different cooling constant in the two rating periods, the usual isoperibol methods for determining the cooling constant and the convergence

temperature do not apply exactly. In addition, the

difference between the final observed calorimeter temperature and the temperature of the added body must

be taken into account. Various experimental procedures have been used. The experiment will be analyzed in some detail to indicate advantages of particular procedures and

methods of estimating some of the errors involved.

The analysis on the basis of the two-body model is related to the real problem in about the same way that a one-body model relates to a combustion or solution

calorimeter. The one-body model—a single body with

temperature varying in time but uniform in spacepredicts the correct formula for calculating the corrected temperature rise for real calorimeters providing that

the energy equivalent and cooling constant are deter- mined experimentally and that initial and final temperatures are taken after the temperature in the rating

periods can be represented by a single exponential function of time. These provisions take care of most of the

differences between the simple model and real calorimeters. The energy equivalent and cooling constant of a

receiving calorimeter can be determined experimentally

13 W. A. Roth and F. Becker, Kalorimetrische Methoden zur Bestimmung chemischer Reaktionswarmen (Frederick Vieweg und

Sohn, Brunswick, Germany, 1956). 104-4210
so that dependence on theory is confined to the effect

of adding the relatively small heat capacity of the dropped body to the large energy equivalent of the

calorimeter. The basic relationship is derived from application of the first law to the system calorimeter plus dropped

body by equating energy measured by the calorimeter

to the decrease in the enthalpy of the dropped body

Hf—Hi less the small heat Ql "lost" in dropping:

h-Vo-t-c (e-ek ] di Hf —Hi—QL . (18)

Since we are now treating real calorimeters, the quantity Ki is the energy equivalent determined by calibration. In (18) Hf is the enthalpy of the dropped body

at the temperature of the furnace, Hi is its enthalpy

at the final temperature of the calorimeter, and Ql

allows for heat lost in transferring the body from the furnace to the calorimeter, for heat radiated directly

from the furnace into the calorimeter during the transfer, and any other small heat quantities associated

with the transfer operation. In careful work Ql is usually accounted for by experiments made with a

capsule and a capsule plus sample in such a way that

Ql is the same for both experiments and their differ- ence is a thermodynamic property of the sample. In our

analysis of the calorimetric part of the experiment, it is sufficient to note that the right-hand side is the sum

of an unknown heat Ql and a thermodynamic quantity

Hf—Hi, which we may treat in accord with thermodynamic theory.

The enthalpy of the dropped body Hi is, in general, not constant during the final rating period because the temperature is changing. The temperature of the dropped body and, consequently its enthalpy, must

also change as long as the calorimeter temperature

changes. One way to avoid this problem is to make

0i=0i as suggested by Jessup.4 Another way which may

be easier experimentally is suggested below.

The inconstancy of the enthalpy of the dropped body

and of the corrected temperature rise may be the source

of the idea of the "unlimited heating period" of King

and Grover. The inconstancy is eliminated by the procedure suggested below and is therefore more a matter of data treatment than of inherent difficulty in the experiment.

The difficulty is overcome merely by treating the

calorimeter by the two-body model in which the inner

body is the dropped body. Using (9), we write the

increase in enthalpy of the dropped body between the

initial and final states of the calorimeter in terms of the observed initial and final temperatures:

K2 (dl -do)a/(a-e)=H1 -H0 , (19)

where Ho is the enthalpy that the dropped body would

have at time to, if it were present in the calorimeter during the initial rating period. Adding (19) to (18) and

rearranging, we obtain

\&i+-£rj Oi-e0+eJ (e-ek )dt =hs -Ho-ql .

(20)

Equation (20) has the virtue that the right-hand side does not depend on the final temperature of the calorimeter. The corrected temperature rise must therefore be

constant and its constancy can be used as a criterion

for deciding when the experiment is complete. We have

found this criterion useful in data analysis.

The cooling constants and the convergence temperature required in (18) and (20) cannot, in principle,

be determined directly from the experimental data

because the dropped body is absent during the initial rating period but present during the final rating period. For some work, it may be adequate to ignore the change

in cooling constant due to the dropped body and proceed

by ordinary isoperibol methods. For more accurate work with a given calorimeter, the change in cooling constant can be accounted for. We proceed to develop

methods for obtaining the constants from the data. The

formulas developed can also be used to estimate the

error in using ordinary isoperibol methods.

The relation between the cooling constants is evident

from their definitions in Table I: c/e=l +laK2 /{a-e)Ki']. (21)

We solve (21) for e, substitute into (7), and rearrange

to obtain an expression for the final rating period in terms of c {6 = dd/dt)

[l+aAV(a-e)A'1 ]01 =-C (01 -04 ), (22) For the initial rating period without the dropped body, we can write

6o=-e(80 -6k ). (23)

Subtracting (23) from (22) gives an expression for the

cooling constant c required in Eq. (18)

11+aK2/ (a- e)Ki~]ex-80 (24)

An expression for the cooling constant e required in Eq. (20) is obtained by substituting for c from (21)

into (23) and subtracting (7) for the final temperature

0i

t=[l/(^o-0i)]{0i-0o/[l +aAV(a-e)A'1 ]!. (25)

The temperatures and time derivatives of temperatures

in (24) and (25) can be obtained from initial and final rating periods; K\ is obtained by electrical calibration and Ki from known weights and heat capacities in the

literature. The contribution of a suspension wire to K2 can usually be neglected. The ratio a/(a—e) is close to one; \/a is the time constant for the dropped body

cooling to the calorimeter and should be about 10 min

or less; 1/e is the time constant for the ralorimeiter con- 105-4211
taining the dropped body cooling to the environment

jacket and is typically about 500 min. It is usually

sufficient therefore to take a/ (a—e) to be one, although

the time constant l/a should doubtless be calculated

for other reasons. If the apparatus is arranged so that an experiment for a furnace temperature 1000° above

the calorimeter temperature causes a 3° increase in the

latter, then K2 /Ki is approximately 1/300. The quantity

aK2/{a-t)Kx in (24) and (25) is therefore about 0.003 and need not be known accurately for the determination

of the cooling constant. In fact, this uncertainty can

be made very small by making the final temperature

near the convergence temperature in (24) as suggested

by Jessup,4 or by making the initial temperature near

the convergence temperature in (25). Other reasons

for such experimental arrangements are discussed below.

If (20) is to be used for data reduction then the energy equivalent must be determined with the dropped

body in place or a suitable correction made. Ordinarily,

only K\ is measured and the question is whether

aK2/(a—e) can be calculated with sufficient accuracy.

If Ki=3Q0 K2 and an uncertainty in the energy equivalent of 1/10 000 is permissible, then a value of aKil (a—e) is required, good to about 3%. The heat

capacity K2 can usually be calculated with sufficient accuracy from data in the literature, and the calculation

hinges on knowing a/ (a — e) with sufficient accuracy.

Several methods might be used to obtain a value for a=h2/K2 . Calculation from first principles may be

adequate, especially if one is sure that a»«. A few comparisons with measured energy equivalents should give a good test of the calculation. Curve fitting (5) might

give useful values of 2p—e, which is a good approximation to a(Ki+K2 ) /K\. Measurement of the cooling constants in the final rating period both with and

without the dropped body give the ratio of energy

equivalents, but this procedure does not appear to be

accurate enough. Electrical calibration with and with- out the dropped body together with K2 calculated from

known weights and heat capacities should give a good

value for h2 , but this value may be considerably different

for an empty capsule and for one filled with a powder,

for example.

In applying any of these refinements, one must keep

in mind that the theory treats two bodies, each at a uniform temperature. Calibration takes care of lags

in the calorimeter, but large departures from uniform

temperature occur in a capsule filled with an evacuated

powder, for example.

Once either cooling constant is known with sufficient accuracy, the convergence temperature 6u can be deter- mined in the usual way from data for one of the rating

periods.

The remaining problem in connection with data

analysis by either (18) or (20) is that the reference temperature of the dropped body is not in general the same as the corresponding observed temperature of the calorimeter. The desired relation is obtained by

subtracting d—dk from both sides of (9)

e-0=[e/(a-e)](0-0*). (26)

The ratio e(a— e) is approximately e/a which is on the order of 0.02. The error in taking the observed temperature as the reference temperature of the dropped

body can be made as small as desired by making the

final calorimeter temperature near the convergence

temperature for (18) or making the initial temperature

near the convergence temperature for (20). These are

just the conditions required for the best determinations

of the cooling constants in (24) and (25). Substitution

from (7) into (26) gives an alterative form in terms of the rate of change of the temperature.

The procedure suggested by King and Grover3 has a weakness not present in either of the procedures sug- gested here: the heat flow from the dropped body to the calorimeter is assumed to follow Newton's law of cooling (3) from the moment it enters the calorimeter. They recognize the nature of the approximation:

"Actually the rate is undoubtedly a more complicated

function of 0 — For a hot capsule, it is likely that the initial rate is nearly proportional to the fourth

power of its absolute temperature, which would give an algebraically greater correction to the temperature

rise. It might be argued that, since heat leak accounts

for only about one percent of the total energy, their approximation for the heating period may be adequate.

It does appear to be adequate for some work. Even so, there appears to be no compelling reason to use the

inferior theory.

MACLEOD'S COMPARISON OF PROCEDURES

Macleod5 set out to test the adequacy of the King

and Grover procedure with actual experimental measurements. He presents the experimental data for an

electrical calibration and an enthalpy experiment in

his isoperibol calorimeter and compares the corrections

to the temperature rises calculated by various methods.

His thesis is that the method of King and Grover

for isoperibol data analysis is superior to Dickinson's

method, which is essentially equivalent to the methods we have advanced. His basic arguments are (1) that data treated by the method of King and Grover agree with data taken by the adiabatic method in the same

calorimeter, and (2) that these data yield enthalpies

for aluminum oxide in better agreement with values in the literature. In Macleod's calibration experiment, the calorimeter

initially comes to a constant temperature so that the

initial temperature is equal to the convergence temperature. Electrical energy is supplied for 46 min and

the calorimeter temperature passes through a maximum

at 48.5 min. After 185 min, the calorimeter temperature

decreases exponentially with time. The corrected temperature rise calculated according

to the left-hand side of Eq. (18) is shown in Table II.

106-4212
The corrected temperature rise decreases by 0.2%

between 48.5 and 100 min and then increases. From

185 to 275 min the corrected temperature rise is constant to about one part in 14 000. If the simple one-body

model is an adequate representation of Macleod's

calorimeter, the corrected temperature rise will be the same for all temperatures after the end of the heating

period. The model fails to describe the calorimeter by

about 0.2%.

If the final temperature is taken during the final rating period, the corrected temperature rise calculated by Dickinson's method is 1427.38 iN, which is 0.11%

less than Macleod's value of 1428.03 juV calculated by

the method of King and Grover. The latter is 0.06%

less than our value at 48.5 min in Table II. The dis- crepancy appears to be due to his use of a trapezoidal

approximation in calculating the time integral of 0— 6k . Our analysis of the enthalpy, experiment shows a

significant discrepancy between the values Macleod

used for c and t. For the two-body model of King and

Grover, which is the basis of Macleod's recommended

procedure, Eq. (21) holds exactly and is probably a good approximation for real calorimeters. To use (21), we need the ratio a/ (a— e). We have shown in the preceding section that this ratio is close to unity. We

can show an equivalent result from Macleod's data. He does not determine a value of a, but it may be

calculated from his value of a+b=aKi/ (Ki+K2 ) if K2/Ki can be estimated. From the size of his graphite

capsule described in his companion paper,14 assuming a

density of 1.8 and a volume of 2.5 cm3 for the sample, we calculate K2 =l.25 cal/°K. He gives ^=2215

cal/°K, from which we calculate a=0.9994(a+6) =

0.10552, whence a/(a— t) = 1.0052. Using these values

in (21) we obtain c/e= 1.00056, which contrasts with

the ratio of Macleod's values of 1.0862. From another point of view, not restricted to any

simple model, the ratio c/e is just the ratio of the energy

equivalent with the dropped body to that without,

assuming only that the coefficient for heat transfer to the surroundings does not change. The experimental

ratio of c/e= 1.0862 requires us to believe that the

addition of a heat capacity of 1.25 cal/°K adds 8.6%

to an energy equivalent of 2215 cal/°K.

At least part of the difficulty lies in attempting to determine the cooling constant from a single rating

period. Although a good fit to the data can be obtained,

goodness of fit is not an adequate criterion for the accuracy of the cooling constant. We can demonstrate

this point by using the same cooling constant to fit the data of both the initial and final rating periods. In Table III we compare differences between the observed

data and equations of the form

0=0o+ {ek -d0){ct+w/2),

in which a value for 0o is determined to give the best M A. C. Macleod, Trans. Faraday Soc. 63, 300 (1967).

Table II. Macleod's electrical calibration experiment.

Corrected temp. Corrected temp.

/i(min) rise", (juV) h (min) rise" (fiW)

A o r 4o. O1/10Q OO 14/8. yo

IOC loo 1 A 07 c; A 14Z/ . oO

CO 1 A OQ 1A 14ZS.o4 i rtc; lyo I'm 1/107 OO . ll

Art 1 A OA 7rt 14Z0. /y Orts 1 A 07 01

Qrt 1 A OA 10 14Z4. LL 01 c J.LO 1 A 07 07 14Z7

.

LI

1 rtrt 1 A O/f 1 rt 14Z4. 1U OO c 1/107 Ort ItLi . Ly

120 1425.41 235 1427.31

1 Af\ 14U 1 A OC 1 1 OA C z4o 1 A 07 A

Q

lAZI .45 160 1426.03 255 1427.28

170 1428.17 265 1427.24

275 1427.16

"Heater off at 46 min; hi/Ki =6.006 min 1 (calr. by Macleod); 6k =

6180.18 juV; lo=0 min.

average fit. For one set, we have used Macleod's values

of c, €, and 0*; for the other set, we have determined 0^ and a single cooling constant by usual isoperibol tech- niques.12 It is evident that the set using the single cooling

constant, in conformity with our conclusion that the

effect of the capsule is small, represents the data as well as the set using two cooling constants. Macleod calculates the corrected temperature rise to be 1422.06 nV by the method of King and Grover and

1420.32 by "Dickinson's" method, using the maximum

temperature, which occurs ahead of the final rating

period. Our value for the corrected temperature rise obtained by (25), using our value of c (or e) and 0* given in Table III and a final temperature at 120 min

later is 1423.88 (N, some 0.13% higher than that given

by Macleod by the method of King and Grover. CONCLUSIONS

The two-body model of an isoperibol calorimeter

shows several interesting features:

(1) The location of the thermometer is critical for satisfying a necessary condition for isoperibol calorimetry that the energy equivalent be the same for both

calibration and unknown experiments. For the ther- mometer located in the outer body the energy equivalent for a heat source in the outer body is the same as the energy equivalent for a heat source in the inner

body; for the thermometer in the inner body, the energy equivalent for a heat source in the outer body

is greater than the energy equivalent for a source in the inner body. We cannot deduce from the simple

two-body model all the restrictions on the locations of thermometer and heat sources in real calorimeters, but,

for the model, the problem arises when one of the sources

to be compared is located in a body outside the body

where temperature is measured. White's statement,

quoted above, about cancellation of lags must therefore be restricted to heat sources which have the same

energy equivalent associated with them. For the two- body model, the criterion for sources to have the same

energy equivalent is that no source shall be located

outside the thermometer.

107-4213
Table III. Comparison of fitting drift-period data.

Initial drift period Final drift period

Macleod Authors Macleod Authors Time obs.-calc.a obs.-cak. b Time obs.-calc. c obs.-calc. d (min) ( MV) (mV) (min) ( MV) ( MV)

-60 +0.02 +0.02

-50 +0.01 0.00 -40 +0.01 -0.01

-30 +0.02 -0.01

-20 -0.03 +0.02

-10 -0.02 0.00

0 -0.04 0.00

"0/, = 1395.86 /J.V; 0o =463.37 juV; c =0.5998 X 10 ^ min i.

11 0L = 1426 yuV; 0o = 463.37 /jV; c =0.582 X10-" min"'.

(2) The energy equivalent is not the sum of heat

capacities but may be either greater or less than the sum. This fact may have implications for heat capacity measurements. If (10) is used for heat-capacity meas- urements by determining the heat capacity Ai of the outer body alone and then with the inner body (sample)

,

what is actually obtained by the difference of the two

experiments is [A~i+aAV(tf-— «) ] — K\. If a^5>e, as it would be for the calorimeter in vacuum at low temperatures, then a/(a — e) is very close to one and a good

value of A'o is obtained from the difference in the two

measurements. At some higher temperature, where

radiation from the outer body is appreciable a/ {a — e) > 1 and the apparent heat capacity is too large. Real

calorimeters are probably too complicated for even this qualitative conclusion to apply, but the general idea that they are subject to systematic error which in- creases with the heat leak appears to be valid. A dis- cission of this problem is given by Cole el al. lb in their section on "Correction for Thermal Gradients within

the Calorimeter."

(3) The corrected temperature rise multiplied by

the proper energy equivalent gives the quantity of heat

exactly, even though the energy equivalent is not a sum of heat capacities. This result illustrates the reason

for experimental calibrations. Calibrations with stand- ard materials are especially useful because they are more likely to produce the calibrating heat in the same

place as the heat to be measured.

(4) The same cooling constant will be observed

during rating periods regardless of the thermometer

location, although the temperatures are not the same.

(5) The cooling constant is the heat-transfer coeffi- cient divided by the energy equivalent determined with

the same thermometer. It is not the heat-transfer coeffi- cient divided by the sum of heat capacities. The cooling K A. G. Cole, J. O. Hutchens, R. A. Robie, and J. W. Stout,

J. Am. Chem. Soc. 82, 4807 (1960).

120 — 0.23 — 0.02

130 -0.13 +0.05

140 -0.04 +0. 10 150 +0.05 +0.16

160 +0.06 +0.13

170 +0.04 +0.07

180 +0.02 +0.01

190 +0.03 -0.01

200 +0.02 +0.02

210 +0.04 -0.08

220 +0.06 -0.09

230 +0.07 -0.13

240 +0.07 -0.13

c

0t- = 1395.86 juV; 00 = 1894.67 fiV ; e =0.5522 X 10"< min"'.

0;. = 1426 fxV; 00 = 1894.46 flV; e =0.582 X10"< min-'.

constant determined by experiment is therefore just the constant required to multiply the temperaturerise correction. The first treatment of the two-body problem by

King and Grover suffers from the imposition of a mathematical condition which is not possible physically and

leads to the conclusion that the final temperature in an

experiment can be taken at the end of a heating period.

The correct two-body model predicts a waiting period

after the end of the heating period before the temperature-time curve becomes a single exponential function

of time. This prediction checks experience.

Their second treatment assumes a particular form for the temperature-time curve during the heating period. In effect, the practical use of this theory requires that the two-body model be an adequate model of the real calorimeter. Alternate procedures suggested, which

avoid this assumption, are preferable on theoretical grounds.

When Macleod's experimental data are analyzed by

our Eq. (20), the corrected temperature rise becomes

independent of the time taken for the end of the experi- ment. There is, therefore, no compulsion to consider

experiments with "unlimited" heating periods, as sug- gested by King and Grover. Macleod concludes that the method of King and

Grover is superior to Dickinson's method for treating

data from isoperibol calorimeters because (1) it gives

agreement with data from an adiabatic method, and

(2) it gives more acceptable values for the enthalpy

of AI2O3. Apart from his dependence on an inadequate

theory, the agreement he found between methods may

depend on small compensating errors. The corrected temperature rise calculated by the method of King

and Grover is too small. The corrected temperature

rise for the calibration experiment is larger than that obtained by more accurate methods, and therefore the energy equivalent he used should be too small. 108-4214
The effect of these various errors on the enthalpy

of AI2O3 is not clear to us. The error in the corrected temperature rise may be partly accounted for when the energy found for the empty capsule is subtracted from

the energy found for the full capsule. The error in the energy equivalent might possibly be compensated by

an error in placement of potential leads for the calibrat- ing heater. Not enough information is given on the lengths of leads, location of potential taps, and thermal

contacts of the leads for an independent judgment to be made.

Regardless of any small errors, Macleod is evidently

right that the heat-exchange correction can contribute

errors of several tenths of a percent in high-temperature

enthalpy measurements. Papers which fail to describe the method of making the correction are therefore suspect at this level of accuracy. It is unfortunate that many papers are vague on this point.

ACKNOWLEDGMENTS

We are grateful to Ward N. Hubbard and Donald R.

Fredrickson of the Argonne National Laboratory for discussions of the practical aspects of this problem.

Reprinted from Journal of Applied Physics, Vol. 39, No. 9, 4206-4215, August 1968

109-4215
Electrical Resistances of Wires of Low

Temperature Coefficient of Resistance

Useful in Calorimetry (10°-380°K)

G. T. Furukawa, M. L. Reilly, and W. G. Saba

Heal Division, National -Bureau of Standards, Washington, D. C. (Received 20 June 1963) THE resistance of some alloy wires was measured in the range 10° to 380°K as a part of the program in the low temperature calorimetry laboratory of the National

Bureau of Standards to simplify and to improve the accuracy in determining the electric power introduced into the resistance heater of adiabatic calorimeter vessels. The

goal is to achieve regularly an accuracy of 0.001% in the determination of power. The total energy introduced is the time integral of the product of instantaneous voltage across the heater and current through the heater. In practice, the energy is calculated from the discrete values of voltages

observed during the heating period, so that to obtain the

highest accuracy, the voltage and current, and therefore the heater resistance, must remain as constant as possible

between readings.

Constantan and manganin are used fairly extensively as heater wires in low temperature calorimetry and, in the range above about 250°K, have a very small temperature

coefficient of resistance. (See Fig. 1.) Below about 250°K,

however, both constantan and manganin wires show large

changes in resistance, manganin more so than constantan. A survey was made, therefore, to find a wire of smaller

temperature-coefficient of resistance at the lower temperatures. The resistances of promising wires were measured

from 10° to 380°K, the range in which heat measurements

are made in low temperature calorimetry. The wires were wound on a cylindrical copper block which was installed

Table I. Composition and room temperature

resistance of wires tested.

Wire

Nominal

composition

weight percent

Nominal

specific resistance

at 20°C

Supplier

Manganin Cu 84, Mn 12, Ni 4 48 Driver-Harris Co.

Constantan

(Advance)* Cu 57, Ni 43 49 Driver-Harris Co.

Karma" Ni 76, Cr 20, Fe, Al133 Driver-Harris Co.

EvanohnV Ni 75, Cr 20, Al 2.5, Cu 2.5 134 Wilbur Driver Co.

" Trade name of the respective suppliers^

Rcprinta . from Tiik Re\ iew ( V SCIEN'TI • u Instruments,

r t/r

o»c1.02

1.00

0.98

0.96

0.94

0.92

0.90

0.88

/ /

/ /

/ /

/

/

KARMA

MANGANIN

• • • • EVAN0HM

CONSTANTAN

-/

J L

50 100 150 200 250 300 350 400

TEMPERATURE.°K

Fig. 1. Ratio of resistances of various wires at low temperatures

to resistance at 273°K.

within one of the laboratory calorimeters in the position

normally occupied by the calorimeter sample vessel. The

resistances were measured at various selected temperatures

maintained constant by means of the adiabatic shield. 1 The temperatures were determined by means of a platinum

resistance thermometer installed in the copper block. The resistance of two alloy wires Evanohm and Karma

was found from the results of the measurements to change

considerably less than constantan or manganin wire below

250°K. (For constantan, a wire of comparable composition sold under the trade name Advance was investi- gated.) Above 250°K, all four wires have comparable low

temperature-coefficient of resistance suitable for calorimeter heaters. The ratios of the resistances to that at 273°K

(0°C) of the four wires are compared in Fig. 1. The nominal

chemical composition and the resistivity at 20 °C of the

wires as given in the literature supplied by the respective

manufacturers are summarized in Table I. The total changes in resistance over the temperature range of meas- urements were 6% and 10% for constantan and manganin,

respectively. On the other hand, the resistance of Evanohm

and Karma wires changed by only about 0.9%. When applied to heat capacity measurements with the usual heating rate of one degree per minute, these newer heaters will change in resistance on the average only about 0.002% to 0.003% per min. With this small rate of change, interpolations should be possible between power readings at one-min

intervals to better than 0.001%, using, for example, a constant current power supply, which is now generally

available with 0.001% stability or better.

1 G. T. Furukawa and M. L. Reillv, J. Res. Natl. Bur. Std. 56, 285

(1956).

110-113
Techniques in Calorimetry. I. A Noble-Metal

Thermocouple for Differential Use

E. D. West

National Bureau of Standards, Washington, D. C. (Received April 4, 1960) A PROBLEM which arises frequently in calorimetry

is the observation and control of the temperature of one body at or near the temperature of another. The temperature difference is frequently detected with one or more

thermocouples. In selecting from the usual thermocouple

materials for operation at temperatures above a few

hundred degrees Celsius, a choice must be made between

the better sensitivity of base metals and the good corrosion

resistance and ease of construction of noble metals. Al- though alloys of gold and palladium have been used to make thermocouples of greater sensitivity than those of platinum and rhodium, such couples have been less stable and less reproducible. 1 These disadvantages are of far less consequence when

the thermocouple wires are used directly between surfaces

at elevated temperatures with more stable leads through

the large temperature gradients to the observation and

control apparatus. For example, if the temperature dif- ference between a body at 1000° and one at 1001°C is measured by two thermocouples brought out to cold junctions, an uncertainty of 0.1% in one of them would be as

large as the temperature difference to be measured; but,

if the alloy wires are kept in the hot region, the same per- centage variation is small compared to the difference measured. The accuracy of the measurement can thus be

made to depend mostly on the wires used for leads. In the process of rebuilding an adiabatic calorimeter for use up to 600°C,2 it was desirable to replace the ChromelAlumel thermopiles, which frequently broke at the silver- soldered junction in the original assembly, with a corrosionresistant combination of comparable sensitivity. Since the

region in which the thermopiles are located is virtually

isothermal, it appeared that gold-palladium might be

useful. An alloy of 60% gold and 40% palladium (Au-Pd)

of commercial purity was obtained at a nominal cost, without specifying close tolerances on the composition. A

check was made of the emf of a couple of Au-Pd and

platinum-10% rhodium (Pt-Rh) by welding a length of Au-Pd wire to a couple of platinum and Pt-Rh and heating

in a tube furnace. The emf of the Au-Pd versus Pt-Rh

thermocouple determined in this way is given in Fig. 1 together with the first derivative with respect to temperature. The curves are close to the calculated values for gold-35.11%-palladium versus Pt-Rh1 and gold-40% pal- ladium.3 For comparison, a curve is included for ChromelAlumel.

60

5 0

i

10

0

1

I

1

j

1

j

1

1

1 1

1

£ —

. • J

ff' /' «r/

/ / —

/ 9 / /

/ f

/ /

/ /

' /

1

ft *

/

/ -/—

y

/ o experimental points . p CHPOMEL-ALUMEL.OE/aT / A'J - PD-PT - Rh, OE/dT 1,1,1,1,1,

CO

55 lu

50 ts>

35

O 200 400 600 800 1000 1200 TEMPERATURE. °C

Fig. 1. Electromotive force of a thermocouple of gold-40% palladium and platinum-10% rhodium.

The thermopile junctions were made up by inserting No. 36 alloy wires through two small holes about 1 mm

apart in gold "tiedown" tabs and brazing them simul- taneously with silver. A 20-junction thermopile was in- stalled in the calorimeter with gold leads out to a cold

junction. The calorimeter has since been used intermittently for about a year. The thermopile is calibrated in place as a regular part of the calorimetric procedure in terms of heat flow per microvolt. At 50°C the heat leak from the calorimeter is 0.4 joules/hr for an indicated "zero"

difference. Although the design of the calorimeter is such

that a heat leak of about this magnitude will be present

at zero temperature difference, ascribing the observed heat

leak to uncertainty in the thermopile results in a calculated uncertainty of about 0.3 /zv (0.4 millidegree C). The "zero"

heat leak is greater by a factor of several at 350°C, but

most, if not all, of this increase is due to the increase in the

radiation heat transfer coefficient. The Au-Pd is stiffer and more difficult to handle than

wire ordinarily used for thermocouples, but this dis- advantage is more than offset by the ease of soldering or welding. Since broken wires of Au-Pd and Pt-Rh can be

repaired without flux and solder, no uncertainty is intro- duced in the weight of the calorimeter.

1 A. A. Rudnitskii, Termoelektricheskie svoistva blagorodnykh

Metallov i ikh splavov (IsdatePstvo Akademii Nauk SSSR, Moscow,

1956). Available as translated document AEC-tr-3724 from Office of Technical Service, Department of Commerce, Washington 25, D. C. A good summary of data on many possible and practical thermocouple materials.

2 E. D. West and D. C. Ginnings, J. Research Nat. Bureau

Standards 60, 309 (1958).

3 International Critical Tables (McGraw-Hill Book Company, Inc., New York, 1929), vol. VI.

Reprinted from The Review of Scientific Instruments, Vol. 31, No. 8, 896-897, August, 1960 111-896
Journal of Research of the National Bureau of Standards Vol. 50, No. 2, February 1953 Research Paper 2392

Calorimetric Determination of the Half-Life of Polonium

D. C. Ginnings, Anne F. Ball, and D. T. Vier 1

The heats of radioactivity of four samples of polonium have been measured with a Bunsen ice calorimeter over a period of about seven months. With samples ranging in

initial powers from 0.17 to 1.4 watts, the half-life values calculated from these measurements

were found to agree within 0.1 percent, or the equivalent of 0.0003 watt, whichever was the

larger. The results with the sample with the largest power gave a half-life value of 138.39

days, with an uncertainty of 0.1 percent (0.14 day). This is in agreement with the value

of 138.3 days (±0.1 percent) reported by Beamer and Easton, who used a different calorimetric method.

1. Introduction

Of all published determinations of the half-life of

polonium, probably the most accurate is that by

Beamer and Easton [l],

2 who used a calorimetric

method and observed a sample for as long as 97 days.

Their method consisted in measuring the temperature

difference between a container with the sample of

polonium and an identical container that was empty.

Both containers were surrounded by an isothermal

jacket, and the relation between temperature differ- ence and power was determined by means of electric calibration experiments. The value of the half-life was found to be 138.3 days (±0.1%). A Bunsen

ice calorimeter is also suitable for measuring radioactive power (and half-life) of radioactive materials.

Because this method is entirely different from that

used by Beamer and Easton, and because much larger

samples of polonium were available, it seemed

worth while to measure the half-life of several samples that were suitable for measurements with the

ice calorimeter.

The Bunsen ice calorimeter seems ideally suited for several reasons to the measurement of the heat

evolved by curie or multicurie quantities of alpha,

weak beta, and with modification [2], other radioactive materials. Eirst, the heat leak is small (perhaps 0.0002 w). Second, the calorimeter requires

very little attention during the measurements,

usually a few minutes every hour or two for ice-bath

replenishment. Third, no electrical or temperature

measuring instruments are required because the

measurement of heat requires only weighing of mercury. Fourth, the calibration factor of the ice calorimeter is a fundamental physical constant,

which has been determined to about 0.01 percent by

electrical calibration experiments [3]. On the other hand, the ice calorimeter in its present

application has an inherent variation, or error, which

is comparable with its heat leak. While this does

not limit the precision of experiments involving about

1-w power, it would limit the precision of measure- ments of much smaller powers. Other ice calorimeters designed specifically for small radioactive

powers [2] have proved sensitive to as little as 0.00003 w. An improved ice calorimeter has been

1 Los Alamos Scientific Laboratory, University of California.

2 Figures in brackets indicate the Hterature references at the end of this paper.

in use at the National Bureau of Standards for some

time in the measurement of heat capacities at high

temperatures [3]. Although this calorimeter was not

intended for measurements of radioactive power, it seemed suitable for measurements on certain samples

of polonium (alpha emitter) furnished by the Los

Alamos Scientific Laboratory, which initially developed powers in the range of 0.17 to 1.4 w. By

measuring the decay of radioactive power of a sample

of polonium over time intervals comparable with its half-life, values were obtained of its half-life.

2. Experimental Details

The ice calorimeter used in these experiments is shown in figure 1. It is the same calorimeter pre- viously described [3]. An ice mantle (I) was frozen

around the central calorimeter well (A) on a system

of copper vanes (F) designed to increase the area of

contact of the central well with the ice. The sample was suspended in the bottom of this well by a small

wire that was pushed over against one side of the

well by the gate G. The heat developed in the

sample melted some of the ice, thereby decreasing

the volume of the ice-water system and causing mercury to be forced into the calorimeter from beaker

B. A small flow upward of dry helium in the calori- meter well was maintained to prevent condensation

of water vapor from the room in the calorimeter and

also to increase thermal contact between the sample

and the calorimeter.

The polonium samples were sealed in glass or metal containers, which were enclosed in brass outer

containers made to fit closely to the central well of

the ice calorimeter. Because the radiation from

polonium is essentially all of the alpha type, the

containers were completely effective in converting

all the radioactive energy into heat within the container. A sample was lowered into the calorimeter

(with the two platinum shields above it, as described elsewhere [4]), and about 10 or 15 min was

allowed for it to come to essentially a steady temperature, the valve V being open. Then the mercury meniscus was adjusted to the upper part of

the scale, C, by partly evacuating reservoir K.

Valve V was immediately closed, thereby causing

the meniscus at C to start to move downward due

to the heat input to the calorimeter. The time was 112-75
Figure 1. Schematic diagram of ice calorimeter.

A, calorimeter well; B, beaker containing mercury; C, glass capillary; E, ice bath; F, copper vanes; G, gate; I, ice mantle; M, mercury; P, Pyrex containers; R, mercury reservoir; T, mercury "tempering" coil; V, needle valve; W, water;

1, 2, 3, and 4, thermocouple junctions. recorded when the meniscus passed an arbitrary zero on this scale, the beaker of mercury (B) was re- placed by a weighed beaker of mercury, and valve

V opened again. At the end of an experiment, the

valve was closed again and the time recorded when

the meniscus again passed its zero. The difference

in the weights of the beaker gave the weight of mercury sucked into the calorimeter in a measured time.

A small correction (perhaps 1 joule) was made for

heat leak. The corrected mass of mercury was con- verted to energy by use of the calibration factor of

the ice calorimeter as previously determined [3], 270.46 abs j/g of mercury for the "ideal" calorimeter

or 270.47 abs j/g for the actual calorimeter used.

From the duration of the experiment (difference in

times at which the mercury meniscus passed the

arbitrary zero), the energy was converted into

average power.

The values of power calculated in the manner described would be correct if the sample and all other

parts in thermal contact with the calorimeter did

not change temperature during the experiment.

However, as heat is put into the calorimeter, the

thickness of the water layer between the ice and the

central well with its vanes increases, and as there is flow of heat across this water layer, the temperature

drop across this water layer must increase. As a

result, the temperatures of the central well and

vanes, and the sample with its container, all in- crease slightly during an experiment, so that part of

the heat produced by the sample does not melt ice. This amount of heat depends on the power of the

sample, the heat capacities of the various parts, and

on the thickness of the water layer at the beginning

of the experiment. The analysis of the correction

for this heat is given as follows.

Consider a system (such as the radioactive sample

plus metal calorimeter well with vanes) separated

from ice by a layer of water. Consider also that the

thermal contact between sample and calorimeter

does not change during an experiment. Let

Q=the total amount of heat (joules) that has been

introduced into the ice calorimeter at any

particular time,

P=the power (j/sec) developed by the sample,

H=the heat capacity (j/deg C) of the system

(sample plus calorimeter well with vanes),

A=the effective area of contact of the system

with ice, cm2

, K=the thermal conductivity of water at 0° C,

0.0052 w cm-Meg-1

, ?n = the average thickness of the water layer, cm,

F=ihe heat of fusion of ice, 333 j/g.

Then the grams of ice melted = Q/F=Q/333.

The volume of water between the ice and the vanes

is the same as the volume of ice melted because any

void created by the difference in density of ice and

water is filled almost instantaneously by water outside the mantle passing through and around the

cracks in the ice mantle. Hence, the volume of

water layer formed = (specific volume of ice) (Q/333) = (1.09) (Q/333) =0.0033$; m=0.0033(<2/A) ; and

the temperature difference across the water film =

Prnf (0.0052) A = (0.0033/0.0052) (PQ/A2

) = 0.63 (PQI A2). Thus the heat stored in the system after Q

joules have been introduced (assuming no temperature gradient in the metal system) = (0.63H) (PQ/A2

)

,

and the heat stored in the water after Q joules have

been introduced (assume linear temperature gradient

across the film) = (4.18) (0.00330 (0.63/2) (PQ/A2

) =

0.0043 (PQ2 /A2), and the total heat stored=(PM2

) (0.63#0+0.0043<?2). If we start an experiment

with Qi joules of heat already put into the calorimeter and a steady state of heat flow from the sample

to the ice mantle, and end the experiment with Q2 joules of heat in the calorimeter, and the same steady

state of heat flow, then the difference in heat stored = (P/A1)[0.6SH(Q2 -Q1 ) +0.0043(Qjj—Q?)!.

The relative error, E, is E=

A2 (Q2 -QX ) [°- 63^-0i)+0.0043(^-0?)], or P E=^2 [0.63H+0.0043(Q2 +0i)].

If E is plotted against (Q2+Q1), the slope of the

resulting straight line is P

Slope =0.0043

and the intercept of this line with the E axis is

Intercept =0.63 —ry113-76
This analysis shows that for any given power P of

the sample, the slope of this line is dependent only on the effective area of contact (A) of the metal vanes

with the ice. This effective area depends, of course, on the length of the sample. The intercept of this

line with the relative error axis depends not only

ipon the area A but also upon the heat capacity, H

of the sample-plus-vane system.

For any given sample with a known heat capacity

and length, values of A and H can be calculated,

using the dimensions and heat capacity of the cor- responding portion of the calorimeter well and its system of vanes. It is believed that a better evaluation of A and H can be obtained by electrical cali- bration experiments, putting in known quantities of

electric heat into the calorimeter over a length

equivalent to the radioactive samples to be measured.

If the heat is distributed in the electrical experiments

the same as in the experiments with the radioactivesamples, the value of A obtained from the electrical experiments should also be the same. However, the

value of H obtained from the electrical experiments

differs from that for the radioactive experiments by

the difference in heat capacities of the electric heater

and the radioactive samples.

The results of the electric calibration experiments

are indicated by the circles in figure 2, which shows

the relative error, E, plotted against (<?i + (?2)- The best straight line through these circles is labeled

"Electric Experiments" and was determined by the

method of least squares to be #=0.000633 +2.992

X

10 _8 (^1 +Q2 ), where Qi and Q2 are expressed in

joules. The electric calibration experiments were made with a power of about 1.4 w to correspond

approximately to the initial radioactive power of

sample 4, which was the largest of the four samples

and therefore had the largest correction for the water

layer. The slope of the solid line (electric experiments) indicated that the effective area of contact

(A) between the ice and the source of heat was about

420 cm2. This is roughly equivalent to a 9-cm

length of the calorimeter well, as compared to an

actual length of the electric heater of about 7 cm. While the value of A obtained from the electric calibration experiments agreed as well as expected

with that estimated from the dimensions, the value

1

a

,Somple 4<!0-7-49)_

O , ' '

, ' ' * ELECTRICAL ^^^EXPERIMENTS O

-

'

' '^^^^

->

e

_ -Sample 4(1-14-50)

•

„• -

'

_ _ - -Sample 4(5-12-50)

a

0 50 100 150 200 250

271.0 o

2 70.6 g

Q, + Q2 (g Hg) Figure 2. Corrections for water layer in calorimeter.

Electrical experiments: ©, 10-11-49; ©. 10-12-49; O. 10-14-49.

of heat capacity H (after correction for the heat

capacity of the heater) corresponded to about a 17-cm length of the calorimeter well, which is considerably more than expected. Some of this differ- ence may be due to the assumption in the theory

that the temperature gradient in the copper vanes is negligible. If the position of the line had been cal- culated entirely on the basis of a 9-cm length of the

calorimeter well, it would have the same slope as the

line given by the electric experiments but would be

shifted to decrease E by almost 0.0003. Because it is believed that the electric calibration experiments give more reliable values of the effective A and H, the

solid line in figure 2 was used as basis for the corrections for the experiments with the radioactive

samples. The dashed lines shown in the figure for sample 4 were calculated on this basis, as well as corresponding lines (not shown) for the other samples.

Values of apparent calibration factor (which is equivalent to 270.47 (l-\-E)) were read from the

dashed lines for the corresponding values of (Qi-\-Q2).

3. Results

The results of the measurements with the four

samples are given in table 1. The mean time of

experiment is given, so that all experiments in one group can be corrected for the radioactive decay to bring them all to the same time (noon, EST) on the

reference date. The mass of mercury was corrected

for the effect of heat leak between the calorimeter

and its surroundings (this effect is usually only a few milligrams of mercury). The quantities Qi and

Q2 are as previously described. Using the quantity

Q1 + Q2, the apparent calibration factor of the ice calorimeter was obtained from figure 2, from the curve for the appropriate sample. The product of

this factor and the mass of mercury, divided by the

duration of the experiment, gives the power at mean

time of experiment. Using an approximate value of the half-life of polonium, this power was converted

to power at noon (EST) on the reference date. The

deviations from mean power are the deviations of the

results of the individual experiments from the mean

power of the group of experiments. The values of

half-life given in the last column are based on the

mean powers and reference dates, and the values

indicated in parentheses are the authors' estimated

uncertainties of the half-life based on both accidental

and systematic errors. It will be noted that more measurements were made with sample 4 than with the other three samples. This was because sample 4 had the highest

power of the four samples, and it was believed that

the highest relative calorimetric accuracy could be

obtained with this sample, resulting in the best determination of the half-life of polonium. The power

of sample 1 was so low that calorimetric errors could

account for the low value of half-life calculated.

The uncertainty in heat leak of the calorimeter was

believed to be about 0.0002 w. This uncertainty,

when compared with the power measured for sample

1 on May 14, 1950 (0.05698 w), could explain most

of the discrepancy with the results with the other

114-77
Table 1. Results of experiments

Date of experi- ment Mean time of experiment

EST

Duration

of experi- ment Mass of mercury0, 02

Apparent

calorimeter

factor 270.47(1+E)

Power at mean

time of experi- ment

Power at noon (EST)

on

reference date

Reference

date

Deviations from mean

power

Mean

power

Half-life

Sample 1

sec 9 9 Hg 9 Hg abs w abs w percent abs w Days

10-3-49

10-4-49

f 3:24 p. m. 3 557.

8

2 3048 0 2 270 49 0. 17523 0 17451

f +0.161 \ 6:36 p. / 12:32 p. m.

m.

12

9

367.

2

928. 0

7

6 98923924

2

10

1017 270

270 4950

. 17474

. 17417

17411 17419 [ 1C- 4-49 J —0.07

] —0.02 > 0. 17423

\ 3:20 p. m. 10 126.5 6 5205 17 23 270 50 . 17418 17430 I +0.04

137 7 5-3-30 1:14 p. m. 20 354.0 4 5269 24 29 270 48 .06016 05694 f +0.07 b (±L0)

5-4-50 1:19 p. m. 19 440.0 4 2913 29 34 270 48 . 05971 05680 1 -0.32

5-14-50 f 2:16 p. m. 21 909.5 4 6221 0 5 270 48 . 05706 05709 j 5-14-50

1 +0.19 | 0.05698

\ 7:14 p. m. 13 948.0 2 9396 5 8 270 48 . 05700 05709 1 +0.19

Sample 2

| 11:10 a. m. 6 168. 5 9 1630 23 32 270 56 0. 40190 0 40183 | +0.04

10-5-49 < 12:45 p. m. 5 224.0 7 7486 32 40 270 57 .40133 40139 1 10- 5-49 \ -0.06 [ 0. 40165]

[ 2:15 p. m. 5 478.

0

g 1294 40 48 270 58 40154 40173 1

1 i n no

I | 138. 52

•> (±0. 4) 4-27-50 _ 1:48 p. m. 16 514.9 8 8470 24 33 270 50 . 14491 14425 f +0. 18 4-28-50. 1:00 p. m. 17 999.8 9 5623 33 43 270 M . 14370 14373 | 4-28-50

\ -0.18 |

o. 14399J

Sample 3

| 1:24 p. m. 5 134. 4 12. 2025 0 12 270 58 0. 64306 0 64323 1 | +0.02 1 10-8-49 < 2:45 p. m. 5 207. 5 12 3623 12 24 270 61 . 64241 64278 > 10- 8-49 < —0.05 > 0. 64312)

1 4:06 p. m. 4 576. 2 10 8695 24 35 270 63 . 64280 64335 1 I +0.04 1 138. 52 4-19-50 1:49 p. m. 12 692.3 11 4817 0 11 270 51 .24471 24358 | 1 —0.01 1 b (±0.2?'

4-20-50 f 11:35 p. m. 10 313.6 9 2898 11 20 270 52 .24367 24365 \ 4-20-50 \ +0.02 } 0. 24361

J

L 2:31 p. m. 10 808.6 9 7279 20 30 270 52 . 24347 24360 1 [ 0.00 1

Sample 1

f 12:55 p. m. 2 634. 7 14. 0020 28 42 270 84 1. 43937 1 43307 1 —0.01

1:35 p. m. 2 766.9 14. 7066 42 57 270 91 1. 43994 1 43382 +0. 04

10-6-49 { 1:28 p. m. 2 622.8 13. 8785 0 14 270 72 1. 43251 1 43296 -0. 02

2:07 p. m. 2 676.2 14. 1607 14 28 270. 78 1. 43279 1 43345 +0.01

1 2:57 p. m. 2 733.6 14. 4582 28 42 270. 84 1. 43249 1 43338 i 10- 7-49 +0.01

( 3:43 p. m. 2 717. 2 14 3735 42 57 270. 91 1.43306 1 43423 +0.07 1. 43327

10-7-49 1 4:28 p. m. 2 736.5 14 4643 57 71 270. 97 1.43226 1 43361 +0.02

I 5:14 p. m. 2 689.3 14 1840 71 86 271. 03 1.42948 1 43105 -0. 15 138. 39

1 6:00 p. m. 2 879.7 15 2113 86 101 271. 10 1. 43202 1 43382 , +0.04 b (±0. 14)

11:00 a. m. 3 170.1 10 2320 10 20 270 64 0. 87353 0 87335 +0.05

11:54 a. m. 3 345.9 10 7884 20 31 270. 67 . 87274 87272 -0.03

1-14-50 12:50 p.

1:44 p. m.

m.

3

3 359.8067.7

10

9 8281 8837

314242

52

270. 270. 7073. 87242

. 87225

87257 87256

1-14-50 -0. 04 -0.04 0. 87294

2:35 p. m. 3 115.

1

10 0448 52 62 270. 74 . 87302 87349 +0.06

3:28 p. m. 3 178.3 10 2384 62 72 270. 78 .87228 87292 +0.00 138.40

" (±0. 18) 10:04 a. m. 8 282.3 14 8070 3 18 270. 56 .48370 48350 f +0.00

12:25 p. m. 8 395.9 15 0148 18 33 270. 58 .48389 48393 +0. 10 5-12-50 0. 48342]

2:46 p.

5:00 p. m.m.

8

7

534.5 439.215

13 21932613

33

48

48

61

270.

270. 6163

. 48257

.48243 48284

48293

5-12-50 -0. 12 -0. 10

6:55 p. m. 6 260.2 11 1775 61 72 270. 64 .48322 48391 +0. 09

8:43 p. m. 6 947.3 12 3852 72 85 270. 66 . 48252 48339 0.00

» Experiment weighted one-third because of short duration of experiment.

h Figure given for uncertainty based upon authors' estimate of both accidental and systematic errors.

samples having higher power because it would re- quire an increase of only 0.0003 w in the value observed on May 14 to agree with the other samples.

It is interesting to note the corresponding effects of an uncertainty of 0.0003 w on the other samples

having higher powers. With samples 2 and 3, this uncertainty in the May values would result in halflife uncertainties of about 0.21 percent (0.29 day)

and 0.12 percent (0.17 day), respectively. With

sample 4, however, the same power uncertainty in

the values on January 14 results in only 0.04 percent

(0.06 day) uncertainty in the over-all half-life. The uncertainty in heat leak is probably the largest

error in the measurements with samples 1, 2, and 3. With sample 4, however, the heat leak uncertainty is

probably comparable with all other errors. In addition, sample 4 was observed at an intermediate date

(0.7 half-life) in an effort to detect any change in the

decay constant with time.

The measurements with the four samples agree

within ±0.1 percent, or 0.0003 w, whichever is the

larger. The slightly different half-life values on

sample 4 for the two different periods are not

significant because the difference is much less than the

experimental error. There is no significant evidence,

therefore, of a change in the decay constant, such as would occur either if the polonium was contaminated

with radioactive impurities having values of half-life different from polonium, or if some secondary chemical or nuclear reaction produced heat that was not

115;-78
directly proportional to the radioactive energy of the

polonium sample. In addition, the polonium samples used were of a purity that should have precluded

the possiblity of appreciable contamination by other

radioactive elements. The polonium had been

purified both by distillation and by electrodeposition on platinum foils from dilute nitric-acid solution

of polonium nitrate. Of course, the stable lead

isotope formed from the decay of polonium was pres- ent but could not affect the results of this investigation. The best value of the half-life of polonium was

estimated from the two values for sample 4, giving more weight to the earlier value, where the sample

had a larger power. On this basis, the authors believe that the best value of the half-life derived from

these measurements is 138.39 days. It is believed

that the calorimetric uncertainties (based upon both

accidental and systematic errors) in the experiments

may result in an error in this value of ±0.1 percent

(0.14 day).

The results of these measurements are in agree- ment with the value reported by Beamer and Eastern

[1] of 138.3 days ±0.1 percent, determined calori- metrically by another method.

4. References

fl] William H. Beamer and William E. Easton, J. Chem.

Phys. 17, 1298 (1949).

\2] Swietoslawski, Microcalorimetry, p. 66 (Reinhold Publishing Corporation, New York, N. Y., 1946).

T3] Defoe C. Ginnings, Thomas B. Douglas, and Anne F. Ball,

J. Research NBS 45, 23 (1950) RP2110.

f4] D. C. Ginnings and R. J. Corruccini, J. Research NBS

38, 593 (1947) RP1797.

Washington, July 15, 1952.

116-79
JOURNAL OF RESEARCH of the National Bureau of Standards—A. Physics and Chemistry

Vol. 69A, No. 3, May-June 1965

Heats of Transformations in Bismuth Oxide by Differentia

Thermal Analysis

Ernest M. Levin and Clyde L. McDaniel

(January 5, 1965) DTA was chosen as a convenient method for resolving differences in the reported heat of transition and heat of fusion of Bi2 03 . The heat of the low to high transition of K2 S04 (at 583 °C) and the heat of fusion of Ag (at 960.8 °C) were used as internal standards. These standards were mixed directly with

the Bi2 03 in three weight ratios. The heating schedule for each weight ratio was 3°/min, 9°/min, and

3°/min. For evaluating internal consistency, DTA determinations were made for mixtures of the two

standards. Linearity was obtained within limits between the weight ratio of Bi2 03 and standard and

the corresponding ratio of peak areas. The heat of transition of Bi2 03 (mon'-*

C cubic was found to be 9.9 ±0.5 kcal/mole and the heat of fusion (cubic^*

C

liq.) 3.9 ±0.2 kcal/mole. The uncertainties

are estimated limits of error, based on internal consistency and on the values of the standards.

1. Introduction

By application of the Clausius-Clapeyron equation to the liquidus curve of the Bi2 03-PbO system [I], 1 K. K. Kelley determined the heat of fusion of B12O3 to be

6.8 kcal/mole [2]. This value is listed in tables of ther- modynamic data [3, 4]. Levin and McDaniel [5] applying the same Clausius-Clapeyron equation to the Bi2 C»3-B2 03 system obtained a heat of fusion value

of 2.O5 kcal/mole. Gattow and Schroder [6] and Gattow

and Schiitze [7] have used these two values in conjunction with differential thermal analysis (DTA) data to calculate the heat of transition of monoclinic- to cubicbismuth oxide (see table 1). They found that the area

of the peak representing the monoclinic to cubic transition was 4.10±0.11 times the area of the peak

representing the cubic to liquid transformation; and,

consequently, the heat of transition should be 4.10

X the heat of fusion.

Table 1. Heats of transformations in bismuth oxide

Heat of transformation

Investigator Method

Transition (mon —* c) Fusion

(c — liq)

K. K. Kelley (1936) (2) Bi2 03

--PhO liquidus kcallmole kcallmole

6.8

Levin and McDaniel (1962) [5] Gattow and Schroder (1962) [6] Gattow and Schiitze (1964) [7] Levin and McDaniel (1964)

[1) Bi 2 03

- DTA"

DTA" DTAC

"B2O3 liquidus

27.9 ± 1.0 8.4 + 0.3

9.9 ±0.5

2.05

3.9 ±0.2

" Heat of transformation = (4.10±0.11) X heat of fusion (6.8 kcal/moie).

6 Heat of transformation = (4. 10 ±0.11) X heat of fusion (2.05 kcal/mole).

c Using K2 S04 and Ag as internal standards.

The two reported values for the heat of fusion of Bi2 0.; differ by a factor of about three. The value of 6.8 kcal/mole obtained from the Bi2 03-PbO diagram

is suspect for two reasons: First, a reinvestigation of the Bi2 C»3-PbO system [8] has shown Belladen's

simple liquidus diagram to be incorrect, inasmuch as PbO exists in solid solution with Bi2 0.j at the liquidus

Second, the sum of the reported entropy of transitior and of fusion, (6800 27900

5j, is about 7 cal/°K/^

1 Figures in brackets indicate the literature references at the end of this paper.

\1098 1003

atom, an abnormally high value. Because of the increasing importance of Bi2 03 in the electronics and ceramics industries, it is desirable to verify the basic thermodynamic data. As equipment

for direct calorimetric measurement was not available,

differential thermal analysis, using internal standards, was selected as a convenient, independent method for determining heats of transformation.

2. Equipment

The differential thermal analysis equipment was

built in the laboratory and is of conventional design.

The furnace heating element consists of a ceramic core

10 in. long X 2

3

/s in. o.d., wound with 20 gage, 80 per- cent Pt: 20 percent Rh, wire. Linear temperature rise with time is accomplished by means of a program controller and a pneumatically activated variable auto- transformer. Heating rates of 3°/min and 9°/min are obtained by controlling the percentage of time during

which the set point is driven. Using a multipoint re- corder, the emfs of the sample thermocouple and of the

differential thermocouple are plotted as a function of time. Determinations are made at overall sensitivities of 14/LtV/in.

To minimize errors that might be caused by poor

thermal diffusivity, a special holder assembly is used.

117-237
The two thermocouples (Pt — 90 percent Pt:10 percent

Rh) from the holder assembly are welded, near the bottom, to Pt containers. The containers are made

from Pt tubing and measured 16 mm long X 2.6 mm

i.d. X 3.0 mm o.d. The tubes contain a total of 0.2

to 0.4 g of material, depending on the substances and

weight ratios studied. To reduce the effect of air currents in the furnace, the Pt tubes are covered with

thin ceramic thimbles.

3. Method

The usual procedure for measuring heats of trans- formation by DTA depends on calibration of the equipment with a known weight of a standard, e.g., benzoic

acid, AgN03 , KN03 [9, p. Ill] and [10, 11]. The cali- bration can be expressed in terms of calories per unit of integrated peak area, in the differential temp. -time curve representing the transformation. Assuming

approximate constancy of the calibration factor, the

unknown heat of transformation for a substance can

be determined from the peak area in its differential temp. -time curve. The method depends on conditions that are seldom

closely realized. First, the geometry of the physical

arrangement and other operating conditions should

be exactly the same for the determination of the un- known as for the calibration with the standard.

Second, and even more unlikely, such thermal properties as conductivity, diffusivity, and specific heat

should be essentially identical for the two samples.

A method using internal standards avoids the problems inherent in a separate calibration method.

Therefore, several high-purity chemicals, with appropriate temperatures and heats of transformations were

tried, in a search for internal standards.

Two substances were found satisfactory for cali- brants: (1) Finely ground crystalline K2 S04 with a heat

of transition (a5?Vr

/3) of 2.14 kcal/mole [3, 12]. (2) Fine, precipitated Ag powder with a heat of fusion

(5

9-6M^ liq.) of 2.61 kcal/mole 2 [13]. The transfor- mation temperatures in these two substances bracket

the transition temp, of Bi2 03 (monoclinic 7 H>

°C cubic)

and the fusion temp, of BijOs (cubic 8?V( ' liquid).

Two additional substances, NaCl and Li2S04 , were

found to be unsatisfactory as internal calibration

standards.

DTA experiments were carried out for Bi203 : K2SO4

mixtures in wt. ratios of 3.46:1, 1.72:1, and 1.00:1;

and for Bi20.3 : Ag mixtures in wt ratios of 4.32:1,

2.16 : 1, and 2.00 : 1. Mixtures were made in 2g batches

by shaking in a mechanical mixer accurately weighed

amounts of dried starting materials. As will be shown

below under "Derivation of Equations" the heat of

transformation calculations are not based on the actual

weights of the two substances in the sample holder

but only on the formulated ratios. Each mixture was given a preliminary heat-cycling treatment by heating the mixture at 12 °C/min to about

2 The literature values reported for the heats of transformations in K2 SO< and Ag vary over a range of about 10 percent. The values selected here are shown later in this paper

(see Internal Consistency! to be self-consistent.

775 °C (above the transition of K>S04 and Bi2 03 but

below the melting point of Bi 2 03 ) and then cooling

to room temperature. The preliminary heat treat- ment was followed by three successive cycles of heat- ing to above the mp of Bi2 03 in K2 S04 mixtures and

above the mp of Ag in Ag mixtures. The heating and

cooling rates for the three cycles were 3°/min, 9°/min,

and 3°/min, respectively. Only the peak areas in heating curves were considered, as previous work,

using both DTA and high-temperature x-ray tech- niques [14], had shown that the stable high-temperature cubic phase is supercooled below the equilibrium

transition temperature of 730 °C; and at about 650 °C

a metastable tetragonal and/or body-centered cubic

phase is formed, which in turn, transforms back to the stable monoclinic form.

To check on the internal consistency of the method

and to evaluate the accuracy, DTA determinations were made with mixtures of the two standards, at the same heating rates and at weight ratios of K2S04 : Ag

of 1.36:1 and 4.00:1.

It should be noted that a number of investigators

[9] have used internal standards for quantitative

estimation of a phase. Barshad [11] has proposed

using "indicators" either mixed with the sample or in separate layers, for direct temperature calibration of a DTA curve. However, the use of internal standards

for heat of reaction measurements as herein proposed

has not been previously reported, according to the

best knowledge of the authors.

An obvious and valid a priori criticism of the internal- standard method is the possibility of obtaining errone- ous results if reaction occurs between the bismuth

oxide and the standards during the heat-cycling treat- ments. This possibility was foreseen and was shown

to be minimal by a number of observations.

(1) The ratio of the areas under the peaks representing the monoclinic to cubic transition and the cubic to liquid transformation for pure Bi2 03 could be compared with the corresponding ratio when standards were mixed with the Bi>03 . (2) Ratios of corresponding areas for successive

heat cycles could be compared with each other, and

any discrepancies noted.

(3) At the conclusion of each series of determinations for a given weight ratio, the mixture was examined

by x-ray powder diffraction techniques to check for any new phases that might have formed by reaction

of the starting materials.

(4) Finally, experimental results could be checked

for conformance to theory.

By the criteria listed above, it was possible to evaluate the individual experimental data and to eliminate

the few values which were obviously in error. However, even in these instances, the evidence did not indicate chemical reaction of the Bi2 03 , but pointed

to physical factors.

4. Derivation of Equations

It can be shown that to a close approximation [9, p. Ill] the total heat of reaction in a DTA determination

118-238
is given by:

AH =

C-^(ydt = ^AC g J g

(1)

where, /Y = heat of transformation per g

c — geometrical shape constant Ks = thermal conductivity of the sample

g=mass of reactive component in sample

ydt= A = peak area for the transformation.

If two substances, designated by subscripts 1 and 2, are considered in a mixture, eq (1) may be applied to each substance. Assuming no reaction between the

substances, constancy in c, and approximate constancy

in Ks (now the combined thermal conductivity of the

mixture), the following expression is readily obtained:

AH1 _Alg2

(2)

As A//i and A//2 are constants, g-ilg\ is the weight

ratio of the binary mixture, as formulated, and AJA2

is the experimentally measured peak area ratio of the

two transformations, the basic equation for an unknown

heat of transformation becomes:

(3)

It may be noted that eq (3) is a straight line that passes through the origin and with slope, m, equal to

(AilA-2)l(gilg2). Thus, over the range that the assumptions made in the derivation hold true, a linear rela- tionship should exist between the formulated weight

ratios and the corresponding measured peak area

ratios.

If the heat of transformation is desired directly in kcal/mole rather than on a gram basis, eq (3) may be

transformed to:

Li — L2 (4)

where, L\ and L2 are the heats of transformation of sub- stances 1 and 2, respectively, in kcal/mole, and

Mi and M2 are the corresponding molecular weights.

Applying eq (4) to the specific case of Bi203 : K2SO4

mixtures:

LBi20: =2.U 465.96\ (A

174.27/ \A

gV\2Q3

i>K 2 SOj 5.722mi

where, LBi2U3 refers to the heat of transformation (transi- tion or fusion), in kcal/mole;

2. 14 = the heat of transition of K2SO4, from the a to

fi form, in kcal/mole;

465.96/174.27 = the molecular weight ratio of Bi2 03 to K2SO4; and

TOi = the slope of the line obtained by plotting as ordinate the ratio of the peak

areas representing the particular

transformation of Bi2 03 to the transi- tion of K2SO4 {A BiM .JAk2SOa ) and plotting as abscissa the corresponding

weight ratio of Bi2 03 to K2 S04 (^BhOs/gfaSO,)-

Applying eq (4) to the case of Bi2 03 : Ag mixtures:

W>3 = 2.61 f^V^)/f^= 11.274m2

107.87 l Ag #Ag

(6)

where, 2.61 =the heat of fusion of Ag, in kcal/mole,

465.96/107.87 = the molecular weight ratio of Bi2 03 to K2SO4, and mi is the slope of the line A

obtained by plotting ^' z °3 as ordinate

^Ag

gBi2 Q:l 1 versus as abscissa.

#Ag

Applying eq (4) to the case of mixtures of the two

standards, K2 S04 and Ag:

'K2 S0j

(7)

where, LK2so4 = l he heat of transition of K2SO4, in kcal/mole;

2.61= the heat of fusion of Ag, in kcal/mole

174.27/107.87 = the molecular weight ratio of K2 S04 to Ag; and

m3 = the slope of the fine obtained by plotting

'K...SH1 gK2 SQ4 as ordinate versus as ^Ag #Ag

abscissa.

Inasmuch as DTA determinations were made in binary combinations of the three substances, Bi2 03 , K2SO4, and Ag, it is possible to evaluate the internal

consistency of the method. From eqs (5), (6), and (7), where mi, m.2, and m3 are given in terms of the specific

ratios, it follows that any one ratio can be determined

independently from the other two, for example:

'Bi20.t A Ag#Ag _^K2 SO

gBi2 03

gAg

Ag gK2 S04

'BizQa gK2 SQ4 ^K2 SO) (3Bi20:i

(5) or my/mi = m3 .

(8)

(9)

119-239
5. Results and Discussion

5.1. General

Figure 1 shows a reproduction of the DTA curve for one of the Bi203 : K2SO4 mixtures. The various trans- formations within the phases are labeled. Peak areas were obtained by tracing the curve on millimeter ruled

graph paper and averaging several counts. The modification of the sample holder in conjunction with the amplification of the equipment was found to be sensitive

to heat of reaction effects. In a 1:1 mixture of

BizC-i : K2SO4, for example, 0.1192 g K2 S04 absorbed

a calculated 1.4635 calories of heat at the transition

and produced an area under the peak of 208 mm2

, or about 0.007 cal/mm2

. No corrections were applied

to the area data for change in thermocouple (Pt-90

percent Pt : 10 percent Rh) sensitivity with temperature. Attempted corrections did not improve the re- sults; furthermore, the use of two standards whose

transformation temperatures bracketed those of BiaOs

provided automatic compensation.

The experimentally determined transformation ra- tios for pure Bi203 and the binary mixtures between

Bi2 0:s, K2SO4, and Ag are given in table 2. Transformation ratios as a function of weight ratios are plotted

in figures 2, 3, and 4. Slopes of the lines and standard deviations of the slopes were determined by the

method of least squares for lines passing through the

origin. If the assumptions used previously in deriv- ing the linear relationships hold, then the origin

constitutes a valid fixed point, for obviously as gBi2 o.) in the mixture approaches 0, so does ABi203 and con- sequently so do the ratios gBi 2 o3 /gK2 so< and ^Bi 2o3 /^K2 so4

- Examining the transformation ratios (table 2) as a function of the 3°/min and 9°/min heating rates or as

a function of the heating cycle (1st, 2d, or 3d), no overall trend of statistical significance can be discerned.

The average ratios of the Bi203 transformations (M-^cl

c-^T) of 2.54 and 2.52 for the Bi2 03:K2 S04 mixtures

and of 2.53 for the Bi 2 03 : Ag mixture (4.32 : 1) are in good agreement with each other and with that for pure

Bi2 03 , 2.46. However, the ratios of 3.20 and 2.80 for the Bi203 transformations in the Ag mixtures (2.16:1

and 2.00 : 1) appear high. The heat of fusion of Bi2 03

is 2/5 that of the heat of transition, and the shape of the fusion peak tends to be low and flat (see fig. 1). Therefore, as the amount of Bi203 decreases in the

mixture, the peak area for fusion becomes less defined

and broader tending to give a low area count.

It may be noted in figure 2 for the Bi203 :K2S04

mixtures that the curves deviate from linearity above a

2 : 1 wt ratio of Bi2 03 : K2SO4 This deviation is not due to any significant reaction between Bi2C>3 and

K>S04 but to poor thermal properties of the Bi2 03

mixture. For the mixtures containing Ag, which is a good thermal conductor and which has been used to improve thermal transfer [9, 15], linearity extends

beyond the 4: 1 ratio of substance to Ag (fig. 3 and 4). Therefore, the area ratios for the 3.46 to 1 wt ratio of

Bi 2 03 to K2SO4 were not used in computing the slopes.

14/j.V/in.

Bi2 03

: K 2S04

(1.72: 1) wt. ratio

250mm2 686mm2

291mm2

( M—- c)

I -

730 °C r

825 °C

583 °C

TIME

FIGURE 1. Differential thermal analysis curve for third cycle of heat treatment o/Bi203 : K2 S04 mixtures of weight ratio 1.72 : 1.

Approx. 0.2 g of sample in Pt tube was heated in air at 3°/min. The temperature of sample container was measured with Pt —90 percent Pt: 10 percent Rh thermocouple; reference

material was compacted alumina powder. Areas under peaks were obtained by counting squares in tracings of the peaks on millimeter ruled graph paper. a — = transition of K2 SG\| M —* c = monoclinic to cubic transition of BijOi

c —* I = fusion of cubic Bi20.i. 120-240
Table 2. Ratio of peak areas between transformations in Bi2 03 and in binary mixtures o/~Bi2 03 , K2 S04 , and Ag, as a function of

heating rates and weight ratios*

Composition

wt. ratio

Transformation

ratios ° AilAt

Ratio of peak areas at heating rates:

3°/min 9°/min 3°/min Average

Bi 2 03 (pure)

M-+c

c — / 2.47 2.57 2.33 2.46

B12O3 : K^SO* mixtures

77.6 Bi2 03 M-» c 2.86

4.67

2.18

4.87

2.58

4.57

2.54

4.70

22.4 K2 SO,

(3.46:1) c-*l M-*c

a-/3

c->/

1.63 2.23 1.92 1.93

63.3 Bi2 03

36.7 K2 SO.

(1.72 : 1)

A/ — c c-> / M->c a^P

2.51

3.03

2.70

2.94

2.36

2.74

2.52

2.90 c— I a-/3

1.21 1.09 1.16 1.15

50.0 Bi203 Af — c»

1.61 1.61 1.62' 1.61 50.0 K2SO, a^P

(1.00:1)

B12O3 : Ag mixtures

81.2 Bi 2 03 18.8 Ag M —

c

c— / 2.56 2.52 2.51 2.53

(4.32 : 1) s-W

3.91 3.82 3.96 3.90

/ 5->/

1.52 1.51 1.58 1.54

68.35 Bi2 03 M^c 3.10'" 3.29" 3.20"

31.65 Ag C—/

(2.16:1) 2.14 r 1.68 1.91

c-» / 0.69' 0.51 0.60 s-»;

66.7 Bi2 03 A/ —

c

2.80 2.80"

33.3 Ag c—

/

(2.00 : 1) A/—

c

1.99 1.72 1.86 s-*/ c— / 0.61 0.61 $-»/

K2 S04 : Ag mixtures

57.7 K2SO«

42.3 Ag S — / 0.637 0.638 0.604 0.626

(1.36:1)

80.0 K2 SO,

20.0 Ag s-»/

2.27 2.16 2.07 2.17

(4.00:1)

"Sample weights varied from 0.2 to 0.4 g, depending on the particular mixtures. Samples were contained in Pt tubes and heated in air. Sensitivity on the differential temperature scale was 14 (iv/in.

a Refers to ratio of peak areas between the indicated transformations:

Af —»c, monoclinic to cubic transition of Bi 2 03 phase at 730 "C

c—*l, cubic to liquid transformation of Bi 2 0 3 phase at 825 °C a—» p, low to high transition of K2 SO< phase at 583 °C s—* /, solid to liquid transformation of Ag phase at 960.8 °C.

b No values for and ratios as c —* I transformation of Bi2 03 is not well

c * / p

denned.

0 12°/min heating rate. Area for c—* / transformation of Bi 2 Q3 appears low.

0 2 4

9 Bi 2 0 3 q K 2 S04

FIGURE 2. Peak area ratios versus weight ratios for mixtures of

Bi2 03 and K2 S04 .

gBiio,/«Kiso. refers to the weight ratio. ^biiOiMkjSO, for ^»pe of line m, refers to area under transition of Bi 2 03 area under transition of K2 S04 . /fBiiOiMi^so. f° r sl°P e °f h ne m/ refers to area under fusion of Bi 2 03 -^area under transition of K2SO4. Slopes calculated by method of least squares. ^Bhoi = 5.722m, (see eq (5). in text). £lr Bi2 03 = 5.722 x 1.66 9 = 9.55 kcal/mole. S.D. m„ = 0.031.

Z./Bi 2 03 = 5. 722 x0.671 = 3.8, kcal/mole. S.D. m/ = 0.020.

1 1 1 1

4

/m,r = 0.902 5

2 •

•//

/* •

.—^rn t = 0.342 3

•

0 1 1

1 0 2 4

g Bi 2 03

FIGURE 3. Peak area ratios versus weight ratios for mixtures of

Bi 2 Os and Ag.

gBiio3 /gA« refers to the weight ratio. A^qJA^, for slope of line m„ refers to area under

transition of Bi 2 03

-^- area under fusion of Ag. ^biioJ^ak Ior slope of line mt refers to area under fusion of Bi2 03 -^-area under fusion of Ag. Slopes calculated by method of least squares.

Z. Bll0l = 11.274m2 (see eq (6). in text). L,r Bi 2 03 = 11.274 x 0.9025 = 10.1, kcal/mole. S.D. m„ = 0.019.

Z.,Bi 2 O3 = 11.27 X0.3423 = 3.86 kcal/mole. S.D. m/ = 0.015.

121-241
g K2 S04

FIGURE 4. Peak area ratios versus weight ratios for mixtures of K2SO4 and Ag.

#k»sii./«a« refers to the weight ratio. /* K.so.M*« for slope of line mlr (DTA) refers to the area under the transition of K2 SO f area under the fusion of Ag. Slope for solid line calculated hy method of least squares; slope for dashed line calculated from literature values.

Lkiso. — 4.217m3 (see eq (7), in text).

i., r K2 SO, = 4.217 x0.533 = 2.25 kcal/mole. S.D. mlr,= 0.014.

i., r K2 SO,, from literature [3. 121 = 2.14 kcal/mole.

5.2. Heats of Transformations

By application of eq (5) to the slopes in figure 2:

Ltr Bi 2 03(M^c) = 5.722 X 1.669 = 9.55 kcal/mole

S.D. mtr = 0.031 (0.30 kcal/mole)

LyBig03(c->/) = 5.722 X 0.671 = 3.84 kcal/mole

S.D. mf = 0.020 (0.08 kcal/mole)

Similarly, by application of eq (6) to the slopes for the Bi 2 03 : Ag mixtures (fig. 3):

L, r Bi 2 03(M^c) = 1 1 .274 X 0.9025 = 10.

1

7 kcal/mole

S.D. mtr = 0.019 (0.19 kcal/mole)

L/Bi203(c->/) = 1 1 .274 X 0.3423 = 3.86 kcal/mole

S.D. mj = 0.015 (0.06 kcal/mole).

The standard deviations of the slopes for the

Bi2 03 :Ag mixtures are somewhat lower than for the

Bi2 03 : K2 S04 mixtures because of the additional data,

for the high weight ratio, that could be used in the

calculations. Certainly, the difference in the heat of fusion of Bi2 C»3 obtained from the two standards is not statistically significant. The difference in values

for the heat of transition is of questionable significance.

5.3. Accuracy

The linear relationship between area ratios and

weight ratios for mixtures of the two standards can be

seen in figure 4. The experimentally determined slope

(0.533) is 4.7 percent greater than the theoretical slope

(0.508) derived from the literature values. The differ- ence between slopes is about twice the standard deviation of the experimentally determined slope. The

agreement is good considering that the binary mixture

of standards presents the most extreme in physical

conditions of the three binary mixtures. In the

K2 SC»4 : Ag mixtures, the area of the solid-solid transi- tion of K2 S04 at 583 °C is compared to the area of the

solid-liquid transformation of Ag at 960.8 °C. Substituting in eq (7) the slope of the transformation

ratio shown in figure 4 (0.533) gives a value of 2.25 kcal/mole for the heat of transition of K2 S04 , compared

to 2.14, the literature value. The agreement between

these two values, as well as for the slopes, tends to substantiate the standard values used in the calculations, namely, 2.61 kcal/moie for Lf of Ag and 2.14

kcal/mole for Lir of K 2 S04 . Attempts to correct for the change in thermocouple sensitivity with temperature or the use of other literature values for the heats

of transformation of the standards has a detrimental

effect on the agreement.

5.4. Internal Consistency

As shown in the development of eqs (8) and (9), it is possible to check the internal consistency of the results through a calculation which does not involve any heat

of transformation values. From eqs (8) and (9): —m2 „ _^k2S01 c?Ag — m3 — —

m-\ AAl, gK2 so4

Substituting the values for the slopes mt , m2 , and

iris, as given in figures 2, 3, and 4, respectively: For

transition data, ?'??^5 = 0.541 (calc.) versus 0.533

I.669 0.3423 (expt.). For fusion data, '

' =0.510 (calc.) versus

O.6/1

0.533 (expt.).

The internal consistency calculations give deviations

between the experimentally determined slope, m3 , and

the calculated one, /7i 2 /mi, of +1.5 percent, for the

transition data and —4 percent for the fusion data. The average of the two calculated slopes agrees to better than 1.5 percent with the experimentally deter- mined one.

5.4. Conclusion

Consideration of the three criteria, namely, standard

deviation of the slopes, internal consistency, and accuracy, as determined with the binary mixtures of standards, indicate an overall uncertainty of about 5 percent.

122-242
Averaging the results for the heats of transformation

of B12O3 obtained from the mixtures with K2SO4 and

Ag, yields:

LtrBi2 O3(M-*c) = 9.9±0.5 kcal/mole

L/Bi2 O3(r->/) = 3.9±0.2 kcal/mole

The sum of the entropy of transition and of fusion

. /9900 3900\ / equals I JQ03 1098/ /

5 = 2-7 cal' ' g atom' a reasonable value [3].

6. Summary

To avoid problems inherent in a separate heat of re- action calibration of DTA equipment, a technique was

developed which makes use of internal standards.

Binary mixtures of Bi2C>3 and two standards, K2SO4

and Ag, were formulated in three weight ratios and subjected to three cyclic heat treatments, in the DTA

equipment. Small amounts of mixtures, 0.2 to 0.4 g

in total weight, were heated in platinum tubes which

were isolated from the tubes containing the reference

material, AI2O3. Thermocouples, Pt-90 percent Pt:10

percent Rh, of fine wire were welded to the outside of the tubes. The modification of the sample holder and

overall sensitivity of the equipment was found to re- spond to heat effects equivalent to 0.007 cal per mm2 of the area under the peak.

A number of criteria were employed to check on

possible reaction between Bi203 and the standards and

to eliminate erroneous date. These criteria were as

follows: Comparison of corresponding transformation

ratios in successive heat cycles; comparison of the

transformation ratio (M—>c/c—»/) in the Bi203 phase of mixtures with that in pure B^C^; x-ray powder analysis

of mixtures at the completion of a determination; and,

finally, observing the adherence of the data to linearity as prescribed by theory.

Except for the high weight ratio of B12O3 to K2 S04 in the 3.46:1 mixture, plots of ratios of transformation

areas versus corresponding weight ratios were linear

and passed through the origin. The presence of Ag in the Bi2 03 :Ag and the K2 S04 :Ag mixtures contributed

to thermal transfer, and linearity was observed for

all the weight ratios. The data were analyzed according to (1) standard

deviation of the slopes, (2) internal consistency, which

is independent of the heat of transformation of the

standards, and (3) agreement between calculated and

selected literature value when one standard is mixed

with the other. The heat of transition of Bi2 03 was

found to be 9.9 ±0.5 kcal/mole and the heat of fusion,

3.9 ±0.2 kcal/mole. The uncertainties are estimated

limits of error, based on internal consistency and on

the values of the standards.

The authors express their sincere appreciation to Joan R. Rosenblatt of the Statistical Engineering

Section, who was consulted on the statistical analysis

of the data.

7. References

[1] L. Belladen, II sistema Bi2 0,-PbO (The System Bi2 03 -PbO),

Gazz. chim. ital. 52, II, 160-164 (1922).

[2] K. K. Kelley, Contributions to Data on Theoretical Metallurgy: V, Heats of Fusion of Inorganic Substances, U.S. Bur. Mines

Bull., No. 393, 166 pp. (1936); p. 26; Ceram. Abstr. 16 [5] 162 (1937).

[3] O. Kubaschewski and E. LL. Evans, Metallurgical Thermochemistry, 426 pp, 3d ed., rev. (Pergamon Press, New York,

1958).

[4] F. D. Rossini, D. D. Wagman, W. H. Evans, S. Levine, and I. Jaffee, Selected Values of Chemical Thermodynamic Properties, NBS Cir. 500, (1952) 1268 pp.

[5] E. M. Levin and C. L. McDaniel, The System Bi2 03 -B2 03

, J. Am. Ceram. Soc. 45 [8] 355-360 (1962).

[6] G. Gattow and H. Schroder, "Uber Wismutoxide, III, Die

Kristallstruktur der Hochtemperaturmodifikation von Wismut (Ill)-oxid (S-Bi.,0.,)", Z. anorg. allg. Chem. 318

[3^1] 176-189 (1962).

[7] G. Gattow and D. Schiitze, Uber Wismutoxide, VI, Uber ein Wismut (Hl)-oxid mit hoherem Sauerstoffgehalt (/3-Modifikation), Z. anorg. allg. Chem. 328, [1-2] 45-67 (1964).

[8] E. M. Levin and R. S. Roth, Polymorphism of bismuth sesquioxide. II. Effect of oxide additions on the polymorphism of

Bi2 03

, J. Res. NBS 68A (Phys. and Chem) No. 2, 197-206

(1964).

[9] W. J. Smothers and Yao Chiang, Differential Thermal Analysis:

Theory and Practice, 444 pp (Chemical Publ. Co., Inc., New York, 1958).

[10] F. C. Kracek, The polymorphism of potassium nitrate, J. Phys.

Chem. 34, 225-47 (1930).

[11] Isaac Barshad, Temperature and heat of reaction calibration of the differential thermal analysis apparatus. Am. Mineral. 37 [7&8] 667-694 (1952).

[12] K. K. Kelley, Contributions to the Data on Theoretical Metallurgy. XIII. High-Temperature Heat-Content, HeatCapacity, and Entropy Data for the Elements and Inorganic

Compounds, U.S. Bur. Mines Bull. 584, 1960. 232 pp.

[13] (a) Cavallaro, Atti Real. Acad. Ital., Rend. Class Sci., Fiz., Mat. et Nat. [4-5] 520-526 (1934). (b) F. E. Wittig, Z. Elektrochem. 54, 288 (1950). (c) W. Oelson, Arch.

Eisenhiittenw. 28, 1-6 (1957).

[14] Ernest M. Levin and Robert S. Roth, Polymorphism of bismuth

sesquioxide. I. Pure Bi2 03

, J. Res. NBS 68A (Phys. and Chem.) No. 2, 189-195 (1964). [15] C. J. Penther, S. T. Abrams, and F. H. Stross, Semi-automatic Thermal Analysis Apparatus, Anal. Chem. 23, 1459-66

(1951).

(Paper 69A3-342)

123-243

2. Cryoscopic Measurements

Paper Page

2.1. Comparison of cryoscopic determinations of purity of benzene by

thermometric and calorimetric procedures.

Glasgow, A. K., Ross, G. S., Horton, A. T., Enagonio, D., Dixon,

H. D., Saylor, C. P., Furukawa, G. T., Reilly, M. L., and Henning, J. M. Anal. Chim. Acta 17, 54 (1957).

Key words: Purity by heat measurements 127

2.2. A cryoscopic study of the solubility of uranium in liquid sodium at 97.8°C.

Douglas, T. B., J. Res. Nat, Bur. Stand. (U.S.) 52, No. 5, 223-

226 (May 1954).

Key words: Solubility measurements by calorimetry 153

125

COMPARISON OF CRYOSCOPIC DETERMINATIONS

OF PURITY OF BENZENE

BY THERMOMETRIC AND CALORIMETRIC PROCEDURES

by

A. R. GLASGOW, Jr., G. S. ROSS, A. T. HORTON, D. ENAGONIO,

H. D. DIXON and C. P. SAYLOR

Pure Substances Section of the Chemistry Division

and

G. T. FURUKAWA, M. L. REILLY, and JEANETTE M. HENNING

Thermodynamics Section of the Heat and Power Division, National Bureau of Standards,

Washington, D.C. (U.S.A.)

I. INTRODUCTION

For some time, workers at the National Bureau of Standards have been embarassingly aware of the discordant results sometimes yielded by the two methods upon which we principally depend to assay the purity of nearly pure compounds. Almost always the

thermometric method, by which a stirred sample is frozen at nearly constant rate, had

indicated larger impurity than the calorimetric method, by which an adiabatically controlled frozen sample is melted in stages by the addition of accurately controlled increments of energy. The fundamental physical principles and assumptions are the same in both cases, and the analysis depends upon the measurements of temperature.

The discordances in assays by the two methods were dramatically laid bare when Ones1 and Mathieu2 published comparisons of results obtained at the National Bureau of Standards using a thermometric method with those obtained at the U.S. Bureau of Mines employing the calorimetric procedure. In general, we have tended to assume that the much more elaborate calorimetric

method provides truer results, for reasons that do not need to be elaborated here. Neither method can be considered free of its own pitfalls, however, and it was decided

to attempt a rigorous and objective comparison of the two methods. This depended on

deliberate contaminations of an unusually pure sample, division of the contaminated

samples in such manner that the compositions would not be altered, and independent

determinations of purities by the two methods.

Fortunately for the independence of this comparison, the group at the National

Bureau of Standards who use the calorimetric procedure work in a different building,

in a different division, and under different supervisors from those who use the thermometric procedure. As a consequence, it was possible to plan a coordinated system of comparison in which each group of workers would be unaware of the results being achieved by the other and for both to be totally uninformed about the extent of the deliberate

contaminations that had been made.

References p. 79 127-54
For the sake of objectivity, an elaborate scheme was employed so that no one could

know the real measure of contamination until all results by both procedures had been

reported. Thus the w-heptane with which a highly purified sample of benzene was to be

contaminated was measured by three workers into 6 different weighed glass vessels. After

they had been filled, the vessels were weighed by another worker who kept a private

record of his results. Volumetric amounts of %-heptane were determined by still another

participant. The vessels containing contaminant were entrusted to another worker, a young woman who did not otherwise participate in the study. When requested, she

selected the sealed tubes of contaminant that were broken into the liquid benzene by

another group of workers who alone knew the amount of the benzene to which the

w-heptane was added. Only after all measurements and calculations had been completed were the scattered bits of information assembled from which it was possible to calculate the actual degree of contamination. In the actual performance of analyses we felt that there was no reason to use any

techniques except those presently believed to give the most accurate results. Conse- quently refinements of procedure were employed that can be mentioned here only in the most cursory fashion. It was stipulated that each method would be utilized in the manner believed by its practitioners to be the most dependable. In this there was just one limitation. Although it is our custom when using the thermometric method to de- termine both freezing and melting curves and to base judgments on the data obtained

each way, it was decided in this instance to utilize for the official computations only

those data obtained during freezing.

II. PREPARATION OF SAMPLES

1. Selection of materials

Benzene was chosen as the major constituent with knowledge that it had a number

of disadvantages. Thus, in the fully dried state, it is an extreme desiccant. There is a

long record of difficulties in determining its true melting point or triple point. On the

other hand, its triple point is conveniently close to the triple point of water. Further,

it was believed that some of the anomalies of its properties might be resolved during the

investigation.

The choice of %-heptane as the contaminant was largely based upon the extreme

difficulty of separating it from benzene by regular distillation. Although the boiling

points of w-heptane and benzene are i8° apart, the boiling points of benzene and the

azeotrope, which contains 0.7% of ^-heptane, differ by only o.i°C. All samples for the

investigation were prepared to he between benzene and the azeotrope. For this reason

the fractionation of the samples even in an efficient still would be practically impossible.

It can be totally neglected in connection with the transfers employed in this study.

w-Heptane was chosen also because of a belief that its solution in liquid benzene would

be ideal within the range of the measurements while it would be insoluble in frozen

benzene.

2. Preparation of a "pure" benzene

As starting material, 2 liters of "ACS Reagent Grade" benzene, claimed by its pro- ducers to be "thiophene-free" and found to be of good quality, was chosen. This was

further purified by 5 treatments with concentrated sulfuric acid lasting about 20 hours,

and leachings with 5 portions of distilled water.

References p. 79 128-55
The benzene was transferred to a 2-liter distillation flask fitted by standard unlubricated glass joints to a Widmer column, condenser, adapter, and receiving flask. After about 250 ml of benzene and water had been slowly distilled, and without inter- ruption of the boiling, the condenser, adapter, and receiver were replaced by a similar

assembly of a drv condenser, adapter, and the ampoule D illustrated in Fig. r. After

800 ml were distilled into the ampoule, the ampoule was disconnected from the condenser and stoppered.

Fig. 1. Apparatus for filling the crystallization ampoule.

As the first stage of removing gases and water, the benzene in the ampoule D was

frozen with a bath of solid carbon dioxide. During freezing, the pressure in the

system was kept reduced by intermittent pumping. When the benzene was completely

frozen, the system was sealed at a in Fig. 1 . The benzene was then melted and refro- zen slowly. The gases, including water, which were evolved during freezing, were pumped off from time to time by opening the ampoule to the ballast bulb F. When

the ballast bulb was not open to the freezing benzene, the pressure in it was maintained at approximately io~6 mm Hg by means of a mercury diffusion pump. After

the benzene was completely solidified, it was subjected to the direct pumping of the

diffusion pump for about half an hour during which time the glass of the system,

wherever feasible, was heated with a soft flame. The benzene was melted and was

refrozen while pumping in the same fashion as before. The benzene was again melted.

The desired amount of benzene was transferred to ampoule E, by chilling the ampoule.

This benzene was slowly frozen and degassed as before, chilled with liquid nitrogen and

subjected to the direct action of the pump while the glass was again heated with a

flame. The ampoule with its break-bulb was then sealed. Resinous ethylene glycol phthalate, which is considered as insoluble in benzene, was used on the stopcocks. Two

samples of about 500 ml each were prepared as outlined.

References p. 79 129-56
Greatest reliance for trie purification of the benzene was placed upon the growth of

single crystals by a method developed by Horton3 and derived from that of Tammann

or of Bridgman. In Horton 's apparatus, Fig. 2, the large glass tube contains two

immiscible liquids. Since convection occurs within each liquid but not across the

Fig. 2. Apparatus for growing single crystals of benzene.

interface, we were able to maintain a difference in temperature of approximately 6o°

across the interface of the two liquids, although the temperature distribution

within each liquid was nearly uniform. The upper liquid was kept at about 30°C

References p. 79 130-57
by a coil of heating wire wound around the tube, and the lower liquid cooled to about —28°C by immersion in a refrigerated bath contained in a Dewar-type flask. During a

period of about 10 days, the ampoule of benzene was lowered across the interface be- tween the upper and lower liquids, the slow movement being controlled by a clock mechanism. Fig. 3 is a diagram of the apparatus. At the end of the 10 days, all but about

15 ml of the benzene had frozen. The ampoule was removed from the bath and clamped

in an inverted position. Upon warming the surface of the vessel with the hands, the

surface of the crystal and all of the solid in the crooked capillary melted and drained

into one of the seal-off bulbs b of Fig. 1. Here it was chilled to the temperature of liquid

nitrogen and sealed off from the rest of the sample. A second crystal was grown in the

other ampoule. We believe the impurity in the two crystals of these samples to be less than can be disclosed by thermal analysis.

Fig. 3. Apparatus for mixing the two samples of purified Fig. 4. Apparatus for benzene and distributing the mixture into smaller sample the partitioning of

vessels. samples for analysis

(also used for intro- ducing contaminant) .

The material in these two ampoules was combined and divided into 4 parts. To do

this, the ampoules were sealed into the system shown in Fig. 4. Over a period of several hours the system was evacuated with a diffusion pump while, from time to time, the glass was heated with a flame. The system was then closed by sealing offat a.

References p. jg

131-58
Liquid nitrogen was placed at trap C and solid carbon dioxide packed around the bulb

B. The samples from separate single-crystal growing operations were combined in the

bulb by opening the ampoules at the break-bulbs with a magnetic hammer. The

major part of benzene distilled into the bulb, that which condensed in the trap serving

as a form of stopcock. Finally, the benzene in the bulb was allowed to melt, the liquid

nitrogen bath was removed from around trap C, and the benzene was allowed to flow

through the magnetically controlled distributor D into ampoules. The ampoules were

chilled with liquid nitrogen and sealed off. Four ampoules containing approximately

250 ml each were prepared.

J. Partition and contamination of the portions

The 4 ampoules prepared as described were divided, either with or without intenti- onal contamination. The final samples were subsequently subjected to the thermometric and calorimetric methods of analysis. The contaminations and partitions were performed in the following manners. In one instance a group of thin-wall glass tubes

about 10 cm long and somewhat less than r mm in bore was washed by putting them

upright in a column in which dry, reagent-grade benzene was refluxed for about an

hour. The tubes were then dried in a heated vacuum system. The internal diameters

at both ends of the tubes were measured with a microscope and filar-micrometer

eyepiece. Tubes selected for uniformity in diameter were weighed on a micro balance.

NBS Standard Sample No. 216a w-heptane was introduced into 3 of these tubes by

means of a micro-buret. The ends containing the n-heptane were then cooled with

compact solid carbon dioxide; the tubes were exhausted and sealed off with a flame. The

portion of the tube containing the w-heptane and the portion removed in sealing were

weighed. The length of the liquid in each tube was measured with a travelling microscope,the sealed end of the tube and the meniscus of the liquid having nearly the same

conformation. Thus two measurements were made of the amount of w-heptane in each

tube. For a more highly contaminated sample, ^-heptane was introduced in 3 of the

fragile sample bulbs that are used in combustion calorimetry. The determination of the

amount of contaminant was based solely on the comparative weights.

Apparatus shown in Fig. 5, is similar to that used to partition the original purified

benzene, and was used to divide and contaminate the samples. The tube or bulb select- ed by the young woman not otherwise participating in the work was placed above

the break-bulb of the ampoule. The system was pumped and flamed for about 2 hours

before sealing. The tube or bulb of n-heptane and the break-bulb were broken by the same magnetic hammer. After steps were taken to assure thorough incorporation of the w-heptane into the benzene, the apparatus was inverted and each sample partitioned into ampoules containing 40, 80, and 100 ml by means of the magnetically controlled distributor. These ampoules were then sealed and removed in the usual fashion. One of the samples was divided without contamination. For simplicity of identifica- tion the uncontaminated sample was given the designation A, the first contaminated

sample the designation B, and the second contaminated sample the designation C.

III. THERMOMETRIC ANALYSIS

I. Apparatus

The apparatus used in the determination of the purity of benzene from time-temperature freezing and melting curves is similar to the one developed by Glasgow and

References p. 79 132-59
Tenenbaum4

. The cell and the completely assembled apparatus are shown in Figs. 6 and 7. The seeding devise was not used because preliminary experiments had shown that,

in general, the small degree of undercooling exhibited by benzene made it unnecessary. In order to minimize errors in the experiments, all components used in temperature

measurement were carefully calibrated. The Meyers bifilar, helical, platinum resistance

thermometer and the 10-ohm standard resistance used in the calibration of the Mueller

G-2 bridge were calibrated at the National Bureau of Standards. During the course

of the experiments, the thermometer was periodically checked against the triple

point of pure water. The triple-point cell was of the type used for calibrating thermometers, and the

depth of immersion of the thermometer in the cell was 13 inches. A comparison of the triple point of water in this cell was made with that observed in the cell shown in Fig. 5 with 40 ml of water and with a depth of immersion of the thermometer of 2.8 inches. The results of this comparison are given in Table VIII.

Resistance readings were taken every minute. In addition to these manual readings

the temperature was recorded in two fashions. The first consisted of amplifying the

off-balance signal from the bridge by passing it through a DC high-gain amplifier

(Liston-Becker Model No. 14). This amplified signal was fed into a Brown 10 millivolt recording potentiometer. In order to obtain both a manual and a printed continuous

record of the same experiment, the signal from a copper-constantan thermocouple

junction was balanced out by a Rubicon potentiometer to within 0.01 millivolt of the

total signal generated at the freezing point. The residual signal was fed through the

DC amplifier and into the recorder. The sensing junction of the couple was placed in the middle of the length of the platinum coil, between the glass case of the thermometer

and the thermometer well. A triple-point water cell was used as the reference point.

This cell was equipped with radiation shielding and insulated at the top with glass wool

to stabilize it as much as possible. The entire potentiometer was thermally insulated so

as to minimize thermal e.m.f.'s. Under these conditions it was possible to record to a

precision of approximately o.oooi°C. This precision has been checked by using a triple

point cell of diphenyl ether and one of water. The apparent overall drift over a period

of 1 hour was found to be less than 0.00005 °C. The data, as given in this paper, were handled both by the methods given by Taylor

and Rossini 5 and by Schwab and Wichers6

. Other procedures were employed by

Saylor. Portions of these results will be reported in another paper.

2. Experimental details Extreme care was exercised during the filling of the cell. The cell was cleaned with

chromic acid, and carefully washed with distilled water. It was then evacuated with

a mercury diffusion pump and subsequently heated to I50°C for a period of 24 hours.

All samples were introduced by breaking the break-off tip of the containing ampoule

and pouring the contents directly into the tube. In order to prevent any accidental

contamination of the cell between runs, additional break-off tips were included in the

manifold so that other samples could be introduced into the cell and investigated

without letting air into the cell between runs. The samples were run in the following

order : (1) two samples of A, (2) one of sample B, and (3) one of sample C. The original size of sample was 50 ml. However, for a sample of this size, the freezing

Refere*ices p. 79 133-60
Fig. 5. Modified thermometric cell (silvering of the glass surface of the double-walled jacket,

confining the evacuated space, was removed to show stirrer, thermometer well, and sample holder) 134-61
Fig. 6. Complete apparatus used in the measurement of purity by the thermometric method. 135-62
TABLE T RESULTS OF THERMOMETRY ANALYSIS OF BENZENE, SAMPLE A-I 1

Expt. TfP Tf 'P

Io AT

I 278.6106 278.6188 O.O082 O. OOOI 2

2 278.6072 278.6090 O.OOI8 O.OOOO27

3 278.6107 278.6366 O.0259 O.OOO39

5 278.6138 278.6391 O.0253 O.OOO39

(» 278.6104 278.6325 0.022I O.OOO34

7 278.6108 278.6400 O.0292 O.OOO44

8 278.6126 278.6367 O.0241 O.OOO37

T/p = 278.6109 ± o.oo20°K Tf

'p = 278.6304 ± o.oii 3°K

Variance = 423-io~8 Variance = i39i8-io-8 Standard deviation = ± 0.0021 Standard deviation = ± 0.0118

Purity* = 99 9 70 ± 0.02 mole %

Purity6 = 99.go5 ± 0.006 mole % 1 Melting experiments on 50-ml sample.

experiments exhibited peculiarities which made analysis impossible. The sample

would recover rapidly from undercooling, but then the observed temperature would

TABLE II RESULTS OF THERMOMETRIC ANALYSIS OF BENZENE, SAMPLE A-2 1

Expt. T/P Tf 'P

io AT ^2*

I 278.6690 278.6708 O.OO18 0.000027

2 278.6686 278.6721 O.OO35 0.000053

3 278.6682 278.6696 O.OOI4 0.000021

4 278.6670 278.6683 O.OOI3 0.000020

7 278.6683 278.6706 O.OO23 0.000035

8 278.6693 278.6744 O.O051 0.000078

9 278.6680 278.6708 O.OO28 0.000043

10 278.6679 278.6702 O.OO23 0.000035

278.6683 ± o.ooo6°K r/» = 2 78.6709 ± o.ooi4°K

Variance = 54- io-8 Variance = 254-IO"8 Standard deviation = ±0.0007 Standard deviation = ±o.ooit

Puritya = 99-996 ±0.002 mole %

Purity6 = 99 993 ±0.002 mole %

iMelting experiments on 50-ml sample.

rise steadily, although slowly, until the sample could no longer be stirred. For this reason, Table I shows only melting experiments. When the "melting" bath was placed

around the cell the temperature was observed to fall very rapidly before commencing

to rise. This erratic freezing behavior was suspected to be related to the size of the

benzene sample, so auxiliary experiments were conducted in another similar cell with

reagent grade benzene. The behavior was identical to the more pure benzene. Successive experiments were run wherein 10 ml fractions of the sample were removed.

When the sample size approached 40 ml, a normal freezing behavior was noted.

References p. yg 136-63
The freezing curves, as obtained with this type of apparatus, are generally considered

to be more reliable than the melting curves, and all subsequent measurements on the

benzene consisted of freezing curves only, using a sample size of 40 ml. However, a comparison of Table II with Table III shows that there is no appreciable difference be- tween the data obtained from melting experiments employing 50 ml of sample and

freezing experiments employing only 40 ml of benzene.

As shown in Table I, the purity of the supposedly "pure" benzene is not appreciable

high. We suspected that in some unexplained fashion we had contaminated the sample.

We therefore removed this sample and introduced another identical sample into our

cell, without allowing air to enter the cell at any time. Tables II and III showthe results. Further investigation showed that the first sample was probably contaminated by

water from the cell walls. This water could be considered as "chemi-adsorbed" in contrast to the "physi-adsorbed" water removed by the heating and pumping technique. In view of the relatively large surface area of the cell and the manifold, the observed

lowering in temperature is not unduly large if attributed to water. From this experience,

TABLE III RESULTS OF THERMOMETRY ANALYSIS OF BENZENE, SAMPLE A-2 1

Expt. T/P r, *P h AT N,"

I 278.6684 278.6745 0.0061 0.000093

2 278.6684 278.6718 0.0034 0.000052

3 278.6699 278.6732 0.0033 0.000050

4 278.6692 278.6744 0.0052 0.000079

5 278.6689 278.6734 0.0045 0.000068

6 278.6696 278.6714 0.0018 0.000027

7 278.6692 278.6718 0.0026 0.000040

8 278.6709 278.6736 0.0027 0.00004 1 9 278.6691 278.6716 0.0025 0.000038

10 278.6697 278.6729 0.0032 0.000049

T/p = 278.6693 ± o.ooo5°K Tf» = 2 78.6729 ± oooo8°K

Variance = 56-io~! 1 Variance = I33-IO"8 Standard deviation = ±0.0007 Standard deviation = ±0.0012

Purity 3 .' = 99-994 ±0.002 mole % 1 Freezmg experiments on 40-ml sample.

one might suspect that the benzene in the form of the large single crystal was much purer

than the sample measured and could have been contaminated during the partition process. The partitioning of the samples were done after careful evacuation and "flaming"

of all glass parts at approximately 350-4oo°C.

This higher temperature could account for the smaller contamination. When sample

A-i was transferred from the ampoule to the cell, the cell and manifold were dried by

heating to I50°C while evacuating the system with a mercury diffusion pump backed by

an oil mechanical fore-pump. However, the inclusion of several break-off tip seals in the permanent part of the manifold assemble attached to the cell made possible the

introduction and removal of all subsequent samples without allowing the cell and per- manent manifold to be open to the air. In this fashion, owing to the order in which

References p. 79 137-64
the samples were run, the cell was in each case "conditioned" or purged by material of a higher purity than the sample being tested. The portion of the manifold between the particular break-off tip being used and the new sample being introduced was thoroughly cleaned and dried by first heating and

pumping, followed by a purging of this section with dry benzene. After the removal of

this benzene, the break-off tips of the ampoule and the cell manifold were broken and

the sample was poured into the cell. This technique of purging the entire system with

benzene before introducing the next sample is thought to be necessary in order to assure non-contamination of the sample in the cell itself. All handlings of the samples were preceded by the distillation of a dry sample of benzene, using the manifold as a

reflux column and condenser.

The data given in Table IV are those obtained from the analysis of the recorded ther- mocouple e.m.f. The curves indicate that much of the "randomness" exhibited by the

TABLE IV

RESULTS OF THERMOMETRIC ANALYSIS OF BENZENE, SAMPLE C1

Expt. TfP T, *P AT N*

2 278.6288 278.6798 O.0510 O.OOO777

5 278.6325 278.6784 O.0459 O.OO0699

6 278.6386 278.6874 0.0488 O.OOO743

7 278.6342 278.6549 O.0207 O.OOO315

8 278.6342 278.6630 O.O288 O.OOO439

278.6346 278.6719 00373 O.OOO568

i i 278.6364 278.6692 O.0328 O.OOO499

12 278.6366 278.6643 0.0277 O.OOO422

14 278.6360 278.6634 O.0274 O.OOO4I7

15 278.6358 278.6545 0.0187 O.OOO285

Tttp = 278.6348 ±o.ooi9°K Tf,'p = 278.6687 ±o.oo24°K

Variance = 7i9-io~8 Variance = ii66-io -8 Standard deviation = ±0.0027 Standard deviation = ±0.0034

Purity 0 = 99 948 ±0.004 rnole %

Purity* = 99 942 ±0.002 mole %

1 These freezing experiments tm a 40-ml sample were machine recorded with a thermocouple as the sensing element. They were also manually

recorded with a platinum thermometer as the sensing element. The manually recorded results on the same experiments are shown

in Table VII.

TABLE V

RESULTS OF THERMOMETRIC ANALYSIS OF BENZENE, SAMPLE B:

Expt. TfP Tf *P AT Nt*

1 278.6512 278.6575 0.0063 0.000096

2 278.6505 278.6566 0.0061 0.000093

T,

tp = 278.65ogJ K T,» = 2 7 8.6570°K

Purity" = 99.99! mole %

Purity* = 99-966 mole %

1 These freezing experiments on 40 ml of benzene were machine

recorded with a platinum resistance thermometer as the sensing element.

References p. yg 138-65
manual recording of points is not random. Since the thermocouple is small and lies next to the thermometer well, it is more sensitive to local changes, and the departures as shown by the recorded trace are larger in magnitude than those manually recorded. The

divergence of the two curves, as increasing amounts of sample are frozen, is considered

to arise from the difference between local effects sensed by the thermocouple and the

larger overall effect sensed by the thermometer. Since the thermocouple was not

accurately calibrated, the data in Table IV give only a relative comparison. Table V,

which shows the results of recording the resistance of the platinum thermometer itself does not have this restraint, and may be directly compared with values as given in the

manually recorded experiments. The fluctuations observed on the machine-recorded

data can readily be shown to be real changes. The true fitting of these recorded curves should give better accuracy and precision, since a fit of the manually recorded values is limited by the necessary assumption that the scatter is random.

3. Correlation and explanation of data In order to reduce individual errors a rather large number of experiments have been

run on each sample. In these, the freezing bath was always a solid carbon dioxide slush. The bath immersion was kept constant throughout all experiments. The rate of cooling

of the liquid benzene was varied between 0.3

0 and 0.50 per minute. The warming bath

used in the melting experiments was water maintained at 25°C. These melting experiments took place over a longer period of time and the liquid warming rate was varied

between 0.1° and 0.3

0 per minute.

All curves which were capable of mathematical analysis are given. Some freezing curves exhibited the peculiarity of having a constant slope, and since these are not

capable of mathematical interpretation they are not included. Five experiments on

sample A and four on sample B exhibited this tendency.

TABLE VI

RESULTS OF THERMOMETRIC ANALYSIS OF BENZENE, SAMPLE B1

Expt. T/P T, 'P

/o AT N,*

I 278.6564 278.6594 0.0030 0.000046

2 278.6488 278.6562 0.0074 0.000113

3 278.6526 278.6819 0.0293 0.000446

4 27 8 -6559 278.6697 0.0138 0.000210

5 278.6534 278.6794 0.0260 0.000396

6 278.6527 278.6810 0.0283 0.000432

7 278.6518 2786733 0.0215 0.000327

8 278-6553 278.6936 00383 0.000583

9 278.6550 278.6732 0.0182 0.000277

10 278.6524 278.6607 0.0083 0.000126

1

1

278.6514 278.6901 0.0387 0.000589

12 278.6488 278.6640 0.01 52 0.000231

Tf> = 278.6529 ±0 .ooi6°K t,:p = 278-6735 ±o.oo77°K

Variance = 628-io~8 Variance = i4528-io~8 Standard deviation = ±0.0025 Standard deviation = ±0.0120

Purity" = 99 963 ±0.014 mole %

Purity* = 99-970 ±0.004 mole %

1 Freezing experiments on 40-ml sample.

References p. 79 139-66
In Tables I-VII, purity is calculated using two different TfJP's. When the purity is listed as "purity"", this signifies that the TfJP used is that obtained by averaging the calculated TfJP's for the group of experiments listed in the table above the value. The

"best" or most probable value of TfJP is considered to be the average of the experiments

listed in Table III, and purity, as calculated using this value, is listed as "purity6 ". The

value of the cryoscopic constant A , jpjr~2

, which was used in this calculation is the

'0 A.S.T.M. value of 0.01523 degrees-1

. The minor difference in the value as reported in the following section of this paper is not enough to change the purity values listed herein. The calculation of the mole fraction of the total amount of impurity present in each

sample, N2

*, was made by using the following equation:

N2 * = A{TU*—Tf*) (1)

This simplified equation was derived on the assumption that it is valid only when the

total mole fraction of impurity is small and only when all the impurity remains in the

liquid phase during crystallization and forms an ideal solution with the major component.

TABLE VII

RESULTS OF THERMOMETRIC ANALYSIS OF BENZENE, SAMPLE C1

Expt. TfP lo AT JV2 *

I 278.631 I 278.6551 O.0240 O.OOO36

2 278.6327 2787313 0.0986 O.OOI50

3 278.6341 278.6727 0.0386 O.OOO59

4 2786339 278.6655 0.0316 O.OOO48

5 278.634I 278.6650 O.0309 O.OOO47

6 278.6331 278.6548 0.0217 O.OOO33

7 278.6356 278.6606 O.0250 O.OO038

8 278.6336 2786595 O.0259 O.OOO39

9 278.6339 278.6645 O.0306 O.OOO47

10 278.6351 278.6674 00323 O.OOO49

11 278.6364 278.6771 O.O407 O.OO062

12 ^78.6337 278.6628 0.0291 O.OOO44

13 278.6331 278.7041 O.0710 O.OOIO8

14 278.6329 278.6478 0.0149 O.OOO23

15 278.6344 278.6631 0.0287 O OOO44

16 278.6332 278.6566 0.0234 O.OOO36

f/p = 278.6338 ±o.ooo7°K T/0tp = 278.6692 ±0.01 1 2°K

Variance = i53-io~ 8 Variance = 43415- io -8 Standard deviation = ±0.0012 Standard deviation = ±0.0208

Purity3 = 99 946 ±0.018 mole %

Purity* = 99-940 ±0.002 mole %

1 Freezing experiments on 40-ml sample.

The data is tabulated showing the purity and delta temperature as calculated for each

experiment as well as a purity value determined by the average T/JP and the TfJP

obtained on the second sample of A which is considered to be the best value. The

References p. 79 U+O-67
calculation of the variance and standard deviation is straightforward. The uncertainty

is given in terms of each sample and indicates the probable percision (95% confidence

level) as calculated by usual statistical methods. All temperatures are given in terms

of degrees Kelvin and were obtained by adding the constant 273.16 to the Tf*P and

TfJP values originally calculated in terms of degrees Celsius. There is no readily apparent explanation for Tf*P as calculated from these experiments being lower than previously reported values.

TABLE VIII

CALIBRATIONS AND RELIANCE LIMITS OF RESULTS GIVEN IN TABLES I-VII

H2 0 (triple-point measurements)

(A) In normal triple point cell (13-inch immersion)

(1) at time of sample A-i

if = 25.48183, ±0.000010 abs. ohms

(2) at time of sample A2

R = 25.481804 ±0.000010 abs. ohms

(3) at time of sample B

R = 25.48i862 ±0.000010 abs. ohms

(4) at time of sample C

R = 25.4818^ ±0.000010 abs. ohms

(B) 40 ml distilled and degassed H2 0 in freezing point apparatus (2 experi- ments performed after running sample C)

(1) R = 2548i800 ±0.000018 abs. ohms

(2) R = 25.48i8n ±0.000016 abs. ohms

Bridge and thermometer calibrations

(A) For ice triple point — (N-R)j2 varies between limits of 0.002207 and

0.002246 abs. ohms with average of o.oo22 19 . (B) For benzene samples — (N-R)j2 varies between limits of 0.02221 and

0.02269 with average of 0.02245.

(C) The change in the bridge calibration between start and finish of these experiments is not known, but, in view of previous calibrations, the change

is probably less than —0.000030 abs. ohms. Such a change is of the same

order as the precision in a single calibration.

Reliability of reported T/0 's and Tfs of benzene samples

(A) Assuming an accumulative propagation of error, the absolute value

of the Tftp of benzene should be 5.5I29 ±o.oo2°C.

(B) In terms of the above, the absolute values of the Tftp's reported would

also have the same limits of accuracy.

(C) The errors as expressed above are of the order of magnitude necessary to account for the standard deviations obtained in those experiments relating to sample A- 2.

IV. CALORIMETRIC ANALYSIS

I. Method

The calorimetric method for determining the chemical purity of benzene involved

the measurements of liquid-solid equilibrium temperatures at various precisely known

liquid to solid ratios evaluated from the total heat input, heat of fusion, and heat

capacity. The measurements of liquid-solid equilibrium temperatures were made under

References p. yg 141-68
conditions of saturation vapor pressure of benzene. The method requires considerably more equipment than the thermometric method but offers an advantage in that the

equilibrium temperature can be measured at one's leisure. If temperature equilibrium

is not indicated, then a longer time can be allowed, within reason, until a temperature

equilibrium is attained. Recently, the calorimeters of this laboratory have been pro- vided with automatic adiabatic controls which conveniently permit long equilibrium

times. Previously, when the calorimeters were controlled manually to attain the adiabatic condition, the maximum conveniently allowable equilibrium time was about

2 hours. In the experiments described in this paper, at least 16 hours have been allowed

per measurement in order to attain more closely the liquid-solid equilibrium conditions.

For a substance of high purity, the relation for thermodynamic equilibrium between

the pure crystal and the liquid containing mole fraction impurity N2 may be given by

the simplified equation:

N2 = A(T,tP— Tabs) (2) where

A = AH/°IR[T/0ip] 2

, the cryoscopic constant, AH,, = the heat of fusion at T/JP, R = the gas constant, Tt tp = the triple-point temperature of the pure

substance, and

Tobs = the observed liquid-solid equilibrium

temperature.

When this high-purity substance containing total mole fraction N2* of liquid-soluble, solid-insoluble impurity is partially crystallized, the concentration of the impurity in the liquid phase is greater by the ratio i/F, where F is the fraction melted. The mole

fraction impurity of the solution in equilibrium with the crystal is then given by

N2 = N2 *(ilF) (3) and when equations (2) and (3) are combined,

(N2/A) = (N2 *IA){ijF) = T/JP—Tobs (4) Equation (4) shows that the plot ofT0is with respect to x/F is a straight line and

that, when i/F = 0, IV2 = o and the temperature intercept is the triple-point temperature of the pure material. The slope (N2*/A) of the line determines the total mole fraction impurity of the material.

2. Apparatus

Determinations of the purity of benzene were made in an adiabatic calorimeter

designed for heat-capacity measurements in the range io° to 300°K on substances that can be readily transferred by vaporization7

. Fig. 7 shows a schematic drawing of the

calorimeter.

The sample container, suspended in the calorimeter by a thin-walled monel filling

tube, was constructed chiefly of copper with a capacity of about 106 ml. In order to provide as uniform a distribution of energy as possible to the enclosed sample, tinned

copper vanes were arranged radially from the central re-entrant well, containing a

heater and an encapsulated platinum-resistance thermometer, to the outer wall of the

Reerences p. 79 U2-69
To High Vacuum

To Weighing Container

Terminal Box

To High Vacuum Pump

Leads

Thin-wall Monel Tube

Dewar

Tempering Ring

Leads with Heaters

Tube Thermocouples

Shield with Heaters

Calorimeter Heater

Thermometer

Shield Thermocouples

ig. 7. Adiabatic calorimeter for volatile substances. 143-70
container. The vanes were held in place by means of a thin coating of pure tin applied

to the interior surfaces of the container and so spaced that the maximum separation was

about 4 millimeters. The tin afforded an inert surface to benzene.

A thin copper thermal shell attached to the upper periphery of the container afforded

a nearly isothermal surface, regardless of any localized temperature differences on the

surface of the container, to the adiabatic shield surrounding the container and the

shell. Electronic control equipment was used to adjust the currents in the several

shield heaters so that the temperature of the shield could be automatically maintained

at the same temperature as that of the shell. Sensitive thermocouples placed

between the shield and the shell controlled the operation of the electronic system.

The outer surface of the container, the inner and outer surfaces of the shell, and

the inner surface of the adiabatic shield were gold-plated and polished to minimize

heat transfer by radiation. A high vacuum (io-6 mm Hg) was maintained in the' space surrounding the sample container and the adiabatic shield. The resistance of the platinum thermometer, having the ice-point resistance of about

25.5 ohms, was measured by means of a special Mueller bridge designed for the range

of 0.00000 to 422.11110 ohms. The platinum-resistance thermometer was calibrated

in accordance with the 1948 International Temperature Scale8. The temperatures

in degrees Kelvin were obtained by adding 273.1600 degrees to the temperatures in degrees Celsius*. The electrical input energy was determined from the measurements of the current and potential across the 100 ohm Constantan wire heater and the time interval of heating. The heater current and potential were determined by means of a Wenner

potentiometer in conjunction with a standard resistor and a volt box. The time-interval

of heating was measured by means of a precision interval timer operated on a standard

frequency of 60 cycles furnished by the Time Laboratory of the Bureau. The timer has

been compared periodically with standard second signals and found to vary not more

than ±0.02 second per heating period, which was never less than 6 minutes. All electrical instruments have been calibrated in terms of the standards maintained at the

National Bureau of Standards.

3. Experimental procedure

Oil-diffusion vacuum pumps were used in conjunction with suitable mechanical vacuum pumps to evacuate the calorimeter and the various accessory equipment. The vacuum manifolds contained liquid nitrogen traps to prevent back diffusion of oil into

the apparatus being evacuated. The general procedure for evacuating an apparatus was

to maintain it for at least 24 hours at ioo°C and at io -6 mm Hg as registered at the vacuum manifold. Although the resistance to gaseous flow was minimized, some of the

equipment necessarily contained valves and small diameter tubulations, particularly

the weighing flasks and the calorimeter container.

* The temperatures given are believed to be accurate to ±0.01 degree Kelvin. Wherever temperatures are given to four decimal figures, the last two digits are significant only in the measurement

of small temperature differences. At the Tenth General Conference held in 1954, the General Conference on Weights and Measures adopted a new definition of the thermodynamic temperature scale by assigning the temperature

2 73.1 6° K to the triple-pomt temperature of water. For details regarding the adoption of this new

scale, see reference9. References p. 79 144-71
Each sample of benzene was vacuum-distilled directly from the ampoule, in which

it was received, into a separate weighing container fitted with a valve. After weighing,

the container was attached to the calorimeter transfer manifold and the entire sample

vacuum-distilled into the sample container. When the purity of the uncontaminated

sample (sample A), which was investigated first, was found to be 99.9937 mole %, a

purity considerably lower than anticipated, the weighing containers and all transfer manifolds were thoroughly purged with portions of the sample A and then pumped to a

high vacuum before transferring the subsequent samples. The evacuation of the system

for 24 hours at loo°C and at io-6 mm Hg at the vacuum manifold was considered to be

still insufficient when working with extremely pure substances. Repeated purging and

evacuation were thought to be helpful in cleaning the system. Since another sample of the purest material was not available, tests could not be made to determine

whether the sample A had been contaminated during the transfer to the calorimeter.

The experimental procedure for making the purity measurements was the

following. The heat capacity of the system containing the sample was determined in the

range from about 250 0 to 290°K. Then, the heat of fusion was determined by introducing

a known quantity of electrical energy sufficient to raise the temperature of the system

from just below to just above the triple point and making corrections for the heat

capacity and for the premelting due to the presence of impurity.

The liquid-solid equilibrium temperatures were determined as follows. To avoid local concentration of the impurities, which was considered possible by slow cooling methods,

the sample was rapidly crystallized either in part or in whole, taking the precaution to maintain the filling tube temperature considerably above the melting point of the sample

so that the sample would not condense in the tube. When the sample was partially crystallized, it was allowed to equilibrate by bringing the adiabatic shield into automatic

control. When the sample was totally crystallized, it was heated electrically under

adiabatic control to the desired liquid-solid ratio and allowed to equilibrate. It was

convenient to allow the sample to equilibrate over-night and to observe the liquid-solid

equilibrium temperatures during the morning of the following day. After the liquidsolid equilibrium temperature was established, a known quantity of electrical energy was added sufficient to raise the temperature of the sample to j ust above the triple point

.

If Q is the electrical energy that was added, then Q — jCdT is the energy required to melt the material from the observed equilibrium temperature. The term /CdT is the

heat-capacity correction. Then,

I/F = Lf-(Q-fCdT) (5)

where Lf is the total heat of fusion. In this method any small heat leak that may occur during the prolonged equilibrium interval would not affect the i/F value.

4. Results The results of the measurements of heat of fusion on the benzene samples are given

in Table IX. The results compare favorably with the selected value (9837 abs j mole-1

) given by Rossini et al. 10

. Since sample B was somewhat larger than generally used in the

calorimeter, it was felt that a small amount of the sample could have been condensed

in the tube during the heat-of-fusion measurements. When measurements on all the

References p. 79 145-72
TABLE IX

HEAT OF FUSION OF THE BENZENE SAMPLES

Molecular weight = 78.1140 g; °K = °C + 273.16°

Temperature interval Total energy Corrections Lj „

of heating input heat capacity premelling Total ^ ° K abs > absj absj abSJ

abs j mole-'

Sample A, mass of sample = 76.6591 g 274.9985 to 282.2772 11005.6

275.8612 to 281.2168 10650.4

275.701 1 to 280.8662 10611.4 275.6013 to 282.2809 10899.3

271. 1321 to 281.4924 11556.2

Sample B, mass of sample = 90.3655 g 260.7869 to 281 .5943 15601.4 Sample B, mass of sample = 76.0445 g

261.1786 to 282.3869 13401.5

Sample C, mass of sample = 86.3014 g 268.5729 to 281.0443 13345-9 257.9009 to 280.7212 X5296.1 271.6529 to 281.3753 12785.3

1357-1 10.6 9659.1 9842.4

,,,)S

, 13-9 9665.9 98493

961 .2 13. 1 9663.3 9846.7

1247.8 12.7 9664.2 9847-5

I907.9 5-i 9653 4 9836.6 Mean 98445

Standard deviation of the meana ±2.3

4214.2 4-5 II39I-7 9847.2

3824.8 3.9 95 8 °- 6 9841-3 Mean 9844.2 Standard deviation of the mean ±3-o

2499.7 35.6 10881.8 9849.4

4452.5 16.7 10860.3 9830.0

1957-° 52.0 10880.3 9848.1 Mean 9842.5 Standard deviation of the mean ±6.3

a Standard deviation of the mean as used above is defined as [,L'd2/w(n—i)]'/s; where d is the

difference between a single observation and the mean, and n is the number of observations. TABLE X

LIQUID-SOLID EQUILIBRIUM TEMPERATURES OF BENZENE, SAMPLE A

j/F Treatment of sample^ Tobs b °K

^ calc °K

Tobs 1 calc °K

8.844 H 278.6450 278.6445 0.0005

7-703 C 278.6486 278.6492 —0.0006

5.05I C 278.6603 278.6601 0.0002 3l65 C 278.6672 278.6679 —0.0007

2.221 II 278.6718 278.6718 0.0000

2.088 c 278.6720 278.6723 —0.0003

I.287 c 278.6762 278.6756 O.OO06

I. OOO 278.6768

Triple-point temperature, 278.68o9°K or 5.5209°C.

Slope, —0.0041 1 F°K.

Impurity, 0.0063 ±0.0010 mole %c.

a The symbol C indicates that the sample was rapidly crystallized and the symbol H indicates that the sample was rapidly crystallized and heated to the i/F values given.

t> These temperatures were obtained from the relation °K = °C + 273.1600° and are believed

to be accurate to ;ho.oi 0 K. The last two decimal places are significant only in the measurement

of small temperature differences.

c The uncertainty was estimated by examining the imprecision of the measurements and all known sources of systematic error. The system was assumed to follow the ideal solution law and

to form no solid solution with the impurity.

References p. 79 U6-73
samples were completed, the heat-of-fusion measurements were repeated using about

84 % of the original sample B. The results indicate that a negligible amount, if any, was in the tube during the first measurements.

278.70

I/FRACTION MELTED

Fig. 8. Liquid-solid equilibrium temperatures of the benzene samples at various i/F values.

The observed liquid-solid equilibrium temperatures and the corresponding i/F values

are summarized in Tables X, XI, and XII, for the benzene samples A, B and C, respectively, and are plotted together in Fig. 8. The values of temperatures given

in column 4 of these tables were calculated from equation (4) using the values of 7V2* and

Tf *P as determined from a linear equation fitted to the experimental data by the method

of least squares. The comparison of calculated and observed liquid-solid equilibrium

temperatures gives an indication of thermodynamic equilibrium, of ideality of the

solution, and of formation of solid solution in the range of the experiments.

The cryoscopic constant used in the various calculations was 0.01525 (°K)_1

, based on the triple-point temperature, Tf fP, and the mean heat of fusion obtained on the

TABLE XI

LIQUID-SOLID EQUILIBRIUM TEMPERATURES OF BENZENE, SAMPLE B

zIF

Treatment o) sample* Tobs b °K Tcalc °K

2.100 H 278.6212 278.6221 —0.0009

1-735 H 278-6339 278.6322 O.OOI7

1.484 H 278.6387 278.6391 —O.OOO4

1. 187 H 278.6458 278.6473 —O.OOI5

1.047 H 278.6518 278.6511 O.OOO7

1. 000 278.6525

Triple-point temperature, 278.6799°K or 5.5I99°C.

Slope, —o.o275F°K.

Impurity, 0.042 ±0.005 mole %c.

a See footnote a, Table X.

b See footnote b, Table X.

c See footnote c, Table X.

References p. 79 147-74
purest sample A. The values obtained with sample A are considered to be the most

nearly accurate. The T/JP value 278.68oc) 0 K, when reconverted to degrees Celsius,

becomes 5. 5209X. Considering the imprecision of the measurements and the various

sources of errors, the uncertainty in the value of 5.5209X for the triple-point temperature of pure benzene was estimated to be io.ooSoX including the uncertainty of i 0.0030X in the determination of the temperature. Mathieu11 reported the value

5.524°C for the triple-point temperature of pure benzene.

The samples were allowed to equilibrate at least 16 hours, and the temperatures

observed during the next 4 hours did not change in any instance by more than 0.0002

degree. The prior treatment of the sample, whether it was partially crystallized rapidly

or totally crystallized rapidly and melted to the desired i/F value, did not seem to give

any definite trend in the results. The deviations of the observed liquid-solid equilibrium

temperatures from the calculated values are scattered and are somewhat larger than

those observed in previous investigations in which successive liquid-solid temperatures were observed during a single day by melting the same crystal stepwise and allowing

shorter time intervals (about 1 to 2 hours) for equilibrium 12 ' 13

. The measurements of the temperature using the same bridge and thermometer over a relatively short

TABLE XII

LIQUID-SOLID EQUILIBRIUM TEMPERATURE OF BENZENE, SAMPLE C

ilF

Treatment of Tobs* Tcalc ^obs ^calc sample3' °K "K °K

4-905 c 278.5092 2 78. 5°7 2 0.0020

3-733 H 278.5461 278.5476 —0.0015

2.998 C 278.5716 278.5729 —0.0013

2.492 H 278.5891 278-5903 —0'.OOI2 2.040 II 278.6054 278.6059 —O.OOO5

1-651 11 278.6201 278.6193 O.OO08

1. 321 C 278.631 2 278.6307 O.OOO5

1.226 c 278.6350 278.6340 O.OOIO

1.000 278.6418

Triple-point temperature, 278.6764°!^ or 5.5i64°C.

Slope, —o.o346F°K.

Impurity, 0.053 ±0 005 mole %c .

a See footnote a, Table X.

b See footnote b, Table X.

c See footnote c, Table X.

range of temperature, are considered to be reproducible within about 0.0002 0 from

day to day. The observed deviations greater than these amounts may arise from the

differences in the crystallization process14

, although the crystallization was thought to be well controlled, and the non-equilibrium conditions even after 16 hours. Since the

calorimeter was operated at a temperature very close to room temperature, a small

amount of benzene and w-heptane may have condensed in the filling tube during the long equilibrium period. Both benzene and w-heptane have sufficient vapor pressure

at 5°C to condense on the tube if any portion of the tube is colder than the sample

container. The contribution to the deviation from this source, however, is considered

References p. 79 148-75
to be fairly small, unless there is a preferential condensation of n-heptane, which

is unlikely.

A series of controlled experiments is required to resolve these small differences. Continuous measurements of the liquid-solid equilibrium temperatures could be made at various l/Fvalues by successively melting a crystal formed by both rapid crystallization

and by slow crystallization. These measurements could be made at equilibrium times

equivalent to those involved in manually controlled measurements and at the pro- longed equilibrium times possible in automatic controlled measurements. At the

writing of this report sufficient data have not been accumulated on these measure- ments for presentation.

V. CONCLUSIONS

The analyses by thermometric and calorimetric procedures can now be compared with

the anticipated purities based upon the methods of preparing the three samples A, B,

and C. For this, the assumptions are made that the uncontaminated benzene was pure

beyond any power of either method to disclose the impurity and that the contaminations

had proceeded exactly in accord with the plans and calculations. Table XIII shows two effects that were unexpected before the final assemblage of data. These effects can serve as valuable guides to future work, however. First, the

large divergence between the thermometric and the calorimetric analyses that had

characterized earlier comparisons, both in our own laboratories and elsewhere, is not

displayed. The differences between the analyses on all three samples are roughly of the

order of the statistically estimated uncertainties of the averages andless than deviations

between individual experiments by one method. The inherent evidences of accuracy are good and both groups of workers completed their tasks with a sense of confidence.

Second, both forms of analysis gave results that differed significantly from values

computed by the amount of contaminant that had been added.

TABLE XIII COMPARISON OF THE RESULTS FROM THERMOMETRIC AND CALORIMETRIC ANALYSES WITH THE VALUES COMPUTED FROM CONTAMINATION

Sample

Purity, mole %

Excess of purity computed from amount of deliberate contamination above average of analysis by thermometric and calorimetric processes

Computed front contamination Thermometric

analysis Calorimetricanalysis A iooa 99.994 ±0.002 99-9937 ±o.ooiob O.006 B 99.9964 99-97o ±0.004 99.958 ±o.oo5b 0032

C 99.9610 99-94o ±0.002 99.947 ±o.oo5b 0.017

a The "pure" sample was assumed to be pure beyond the sensitivity of the methods of analysis employed.

b See footnote c, Table X.

It should not be too surprising that the earlier differences between the methods

should have become much reduced. Both sets of analyses were performed under the

conditions mentioned in the introduction -— "that each method would be utilized in the manner believed by its practitioners to be most dependable." The result is that

References p. 79 149-76
there were significant modifications of procedure or interpretation of data by both

groups. In the thermometric experiments the greatest change, except for refinements of temperature measurement were modifications of the means of interpreting data. It has been

known that, when TfJP is calculated by the method of Taylor and Rossini, the values

become progressively higher as purer samples are employed. In the present work,

although the same fundamental method is used, slightly modified criteria were employed to select the usable portion of a freezing curve and for calculation both of

ideal and actual points of initial freezing. In the calorimetric analyses the principle changes were experimental, there being

two important changes of technique. The time of equilibration was greatly increased

both to attain temperature stability and to allow diffusion of impurities within the

liquid phase. Furthermore, the thermal history of each run was changed in such ways

that very little separation of the impurities from the rest of the sample could occur. On the second point, the difference between the analyses and the assumed purity

of the samples as prepared and contaminated, an important clue is found in data of Table I. The first two runs were made on a Friday after the benzene had been introduced

into the freshly heated and exhausted apparatus. The sealed apparatus remained un- used until the following week when the other runs were made and a much larger amount

of impurity was disclosed. On this basis subsequent runs were made by conditioning

the interior of the apparatus with benzene of high purity. This can account for the

difference between Table I and those that follow. Observing, both on the assumed

"pure" sample and on the several contaminated samples, that the impurities found

exceeded those anticipated more or less in relation to the number of times that a benzene

sample had been introduced into a flamed and exhausted glass vessel without contact with air, it is beguiling to infer that flaming with exhaustion does not adequately

prepare glass to receive benzene without contaminating it. In the body of the paper it was suggested that chemi-sorbed water might be a source

of contamination. This inference was drawn before the assemblage of data disclosed

the difference between assumed and determined purities. Whether it is true or not may

possibly be disclosed by experiments now in progress, but in any event the evidence

is strong that it is difficult to manipulate benzene in glass in such manner as to preserve

a state of high purity. The results of this investigation strongly indicate that additional series of closely controlled experiments need be performed to determine (a) the source of discrepancies previously found between the thermometric and calori- metric methods of analysis and (b) the- sources of contamination during the handling

of the benzene samples.

SUMMARY

Workers at the National Bureau of Standards and elsewhere have been conscious of the discordant

results sometimes yielded by two methods for determining purity employing the same physical

principle. A comparison was made on samples of benzene by the thermometenc method, by which

a stirred sample is frozen at nearly constant rate, and by the calorimetric method, by which a frozen sample is melted in stages by the addition of accurately controlled increments of energy under

adiabatic conditions. Benzene, purified by single crystal formation and of very high purity, was contaminated in known amounts by w-heptane and samples of the same level of purity determined by both procedures. Great care was taken to submit samples of the same composition to the different groups employing the two different methods. Further, the actual degree of contamination of the benzene was unknown to both groups until final values of the purity were submitted.

References p. 79 150-77
Results of this comparison showed that the large divergence between the two methods that had

characterized earlier comparisons is not displayed. The differences between the analyses on all three samples are roughly of the order of the statistically estimated uncertainties of the averages and

less than deviations between individual experiments by one method. Comparison of the methods with absolute values of purity could not be made because of contamination of the highly purified sample of benzene with supposedly chemically adsorbed water from

the borosilicate glass walls. RESUME

Des chercheurs au Bureau National des Etalons des Etats Unis et ailleurs se sont rendu compte

du fait que Ton obtient parfois des resultats discordants lorsque Ton determine une purete par deux methodes basees sur le meme principe physique. Dans ce memoire on decrit une comparaison

de determinations de puretes d'echantillons de benzene d'une part par la methode thermometrique

au cours de laquelle un echantillon agite est congele a une vitesse a peu presconstante et, d'autrepart, par la methode calorimetnque oil Ton fait fondre un echantillon congele en etappes en lui fourmssant

des portions d'energie exactement reglees sous des conditions adiabatiques.

Du benzene purifie par formation de cristaux et d'une tres haute purete a ete contamine par des

quantites connues de w-heptane et des echantillons d'un meme degre de purete ont ete examines

par les deux precedes. L'on a pris grand soin de soumettre des echantillons de meme composition aux differentes equipes employant les deux methodes differentes. De plus, les vrais degres de

contaminations du benzene etaient inconnus aux deux equipes jusqu'a ce que les valeurs definitives de puretes furent soumises. Les resultats de cette comparaison ont montre que les grandes divergences entre les deux methodes

qui avaient caracterise les comparaisons plus anciennes ne se produisaient pas. Les differences entre

les resultats des analyses de tous les trois echantillons sont, approximativement, de l'ordre des

incertitudes des valeurs moyennes estimees statistiquement ; elles sont inferieures aux deviations

entre les experiences individuelles par une seule methode. Une comparaison des methodes donnant des valeurs de purete absolues n'a pas pu etre faite a cause de la contamination des echantillons hautement purifies de benzene par de l'eau que l'on suppose etre adsorbee chimiquement a partir du borosilicate des parois de verre.

ZUSAMMENFASSUNG

Forscher im ,, National Bureau of Standards" und anderswo waren sich davon bewusst, dass man

manchmal nicht ubereinstimmende Resultate erhalt wenn man den Reinheitsgrad mit zwei ver- schiedenen Methoden, die sich auf dasselbe physikalische Prinzip griinden, bestimmt. Ein Vergleich

solcher Bestimmungen an Benzolproben wurde nun angestellt, und zwar einerseits mit Hilfe der thermometrischen Methode bei der eine geriihrte Probe mit nahezu konstanter Geschwindigkeit zum Gefrieren gebracht wird, andererseits mit der kalorimetrischen Methode bei welcher eine gefrorene Probe in Etappen durch Zufuhren genau geregelter Energiemengen unter adiabatischen Bedingungen geschmolzen wird. Durch Emzelkristallbildung gereinigtes Benzol von hohem Reinheitsgrad wurde mit bekannten

Mengen re-Heptan verunreinigt und Proben vpn gleichem Reinheitsgrade wurden nach beiden Verfahren gepriift. Es wurde besonders darauf geachtet, dass die verschiedenen Arbeitsgruppen,

die die verschiedenen Verfahren anwendeten, Proben von gleicher Zusammensetzung erhielten. Ausserdem war der wirkliche Verunreinigungsgrad des Benzols beiden Gruppen solange unbekannt,

bis die endgiiltigen Reinheitswerte mitgeteilt waren.

Die Ergebnisse dieses Vergleiches zeigten, dass die grossen Abweichungen zwischen den beiden Methoden, welche fruhere Vergleiche kennzeichneten, nicht auftreten. Die Unterschiede zwischen den Analysen aller dreier Proben waren im grossen und ganzen von der Grossenordnung derstatistisch geschatzten Unsicherheiten der Mittelwerte; sie waren kleiner als die Abweichungen zwischen den einzelnen mit einer selben Methode ausgefiihrten Versuchen. Ein Vergleich der Methoden mit absoluten Reinheitswerten konnte nicht gemacht werden, weil das hoch gereinigte Benzol durch wahrschemlich chemisch adsorbiertes Wasser aus dem Borosilikat der Glaswande verunreinigt wird.

ACKNOWLEDGEMENT

The authors wish to acknowledge the assistance of Marthada V. Kilday, H. B. Lowey, L. A. Machlan, Patricia B. Nails, and O. T. Termini for their help in the various phases of this work.

References p. 79 151-78
REFERENCES

1 M. R. Ones, Physical Chemistry of the Hydrocarbons, Vol. I, Academic Press Inc., New York,

195°. P- 315-

2 M.-P. Mathieu, Acad. roy. Belg., Classe sci., Mem., 28 (1953) Fasc. 2, No. 1639.

3 A. T. Horton, U.S. Patent No. 2, 754, 180, July 10, 1956.

4 A. R. Glasgow, Jr. and M. Tenenbaum, Anal. Chem., 28 (1956) 1907

5 W. J. Taylor and F. D. Rossini, /. Research Natl. Bur. Standards, 32 (1944) 197.

6 F. W. Schwab and E. Wichers, Temperature , its Measurement and Control in Science and Industry,

Remhold Publishing Corp., New York, i94i,p. 256.

7 R. B. Scott, R. D. Rands, Jr., C. H. Meyers, F. G. Brickwedde and N. Bekkedahl,

/. Research Natl. Bur. Standards, 35 (1945) 39.

8 H. F. Stimson, /. Research Natl. Bur. Standards, 42 (1949) 209.

9 H. F. Stimson, Am. J. Phys., 23 (1955) 614.

10 F. D. Rossini, K. S. Pitzer, R. L. Arnett, R. M. Braun and G. C. Pimentel, Selected Values

of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds, Carnegie

Press, Pittsburgh, 1953.

11 M.-P. Mathieu, Bull. soc. chim. Beiges, 61 (1952) 683.

12 G. T. Furukawa, D. C. Ginnings, R. E. McCoskey and R. A. Nelson, /. Research Natl. Bur.

Standards, 46 (1951) 195.

13 T. B. Douglas, G. T. Furukawa, R. E. McCoskey and A. F. Ball, /. Research Natl. Bur.

Standards, 53 (1954) 139.

14 J. P. McCullough, paper presented at the Eleventh Calorimetry Conference , Johns Hopkins

University, September 14 and J5, 1956.

13253 —U.S. Dept. of Comm—DC—1957

Received April 23rd, 1957

Reprinted from Analytica Chi.mica Acta

Vol. 17, Nr. 1, July, 1957

152-79
Journal of Research of the National Bureau of Standards Vol. 52, No. 5, May 1954 Research Paper 2493

A Cryoscopic Study of the Solubility of Uranium in Liquid

Sodium at 97.8° C

Thomas B. Douglas

The equilibrium temperatures, at various stages of melting, of three samples of sodium

were measured with a standard deviation of 0.001 degree. One sample contained uranium

in compact form, and one contained finely divided uranium. Impurities lowered the freezing

points of all the samples by approximately 0.035 degree, but the sodium containing finely divided uranium was found to have a freezing point higher than those of the other two

samples by 0.005 degree, an effect that may be due to a partial purification, of the sodium

by the uranium. After extrapolation to no impurity, the freezing points of the three samples

agree within 0.001 degree. Allowing for errors, it is concluded that the solubility of uranium

in liquid sodium at 97.8° C probably does not exceed 0.05 percent by weight and may actually be many times smaller.

1. Introduction

One of the most sensitive and convenient methods

commonly used to estimate the concentration of a

dilute solution is the comparison of its liquidus

temperatures (freezing points) with that of the pure

solvent, if the solid phases are immiscible. This

method was applied in an attempt to estimate the

solubility of uranium in liquid sodium at 97.8° C,

the triple point of the latter element. The equilibrium temperatures at intervals from 70- to 100-

percent completion of fusion of the sodium were

observed.

2. Experimental Procedure

Three samples were prepared, each containing

6y2 g of sodium from a batch that had been purified

by distillation. In addition to the sodium, the

sample designated as A contained no uranium,

sample B contained 2 g of a solid section of uranium,

and sample C contained 2 g of finely divided uranium

prepared by hydride decomposition. The samples were sealed, by induction welding in an oxygen-free

inert atmosphere, in small cylinders of stainless

steel type 347. Subsequent tests at room temperature and at 150° C indicated leakage through the

seals to be no greater than 4X10-12 cm3 of helium

per second, a rate not taken to indicate a real leak. The apparatus for the cryoscopic measurements

is shown in figure 1 . Each sample was suspended by

a No. 32 nichrome wire in air inside a vertical

furnace, whose core maintained a highly uniform

environmental temperature because it was sur- rounded by a silver pipe 10 in. long and of y2 -in. wall thickness. The temperature of the silver was

measured by a platinum resistance thermometer

whose ice point remained constant to within an amount equivalent to ±0.0005 deg throughout the

measurements. Heat was supplied to the sample at

will by a constantan heater imbedded in a goldplated copper jacket that surrounded the sample

container at an average distance of 0.002 in. A fourjunction differential thermocouple (chromel P versus

constantan), calibrated in place against freezing

sodium, enabled precise measurement of the temperature difference between the silver pipe of the

furnace and the sample.

A detailed systematic procedure was followed in an

effort to make the systematic errors constant and

thereby to secure accurate differences in temperature

among the three samples. With the individual runs numbered chronologically, runs 1, 5, and 9 were on

sample A; runs 2, 3, and 4 were on sample C; and

runs 6, 7, and 8 were on sample B. Run 10 was on a fourth sample of sodium, taken from a different batch

prepared 2 years earlier. Each run was made on a different day.

With the sample in place, the furnace was heated

to a temperature at which melting of the sodium

would just begin, and was then held at approximately

this temperature for the next 3 hr. The sample was then heated lor separated intervals of time until

fusion was clearly complete. Thus at any stage of

the fusion process the fraction of the total fusion

heat that had entered the sample could be taken as a measure of the. fraction of the sodium then present

as liquid. After each such interval of heating, the

equilibrium temperature was measured in the following way. The temperature of the furnace was held

constant (within ±0.0005 deg) at a temperature no more than 0.003 deg higher or lower than the prevailing

sample equilibrium temperature, 1 until the thermocouple reading appeared to be changing by less than

0.0001 deg/nlin. This furnace control was ac- complished by means of a 0.7-w variable auxiliary

heater inside the silver. When the sodium was all crystalline or all molten, the difference between its temperature and that of the furnace decreased by

15 percent per minute owing to heat conduction

through the intervening air spaces. However, during melting the error introduced in this way was

negligible because of the large magnitude of the heat

of fusion and the ease of maintaining then a small

temperature difference.

To each equilibrium temperature found was added

0.012 deg, as the thermocouple reading was found

to approach —0.012 deg when the temperatures of

its junctions were known to be rapidly approaching

1 Reversal of the sign of this temperature difference was used to prove that the thermocouple read the unbiased relative temperature of the sample. 153-223
Figure 1. Apparatus for cryoscopic measurements.

A, Sodium sample (with or without uranium); B, sealed container for sample

(stainless steel type 347); C, suspension wire (Nichrome V); D, platinum re- sistance thermometer; E, isothermal jacket (silver); F, heater for sample (glass- covered constantan); G, thermocouple reference block (gold-plated copper); H,

thermocouple junctions (copper bands or tabs); 1, spacers (nichrome V wire);

J, heater leads (copper); K, jacket for sample container and heater cover (gold- plated copper); L, pins for supporting sample, container; M, auxiliary heater for silver jacket (platinum); N, Inconel tubing; O, alundum tube; P, main furnace

heater (platinum); Q, furnace insulation (silica powder); R, porcelain tube.

equality. In addition, 0.003 deg also was added to correct for the error due to the estimated azimuthal

temperature gradient in the silver pipe.

3. Results and Conclusions

The variation of temperature as the impure

sodium melts may be predicted from Raoult's law.

For very small proportions of impurities entirely

insoluole in the solid solvent (sodium) , this law may

be written in the approximate form

t^-iRTHL^ix.+x,). (1)

In this equation the total mole fraction of all solutes n solution in the liquid sodium has been divided into wo parts. xx designates that part due to solute

hat, if present at all, is sufficient in amount to maintain the liquid sodium saturated with it. (This solute

will be assumed to be uranium only.) x2 designates

that part due to any solute at all times entirely in

solution in whatever liquid sodium is present; t is the equilibrium temperature (in deg C) ; t0 is the

freezing (^triple) point of pure sodium (also in deg C,

the corresponding value in deg K being T0) ; R is the

gas constant; and Lf

is the molal heat of fusion of

sodium.

154-224
It is evident that as fusion of the sodium progresses, the increasing amount of liquid available as solvent

leads to a decrease of x2 but not of X\. x2 may be

replaced by its equivalent, z2 /f, where / is the frac- tion of the sodium present as liquid when the

temperature is t, and x2 is then the value of x2 when

/'is unity. Equation (1) then becomes

t=U-BT%XilLf- (RT2

0x'2 /Lf) (1//). (2)

Substituting numerical values for the known constants (5=8.314 j mole"1 deg K

-\ 210 =371.0° K,

and iy=2603 j mole-1

),

2 eq (2) may be written in the present specific case as follows:

t=t0—440^—440a£(l//>. (3) The points in figure 2 show for various stages of

fusion the individual observed equilibrium temperatures. The chronological number of each run is shown beside its respective points. It may be seen

that for the same sample there is, in general, more

variation from one run to another than in the systematic deviations from linearity of the points of one

run. This is due partly to the errors in the calculated fractions melted, these errors arising chiefly

from the difficulty of determining accurately when

in each run fusion began and ended. The solubility

of the steel container in the liquid sodium 3 should

have caused a constant error of less than 0.001 deg.

This error has been ignored. Temperatures recorded

when fusion was less than 70 or more than 98 percent

complete were always decidedly too high to be in line with the others and were discarded. It seems

likely that these latter discrepancies resulted partly

from lack of the expected thermal and composition

equilibrium, under these less favorable conditions,

as the samples were neither shaken nor stirred. Also,

the solubility of unidentified impurity may have

been exceeded until a large fraction of the sodium

had become molten.

Equation (3) predicts that as fusion progresses, the temperature will increase linearly with the decrease in 1//. In figure 2 the straight line for each

sample was obtained from the observed points by

the method of least squares. The corresponding

numerical values of the coefficients of eq (3), together

with their standard deviations (precision) , are shown

in table 1. Several conclusions may be drawn from

these values.

Table 1. Coefficients of equation (3) for three samples

Sample (o-440ri 440r2

'

A

°c

97. 8199 (±0. 0056)

97. 8208 (±0.0033)

97.8202 (±0.0025)

°C

0. 0349 (±0. 0048)

. 0379 (±0. 0028) .0297 (±0. 0021) B

C

2 D. C. Ginnings, T. B. Douglas, and A. F. Ball, J. Research NBS 45, 23 (1950) EP2110.

3 L. F. Epstein (private communication). 155

9 97.792 • Al0

97.768 I I , i i Z ,_

1.0 1.1 1.2 1.3 1.4 1.5 RECIPROCAL OF FRACTION MELTED Figure 2. Observed equilibrium temperatures. • _, sample A (sodium); Q .sample B (sodium

plus bulk uranium); 3 , sample C (sodium plus finely divided uranium); A. sample D (an earlier sodium sample). The run numbers given with the points are in chronological order.

From consideration of the details of purification

of the sodium, it appears that the impurity with

respect to which the liquid sodium was unsaturated

may well have been largely sodium oxide, Na2 0.

The values of the third column of table 1 give immediately the corresponding values of x'2) the mole

fraction of this type of impurity in the whole sample.

This averages 8X10-5 for samples A and B. This

value corresponds to 0.02 percent of Na2 0 by weight,4 a reasonable amount of impurity from this source as

it corresponds to the order of magnitude of the solubility of Na2 0 in liquid sodium at this temperature.

The corresponding quantity for sample C is some- what lower than that for sample A, the difference

having a standard deviation equal to the difference

itself. It is possible that sample C actually contained substantially less impurity of this type, for

the large surface of the finely divided uranium in

this sample may have led to the removal of a considerable amount of the original impurity. Such a hypothesis is supported by the known ability of

uranium to remove oxygen from Na20 at higher

temperatures.

If it be assumed that sample A, into which no uranium had been introduced, was free of all other

"saturated" solutes, the value of t0 —440a-! for this sample from table 1 gives 97.82° C as the triple point

of pure sodium, and from a consideration of the

* If the effective molecular weight of NS2O be taken equal to its formula weight. 225
various likely instrumental errors, this value is estimated to have an absolute accuracy of ±0.02 deg.

Earlier measurements on another sample of sodium,

using a less stable copper resistance thermometer, had

similarly yielded 97.80 ±0.03° C (see footnote 2).

The differences among the three values of the

second column of table 1 will now be examined.

Unless the uranium in samples B and C was completely protected from the sodium by some insoluble

surface film, the values for these two samples should

be lower than that for sample A by amounts (440^)

corresponding to the solubility of uranium in liquid

sodium at this temperature.5 These differences,

with their standard deviations, are as follows: For

sample B, 440xi = -0.0009° ±0.0067°; and for sample C, 440*1= -0.0003° ±0.0058°. These dif- ferences are thus zero within the precision of their

measurement. The probability that the real differ6 It seems very unlikely that uranium is appreciably soluble in solid sodium.

ences exceed 0.02 deg is very small. This figure

would correspond to a value of xt of 5X10-5

, equivalent to 0.05 percent by weight of uranium dissolved

in the liquid sodium if the dissolved uranium is monatomic. It is accordingly concluded from these

measurements that the solubility of uranium in liquid sodium at 97.8° C probably lies between 0.00

and 0.05 percent.

It seems likely that a radioactive tracer method

would furnish a more definite value for this solubility.

This work was supported by the Atomic Energy

Commission. The author thanks C. E. Weber, of the

Knolls Atomic Power Laboratory, Schenectady,

N. Y., for supplying the sealed samples, and D. C.

Ginnings, of the Bureau, for advice in designing part

of the apparatus.

Washington, December 31, 1953.

156-226
3. Low Temperature

Calorimetry

Page

3.1. Continuously operating He3 refrigerator for producing temperatures

down to %° K.

Ambler, E., and Dove, R. B., Rev. Sci. Instr. 32, No. 6, 737-739

(June 1961).

Key words: Low temperature calorimetry, He3 refrigerator- 159

3.2. Apparatus for determination of pressure-density-temperature rela- tions and specific heats of hydrogen to 350 atmospheres at temperatures above 14° K.

Goodwin, R. D., J. Res. Nat. Bur. Stand. (U.S.) 65C, (Eng. and

Inst.) No. 4, 231-243 (Oct.-Dec. 1961).

Key words: PVT measurements at low temperatures, gas

heat capacities, and densities 162

3.3. Detection and damping of thermal-acoustic oscillations in lowtemperature measurements.

Ditmars, D. A., and Furukawa, G. T., J. Res. Nat. Bur. Stand.

(U.S.) 69C (Eng. and Inst.) No. 1, 35-38 (Jan-Mar. 1965).

Key words: Heat transfer by gas oscillations 175

157

Continuously Operating He3 Refrigerator for Producing Temperatures down to |°K

E. Ambler and R. B. Dove

National Bureau of Standards, Washington 25, D. C. (Received January 13, 1961)

A continuously acting, portable, He3 refrigerator is described. The He3 is recirculated in a system that operates without mechanical pumps. The throttling of the returning liquid is accomplished by means of a porous plug. Good

regulation is obtained by using a system that allows the pressure across the porous plug to vary with the circulation

rate. The lowest temperature reached while circulating is 0.26°K at zero "external" heat input, and 0.40°K at 2mw.

TT is well known that the relatively high vapor pressure

at any given temperature and absence of film flow in He3 constitute considerable practical advantages over He4

for producing very low temperatures by evaporation under

reduced pressure. Although a lowest temperature12 of 0.71°K has been reached with He4

, a more usual limit for convenient operation is in the range 1° to 0.8°K. With

He3

, temperatures down to 0.35°K can be reached very

easily, while a practical limit could be taken to be 0.25°K.

A number of He3 cryostats have been described,3-6 most

of which have been discussed and compared in a review

article7 on He3

. We wish to describe a cryostat in which the lowest temperature reached comes close to what might be

considered a lower practical limit, and which can, with good

temperature regulation, cope with rather large heat inputs.

Novel features in the design consist of an automatic device

for throttling the liquid He3 returning to the evaporator,

and the use of a mercury ejector pump (without mechanical

backing pump) for circulating the He3

. The cryostat was designed in connection with experimental work on nuclear reactions with oriented nuclei,

and in this connection it is worth noting a fact that has

been realized for some time, viz., that at the temperatures

obtainable with a He3 refrigerator a significant degree of nuclear orientation can be obtained with a number of nuclei (e.g., Ho, Tb, U, Np), without further cooling (i.e., by magnetic cooling). It was desirable that the refrigerator

have the following features

(a) It should be continuously operating; therefore, a

refluxing system for the He3 is used.

(b) It should be portable and self-contained in order

to be movable from one particle accelerator to another.

(c) It should be fast, i.e., it should be possible to recycle

from the lowest temperature to 1°K, or higher, quickly.

1 W. H. Keesom, Communs. Kamerlingh Onnes Lab. Univ. Leiden No. 219(a), 1 (1932); Proc. Roy. Acad. (Amsterdam) 35, 136 (1932).

2 B. G. Lasarev and B. N. Eselson, J. Exptl. Theoret. Phys. U.S.S.R.

12, 549 (1942).

3 S. G. Sydoriak and T. R. Roberts, Phys. Rev. 106, 175 (1957).

4 G. Seidel and P. H. Keesom, Rev. Sci. Instr. 29, 606 (1958).

6 H. A. Reich and R. L. Garwin, Rev. Sci. Instr. 30, 7 (1959).

6 V. P. Peshkov, K. N. Zinov'eva, and A. I. Filimonov, J. Exptl. Theoret. Phys. U.S.S.R. 36, 1034 (1959) [translation: Soviet Physics —JETP 9, 734 (1959)].

7 V. P. Peshkov and K. N. Zinov'eva, Repts. Progr. in Phys. 22, 504 (1959).

In this way measurements can be done alternately with

oriented and unoriented nuclei. Before describing the apparatus, we should like to mention one fact that is of importance for the detailed design

of targets refrigerated to such low temperatures in this way, viz., that allowance must be made not only for the

relatively low thermal conductivity of liquid He3

, but also

for the Kapitza thermal boundary resistance. 7 We shall discuss these points in a later paper on the detailed design

of a scattering chamber. For the present we shall give details of the refrigerator only.

The cryostat is shown schematically in Fig. 1. The overall diameter of the cryostat, which is about 10 cm ex- clusive of helium and nitrogen Dewars, is determined by

J

1-inch

Fig. 1. Schematic diagram of the He3 cryostat. The He4 Dewar and nitrogen Dewar are not shown. 159-737
the diameter of the pumping tubes required, i.e., 2 cm at

liquid helium temperatures, 4 cm at liquid nitrogen temperatures, and 10 cm at room temperature. The over-all length of 100 cm is determined by the allowable evaporation rates of the refrigerant liquids. The He4 Dewar has a

capacity of about 1-J liters, and starting from liquid nitro- gen temperature, may be filled by taking \\ liters from

the transport Dewar. The average evaporation rate allows an operational time of about 15 hr, although, of course, by

repeated transfers the cryostat can operate indefinitely.

A separately pumped He" space A, which is filled from the He4 Dewar through a needle valve V, is incorporated to allow a low temperature to be reached (0.82°K) with

smaller, more portable, 8 pumps than normally required

when the helium Dewar is pumped directly. A lower temperature at A yields a smaller heat influx into the He3 evaporator E, both through heat conduction and by the

refluxing liquid He3

. The vapor pressure of He3 at the temperature of A is about 3 mm Hg, so that by placing there the He3 condenser

C, a system is obtained that will operate with a maximum

pressure in the He3 system slightly in excess of this. Thus

the vapor is condensed from a pressure well below the backing pressure of many mercury ejector pumps, and a system can be constructed without using mechanical pumps

of any kind. This gives a simple, quiet, fast system which

can be made vacuum tight very easily, and which requires,

furthermore, a minimal amount of He3

. No special meas- urement was made to see how little was needed for operation, although the 2 cm3 of liquid He3 available tousproved

to be more than sufficient. Since most of this is used infilling the "dead volume" of the condenser and associated tubes,

it is felt that by suitable minor modifications, it should be

possible to operate with a significantly smaller amount of liquid He3

. Although we should like to emphasize that the mercury

ejector pump used9 would have been adequate by itself, an oil diffusion pump with a nominal speed of 300 liters/sec was also incorporated in series. This enabled us to use a

previous pumping and circulating system,10 originally

designed for use with another less suitable type of ejector

pump. The oil pump was used without trap or baffle. Apart from liquid nitrogen cooled traps on both sides of the mercury pump and a very small trap T packed with copper wire and placed in the He4 Dewar, no special clean- ing of the He3 is done.

8 We used a Welch mechanical pump, type 1397, and a Consoli- dated oil diffusion pump, type MCF 300.

9 We used an Edwards high vacuum pump, type 2M4

10 Preliminary measurements show, nowever, that changing the temperature of the space A through the interval 0.8° to 1°K does not

alter significantly the overall performance of the He3 refrigerator. It appears, therefore, that both oil diffusion pumps, i.e., that used in pumping the He3 and that used in pumping the He4

, may be omitted. This leaves an extremely simple and compact arrangement, involving

only one mechanical pump for pumping the He4

, and one ejector pump for pumping the He*.

(a) (b)

Fig. 2. Details of two different types of evaporator used in the He3 cryostat.

The throttle H which allows the liquid He3 to expand into the evaporator consists of a plug of porous stainless steel. 11 The plug is swaged inside a copper tube which is in turn connected thermally to the evaporator £see Fig. 2(a)].

The pressure across the plug adjusts automatically to the

circulation rate, by a rise in the discharge pressure of the

ejector pump. With this arrangement there is no possibility

of troublesome vapor locks forming on the one hand; and

on the other hand, regulation is achieved with quite a small net change of liquid He3 in the evaporator. The minimum

pressure across the throttle is approximately equal to the vapor pressure at 0.82°K, i.e., about 3 mm Hg, and the maximum pressure is equal to the largest tolerable dis- charge pressure of the ejector pump (~35 mm Hg). The

maximum heat input (2mw) at which the refrigerator

will operate at present is governed by the pressure, at the discharge side of the ejector pump, rising above this value. At this heat input, the circulation rate is about the maximum that can be carried by the pumps.

The use of a storage container with a large volume

enables the He3 gas to be stored very simply after the ex- periment at the discharge pressure of the ejector pump.

Other components shown in Fig. 1 are the tube G, for pumping the He4 bath, the tube P, for pumping the He3 bath, and the tube D, for measuring the He3 vapor pressure.

S's are radiation baffles, L is a platinum to soft glass seal for bringing electrical leads into the vacuum case, and J

is a fitting that may be interchanged, as required, for the performance of different experiments. The copper link K

connects thermally all tubes in the vacuum case to the

11 We found that a cylinder, \ in. long, \ in. diam., of Micrometallic

Corporation, type H porous stainless steel to be suitable. 738
He4 pumping tube in such a way that maximum use12 is made of the latent heat in the He4 film creeping up G. The

volume available for experiments at He3 temperatures is about 500 cm3 with the present arrangement.

Measurements have been made with two types of evaporator shown in detail in Fig. 2(a) and (b). The temperature was determined by means of the He3 vapor pressure3 transmitted on a static line (0.386 cm radius) and measured on a McLeod gauge. Corrections were applied for thermomolecular pressure.

13 An electrical resistance F is used to provide a heat input, when required, and is used both to check the performance of the refrigerator and to recycle the temperature rapidly by evaporating off the liquid He3

. Copper fins B are included to give a large surface area for heat transfer. The results obtained with the apparatus shown in Fig.

2(a) are given in Fig. 3, where we have plotted vapor pres- sure and temperature against the heat dissipated in F. We should point out that the pressure at the intake of the He3 pump remained low throughout the run so that the

pressure given in Fig. 3 is for all practical purposes the

pressure drop down the pumping tube. The lowest temperature reached was computed to be

0.26°K. Since the thermomolecular pressure corrections

at these temperatures were very large, it was decided to verify these measurements by using a magnetic thermometer, calibrated only at the higher and more certainly established temperatures. In order to do this it was neces0 500 1000 1500 2000 HEATER INPUT -/i watts

Fig. 3. Performance .of the He3 cryostat using evaporator shown in Fig. 2(a). The abscissa is the heat input, the right-hand scale of the ordinate refers to the temperature reached, and the left-hand scale

to the pressure in the evaporator.

12 E. Ambler and N. Kurti, Phil. Mag. 43, 1307 (1952).

13 T. R. Roberts and S. G. Sydoriak, Phys. Rev. 102, 304 (1956).

0 1 .0 2.0 3.0 4 0 l/T

Fig. 4. Throw of ballistic galvanometer 6 against l/T, where T is the temperature determined from vapor pressure measurements,

obtained using the apparatus shown in Fig. 2(b).

sary, for practical reasons, to alter the apparatus to the form

shown in Fig. 2(b). The vapor pressure bulb N is sealed with a gold O-ring O, and contains a \ in. diam sphere of chromic methylammonium alum M. The change in sus- ceptibility of the salt was determined ballistically, using a niobium primary Pr, and copper secondary Sc, with compensator Sc' wound around N. From the vapor pressure measurements we computed the temperature as before,

and plotted the reciprocal against the ballistic throw 5 in Fig. 4. Since it is known that the susceptibility of the

salt shows little deviation from Curie's Law in this temperature range, this plot should give a straight line. It can be seen that this is so except for the points at the lowest temperatures, where there appears to be a small deviation. This deviation is thought to arise through the evaporator

being at a temperature slightly lower than the salt space, and the vapor pressure indicated of course being that of the coldest part of the system, viz., the evaporator. On

assuming this to be the correct explanation, we can con- clude from Fig. 4 that the salt cools to nearly 0.27°K and

the evaporator to 0.26°K; the latter figure is in good agree- ment with the measurement using the evaporator shown in Fig. 2(a). Finally we should point out that an important advantage

of an arrangement of the type shown in Fig. 2(b) over that shown in Fig. 2(a) lies in the fact that in the former case

a completely enclosed He3 system can be built, which need

not be broken into on changing specimens or setting up

a different kind of experiment.

Reprinted from The Review of Scientific Instruments, Vol. 32, No. 6, 737-739, June, 1961

161-739
JOURNAL OF RESEARCH of the National Bureau ot Research—Engineering and Instrumentation

Vol. 65C, No. 4, October-December 1961 Apparatus for Determination of Pressure-Density-Temperature Relations and Specific Heats of Hydrogen to

350 Atmospheres at Temperatures Above 14 °K*

Robert D. Goodwin

(June 20, 1961)

Method and apparatus are designed for more rapid determination of accurate, closelyspaced, PVT and specific heat data than realized by previous procedures. A sequence of pressure-temperature observations at nearly constant density is made by a modified Reichsanstalt method. Temperatures of the essentially adiabatic piezometer are regulated by

electric heating under control of the measuring thermometer. Instruments for measure- ment and control are integrated with a high-pressure calorimeter for compressed liquid and

fluid. Calorimetric experimentation is accelerated by use of an electronic battery for the

calorimetric heat supply and of a d-c power regulator developed for automatic shield control. Details are given of the PVT calibrations, adjustment computations, and comparisons with

independent data.

1. Introduction

The high-density physical properties of hydrogen

are needed for technological applications [5, 10]. Thermodynamic functions may be computed from

certain thermal data combined with a wide range of

precise mechanical properties (PVT) and vaporpressure data [1, 2, 3, 9]. The purpose of this paper

is to describe the essential features of apparatus

used to obtain PVT data for parahydrogcn from 16 to 100 °K and from 2 to 350 atm, and to obtain specific

heats of compressed liquid and fluid in the same

range. Advent of high-speed digital computers

renders practical the handling of a large quantity of

data, produced by closely-spaced observations with

accelerated methods to be described.

2. Experimental PVT Method

The PVT method and its numerous calibrations are emphasized in preference to the better-known

calorimetric techniques, outlined below. The popular Burnett method for PVT determinations [17] is not suitable for compressed liquids [9]. That of

Holborn and coworkers [20, 21, 22], termed the

Reichsanstalt method [2], involves essentially direct

measurement of each variable. As employed by

Michels and coworkers, a sample of fluid of known

PVT behavior at normal temperature is confined in the piezometer and pressure gage system at that

temperature. Pressure of the sample then decreases

rapidly with temperature of the piezometer [25]. In the Ohio State University modification for gaseous

states, adjustments for obnoxious volumes of capillary and gage were eliminated by placing a valve in the cryostat. This necessitated an independent de-

* Contribution from the Cryogenics Engineering Laboratory, National Bureau

of Standards, Boulder, Colo.

termination of the amount of sample following every

P-T determination [24]. For liquid states they employed a boiling hydrogen thermostat. Successive

small portions of the sample were released from the

piezometer or "pipet" to obtain a series of isothermal P-v determinations from a given filling, each

P-v point again requiring an independent volumetric determination [23]. Average time per determination is greatly reduced

in the present method. Temperature of the nearly

adiabatic pipet is varied to obtain a series of P-T

determinations at nearly constant density. Temperatures are automatically controlled at exact, in- tegral values, to permit handling the data as isotherms. Only one determination of the amount

of sample is required following each experimental

"pseudo-isochore". The portion of the total sample

which was in the pipet during each P-T determination

is calculated by subtracting the computed amounts

residing simultaneously in capillary and diaphragm

cell under those conditions. For this small adjustment, the known and estimated PVT behavior of

normal hydrogen is employed.

With reference to figure 1, a sample of the experimental fluid is confined by valve C-4 to the following

system: the heavy-walled copper pipet, the stainless

"transition" capillary tube in the cryostat, the capillary tubes and valves at room temperature, and the

pressure-sensitive diaphragm cell (N. P. D.). Vol- umes of these elements are calibrated independently.

The latter transmits pressure of the fluid to the oil of a piston-type, deadweight gage- With reference to

figure 2, liquid hydrogen refrigerant resides in the

tank. The pipet is cooled strongly as required by

liquid hydrogen reflux action from hydrogen gas in- troduced to the thin-walled, stainless steel "reflux"

tube supporting the pipet. For automatic temperature regulation by electric heating, under control of

162-231
B-l B-2

Figure 1. Pneumatic apparatus for PVT determinations.

A, Connection to thermal conductivity analyzer. B-l, Absorbent bomb at 7ii °K.

B-2, Iron-oxide, ortho-para catalyst bomb at lif.O °K.

U-3, Thermal pump bombs.

C, Check valves COMM., Commercial hydrogen.

D, Bursting disk. DWG, Dead weight gage. G, Gas buret. L, Mercury leveling screw.

M, Precision manometer. NPD, Null pressure detector.

!', Oil press. K, Relief valves.

S, Sampling connection. T, Reflux gas dose tank. V, Philips vacuum gauges. W, Water-bath thermostat. X, Exterior vent lines.

the platinum resistance measuring thermometer, gas

pressure in the reflux tube is reduced to provide controlled cooling by gas convection, aided by a copper

rod suspended in this tube.

An experimental run consists of measurement of a sequence of pressure versus temperature points, beginning at the lowest, temperature. The total quantity of confined fluid then is determined by releasing

it as gas into volumetric system I) of figure I and

measuring P, V, and T at about normal conditions,

accounting also for the gas remaining in till obnoxious

volumes and in the pipet at this pressure. Experimental time required for filling and ,,x>tying the

pipet is greatly reduced through capaonity of the

commercial, null-pressure diaphragm instrument to withstand high-pressure imbalance without damage.

About 30 points on a pseudo-isochore tire determined

routinely in 8 hr by 2 or 3 men.

3. Sample Preparation, Handling, and

Analysis

By mass-spectral analysis, electrolytic hydrogen

in clean steel cylinders at 2,000 psig contains less than 5 ppm helium and 100 ppm air, respectively.

The preparation system on the left of figure 1 litis three functions. Impurities are absorbed at 76 °K

in B-l on 20 ml of 1.6 mm diam extrusions of "molecular sieve" silica [71]. The paramodification of hydrogen is produced catalytically in B-2 at 19.6 °K

on 10 ml of "30-100 mesh" particles of an iron oxide,

batch 48-C, used in activity studies [72]. Small disks

of sintered stainless steel retain the fine solids in their

containers. Two stainless steel bombs, B-3, each of

about 20 ml capacity, may be immersed in liquid

nitrogen to provide a two-stage, thermal pump for

boosting the parahydrogen pressure. Solidification

of hydrogen at the catalyst is avoided by placing the

catalyst ahead of these pumps in the train. The hydrogen cylinders, preparation system, liquid hydrogen transport Dewar, cryostats and vacuum pumps

tire separated from the instrument room by an ex- plosion-proof Willi. Valve manifold C in the instrument room uses a bourdon gage as a doser for filling

the pipet. to selected densities and for controlling re- lease of the pipet sample to the gasometer system D.

Systems B and C of figure 1 tire assembled with

Jie-in. o. d. stainless steel tubing and high-pressure

midget valves with solid stems and polytetrafluoroethylene O-ring packings. Shop-fabricated gage connectors force a small, drilled, metal cone against a

conical recess on the gage stem. This special fitting

is necessary to avoid contamination of the gas. Bourdon gages for hydrogen must be phosphor-bronze,

beryllium-copper, or type 316 stainless steel [75]. Analysis for parahydrogen is performed on gas

bled from valve C-S at 100 ml NTP/min through a thermal conductivity instrument [58]. Calibration

depends upon parahydrogen produced independently.

In preliminary studies the rate of conversion of parato orthohydrogen in the pipet at pressures up to 4,500

psi was in the order of one percent per day at 76 °K

and 25 to 30 percent per day at 275 to 300 °K. The

vapor pressure of parahydrogen was measured at the

beginning of a number of PVT runs [66]. Following one of the routine, 8-hr PVT determinations, the

presence of parahydrogen again was confirmed by

it vapor pressure measurement.

4. Cryostat and Piezometer

Descriptions and summaries of low temperature

techniques are available [11, 12, 13, 14, 38, 46].

163-232
^ CAPILLARY

Figure 2. Piezometer region of PVT cryostat.

(Shield is misspelled io the above figure.) Figure 2 shows a cross section of the lower portion

of the cryostat. A 25-ml pipet sample cavity,

5/8-in. diam, is bored into a two-in. diarn, solid copper cylinder 8.5-in. long. To avoid oxidation,

the plug is brazed with helium in the cavity. Metal

stress is about one half the internal pressure. Helical

grooves on the cylinder carry a 32-gage, 500 12 constantan wire heater. The platinum thermometer

is tinned and cast into the pipet with Rose's alloy.

Above the pipet on the supporting, thin-walled,

stainless steel tube, a guard ring thermally tempers

electric wires leading to and wound on the pipet

;

the ring is automatically controlled at pipet temperature by a gold-cobalt versus copper thermocouple [40, 44] and a 36-gage, 100 ft constantan

wire heater. A cold ring, integral with the refrig- erant tank, tempers electric wires entering from room temperature. Before it was mounted and

wound in the cryostat, the bundle of 3(5-gage,

low-level wires was constructed as a unit with all wires lightly varnished together parallel in a plane

to insure good thermal contact on the rings. The

levels of cooling through the reflux tube which do

not disturb the temperature-versus-pressure rela- tionships are determined experimentally. About 10 milliwatts cooling normally is used.

An evacuable copper can, soldered to the tank

with Rose's alloy, encloses the pipet. A Dewar

vacuum jacket immersed in an open Dewar of liquid nitrogen protects the can and the tank.

A permanent liquid hydrogen transfer line with

built-in valves enters the cryostat refrigerant tank

through an O-ring seal, with the amount of refrig- erant in the tank shown by an electronic level- indicator instrument. Suitable valves and safety

devices on the vent from the tank permit the use

of a rotary oil pump to attain the triple-point

temperature of the refrigerant.

5. Measurement of Sample Volume

5.1. Normal Pipet Volume

This volume is required for computation of

density. By ignoring the adjustments contained

in eqs (10.1-1) and (10.3-1) there is obtained the

rough approximation for sample density,

a « (Pm/R Tb ) ( VJV„) , (5.1-1)

where Pm , Tb and Vg refer to the gasometry system

and V0 is pipet volume. Whereas the ratio VK /V0 dominates the computation of eq (10.3-1), it is a

practical convenience to perform absolute cali- brations.

The pressure and temperature-dependent volume

of the pipet is required. Connection to the pipet

cavity is made with a 3-in. length of 0.35 mm

stainless capillary brazed to the pipet drill hole,

figure 2. The pipet was briefly tested to 8,000 psi.

A midget valve was attached to the capillary,

the pipet evacuated, and freshly boiled water

admitted to the pipet. The three determinations

yielded an adjusted volume of 25. 83± 0.016 cm3 at 25 °C. Volume -at room temperature after mounting in the cryostat was determined by ex- panding hydrogen from the pipet at about 1,000

psi into the gasometer system of section 6. Seven

determinations yielded adjusted volume 25.854

±0.037 cm3 at 25 °C. Following two series of highdensity experiments for PVT data to 5,400 psi,

low-density experimental results violated general,

low-density, limiting gas behavior. Six redeterminations of pipet volume by gas expansion yielded

normal volume 25.91 3± 0.009 cm3 relative to the

gasometer volumes, in agreement with deductions

from low-density behavior. The first series of

PVT experiments is rejected, and the increase of

molal volume by factor 1.00263 is applied to all other data. The annealed pipet is thus assumed to have deformed in use. With this correction, the

estimate of error in normal pipet volume is 0.5

parts per thousand.

5.2. Elastic Stretching of Pipet

Circumferential and longitudinal stresses in a closed-end cylinder are, respect ively,

Sc =kP/(R-l) and S^P/(R2 -1), (5.2-1)

where P is excess internal pressure, R is the ratio

of external to internal diameters, and k incorporates

both end-effects and relative behavior of thick

walls. With modulus of elasticity E, relative

diameters, lengths, and volumes are, respective^,

D/D0 =l+kP/E(R-l) (5.2-2)

L/L0 =l+P/E(R2 -l) (5.2-3)

V/V0- 1 = (P/E)[(R2 - 1 )~ l + 2k(R- 1 )-']. (5.2-4)

164-233
The temperature-dependence of E from [73] in T °K is #=1.15 • 106 [l-4.35 • l(T 4 r], atm, (5.2-5)

and the behavior of k by comparison with [70, 74, 79]

is k=a(R-l)[(R2 +l)/(R2 — l)+m]=l.ll (5.2-6)

by introducing R=3.2, a = l/3 for end-effect and

m=0.3 for Poisson's ratio. Within the accuracy of

above estimates, therefore,

\ = V/V0 =1 +1 10- 6 [l+4.35- 10-T]-Patm . (5.2-7)

5.3. Thermal Contraction of Pipet

Thermal expansivity of copper [78] in the form

a=(L0 —L)/L0 as a function of temperature is used

to compute a table of V/V0 versus temperature.

For use with computing machines, this is fitted by a quadratic polynomial on the Kelvin temperature

scale,

V/V0 =a+bT+cT\

F„=25.913 cm3

; a =0. 990069; 6=1.667 • 10" 6

; c=1.317 • 10- 7

. (5.3-1)

6. Measurement of Amount of Sample

6.1. The Gasometer

The fluid contained in the pipet, the capillary, and

the diaphragm cell is released into the gasometer

system D (fig. 1). This is a set of spherical glass

standard volumes in a precision water-bath thermostat, and a valve manifold with precision mercury

manometer [48] in a circulating-air cabinet. Elevation of each arm of the leveled manometer is read

to ±0.05 mm by a highly reproducible lightbeam

and photocell arrangement. A standard volume is selected such that the pressure is in the upper range

of the manometer; i.e., 500 mm or greater. The

instrument room temperature is controlled to about

±0.5 °C. To compromise between low obnoxious

volumes and adequate pumping speeds, the manifolds are %-iri. copper tubing of 0.19-in. diam bore.

For leak-free behavior, bellows-sealed valve seats and gaskets are a plasticized vinyl chloride polymer.

Bellows volume increase per single turn is 0.15 cm3

. This adds to standard volumes of 10 liters or more

used for most determinations. Ionization gages

serve for vacuum leak testing.

6.2. Gasometer Calibration

Volumes of the 1- and 2-liter spherical glass flasks are determined by weighing them with water on a 3-kg analytical balance against class Q weights.

The 6-liter flask is weighed on a 20-kg single-beam

platform balance against calibrated weight slugs.

Adjustment is made for air buoyancy, water density,

165

and thermal expansion of the borosilicate glass [76]. Volumes at 300 °K are given by the second column

of table 1

.

Table 1. Calibration of gasometer flask volumes

Nomina]

volume

Water

weighing Gas expansion Assigned

1 L

2 L

6 L

22 L

Ratio, 2 L/1L

ml

994. 48

2, 03fi. 35

6, 429.

1

ml

(994. 48)

2, 037. 5±0. 7

6, 427 ±3. 0 21,226±3. 0

2. 0488

ml

994. 1

1

2, 036. 7

6, 427 21,226

2. 0477

After determination of all manifold volumes in- cluding the manometer, the 2 -liter flask is calibrated

b}^ gas expansion relative to the 1 -liter flask; each

successive flask then is calibrated relative to the sum

of all smaller flasks. With all adjustments the

results shown in the third column are obtained.

Absolute volume standard is selected as the sum of

volumes of the 1- and 2-liter flasks by water weighing, and the ratio of these two volumes by gas

expansion is selected for assigning the values shown

in the last column. Pressure-dependence of the

flask volumes was computed from physical dimensions and mass of the individual flasks and the modulus of elasticity [76]. The nearly uniform results were confirmed experimentally upon a flask filled with water extending into a capillary neck,

( 1 / V) (d VIdP) = 1 • 1 0

- 4 atm

1

. (6.2-1)

6.3. Adjustment for Capillary and Cell

The amount of sample in the pipet is the total amount behind valve 4 of figure 1, determined by

gasometry, less amounts in capillaries and in the

diaphragm cell under conditions of measurement

for each P-T point. The rapid experimental method

is justified provided these latter amounts can be

estimated with sufficient accuracy. This is attained

with a diaphragm cell volume which is small relative

to the pipet, and by utilizing known and estimated

gas-imperfection behavior of normal hydrogen.

A volume of 0.655 cm3 for capillary tubing and

diaphragm-cell exterior to the top of the cryostat

and up to the. pipet valve C-4 is obtained by weighing

mercury out of the tubing and by finding differences

with suitable gas-expansion methods. The quantity

of hydrogen in these obnoxious volumes is computed

from their temperatures, the pressure, and the

compressibility factor for normal hydrogen [65]. The volume of the 71 -cm-long, transition capillary

from the top of the cryostat to the guard ring is yc =0.0672 cm3

, or 0.26 percent of pipet volume.

The amount of fluid in the capillary is computed by

calculating the temperature Tx , corresponding to any

position at a fraction x of capillary length from the

ring at pipet temperature T0 to the top of the

cryostat at room temperature Tu from thermal

conductivity K of stainless steel [77] by the relation,

-234
*=[£' KdT-£'KdT}U?K"T-£'KdTT

(6.3-1)

The number of gram moles of fluid in the capillary is Nc =(PVc/RT0)d (6.3-2)

d=T0J

l dx/TxZx . (6.3-3)

where

Indices o refer to the ring or pipet, x to relative

position along the capillary, and Z = Pv/RT where

v =mo\&\ volume. By known [23, 64, 68, 69] and

extrapolated [3] data for Z, the capillary factor 0 for hydrogen is determined at a sufficient number of

sensitive points for smoothing, taking note of liquidvapor discontinuities; results are summarized by

figure 3. The ratio of amount of fluid in the tran - sition capillary to amount in the pipet is necessary

for an estimate of required accuracy. This ratio is (VJV„) 4>, where <p=Z0d is summarized by figure 4. Due to the small value of VJV0 , a ten percent error

in <p would correspond to a relative error well under

0 03 percent in density of the pipet sample at temperatures < 100 °K.

Figure 3. Capillary factor, 6.

?o 90 no

TEMPERftruRE r 0

.°K

7. Measurement of Pressure

7. 1 . Piston Gage and Diaphragm Cell

The commercial, dual-range, precision, dead -weight

gage and null-detector operate in the oil-filled F-manifold, figure 1 [52, 53, 57, 59]. The diaphragm,

with adjustable electric contacts to indicate null

position, is centered by use of an open-tube manometer. The oil pressure is adjusted to the experimental gas pressure with the screw-type oil press P. Prior to placing weights on the piston gage, the

approximate pressure is read from bourdon gages. Piston diameters of about 0.182 and 0.407 in. are measured with a light-wave micrometer to ±5

million ths of an inch. Tolerance on the weights,

determined by comparison with class S standards

[54], decreases from 0.05 percent on the 1 psi weight

to 0.002 percent on the 1000 psi weights. Adjustments to gage readings are made for temperature,

pressure, acceleration of gravity, and barometric

pressure. Observed sensitivity of pressure measure- ment with the small piston varies from under

±0.05 psi below 500 psi to under ±0.5 psi at 5000

psi.

As compared with known diaphragm-detectors

[49, 61], the commercial instrument used here

withstands extreme pressure imbalance without

damage, but exhibits temporary hysteresis effects up to about ±0.05 psi. A measured shift of null- point with absolute pressure is applie 1 by the

relation

P ,+ (1.00002)Po (7.1-1)

Table 2 summarizes estimates of accumulated errors

at different pressures.

Table 2. Estimates of accumulated pressure

errors

2 20 200 Gape pressure, atm

Error, atm X HP

Barometer 0. 50 0.50 0.50 Diaphragm cell 4.00 4. 00 4.00

1'iston-cylinder iliameter.-- 0. 06 0. 60 6.00

.67 1.52 4.07

5.23 fi. 62 14. 57

Kelativo error {&PIP)-W... 2.6 0.33 0.073

Figure 4. Capillary relative content, <j>.

Thermal equilibrium of the fluid sample, following

a step-increase of temperature, is found by pressure

observations to be established nearly as rapidly as the heating rate of the massive pipet. Occasional

pressure balances are taken an hour apart to confirm

this inference from the steady behavior of single

observations.

7.2. Adjustment for Capillary Column

The column of cold fluid standing in the transition

capillary tube produces an additional pressure Pc at the pipet,

PJP=JMLC6/RT0 166-235
using symbols of section 6.3, pressure conversion

factor J, molecular weight M, and capillary length

Lc =ll cm. Since JMLJR= L68 • lO" 3 °K for hydrogen, the adjustment for capillary column pressure

is negligible.

8. Measurement of Temperature

8.1. Method and Instruments

The potentiometric method of figure 5 is employed

with a 25-ohm platinum resistance thermometer cali- brated by the NBS Temperature Physics section and

a six-dial microvolt potentiometer [41, 42, 46]. The

low-impedance, unsaturated standard cells are protected from occasional extreme temperatures of the

laboratory by two concentric boxes of 1/2 -in. aluminum in a plywood case [43]. The upper potentiometer current supply is stabilized by placing a lead-acid

battery across an isolated, rectified, and filtered a-c source [60]. A 25-v, 200 amp-hr, thermally insulated

and shielded battery, of a similar, low internaldischarging type, supplies the stable thermometer

currents which flow in the calibrated precision standard resistors. The microvolt switch is wired so that

the thermometer potential connections to the potentiometer can be reversed when the thermometer

current is reversed. Microvolt galvanometer amplifiers with floating input circuits are coupled to 50-^a

panel galvanometers in suitable damping and rangechanging circuits. To minimize spurious effects in the thermometer and thermocouple potential circuits,

the continuous copper wires from the pipet in the

cryostat are joined by a special solder [45] to unturned, copper cable wires near the cryostat on copper

lugs in an iron-shielded, heavy aluminum box. The

cryostat wires and shielded cables run in iron conduits. The cryostat and all electrical instruments

are interconnected and grounded to the earth with

heavy copper conductors.

8.2. Procedure and Calibration

When the instrument room air conditioner is started, spurious potentials up to ±0.1 microvolt

arise in the galvanometer circuit. These potentials

are observed by use of an internally-shorted emf

position on the potentiometer and are bucked out

at the galvanometer amplifier. When the cryostat

is cooled with liquid hydrogen, a 0.35-^v spurious

potential, which is nearly independent of pipet temperatures up to 40 °K and increases with higher

temperatures, appears across the thermometer potential leads in the absence of thermometer current. Potential measurements with reversed thermometer

currents show the effect to be independent of current. Thermometer currents are adjusted to exact in- tegral milliampere values. To a corresponding,

tabulated, thermometer potential is added the spuri- ous thermometer potential to obtain a potentiometer

dial setting yielding an automatically-controlled,

integral-valued temperature. A thermometer current

of 5 ma is used at temperatures below 35 °K; 2 ma,

from 35 to 75 °K; and 1 ma, at 75° and above.

Thermometer heating by the 5 ma current produces

an error of 0.0007 °K at 40 °K. All measurements

occur in the low range of the potentiometer.

The specified error limit of the potentiometer low

range is 0.01 percent of reading plus 0.02-^v. The

calibrated value of the 1-ohm standard resistor is 0.99999±0.00001 ohms. Apparently satisfactory

agreement was found between the platinum thermometer calibration tables and measurements with

above procedures for the ice-point and for vapor

pressures of high-purity nitrogen and of parahydrogen, as described in section 11. The accuracy of temperature measurements is summarized by table 3. It is based on the thermometer characteristic and currents, the potentiometer specifications, and a latitude of 0.05 nv for

bucking out spurious potentials. Thermometer

calibration uncertainties are not included.

Table 3. Estimates of accumulated temperature errors

T, °K

Thermometer Potenti- ometer

error, fV

Errors, ST, °K 103 ST/T, X10«

i, ma R, a ilR/dT Potenti- ometer

External ±0.05 jiv

15 5 0.049 0. 0074 0. 045 1.22 1.35 170

20 5 .112 .017 .076 0.89 0.58 74

40 2 1.07 .075 .234 .62 .13 19 70 1 4.05 . 109 .485 .89 .09 13

100 1 7.25 .109 .745 1.37 .09 15

ANKI

BUCK1NS

CIRCUIT

STANDARD

CELLS

BOX

MICROVOLT

AMPLIFIER

METER

DAMPING, RANGE

MICROVOLT SWITCH

PIPET

THERMOITL

BATTERY, CURRENT

CONTROLS

MICROVOLT

POTENT lOMETEf

STABILIZED BATTERY

CIRCUIT

MICROVOLT

AMPLIFIER

METER

DAMPING, RANGE

POWER

REGULATOR

POWER

SUPPLIES

METER

RANGES

PIPET HEATER

UAHU METER

DAMPING, — RANGE —

POWER

REGULATOR METER

RANGES

GUARD HEATER

Figure 5. Temperature measurement and control methods. 167-236
9. Regulation of Temperature

Precisely controlled electric heating compensates

for crudely adjusted, spontaneous cooling (section 4).

The pipet temperature can be controlled [29] from

a thermocouple, relative to the temperature of the

refrigerant tank (upper left of figure 6), by a wide

range microvolt bucking circuit, a microvolt amplifier [56] and a d-c power-regulator [50]. For all PVT measurements the pipet temperature is controlled from the platinum resistance thermometer

and potentiometer. There is no perceptible noise at 0.0002 °K sensitivity. The accuracy of controlled

temperature is equivalent to the described accuracy

of measurement. To maintain a steady temperature

during other operations with the potentiometer, the

power regulator input signal switch is opened and

the steady-state heating carefully adjusted by the

power regulator control before undertaking such operations. If required, the above thermocouple control can be used. The guard ring temperature is controlled with similar instruments.

10. Computation of PVT Observations

10.1. Gasometry

The number, N, of gram moles of hydrogen contained behind pipet valve C-4 is calculated by the

relation,

RN/Pm =[(EVg + Vw )/Tw + VJTa + Vb/Tb]/Zw , m +V0 /T„Zom> (10.1-1

)

where Pm is mercury manometer pressure in atmospheres,

#=82.057 cm3 atm/g mol deg K,

Pm =KgDLm, (10.1-2)

7iC=0.986923.10-6 atm cm2/dyne [4],

</=979.615 dyne/gram in this laboratory room,

#=13.5948-0.00245 • t m , g/cm3 [4], (10.1-3)

£m =manometer mercury temperature, °C,

im =manometer mercury height, cm (brass scale),

.E =glass volume/pressure coefficient = l + 10- 4 CPm -0.825), (10.1'-4)

Ta =air-bath manifold temp, °K,

T6 =NPD temp, °K,

T0 =pipet temp, °K,

Tw =water-bath temp, °K,

Va =vo\ of air-bathed manifold and manometer,

59.66 cm3

,

Vb —vol of lines, gasometer to C -valves, including

gage, 22.37 cm3

, Vg =vol of glass bulbs used, cm3

, F„,=vol of water-bath manifold, 13.00 cm3

, F0 =vol of pipet, cm3

, Fo/ro =25.913[0.990069/To + 1.667. 10-6 + 1.317.10- 7

• T0], (10.1-5)

Zwm (at Tw and Pm) = 1. 000044 +0.000555Pm, (10.1-6)

Z„.m .(at T0 and Pn ) = 1.0007

-1055/7^ for ro >40 °K. (10.1-7)

10.2. Pressure

The pipet fluid pressure P in international atmospheres is p=0.0680457P, +Ps (10.2-1)

where

Pg =deadweight oil gage pressure in psig,

P6 = barometric pressure in atm,

Pt =k(g/g,)[l-2A 10-5 (^-20 °C)] [1 +

4.2- 10 _8PJ- [Nominal wt psi]. (10.2-2)

£=1.00002, eq (7.1-1),

(g/gs ) =979. 615/980.665,

tK —deadweight gage temperature, °C,

Pb =KgD Lb as in eq (10.1-2), (10.2-3)

Lb = barometer height, cm,

f 6 =barometer temp, °C.

10.3. Density

Density, a, g moles cm3

, is calculated by

aV0 =N— (PIR)[VC6IT0 + VaiZa Ta] (10.3-1)

where

Td = temperature NPD, °K,

y«= pipet temperature, °K,

F<=25.913 X[0.990069 + 1.667 • 10-6 To +

1.317 • 10- 7 77], (10.3-2)

Fc =0.0672 cm3

, Vd , volume of NPD and warm capillary =0.655 cm3

, Zd , for gas at P and room temperature in Vd is Zrf =0.99990 +0.000623447 P, (10.3-3)

X, eq (5.2-7),

d, eq (6.3-3) and figure 3. 168-237
1 1 . Checks on PVT Calibrations

11.1. Thermometry Fixed Points

Vapor pressures of a commercial, high-purity

nitrogen and of parahydrogen were measured prior

to the PVT experiments. Examination of experimental technique later revealed failure to compensate some of the spurious potentials. Determination of

these potentials provided adjustments, estimated

accurate within 0.005 °C, which have been applied

in preparing table 4.

Table 4. Thermometry fixed point observations*

P, mm a T„b, Tut AT

Vapor pressure of nitrogen b

625. 05

625. 42

626. 03

631. 75 631.68

75. 732

75. 741

75. 744

75. 825

75. 826

75. 730

75. 735

75. 743

75. 816 75.815

—0. 002 -0. 006 +0. 001 +0. 009 +0.011

Vapor pressure of parahydrogen °

626. 33

626. 72 626.90

628. 18

629. 12

19. 639

19. 645

19. 650

19. 656

19. 656

19. 632

19. 634

19. 635

19. 642

19. 646

+0. 007 +0. Oil +0.015

+0.014

+0. 010

*A11 temperatures in deg K on NBS

1955 scale.

» Mercury column height reduced to 0 °C at standard gravity,

b O. T. Armstrong, 1954.

• Iloge and Arnold, 1951.

11.2. Elevated Vapor Pressures

Initial PVT points of several runs wore taken at saturation conditions to check instrumentation. If the substance is nearly pure parahydrogen, the

observed pressure-temperature relations should agree

with those of Hoge and Arnold. Table 5 presents

Table 5. Elevated vapor-pressures observations

Pots, atm Data from Iloge and Arnold »

T °K II III P, atm dl'MT

22 1.612 1.614 0.417 23 2.069 2. 071 .498

24 2.614 .587 25 3. 246 3. 249 .685 26 3.978 3. 983 3. 985 .790

27 4. 832 4.829 4.832 .904 28 5. 785 5. 792 5. 795 1.020 29 6. 886 6. 889 1. 162 30 8. 121 1.304

31 9.499 9.502 9.500 1.459

32 11.051 11.047 1.643 32 11.051 11.047 1.643 32 11.052 11.047 1.643

» Data of Hoge and Arnold interpolated to NBS 1955 temperature scale.

observed vapor pressures of parahydrogen from the

series II compressed liquid runs and from the series III low-density runs in the vapor and gaseous region.

169

Data of Hoge and Arnold are interpolated to the

NBS 1955 temperature scale of the present work.

Temperature deviations corresponding to pressure

deviations in series II range from 0.0098 deg at 28 °K to 0.0030 deg at 32 °K. The series III range

is from 0.005 deg at 22 °K to 0.003 deg at 32 °K.

11.3. PVT Data for Normal Hydrogen

The first PVT run was made with normal hydrogen

for comparison with known data, table 6. The

Table 6. PVT observations on normal hydrogen

T, °K P, atm v, cm3 /raol Ze.p 1.0026-

Z

e ,p Ziit

28 30. 869 30. 443 0. 4090 0. 4101 0. 4093"

30 45. 357 30. 460 .5612 . 5627 . 5616"

32 59. 738 30. 476 .6933 .6952 . 6945"

36 88. 443 30. 508 .9134 .9160 .914*"

40 116. 969 30. 538 1.0883 1.0911 1. 0902b

45 151.884 30. 574 1.2576 1.2609 1. 259">

50 186. 213 30.007 1. 3892 1. 3928 1. 39281"

« Friedman and Ililsenrath, private communication,

b Johnston and White, Trans. AS ME 72, 785 (1950). •Nonlinear interpolation. known data have been interpolated linearly except

where indicated. Present results for Z in column 4

are multiplied by 1.0026 in column 5 as an adjustment for the pipet deformation which occurred at an unknown time during the experiments. Deviations of the former results are within 0.07 to 2.6 parts per thousand; of the latter within 0.00 to 2.2

parts per thousand.

11.4. Virial Coefficients

Corresponding to the virial equation,

Z = Pr/RT=l±B/v+V/v2 + • • • , (11.4-1)

the data function,

4> = nT(Z-l)v=RTB+RTC/v+ • • •

, (11.4-2)

exhibits satisfactory linear dependence on density

at each temperature when the recalibrated pipet

volume, T "0 = 25.9 13 cm3 is used for computation of

experimental densities below critical. Unsmoothed

values of UTJi and R TO, determined by least squares,

are given by table 7. These new data are equivalent

to an equation of state for parahydrogen at densities

up to 9 g mol/liter. For comparison are given

values for normal hydrogen calculated from the

smoothed table 19 of H. W. Woolley et al. [69], and

values for KTB onlv, smoothed bv us from the

"smoothed" table CIV of A. S. Friedman [19]. Negative third virial coefficients in the latter table

below 50 °K suggest that corresponding second virial coefficients are too small in absolute value. Our

closely-spaced data suggest a so-called lambdapoint maximum in the third virial coefficient at the

critical temperature. The criteria of its validity

have not been investigated. Concerning comparison

of results, it recently has been shown that second

virial coefficients for parahydrogen may be about 1 percent smaller in absolute value than for normal

hydrogen at liquid hydrogen temperatures, in 238
agreement with these results [63]. Quantitative

study of the ^-density behavior before and after correction of the pipet volume suggests accuracy of

volumetric calibrations within one part per thousand.

Table 7. Virial coefficients, parahydrogen

Units of cm3

, g mol, atm, deg K

-RTB10-5

T, °K

2125

26

27

28

29

30

3132

33

3435

36

3738w

40

4244

ir,

48

50

55m

65

70

75

XII 8590

95

100

Exp

2. 229*

2. 185*

2. 139J 2.098

2. 059

2. 023

1.987 1.952

1.917 1.883

1.848

1.814

1.780

1.747

1. 714

1. 683

1.651

1.591 1.533

1.478

1. 423

1.369

1.239

1. 116

0. 992

. 873

.762

.647

.531 .417

.310

.205

(»)

2. 247

2. 159

2. 075

1.996

1.921"

1.849

1.781

1. 715

1. 653

1.591

1.473

1.360 1.224

(»)

2.20

"2.11"

2" 02"

1.95

1.88"

1.81 T75"

I. 70

1.64

1. 59

1. 49

I Hi

1. 28

1. 16

0.94

"".65"

RTC-10^

Exp

3. 053*

3. 432*

3. 273|

3. 519

3. 647

3.826

3.938

4.021

4. 096

4. 124

4. 110

4. 103 4.073

4.043

4 1 121

1

3.998

3. 966

3 934

3. 920

3. 922

3. 929

3. 926

3.971

4. 074

4. 143

4. 232

4 414

4. 514

4. 587

4. 688

4.849

5. 007

(»)

4.089

4.020"

3. 962 3.914

3. 846

3.811

3. 804

a H. W. Woolley et al., J. Research XBS 41, 379 (1948) R1M932, normal Il 2 . b A. S. Friedman, Ohio State dissertation (1950), normal 11 2 . •Based on only two data points. {Based on only three data points.

12. Comments on Overall PVT Accuracy

Requests for a statement of overall accuracy of

data in the form Z=Pv/RT are commonplace.

This accuracy depends not only on calibrations, but

also on all the adjustment computations and the

particular conditions defining the state of the fluid. The relative error in Z is the sum of relative errors in experimental variables,

bZj&P 8v_5T

Z~P + v T'

Estimation of pressure errors is indicated by section

7.1. and table 2. The complexity of error estimates

for molal volume, v, is appreciated by reference to eq (10.3-1). In view of sections 5 and 6, table 1, and the unpublished details of calibration and adjustment of obnoxious volumes, we venture the

experimentalist's opinion that error in v generally is under two parts per thousand. Temperature errors,

in view of tables 3, 4, and 5, are within 0.02 °C

except near 14 °K, comparable to uncertainty in the low temperature scale [38]. Value of the gas

constant used for present computations is R— 82.057

cm3 atm/g mol deg. It may be noted that at high

densities, any isotherms of pressure as a function of

density are highly sensitive to errors in density, due

to the relatively incompressible state of the fluid, a situation giving spurious indications of low precision in the measurement of pressure.

13. Calorimetric Apparatus

13.1. Introduction

Measurements of the volume, mass, and temperature of a fluid sample are necessary to define the

state corresponding to each specific heat determination. For high pressures the PVT pipet must be

massive so that its volume will be calculable. The

PVT data are obtained first because they are used

for calibration of the volume of the thin-walled

calorimeter as a function of temperature and pressure. Calorimetric methods have been reviewed

[29] and the calorimetry of some compressed fluids described [28, 30, 33, 34,' 35, 36]. The purpose of this

section is to provide a brief description of some

improved instrumentation and of the integration of

calorimetric with PVT apparatus. Calorimetric

calibrat ions will accompany the publication of results.

13.2. Cryostat and Calorimeter

The calorimeter resides in an additional cryostat

of basic construction identical with that for the PVT

pipet, with the high-pressure hydrogen capillary,

vacuum, and liquid-transfer plumbing in parallel

through suitable valves. Alternation of experiments

requires no dismantling. Figure 6 is the calorimeter region of the cryostat, and figure 7 is the

calorimeter section. All parts are copper except for

GUAfiO RING

Figure 6. Calorimeter region of calorimeter cryostat.

(Shield is misspelled in tbo above figure.) 170-239
f f

THERMOCOUPLE WELL

CAPILLARY

HEATER

THERMOMETER WELL

Figure 7. Calorimeter section.

sphere, capillary tube, and the guard-ring suppor t tube. The 2-in. diani, type 316 stainless steel,

spherical calorimeter has a nominal wall thickness of

0.06 in. It is fabricated from spun hemispheres,

welded together, with addition of a 1 -in. -long neck of

}i-m. tubing. The spherical shape is improved by

expansion with water pressure. Yielding to a per- manent volume increase of 10 percent was observed

with a pyenometer surrounding the calorimeter. It occurred at pressures from 5,000 to 6,400 psi,

corresponding to metal stress roughly N.3 times these

values. Elastic behavior following this deformation was AV/VaP= 1.59 • 10~ 5 atm-1

, corresponding

roughly to a circumferential modulus (3r//4/) VAP/AF=23- 106 psi, where <l is diameter and t is wall-thickness. After electroplating copper inside

and outside to about 0.2 mm thickness, avoiding

sulfate electrolytes, the

cm3

, determined by gas

orimeter in the cryostat.

wire heater is varnished

and shielded by the

which serves also as

normal volume

expansion from

is 72.35

the cal- The 100-ohm, constantan

directly onto the sphere,

lightweight calorimeter case, the wire spool for thermally

anchoring thermocouple and thermometer leadwires. The }i6-in. o.d. stainless steel capillary has

a bore diameter of 0.0345 cm. This relatively

large bore is essential for rapid filling and emptying

of the calorimeter. Volume of this capillary,

including a valve at the head of the cryostat, is 0.080 cm3

.

Adiabatic shielding is in two parts: the guard

ring, and attached, lightweight shield can. The

ring tempers all electric wires, pressed into individual, longitudinally machined grooves. These

wires lead from similar grooves in the cold ring and

lead to the calorimeter case. Separate heaters are wound on the guard ring, the cylindrical surface of

the shield and as a plane spiral on the bottom of the

shield can. The two shield heaters operate in a divider circuit from a single regulator. These

heaters are automatically controlled from thermopile 1 and thermocouple 2 respectively of figure 6. Thermocouple 3 serves for manual adjustment of the

side-to-bottom heat divider. Thermocouple 4

serves for automatic temperature control of shields

and calorimeter, during gas-expansion calibrations

of the calorimeter volume, with reference to the re- frigerant tank temperature.

To facilitate control of the calorimeter temperature during some calibrations, a small heat leak is introduced to the present apparatus. Thermal

contact between electric wires and tempering ring

is reduced to obtain the calorimeter cooling drift described in section 13.4 The caiorimetric method

therefore may be described as quasi-isothermal.

13.3. Control and Measurement of Heat

The control circuits for caiorimetric heating are

indicated by figure 8. Although they are conventional in principle, a useful simplification is application of an electronic battery: a 0.5 amp,

transistorized, d-c power supply, continuously adjustable to 0.02 v from 0 to 32 v, with regulation

and stability better than 0.002 v. The nns ripple is 0.001 v. The battery source impedance, Rh of the

figure, is readily adjusted equal to the calorimeter

heater resistance when the battery potential in- dicated by P-\ is twice the heater potential indicated

by P-2 [31]. To provide time for potentiometric

measurements of the heater power, and for shield

temperature adjustments, a temperature rise of

about 2° in a fixed interval of 10 min at all temperatures is realized by adjusting the battery potential.

This adjustment does not affect Rb , in contrast to behavior with conventional batteries and rheostats.

Relay coils are operated with direct current to reduce induction of spurious a-c effects in the lowlevel circuits. Potentials are measured with the 6-dial microvolt

potentiometer and with a type K-3 universal potentiometer, each indicating through an electronic

galvanometer [5G], as in figure 5. Potentials to be

measured are connected to each potentiometer by

high-quality, commercial, microvolt selector switches.

Four measurements of heater potential and current

are made in 10 min. Heater power is constant to better than 1 part in 10,000. The standard electric,

clutch-type, synchronous stopclock utilizes local,

60- c/s, powerline frequency for the time standard.

The NBS Time Standards Section finds that this

frequency usually is accurate and constant to well

within 0.03 percent.

171-240
24 u,d-c POWER

SUPPLY

117 v POWER LINE

24 v, d-C. INTERVAL SIGNAL

PRESET

INTERVAL

TIMER -RELAY

ELECTRIC

STOP CLOCK

60 C/S , 0.03 °/o

-•SHIELD POWER

Figure 8. Calorirnetric heat control methods.

13.4. Measurement of Temperatures

The calorimeter platinum resistance thermometer

is calibrated and the thermometric technique checked

as described for PVT determinations. Imperfections of adiabatic shielding yield emptv calorimeter

drift rates from —0.0009°/mm at 20 °K'to -0.0019°/

min at 100 °K. These are linear in time.

Five temperature observations in 5 min precede

a heating interval. Nonlinear equilibration fol- lowing the interval requires a few minutes, and is observed with a recorder. Five similar temperature

measurements follow. Temperature-time behaviors

are extrapolated to mean time of the heating in- terval, by a least-squares computer program, at which time is taken the calorirnetric temperature

increment.

13.5. Control of Shield Temperatures

The different methods, isothermal and adiabatic

shielding, are useful for different purposes [37]. The

adiabatic method is selected here for rapid adjustments in the range 20 to 100 °K where thermal

transport is almost entirely conductive. Goldcobalt versus copper thermocouples indicate temperature differences between the calorimeter and the

guard ring and shield respectively. An individual

regulating system is employed for each of the latter. An improvement of present instrumentation, in- dicated by the bottom row of figure 5, is its simplicity

relative to current practices [27]. Control instruments are the microvolt amplifier [56] and the power

regulator [50]. Two factors contribute to satis- factory operation. (1) Thermocouples are so placed on shields as to give rapid but average response.

The heater windings and powers are designed to match the areas and masses of metal to be controlled. (2) The power regulator contains a solenoid

relay, operated by the heating interval signal,

figure 8, which automatically boosts the shield

heating to a manually pre-set level. This eliminates

the delay otherwise required for development of the

temperature difference normally utilized for automatic control. The booster circuit does not affect the low output impedance of this regulator, thereby

avoiding the loss of power-gain and temperatureregulation otherwise suffered when resistances or other impedances are inserted in the heater circuit

for boosting control. Because automatic resetting

instruments are not necessary for the present work,

the normal steady-state heating also is manually

adjusted at the power regulator. For calibration

work, the shield versus calorimeter temperature dif- ferences may be recorded from the microvolt amplifier output signals by means of simplified stripchart instruments. A typical chart shows that,

with routine error in adjustment of the boost heat

level, the guard ring-versus-calorimeter temperature

difference peaks at 0.001 °C at the start of an interval

and decays to within 0.0001° in 20 sec. The same

behavior with opposite sign follows the ending of an interval. Relative change in the steady heat-leak over the copper wire bundle between guard ring and

calorimeter is negligible during a heating interval.

The numerous machined parts for the cryostats were made in the XBS, Boulder shop under S. Landis. The skillful assembly and silver-soldering

of these parts as well as the construction of the liquid

transfer and hard vacuum systems by Cryogenic

Division instrumentalist W. R. Bjorklund greatly

advanced the project. D. E. Diller placed all of the

small electric wiling in the cryostats, intercalibrated

the gasometer glass volumes, performed the gas- expansion calibrations of the pipet, checked fixedpoints of the platinum thermometer, and measured

null-point shift of the diaphragm cell in addition to other important contributions. L. A. Weber as- sisted witli the many details of placing the PVT

apparatus in final operating condition. B. A. Younglove determined mechanical properties of the

calorimeter and with D. E. Diller placed the calo- rimetry in successful operation. Hans M. Roder, in programing the computer work, devised subsidiary

equations presented in sections 5.3 and 10. Continuing encouragement from Robert J. Corruccini

and Russell B. Scott have been essential in bringing

this long task to completion.

172-241
14. References

14.1. General

[1] Stanley H. Bransom, Applied thermodynamics (D. van

Nostrand Co., Ltd., London, 1961).

[2] F. Din, editor, Thermodynamic functions of gases, 1 (Butterworths Scientific Publications, London, 1956).

[3] B. F. Dodge, Chemical engineering thermodynamics

(McGraw-Hill Book Co., Inc., New York, N.Y., 1944).

[4] W. E. Forsythe, Smithsonian physical tables, Ninth re- vised ed. (Smithsonian Institution, Washington, D.C.,

1956).

[5] Lawrence Lessing, The master fuel of a new age, Fortune

63 (5), 152 (1961).

[6] A. Michels, High pressure research, Research 9, 99 (1956)

.

[7] A. Michels, J. C. Abels, C. A. Ten Seldam, and W. deGraff, Polynomial representation of experimental data;

application to virial coefficients of gases, Physica 26, 381 (1960).

[8] J. B. Opfell and B. H. Sage, Application of least-squares

methods, Ind. Eng. Chem. 50, 803 (1958).

[9] J. S. Rowlinson, The properties of real gases, Handbuch

der Physik, vol. XII, S. Fluegge, ed. (Springer-Verlag, Berlin 1958).

[10] R. B. Scott, Liquid hydrogen for chemical and nuclear

rockets, Discovery 21 (2), 74 (1960).

14.2. Cryogenic Technique

[11] J. G. Aston and H. L. Fink, Application of low temperatures to chemical research, Chem. Revs. 39, 357 (1946).

[12] F. Din and A. H. Cockett, Low temperature techniques

(Geo. Newness, Ltd., London, 1960).

[13] R. B. Scott, Cryogenic engineering, D. van Nostrand,

Co., Ltd., London (1959).

[14] G. K. White, Experimental techniques in low-temperature physics (Clarendon Press, 1959).

14.3. PVT Methods

[15]

[16] J.

[17]

[19]

E. P. Bartlett, H. C. Hetherington, H. M. Rvalues, and

T. H. Tremearne, The compressibility isotherms of hydrogen, nitrogen and a 3:1 mixture of these gases at temperatures of —70, —50, —25 and 20° at pressures up to 1000 atmospheres, J. Am. Chem. Soc. S2, 1363

(1930). A. Beattie, The apparatus and method used for the measurement of the compressibility of several gases

in the range 0° to 325° C. Proc. Am. Acad. Arts. Sci. 69, 389 (1934). E. S. Burnett, Compressibility determinations without

volume measurements, J. Appl Mechanics 3, 136

(1936).

[18] D. Cook, The second virial coefficient of carbon dioxide

at low temperatures, Can. J. Chem. 35, 268 (1957). A. S. Friedman, Pressure-volume-temperature relation- ships of gaseous hvdrogen, nitrogen and a hydrogennitrogen mixture, Thesis, The Ohio State University,

(1950).

[20] L. Holborn and H. Schultze, On the pressure balance and

the isotherms of air, argon and helium between 0 and

200°, Ann. der Physik 47, 1089 (1915).

[21] L. Holborn and J. Otto, On the isotherms of helium,

nitrogen and argon below 0°, Z. Physik 30, 320 (1926).

[22] L. Holborn and J. Otto, The isotherms of helium, hydro- gen and neon below -200°, Z. Physik 38, 359 (1926).

[23] H. L. Johnston, W. F. Keller, and A. S. Friedman, The

compressibility of liquid normal hydrogen from the

boiling point to the critical point at pressures up to 100 atm., J. Am. Chem. Soo. 76, 1482 (1954).

[24] H. L. Johnston and D. White, Pressure-volume-temperature relationships of gaseous normal hydrogen from its boiling point to room temperature and from 0-200 at-

[26] mospheres, Trans. ASME 72 (6), 785 (1950). A. Michels, T. Wassenaar, and Th. N. Zwietering, The

experimental determination of the equation of state of fases at temperatures between 0° and —180° C,

'hysica 18, 67 (1952).

[26

[27

[28

[29

[30

[31

[32

[33

[34

[35

[36

[37

[38

[39

[40

[41

[42

[43;

[44

[45

[46

[47

[48

14.4. Calorimetric Methods

J. G. Aston and M. L. EidinofT, The low temperature

precision adiabatic calorimeter adapted to condensed

gases from 10 °K. to room temperature, J. Am. Chem.

Soc. 61, 1533 (1939). W. J. Cooper, R. H. Forsythe, J. F. Masi, and R. E.

Pabst, Ix)w temperature adiabatic calorimeter with

automatic shield control, Rev. Sci. Instr. 30, 557

(1959) . A. Eucken, On the thermal behavior of some compressed

and condensed gases at low temperatures, Verh. deut. Phys. Ges. 18, 4 (1916). R. W. Hill, Low-temperature calorimetry, Progress in Cryogenics, vol. 1, K. Mendelssohn, ed. (Heywood and

Co., Ltd., London, 1959). H. J. Hoge, Heat capacity of a two-phase system, with

applications to vapor corrections in calorimetry, J. Research NBS 36, 111 (1946) RP1693.

H. J. Hoge, Circuits for minimizing transient effects on

energy measurements in calorimetry, Rev. Sci. Instr. 20, 59 (1949). Hugh M. Huffman, Low-temperature calorimetry, Chem.

Revs. 40, 1 (1947). O. V. Lounasmaa, Specific heats at low temperatures,

Thesis, University of Oxford, Brasenose College, 1958. (Helium Cv and PVT.)

A. Michels and J. C. Strijland, The specific heat at constant volume of compressed carbon dioxide, Physica

18, 613 (1952). E. B. Rifkin, E. C. Kerr, and H. L. Johnston, Condensed

gas calorimetry. IV. The heat capacity and vapor

pressure of saturated liquid diborane above the boiling

point, J. Am. Chem. Soc. 75, 785 (1953).

P. A. Walker, The equation of state and the specific heat

of liquid argon, Thesis, Queen Mary College, Univ. of London (1956). D. M. Yost, C. S. Garner, D. W. Osborne, T. R. Rubin,

and H. Russell, Jr., A low temperature adiabatic calorimeter. The calibration of platinum resistance ther- mometers, J. Am. Chem. Soc. 63, 3488 (1941). 14.5. Thermometry

Anonymous, Symposium on Temperature, Its Measure- ment and Control in Science and Industry (Columbus,

Ohio, March 27, 1961), Abstracts, 116 pp., $5.00, American Institute of Physics, 335 E. 45th St., New York, N.Y.

T. M. Dauphinee and H. Preston-Thomas, A copper re- sistance temperature scale, Rev. Sci. Instr. 25, 884

(1954). N. Fuschillo, A low-temperature scale from 4 to 300 °K

in terms of a gold-cobalt vs. copper thermocouple, J. Phys. Chem. 61, 664 (1957).

F. K. Harris, Electrical Measurements (John Wiley &

Sons, Inc., New York, N.Y., 1952). H. J. Hoge and F. G. Brickwedde, Establishment of a

temperature scale for the calibration of thermometers

between 14° and 83 °K, J. Research NBS 22, 351

(1939) RP1188.

E. F. Mueller and H. F. Stimson, A temperature-control

box for saturated standard cells, J. Research NBS 13,

699 (1934) RP739.

R. L. Powell, M. D. Bunch, and R. J. Corruccini, Lowtemperature thermocouples—I. Gold-cobalt or con- stantan versus copper or "normal" silver, Cryogenics

1 (3), 139 (1961). Bruce K. Smith, Low thermal soldering procedures for copper junctions, Electronic Design 7 (28), 82 (1989).

It. F. Stimson, Precision resistance thermometry and

fixed points. Temperature, vol. 2, H. C. Wolfe, editor (Roinhold Publ. Corp., New York, N.Y., 1988). H. F. Stimson, Heat units and temperature scales for calorimetry, Am. J. Phys. 23, 614 (1988). 14.6. Instruments

W. G. Brombacher, D. P. Johnson, and J. L. Cross, Mercury barometers and manometers, NBS Mono. 8

(1960) . 173-242
[49] D. 0. Coffin, High-pressure gas-to-liquid transducer, Rev.

Sci. Instr. 29, 896 (1958).

1 50] R D. Goodwin, An improved d.c. power regulator, Advances in cryogenic engineering, vol. 5, K. D. Timmerhaus, ed. (Plenum Press, New York, N.Y., 1960).

[51] P. C. Hoell, Low-level d.c. amplifier with whole-loop

feedback, Rev. Sci. Instr. 29, 1120 (1958).

[52] D. P. Johnson and D. H. Newhall, The piston gauge as a

precise pressure-measuring instrument, Trans. ASME

75, 301 (April 1953).

[53] F. G. Keyes, High-pressure technic, Ind. Eng. Chem. 23, 1375 (1931).

[54] T. W. Lashof and L. B. Macurdy, Precision laboratory standards of mass and laboratory weights, NBS Circ. 547 (1954).

[55] L. LeBlan, The precise measurement of pressures, Chimie

et ind. 61, 235; 349 (1949).

[56] M. D. Liston, C. E. Quinn, W. E. Sargeant, and G. G.

Scott, A contact-modulated amplifier to replace

sensitive suspension galvanometers, Rev. Sci. Instr. 17, 194 (1946).

[57] A. Michels, Calibration of pressure-balance in absolute

units, Proc. Kon. Ak. Amsterdam 35, 994 (1932).

[58] J. R. Purcell and R. N. Keeler, Sensitive thermal conductivity gas analyzer, Rev. Sci. Instr. 31, 304 (1960).

[59] H. H. Reamer and B. H. Sage, Experience with pistoncylinder balance for pressure measurements, Rev. Sci. Instr. 26, 592 (1955).

[60] E. E. Watson, Constant current supply for the potentiometer, Am. J. Phys. 27, 404 (1959).

[61] D. White and J. Hilsenrath, A pressure-sensitive

diaphragm-type null detector, Rev. Sci. Instr. 29,

648 (1958).

14.7. Fluids Properties

[62] G. T. Armstrong, Vapor pressure of nitrogen, J. Research

NBS 53, 263 (1954) RP2543.

[63] J. J. M. Beenakker, F. H. Varekamp, and H. F. P. Knapp, The second virial coefficient of ortho and para hydrogen at liquid hydrogen temperatures, Physica

26, 43 (1960).

[64] A. S. Friedman and J. Hilsenrath, The thermodynamic

and transport properties of liquid hydrogen and its isotopes (private communication).

[65] Joseph Hilsenrath et al., Tables of thermal properties of

gases, NBS Circ. 564 (1955).

[66] H. J. Hoge and R. D. Arnold, Vapor pressures of hydrogen, deuterium, and hydrogen deuteride and dew-point

pressures of their mixtures, J. Research NBS 47, 63

(1951) RP2228.

[67] V. J. Johnson, editor, A compendium of the properties of materials at low temperature. Part I, Properties of

fluids. Part II, Properties of solids, WADD Technical Report 60-56, Office of Technical Services, U.S.

Dept. Commerce, Washington 25, D.C.

[68] R. B. Stewart and V. J. Johnson, A compilation and

correlation of the P-V-T data of normal hydrogen

from saturated liquid to 80 °K, Advances in Cryogenic

Engineering, vol. 5, K. D. Timmerhaus, ed. (Plenum

Press, New York, N.Y., 1960).

[69] H. W. Woolley, R. B. Scott, and F. G. Brickwedde,

Compilation of thermal properties of hydrogen in its various isotopic and ortho-para modifications, J. Research NBS 41, 379 (1948) RP1932.

14.8. Solids Properties

[70] J. H. Faupel and A. R. Furbeck, Influence of residual

stress on behavior of thick-walled closed-end cylinders, Trans. ASME 75, 345 (April 1953).

[71] M. J. Hiza, Cryogenic impurity adsorption from hydrogen, Chem. Eng. Progr. 56 (10), 68 (1960).

[72] R. N. Keeler and K. D. Timmerhaus, Poisoning and

reactivation of ortho-parahydrogen conversion catalyst, Advances in Cryogenic Engineering, vol. 4, K. D. Timmerhaus, ed. (Plenum Press, New York,

N.Y., 1960).

[73] R. M. McClintock, D. A. vanGundy, and R. H. Kropschot, Low-temperature tensile properties of copper and four bronzes, ASTM Bull. No. 240, p. 47 (TP 177)

(Sept. 1959).

[74] A. Michels, The behavior of thick-walled cylinders under

high pressures, Proc. Kon. Ak. Amsterdam 31, 552

(1928).

[75] R. L. Mills and F. J. Edeskuty, Hydrogen embrittlement

of cold-worked metals, Chem. Eng. Prog. 52 (11), 477

(1956).

[76] G. W. Morev, The properties of glass (Reinhold Publ.

Corp., New York, N.Y., 1954).

[77] R. L. Powell and W. A. Blanpied, Thermal conductivity

of metals and alloys at low temperatures, NBS Circ. 556 (Sept. 1, 1954)'. [78] T. Rubin, H. W. Altman and H. L. Johnston, Coefficients

of thermal expansion of solids at low temperatures,

J. Am. Chem. Soc. 76, 5289 (1954).

[79] S. Timoshenko, Strength of materials II, 2d ed., eq. (208) (D. van Nostrand Co., Inc., New York, N.Y., 1941).

(Paper 65C4-76)

174-243
JOURNAL OF RESEARCH of the National Bureau of Standards—-C. Engineering and Instrumentation

Vol. 69C, No. 1, January-March 1965

Detection and Damping of Thermal-Acoustic Oscillations

in Low-Temperature Measurements

David A. Ditmars and George T. Furukawa

(June 8, 1964)

The spontaneous thermal-acoustic oscillations in nonisothermal columns of helium,

hydrogen, nitrogen, argon, and oxygen gas have been investigated. The pressure fluctua- tions were measured with a barium titanate transducer and the particle displacements

observed by a smoke technique. The observed pressure oscillations were often nonsymmetrical and of sufficient amplitude to indicate the necessity for a nonlinear approach in a

theoretical treatment of the oscillations. An adjustable "Helmholtz resonator" attached

at the warm end of the oscillating column was found to damp completely the oscillations and

eliminate the energy transfer which they caused.

1. Introduction

Spontaneous pressure oscillations in gaseous col- umns, along which there is a temperature gradient,

often hamper cryogenic work. An excellent review

of this oscillation phenomenon has been given by

Wexler [6].

1 While there are at least three reports

of such oscillations having been used to advantage

[1,2,3], they are most often undesirable. They can

introduce errors in vapor-pressure measurements

and sometimes make the measurements impossible

to obtain [1,4]. Frequently, the oscillations cause a large uncontrollable energy transfer from hot to cold regions, making calorimetric measurements

difficult or impossible.

Experience gained with a calorimeter at the

National Bureau of Standards confirmed Wexler's

observation [6] that the energy transfer due to gas

oscillation from the room temperature region to the

4 °K region can be as much as 1000 times greater

than the energy transfer by thermal conduction.

It was decided to investigate the possibility of

damping the oscillations by some device added

externally.

Experiments with a simple auxiliary apparatus

showed this solution to be promising. This apparatus was then used to investigate further

the factors affecting the cause and suppression of

the oscillations. In the course of this investigation, an adjustable "Helmholtz resonator" attached at the warm column end proved to be a reliable and

effective damper.

2. Apparatus

The auxiliary apparatus shown in figure 1 consists

basically of a tube T extending down into a Dewar

containing a cryogenic liquid boiling at atmospheric

pressure. The lower end of the tube T was always

open and the upper end was closed by a pressure

1 Figures in brackets indicate the literature references at the end of this paper.

transducer and a device used to suppress the gaseous

oscillations. The Dewar, of two-liter capacity, was generally

used with less than a liter of liquid. When the

liquid was helium, the Dewar was immersed in a

liquid nitrogen bath.

Temperatures along the tube T were occasionally

measured with thermocouples. Typical temperature gradients along the tube ranged from 1 to 2 °C

per mm when the Dewar contained 1 liter of liquid.

The only means of changing the temperature gradient

along the tube was to add or withdraw cryogenic

liquid in the Dewar, keeping the same apparatus

dimensions.

Figure 1. Auxiliary apparatus for studying thermal-acoustic

oscillations. 175-35
A barium titanate tube, cemented onto the upper

end of T, served as a pressure transducer. This

transducer (2 in. long, % in. o.d. with a }U in. wall) •was silvered on the inside and outside and polarized

through the wall thickness. A static pressure cali- bration showed that the transducer had a sensitivity

of 7 mV/torr 2 differential pressure across its walls. This potential was measured with a vibrating reed

electrometer and was a linear function of pressure

in the range covered, 0 to 30 torr. The sensitivity

should be independent of frequency at the low

frequencies involved in these experiments (less than

60 Hz). The transducer output was fed directly

to a sensitive oscilloscope. Because of the low

impedance of the oscilloscope, the trace, at low

frequencies (2 to 10 Hz), represented more nearly

the time derivative of the average pressure fluctuations inside the transducer than the pressure itself. Additional circuitry or a dynamic calibration of the

transducer-oscilloscope system would be necessary

to interpret the trace directly as a pressure at low

frequencies.

Some direct visual observations of the wave motion

were made when T was a glass tube by introducing

a smoke of finely divided Ti02 particles into the

tube. In the case of oscillations over liquid helium,

that part of the energy dissipated in the liquid by

the oscillating gas column was measured by passing

the gas evolved from the Dewar through a flowmeter.

Pressure and net mass flow of gas in the tube were not controlled in these experiments. The

mean pressure in the tube was always within a few

torr of atmospheric and the net gas flow in the tube was zero. This is not to imply that oscillations occur only under these conditions. For instance, in the calorimeter referred to above, oscillations have

been detected at pressures below 400 torr and also

in tubes through which a net helium gas flow existed.

3. Results

3.1. Generation and Observation of Oscillations

The literature contains only references to oscilla- tions in helium or hydrogen gas columns over baths

of liquid helium or hydrogen, respectively. The

present work has shown the phenomenon to be of a more general nature. For instance, gaseous

columns can also be made to oscillate over baths

of liquid nitrogen or oxygen. Columns of helium,

hydrogen, nitrogen, argon, or oxj^gen gas were

readily made to oscillate over a liquid oxygen bath.

Evaporation caused by oscillation energy transfer

to nitrogen or oxygen baths in the present experiments was small and could not be distinguished from

evaporation due to other sources of heat leak to the baths. Two conditions had to be met, however,

for the oscillations to occur with the higher temperature baths: (a) The open tube end had to extend

several tube diameters beneath the bath surface,

and (b) the Dewar volume above the surface had

to be flooded with helium or hydrogen gas. This

2

1 torr = 1/760 normal atmosphere = 133.322 N/m2.

Figure 2. Pressure oscillation at closed end of He gas column.

Open end 1.5 cm above liquid lie surface. "O" indicates sweep position without

oscillation.

is in distinction to helium or hydrogen gas columns

which oscillate in tubes whose open end is either

above or below the surface of a liquid helium or hydrogen bath respectively. Probably the most

important effect of the flooding was the increase in the surface heat-transfer coefficient [14] at the

exterior tube wall. This also altered the bath composition and the tube temperature gradient. Experiments performed, in which these latter effects were eliminated or produced independently of any

change in the heat transfer coefficient, showed that

helium or hydrogen gas had to be present for oscilla- tions to be sustained.

To obtain a column of a gas other than that of the

bath species, the tube T, removed from the Dewar, was first flushed by introducing the desired gas

through an opening in the upper tube end. The

tube was then lowered into the Dewar until its lower

(open) end was beneath the bath surfr.cs and the gas

flow gradually reduced to zero. This procedure was

followed, for instance, to obtain a column of helium

gas above liquid nitrogen. The amplitude and

period of the ensuing oscillation were recorded as soon as they reached stable values in order to minimize the effect of contamination of the helium

gas column with nitrogen. The observed frequency was always several times that of a nitrogen gas

column oscillating under the same condition—as much as eight times in one instance. By way of

comparison, a similar gas column resonating in its lowest acoustic mode with helium would normally

exhibit a frequency which is about three times that

when resonating with nitrogen in the same mode.

A helium column oscillating with the open tube end

below the bath surface displayed approximately

equal frequencies with baths of helium or nitrogen

though the amplitude over the helium bath was

several times that over the nitrogen bath.

At low amplitudes the pressure oscillations

appeared sinusoidal, but with either increasing

amplitude or increasing temperature gradient, a nonsymmetrical distortion appeared (fig. 2). The

time between a pressure maximum and the followingpressure minimum exceeded half the period.

176-36
Using the smoke technique referred to above,

observations were made with a glass tube of 2 mm

i.d. and 0.8 mm wall thickness, containing a nitrogen

gas column oscillating at about 5 Hz over a liquid

nitrogen bath. No displacement nodes were observed other than at the closed end. The displacement amplitude of the smoke particles increased

monotonically along the tube length and was as great as ±8 mm near the open (cold) tube end.

The amplitude of this oscillation was 5 to 10 times

less than typical amplitudes of helium gas oscillations over liquid helium in which a large energy transfer

occurred. When direct observation of the liquid

meniscus in the tube T was possible (i.e., with glass

tubes), the mean position of the meniscus was below

the bath level, indicating a net positive pressure

within the tube during oscillation.

3.2. Damping the Oscillations

Reported attempts to damp or eliminate thermalacoustic oscillations fall into three main categories:

(1) Changes in apparatus geometry such as employing tubes of greater diameter or closing tubes

at the cold end when possible [2,7]. (2) Insertion of objects such as wire, wire mesh or knotted threads into the oscillating column [5,8,13].

(3) Thermal isolation of the oscillating column

[2,4]. None of these methods was practical to apply

to the calorimeter referred to above. It was possible

to control the oscillations in the auxiliary apparatus

(fig. 1) at any desired amplitude or to eliminate

them completely with an adjustable Helmholtz

resonator attached at the warm end of the oscillating

column. The same technique permitted the control

of the oscillations in the calorimeter. The effect of

the resonator dimensions on its efficiency as a damper

was then investigated using the auxiliary apparatus.

Resonator neck diameters from 0.014 in. to 0.058

in. and lengths up to 2 in. were tried. The neck

dimensions were found to be critical and the best

results were obtained with the neck dimensions

indicated in figure 1. Necks whose diameters or lengths varied from the indicated neck dimensions

by as little as a factor of two provided poor damping.

Oscillations in helium and nitrogen gas columns

ranging in frequency from 2 to 60 Hz and causing

heat leaks of up to 7 W were successfully damped

with the resonator. A typical set of damping curves obtained for helium gas oscillating over liquid helium

is given in figure 3. The distance of the tube end

above the liquid surface was kept constant along any

curve. Larger values of the relative pressure amplitude correspond to lesser values for this distance.

These curves varied considerably in shape with

different oscillating gas columns and different neck

dimensions. They exhibited, however, the common

characteristic of a continual decrease in pressure

amplitude (and associated energy transfer) with

increasing piston extension.

Piston extensions up to three times the minimum

length required for complete damping were in- vestigated and in no instance did the oscillation ever

reappear. No correlation was discovered between

0 5 10 15 20 25 PISTON EXTENSION , Cm Figure 3. Effect of piston extension on pressure amplitude.

Pressure amplitude increased by decreasing distance between cold tube end and

liquid surface.

the piston diameter and the minimum piston extension required to damp an oscillation of given

amplitude ; neither was the natural acoustic frequency

of the damper related in any obvious way to its effectiveness as a damper. Piston diameters from

3/8 in. to 1 in. have been used successfully at extensions not exceeding 50 cm to damp oscillations in the

entire amplitude and frequency range attainable in the auxiliary apparatus with the combinations of gas

columns and liquid baths mentioned earlier. The damper illustrated in figure 1, together with

the oscillating column, constitutes a variable volume

system. Equivalent results were also obtained by

fixing the position of the piston and moving the neck

assembly. In this case, the neck was mounted on

a thin piston which was attached to a rod extending

through a seal in the fixed piston.

In one series of experiments a porous tissue plug- was substituted for the neck assembly. The damping of some oscillations was possible with this arrangement.

4. Discussion

The neck assembly is the vital part of the damper

shown in figure 1. Since oscillations cannot be

sustained in a tube open at the warm end, one could,

in principle, attach a large closed volume onto the

end of any tube to simulate an open end condition

and thus damp the oscillations without use of the

neck assembly. In practice, the volume required is often rather large and cumbersome. Damper ex- periments performed with the neck assembly removed

have shown that the volume changes alone caused by

retraction of the piston have little effect on the

oscillation amplitude.

The resonator clamper has several advantages.

No modification of apparatus design in the cold

region and no obstruction in the oscillating tube is required. This is an important consideration if a pumping tube is oscillating. Connections can be

177-37
provided so that the damper can be removed and

it can be designed to be vacuum or pressure tight

if the gas column is oscillating at a mean pressure

considerably different from atmospheric. In the

application to the above calorimeter, the piston was

designed to be vacuum tight.

The coupling between the damper and oscillating

system is not fully understood. Several workers

[9,10] have investigated the nonlinear impedance of a Helmholtz resonator at large amplitudes and have

tried to correlate it with energy dissipation in vortices near the resonator neck. The flow pattern near the neck of a damper used in the present ex- periments was observed by the smoke technique

and appeared to be a pulsating jet similar to those

described in [9]. A number of variables, probably not all independent of one another, determine whether or not a given

system will perform sustained oscillations and if so, what the wave form and associated energy transfer

will be. With a given temperature distribution

throughout the system, the essential requirements seem to be that the gas column have a diameter

small enough (usually less than }{ in.), that the cold

tube end be open to a volume whose characteristic

dimensions are large compared to the tube diameter,

that the warm end be terminated with a high acoustic impedance, and that the tube be in good thermal

contact with its surroundings. This contact need

not be due to a conducting gas but can be provided

by metal contact with heat sources or sinks along

the tube length as was observed in the above calorimeter.

Kramers [15] has attempted to treat the gas oscil- lations analytically assuming small amplitudes of

vibration. This linear approach did not account

for the observed phenomena, a result which is plausible considering the oscillation amplitudes en- countered in the present work. The possible exist- ence of such oscillating states of a thermal system

has been treated in some detail from an energy standpoint by Milne [11]. Milne's theory predicts periodic

fluctuations with just the asymmetry observed in

these experiments. Squire [12] has speculated that

the occurrence of the Boyle temperature in the oscillating column may play a role in initiating the

oscillations. Since a column of helium gas readily

oscillates over liquid nitrogen, this evidently need

not be a decisive role. Since thermal-acoustic oscillations so often hamper low temperature experiments, the need for a

fuller understanding of them is great. It is felt that an apparatus specifically designed to reproduce

known temperature gradients would be valuable in

future experimental investigation.

5. References

[1] K. W. Taconis, J. J. M. Beenakker, A. 0. C. Nier, and

L. T. Aldrich, Physica 15, 733 (1949).

[2] J. R. Clement, Proc. 1954 Cryogenic Engineering Conf.

(1954).

[3] D. Ter Harr, Proc. Paris Conference on Low Temperature Physics, p. 347 (1955). (See appended discussion.)

[4] F. E. Hoare and J. E. Zimmerman, Rev. Sci. Instr. 30, 184 (1959).

[5] O. V. Lounasmaa, Ann. Univ. Turku, Al, No. 39 (1959).

[6] A. Wexler; in F. E. Hoare, L. C. Jackson, and N. Kurti

(Eds.), Experimental Cryophysics, p. 155 (Butterworths, London, 1961).

[7] A. Van Itterbeek and W. H. Keesom, Comm. Leiden

209C.

[8] R. B. Scott, Cryogenic Engineering, p. 118 (D. Van

Nostrand Co., Inc., 1959).

[9] U. Ingard and S. Labate, J. Acoust. Soc. Am. 30, 211

(1950).

[10] F. Barthel, Frequenz 12, 72 (1958).

[11] E. A. Milne, Quart. Journ. of App. Math. 4, 258 (1933).

[12] C. F. Squire, Low Temperature Physics, p. 23 (McGrawHill Book Co., Inc., New York, N.Y., 1953).

[13] H. Plumb, private communication.

[14] M. Jakob, Heat Transfer, I (John Wiley & Sons, Inc., New York, N.Y., 1949).

[15] H. A. Kramers, Physica 15, 971 (1949).

(Paper 69C1-183)

178-38
4. High Temperature

Calorimetry

Paper Page

4.1. High temperature drop calorimetry.

Douglas, T. B., and King, E. G., Chapter in Experimental Thermodynamics, Ed. J. P. McCullough and D. W. Scott, Vol. 1, Calorimetry of Non-reacting Systems, Chapt. 8, 293-331 (Butterworth &

Co., London, England, 1968).

Key words: Enthalpy measurements at high temperatures;

ice calorimeter; isoperibol calorimeter; furnaces 181

4.2. A calorimetric determination of the enthalpy of graphite from 1200

to 2600° K.

West, E. D., and Ishihara, S., Advances in Thermophysical

Properties at Extreme Temperatures and Pressures, Am. Soc. Mech. Engineers (1965).

Key words: Drop calorimetry; high temperature calorimetry . 220

4.3. Dynamic measurements of heat capacity and other thermal properties of electrical conductors at high temperatures.

Cezairliyan, A., and Beckett, C. W. (Abstract).

Key words: Radiation emittance; electrical resistivity; heat

capacities; pulse calorimetry 226

4.4. The vapor pressure, vapor dimerization, and heat of sublimation of aluminum fluoride, using the entrainment method.

Krause, R. F. Jr., and Douglas, T. B., J. Phys. Chem. 72, No. 2, 475-481 (Feb. 1968).

Key words: Heat of sublimation, vapor pressures at high

temperatures 227

179

Reprinted from*

Experimental Thermodynamics

Volume I

CHAPTER 8

High-temperature Drop Calorimetry

Thomas B. Douglas

National Bureau of Standards, Washington D.C., U.S.A. Edward G. King

Albany Metallurgy Research Centre, Bureau

of Mines, Albany, Oregon, U.S.A.

Contents

I. Introduction . . . . . . . . . . . . . . 294

1. General Requirements . . . . . . . . . . . . 294

2. Advantages and Disadvantages of the Drop Method . . 295

A. Cases for which the Drop Method is Unsuitable . . . . 295

II. The Furnace 296

1 . Furnace Design and Operation . . . . . . . . . . 296

A. General Type of Furnace Most Commonly Used . . . . 297

(1) Materials of Construction .. .. .. .. 298

(2) The Heaters 298

(3) Heat Transfer and Temperature Gradients . . . . 299

B. Furnaces with a Good Heat-Conducting Core . . . . 300

C. Furnaces Operating Above 1500°C 302

D. Automatic Temperature Control of the Furnace . . . . 303

2. Temperature Measurement . . . . . . . . . . 304

A. The Thermocouple . . . . . . . . . . . . 304

(1) Calibration 304

(2) Common Sources of Thermocouple Error . . . . 305

B. Use of Other Temperature-Measuring Instruments . . 305

3. The Sample in the Furnace . . . . . . . . . . 306

A. The Container 306

(1) Choice of Material 306

(2) Container Design; Enclosing the Sample . . . . 307

B. Suspending and Dropping the Sample . . . . . . 308

(1) Suspension and Dropping Mechanisms . . . . 308

(2) Time in the Furnace ... .. . , .. .. 309

III. The Calorimeter 310

1. The Isothermal Calorimeter .. .. .. .. ..310

A. Design of the Ice Calorimeter . . . . . . 310

B. Assembly 312

C. Calibration Factor 313 D. General Procedure of Operation .. .. .. ..313

E. A Typical Experiment .. .. .. .. ..314

F. Tests for Accuracy . . . . . . . . . . . . 316

G. Hunting Causes of Trouble .. .. .. .. ..317

2. The Isothermal-Jacket, Block-Type Calorimeter . . . . 318

A. Design and Construction .. .. .. .. ..318

B. Additional Measuring Equipment . . . . . . 319

C. A Typical Experiment . . . . . . . . . . 320

D. Calibration Factor 322

IV. Treatment of the Data 322

1. Correcting to Standard Conditions . . . . . . . . 322

A. Correction to a Basis of a Pure Sample . . . . . . 322

(1) Correcting for Insoluble Impurities . . . . . . 322

See complete ref • on page 3t»X.

181-293
(2) Correcting for Soluble Impurities . . . . . . 323

B. Correcting for Vaporization Inside the Container; Correcting

to a Different Pressure . . . . . . . . . . 323

2. Smoothing and Representing Enthalpy Values . . . . 325

A. Graphing . . . . . . . . . . . . . . 325

( 1

) Choice and Treatment of Measurements . . . . 326

B. Representation by Equations . . . . . . . . 326

(1) Theoretical and Semi-Theoretical Equations. .. .. 326

(2) Empirical Equations . . . . . . . . . . 326

C. Treatment of Fusions and Transitions . . . . . . 328

3. Derivation of Other Thermodynamic Properties from Relative Enthalpy 328

4. Precision and Accuracv . . . . . . . . . . . . 329

V. References .. . . 330

I. Introduction

The determination of accurate high-temperature enthalpies provides a

valuable tool in the study of materials and processes at elevated temperatures.

As interest in high-temperature research increases, impetus is given to experimental methods that will extend the temperature range of measured

enthalpies.

The enthalpies of the simpler, ideal gases can be determined much more

accurately from spectroscopic data than by measurement. Calculation

methods may also be accurately applied for less simple gases with molecules

in a single electronic state and without internal rotations. In these cases molecular-constant data must be available, i.e., molecular-structure and

vibrational-frequency data. At present, enthalpies of solids and liquids must be determined experimentally; and most of the accurate data for solids and liquids, above 100°C,

have been provided by drop calorimetry. With this method a sample is heated to a known temperature and is then dropped into a calorimeter

(usually operating near room temperature), which provides measurement of

the heat evolved by the sample in cooling to the calorimeter temperature.

Currently the major applications of enthalpy and enthalpy-related data

are to problems in microstructure, heat transfer, and chemical thermodynamics. In particular, the last application is of great importance. If room-temperature values of enthalpy, Gibbs energy, or entropy have been

obtained by other means, the values may be extended to the limit of the high-temperature measurements. In many cases equilibrium vapor pressures can be calculated more accurately than they can be directly measured. If vapor pressure measurements do exist, the measured enthalpies and derived

data can be used in a complementary way.

1. General requirements

The general requirements for drop-calorimetry operation of high accuracy

may be considered in terms of (i) the sample, (it) the furnace, and (Hi) the

calorimeter.

(i) The substance measured must not change irreversibly to a significant extent during the measurements. Such a change can occur through decomposition, reaction with the container, or deterioration caused by container

182-294
leakage. In passing from the higher (furnace) temperature to the lower

(calorimeter) temperature, the amount of heat evolved by the sample is meaningful only if the forms of the sample at the two temperatures are

defined.

(ii) The accurate determination of the average temperature of the sample

referred to some well defined temperature scale (usually the International

Practical Temperature Scale) is the most important requirement of the furnace. The heat lost by the sample as it drops through the region between

the furnace and the calorimeter must cancel out through empty-container

measurements. This requirement dictates a high and reproducible rate of

fall (most easily accomplished by a close approximation to free fall) and

constancy of surface emissivity, because these factors strongly affect radiation

losses which predominate at high temperatures.

[Hi) The calorimeter must be capable of measuring the heat delivered

by the sample with high accuracy, a requirement which entails the accurate determination of the heat losses from the calorimeter itself. In designing calorimetric apparatus for high accuracy and choosing

materials of construction, intuition is a poor substitute for relatively simple

calculations, even ones which may be in error by as much as a factor of

two or three. This is especially true of questions involving heat transfer. For considerably lower requirements in accuracy, a much simpler furnace

and type of calorimeter can replace those subsequently described in this chapter; in this case, simple calculations or tests may indicate an otherwise

unsuspected degree ofsimplification in construction and operation which may

be safely adopted.

2. Advantages and disadvantages of the drop method

Advantages and disadvantages of the drop method compared with other

calorimetric methods are discussed in Chapter 1, Section V. Perhaps the

greatest advantage of the drop method over the adiabatic method is that the precise calorimetric measurements are made at or near room temperature where suitable conditions are most easily maintained. Above 500°C or so the drop method at present excels applications of the adiabatic method in accuracy as well as simplicity. With high-temperature adiabatic and iso- thermal-jacket calorimeters there is considerable difficulty in temperature

control and in accounting for heat losses by radiation.

With the drop method, enthalpies of transition and fusion are obtained

by the difference between two measured quantities of heat. If these quantities are large, the errors in the enthalpies of transition or fusion may be corres- pondingly large. This may be regarded as a weakness of the drop method

;

however, this effect is partially cancelled by systematic procedure.

A. Cases for which the Drop Method is Unsuitable

The success of the drop method depends upon complete return to the same, defined, thermodynamic reference state after each measurement. The

method inherently involves the rapid cooling of the sample. Sometimes,

during cooling, a sample fails to complete a solid-solid transition or fails to completely crystallize upon returning from a fused state. If the calorimeter

is normally precise, such cases will usually make themselves known through

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lack of precision or through continued heat evolution to the calorimeter over a longer period of time than usual (sometimes over a period of many

hours). If the time is too long or the results inconsistent, the drop method is unsuitable and must be abandoned. If the behavior is consistent and

measurable, the difficulty may be resolved through use of auxiliary calori- metry such as solution calorimetry by which enthalpies are referred to a

desired reference state. Particularly uncertain are drops from the liquid state if the solid-composition line is not vertical. Changes of composition of solid phases will occur upon cooling, with resultant indefinite final states. Such cases can usually

be predicted if phase diagrams are available.

II. The Furnace

Invariably the furnace involves a vertical cylindrical cere surrounding

the sample. Sometimes the core is heated by means of its own electrical resistance, but more commonly through the electrical resistance of one or more suitable wire windings on it. Sometimes at the higher temperatures

inductive heating is used instead. Reference may be made to published descriptions of some of the furnaces

designed specifically for drop calorimetry. Important contributions to precision in operation were made by White36 ' 37 . Southard33 described a wire-wound furnace suitable for use up to 1500°C. His design has been used

and described more fully by Kelley, Naylor, and Shomate19

, and its essential features have been adopted by numerous other investigators, such as Ginningsand Corrltfccini10 The U.S. National Bureau of Standards6 improved

the temperature profile of a furnace for use to 900°C by means of thick

silver tubes surrounding the core. Nickel was used for the same purpose by

Oriani and Murphy28

, Dworkin and Bredig3

, Gilbert7

, and others. Graphite was used for this purpose for the temperature range 900-1 650 °C by Lucks

and Deem24 . Douglas and Payne2 have presented design calculations for a

furnace operating up to 1500°C. Fomichev, Kandyba, and Kantor5 used a

solid tube of platinum as a resistance heater, and nickel tubes to equalize

the temperature. These last workers also describe a vacuum furnace for the range 900-3000 °K with a graphite heater, together with a system of

coaxial graphite and metal shields. Levinson23 used a graphite resistance furnace for measurements in the range 1000-2400°C. Olette's27 furnace

follows the design of Southard's33

, but gives measurements to as high as 1900°C. The furnace of Kirillin, Sheindlin, and Chekhovskoi20 > 21 is heated

by tungsten windings and has been used up to 2400°G. Hoch and Johnston12 have described a furnace in which the sample is heated by radio frequency

induction in the temperature range 700-2700°G.

1. Furnace design and operation

In designing and constructing a furnace, ease of operation and ready

access for repairs are certainly important (along with superior performance)

if the purpose of the undertaking is a satisfactory rate of production of a body

of data. For example, the ability to easily swing or hoist the furnace away

from the calorimeter is an advantage. It is convenient to be able to exchange

heater windings and thermocouples without disturbing other parts. Easy and

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rapid return of the specimen from the calorimeter to the furnace and

readying conditions for a succeeding measurement deserve consideration.

A. General Type of Furnace Most Commonly Used

Most accurate drop calorimetry to date has been performed with wirewound, resistance-heated furnaces at temperatures of 1500°C or lower.

The cross-section of such a furnace is diagrammed in Figure 1 and may be

considered typical. However, the following discussion will present several alternative features.

Figure 1. Diagram of furnace and copper-block calorimeter A, Alumina winding tube

B, Alumina tube

C, Mullite D, Alumina powder

E, Magnesia brick

F, Refractory plug

G, Porcelain tube H, Stainless steel holder

T, Thermocouple

J, Brass dropping tower

K, Copper cooling coil L, Copper block M, Gates

N, Resistance thermometer

0, Receiving "well"

P, Heater

R, Oil level

185-297
(1) Materials of Construction. For operation up to 1500°C, the furnace

core (or cores, if there are two or more coaxial ones) is usually a tube of

alumina. The core, A, shown in Figure 1 (inside diameter 2-5 cm, wall

thickness 0-5 cm, length 58 cm) is a porous tube made of alumina. It is sometimes desirable to pass an inert gas through the core, partly to prevent

oxidation of the heater winding, sample container, or suspension wire. This protection is not essential when platinum (or platinum-rhodium alloy)

is used throughout for these purposes. The top and bottom plates of the furnace shown are of ordinary steel plate. The outside boundaries of the furnace are water-cooled through use of copper tubing. This is mainly for convenience, so metal sheet all around

should be satisfactory. If metal sheet is used, stainless steel is recommended.

The furnace pictured is disengaged from the calorimeter by means of a hand-operated, geared hoist (not shown).

The bottom of the alumina core fits into a short section of mullite tube

which in turn fits into a recess in the bottom plate of the furnace. This

arrangement serves to center the core. No centering device is used for the top

of the furnace; the furnace packing material serves to hold it in place.

However, some workers have found it convenient to silver-solder stainless

steel rings to the top and bottom plates.

Surrounding the alumina core and fitting closely to it is a second tube of

alumina, B, 0-6 cm thick. About midway in the insulation space is located a tube of refractory mullite, C, and the space inside it is packed with pure

alumina powder. The repair and replacement of the furnace winding is easily accomplished with this arrangement. The space outside the mullite

tube is filled with magnesia brick. As an alternative, the insulating space between the core and the outside

container may be occupied by several concentric, highly polished metal

cylinders which serve as radiation shields.

(2) The Heaters. Although a furnace may be heated by passing an electric current through a conducting core, the electrical resistance of the core must be relatively high unless very large currents are used, requiring unusually large or water-cooled leads. This difficulty is usually avoided by

passing the heating current through a wire which may be wound on the

furnace core. The main requirement of the heater is that it surround the sample with a

region whose temperature varies as little as possible so that the mean temperature of the sample may be ascertained accurately. Constancy of furnace

temperature implies a steady state in which the heat losses are balanced by

the output of the heaters. A variation of the heating current by 1 per cent

will vary the steady-state temperature of the furnace by approximately

20° in the neighborhood of 1000°C, an example which illustrates the fact that approximate constancy of furnace temperature depends more upon the thermal inertia (large heat capacity) of the furnace than is often realized. The furnace power is nearly always supplied by one or more heaters wound on the core, which may be purchased with grooves on the outside for uniform heater spacing. Frequently more power is supplied to the ends of

the core than the middle to compensate for the heat losses from the top and

bottom of the furnace. This may be accomplished by shunting part of the

186-298
current from the center portion of a single winding or by having three

separate windings with independent controls. In practice, the center heater

usually extends over the middle 65-80 per cent of the core. Care must be

taken that the temperature profile of the furnace does not have or develop

unwanted humps or hollows. Although a single winding has a narrower

constant-temperature zone, it is free from this defect. When massive cores are employed within the main heaters, additional

secondary heaters are advisable to prevent temperature lags and to aid in controlling the core temperature. These heaters may be wound around a

separate core immediately surrounding the sample, or if the massive core

is a sufficiently good heat conductor, be located within the conductor itself. The use of the secondary heaters can be more important if automatic temperature control is employed.

Power is conveniently supplied by means of variable autotransformers.

If more than one heater section is used, it is advisable to feed each section

by its own transformer.

Nichrome (Ni-Cr 80:20) wire is used most often for heater windings at lower temperatures. It has a fairly low temperature coefficient of resistivity,

but cannot be used in air much above 1000°C because of excessive oxidation.

Platinum-rhodium windings are suitable for continuous use up to about

1500°C, but in air they deteriorate rather rapidly above this temperature.

Platinum containing 10 per cent rhodium has about three times the resistivity at 1500°C as at room temperature, but this is no real disadvantage. Plati- num containing 20 per cent rhodium is sufficiently flexible for winding on the core if annealed ; its advantage is mainly a slightly higher melting point.

For still higher temperatures a more refractory winding is needed. Lucks

and Deem24 used molybdenum windings up to 1650°C, surrounding the wire

with a protective atmosphere. Main heater wire should not be too fine,

because of decreased mechanical strength and shorter life. A diameter of

from 0-05-0-1 cm has been commonly used. Care should be taken to wind

the heaters firmly and uniformly.

The single-winding heater used in the furnace shown in Figure 1 is made

up of 58 ft. of B and S No. 18 (diameter, 0-1 cm) platinum containing 20

per cent rhodium on the spirally grooved alumina core. AC power is supplied

by means of a voltage stabilizer and two 7-5 kVA variable autotrans- formers in series. This scheme permits sensitive manual control. The power

consumption at 1500°C is about 1700 W.

(3) Heat Transfer and Temperature Gradients. Despite the practical importance

of enthalpy measurements at high temperatures and the simplicity of the drop method, the results of different investigators on the same materials

have often varied by several per cent. This type of calorimetry is thus seen

to be less developed than techniques at low temperatures. The principal reason for disagreement undoubtedly lies in measuring the sample temperature in the furnace. The singly wound furnace shown in Figure 1 provides an axial temperature gradient of less than 0-1 per cent of the temperature

(Celsius) per inch over the range 100-1500°C. Refinement may be made to improve and lengthen this 'hot zone'. The use of multiple heaters (Ginnings

and Corruccini10

) provided a few tenths of a degree per inch at 1100°C

in a furnace 46 cm long. The use of innermost, heat-distributing tubes of

187-299
silver provided the U.S. National Bureau of Standards6 with virtually no temperature gradient within the masses of silver. This furnace is fully described

in a subsequent section. Fomichev et al. 5 used nickel tubes and obtained a

precision of measurement of 0-1° up to 1500°K.

It is desirable to reduce the temperature difference between the inner

furnace wall and the sample as much as possible. This is particularly important if the temperature of the sample is measured by means of a thermocouple whose junction is attached to the wall. Also, the presence of a gas surrounding the sample (a few mm Hg suffices) will minimize the wall- to-sample gradient, as will fusing the sample in its container if this is possible.

Heat transfer between the container and wall is increased by reducing the

gap between them. Consideration should be given also to the heat-transfer

coefficient of the gas to be used in the furnace. When the conditions are favorable and the nearly isothermal part of the core is not too short, the

sample will radiate an insufficient amount of power from the bottom of the

furnace to invalidate its temperature measurement.

B. Furnaces with a Good Heat-Conducting Core

A good heat-conducting core is provided by a material of high thermal

conductivity and by using a large cross-section of the material. The result

is an unusually large total heat capacity. The major consequences in the

performance of the furnace compared with that described in Section II-l-A

are, first, that axial temperature gradients and errors in measuring the sample

temperature can be made smaller or alternatively that they can be made

equally small with considerably less effort, and second, that the inertia of

the furnace to temperature change becomes so large that the temperature can easily be kept constant to 0-01 0 or better by simple control by hand.

A few examples of such furnaces and their major differences from the more commonly used type will be discussed. The U.S. National Bureau of

Standards6 constructed a furnace having a core of silver, which is resistant to corrosion, has the highest thermal conductivity of any metal, and can be

used up to its melting point, 962 °C. A cross-section of the furnace is shown

in Figure 2. The main furnace heater was made in three separate sections corresponding in elevation to the three silver cylinders, J, A, and L, which

were located inside the alumina. The silver cylinders are supported and

separated by porcelain spacers, Y, having a far lower thermal conductivity

than silver, so that the end silver cylinders, J and L, need to be maintained

at a temperature no less than a few tenths of a degree of that of the central

silver cylinder, A', for the gradients in cylinder A" to be negligible. Coaxially

with the silver and porcelain cylinders are Inconel tubes which enclose

the sample container, D, with its suspension wire and shields, S. Helium

flows upwards past the container and escapes from a small orifice at the top.

(Care must be taken that cold air cannot fall into the lighter helium in the furnace.)

Figure 2 shows some of the vertical holes, N, drilled through the silver and porcelain and placed 90 degrees apart azimuthally. These holes contain

the platinum resistance thermometer, the platinum-rhodium thermocouple,

and the differential thermocouples between the end silver cylinders, J and

L, and the central cylinder, K. In one of these holes are placed three small

188-300
0 2 5 10 cm

Figure 2. Diagram of silver-core furnace and ice calorimeter A, Calorimeter "well"

B, Beaker of mercury

C, Glass capillary

D, Sample container

E, Ice bath

F, Copper vanes

C, Gate

I, Ice mantle

M, Mercury

N, Inconel tubes

P, Pyrex vessels

if, Mercury reservoir

S\ Platinum shields T, Mercury "tempering" coil

V, Needle valve W, Water

Y, Porcelain spacers JH, KH, LH, Furnace heater leads

/, K, L, Silver cylinders

189-301
secondary heaters, running parallel to the axis of the furnace and located

at the elevations of the three silver cylinders. The temperature of the silver responds to sudden changes in the main-heater currents in 3-6 min, but to changes in the secondary-heater currents almost completely within 1 min.

For furnace insulation, powdered silica (Silocel) is used. The operation of the furnace is normally limited to 900°C, to provide

a margin of safety against melting the silver, and a thermocouple-reading

meter (Sym-ply-trol) monitors each silver cylinder to shut off the heating

current automatically should the temperature accidentally become a few

degrees higher. A fourth such monitoring device shuts off the heating currents

if the platinum resistance thermometer is in place and the furnace temperature exceeds about 625 °C. Some investigators have accomplished the same objectives by using copper

instead of silver. Pure copper has a higher melting point (about 1083°C,

but it has been reported that dissolved oxygen can lower the melting point

by as much as 20°) ; however, at all except relatively low temperatures the

copper must be protected by an inert atmosphere. Other investigators have

replaced the silver by nickel, which has only about 20 per cent of the thermal

conductivity of silver but still provides a similar advantage; the nickel has a still higher melting point, but must of course be protected from excessive

oxidation. Lucks and Deem24 have used a silver furnace of the above design

up to 900°C, separating the silver cylinders by alumina spacers. From 900-

1650°C they used a similar furnace in which the silver was replaced by

graphite and the alumina by refractory brick; the graphite was protected

from oxidation by an atmosphere of 95 per cent argon-5 per cent hydrogen.

C. Furnaces Operating Above 1500°C

Although a relatively small amount of enthalpy data above 1500°C has

been reported, designs of several calorimeters have been published for measurement to as high as 3000°K. The furnaces for two of these calorimeters

will be described briefly.

Hoch and Johnston12 have designed a furnace to be used in drop calori- metry to 3000 °K. The sample is heated inductively, the radio frequency

being supplied by a 20 kW General Electric RF generator through a "work coil" consisting of water-cooled, 0-25 in copper tubing. The sample,

heated in the center of this "work coil", is suspended by means of a tantalum

wire. The tantalum wire is attached to an iron cylinder which is held in place by an external electromagnet. This arrangement provides a dropping

mechanism for the sample. Thus, the furnace is essentially a vacuum-tight

shell containing the coil and sample. The sample temperature is measured

by sighting holes in the sample container with a disappearing-filament optical

pyrometer. The furnace and attached calorimeter are sealed vacuum tight

with O-rings and the system is evacuated with an oil diffusion pump. A

small amount of helium is introduced after dropping the sample to facilitate heat distribution. The furnace walls are wound on the outside with copper

tubing. The tubing is used to help degas the furnace when heated by steam

and then to cool it during a run. The furnace is about 34 cm long and 25 cm

in diameter.

Fomichev et al. 5 describe a furnace for use at 1000-3000°K. Heating is 190-302
accomplished by means of a graphite tube with an internal diameter of

4-5 cm, a length of 60 cm, and a wall thickness of 0-3 cm. Electrical contact

is made with water-cooled flanges of copper or brass. These flanges are attached to springs to allow for expansion of the graphite tube. The heater

is surrounded by nine coaxial shields; the first is made of graphite, the second

and third of tantalum, the fourth, fifth and sixth of molybdenum, and the

remaining three of stainless steel. All outer surfaces of the furnace are watercooled. In addition, two water-cooled screens are provided above the top

and below the bottom of the central furnace openings. These screens can

be moved to one side by means of bellows. Temperature is measured by

optical pyrometry, utilizing a reflecting prism which is located along the

central axis and between the sample and the calorimeter. The prism is moved out of the way with a bellows. All parts of the apparatus are vacuumtight, and different parts may be sealed off so that samples may be placed

in the furnace without disturbing the furnace temperature. The sample is suspended in the furnace by a Ol mm tungsten wire which is melted to release the sample. An inert gas (at a pressure of 10-20 mm Hg) is used

during the measurements, as it improves the general performance. Power

is supplied through stepdown transformers. At 3000°K the power consumption is 40 kW.

D. Automatic Temperature Control of the Furnace

The two furnaces illustrated by Figures 1 and 2 use manual control of

heaters. The resulting temperature fluctuations are well within the limits of other uncertainties involved in the measurement of the sample temperature. Manual control satisfactorily provides for the "over-shooting" neces- sary for overcoming the thermal lag of the furnace parts, thus providing a quicker approach to thermal equilibrium. Automatic controls have been

found to be of limited value for these furnaces. The detailed treatment of automatic-control instrumentation can be

found elsewhere. Specific applications to calorimetry are discussed in Chapters 5 and 9. A few general comments may be made here relating to automatic stabilization of furnaces in drop calorimetry.

The important point is to have the response time between the sensing

element and the heater it controls as small as practicable. This sensing

element may reflect the temperature of a point or the temperature of a

region. The former may be sensed by a single-junction thermocouple, the

latter by a multiple-junction thermocouple or an element whose electrical resistance varies sufficiently with temperature. When the furnace winding

is of platinum-rhodium, the temperature coefficient is such that its resistance may be used as the temperature-sensing element.

Furnaces with low thermal inertia, such as those using reflection shields, are more sensitive to small current changes and are best served by automatic

control devices. Furnaces with massive metal inner tubes are very sluggish

to temperature change and will benefit least from automatic controls. The response of the best controls on the market is dependent on three

factors. Briefly, they are: how far the temperature diners from the desired

value, how long it has been so, and how fast it is changing. If the refinements

of control are adequate for the time-lag of response, the major remaining

191-303
problem is likely to be securing a wide enough range of control to handle all likely variations in heater power and furnace heat losses.

2. Temperature measurement

A. The Thermocouple

The most common temperature-measuring device up to 1500°C has been

the thermocouple. Some base-metal thermocouples (such as ChromelAlumel and iron-constantan) have the appeal of large sensitivities. However,

with modern potentiometers reading to one microvolt or less, this sensitivity

is not needed, and for the most accurate work, the base-metal thermocouples

are not preferred over the more stable Pt versus Pt-Rh thermocouple.

Thermocouples of 94 Pt-6 Rh versus 70 Pt-30 Rh3** and 80 Pt-20 Rh versus 60 Pt-40 Rh15 have the advantage ofmaintaining their calibrations for' comparable periods of time at temperatures some 300° higher than the conventional Pt versus 90Pt-10Rh couple. Additional investigation of these and

other thermocouples particularly adapted to high temperatures may

recommend them for measurement in calorimetry. At the present time the

reliable Pt versus 90Pt-10Rh thermocouple (or the Pt versus 87 Pt-13Rh

thermocouple) is the best for accurate work. This couple shows very little change up to 1200°G, and can be used up to about 1500°C with frequent

calibrations. Roeser and Wensel34 have stated that with favorable calibration the uncertainty in interpolated values of temperature should be as small as 0-3° near 1100°C and 2° near 1500°C.

(1) Calibration. Details of thermocouple calibration outside the furnace

are dicussed in Chapter 2. The ideal Pt versus 90Pt-10Rh thermocouple is compfetely homogeneous and free from strains so that its reading depends

solely on the temperatures of its junctions. As the thermocouple is used, the

e.m.f. changes are mainly due to diffusion through the junction and to oxidation. These effects can be made negligible if the working couple is frequently calibrated in situ in the furnace. Calibration below the point of

thermocouple deterioration (about 1500°K) may be accomplished by

comparison with a calibrated thermocouple. A special method of calibration

makes the comparison with the hot junction of a "standard" thermocouple

firmly attached (preferably in a well) to the sample container which is hanging in place in the furnace. Otherwise calibration in situ at one temperature is generally made by

melting a short length of gold wire (at least 1 mm) welded between the ele- ments of the thermocouple. The e.m.f. at the melting point corresponds to the halt in the temperature rise. The assumed temperatures of all fixed

points used for thermocouple calibration should be stated because such

information has sometimes permitted later revision of old data to a basis closer

to the true thermodynamic temperature scale. Roeser and Wensel34 report

that in most cases curves of differences between actual thermocouples and

standard reference tables are linear over the entire range 0-1700°C.

The use of Pt versus 90Pt-10Rh thermocouples above about 1500°K

necessitates frequent recalibrations. It has been found that, in typical

circumstances, the rates of change per 3 h of heating in an oxidizing

atmosphere are about 0-2° at 1600°K, 0-4° at 1700°K, and 1-0° at 1800°K.

192-304
(2) Common Sources of Thermocouple Error. The temperature measurement of

the sample suspended in the furnace requires that the thermocouple junction

and the sample be at the same temperature. Further, the temperature

gradient of the thermocouple along the leads to the junction should be

small. In the furnace shown in Figure 1, the thermocouple leads are brought

into the furnace through a 5 cm-long refractory plug, F, by means of

porcelain tubes, G. The plug is made of zirconium silicate tubing for high

thermal shock resistance. The porcelain tubes are fixed in position with

alumina and cement. The thermocouple leads run along near the furnace

wall to the sample container. The junction touches the top wall of the

suspended container at temperatures below 800 °K, and it is placed within

1 mm of the top above this temperature to prevent welding or other inter- action between the two surfaces. Proximity of the leads to the solid parts

of the furnace is highly desirable to prevent conduction into or away from

the junction; a similar result can be achieved by welding the junction to a band of a highly conducting metal such as platinum which lies firmly against

the inside wall of the furnace. The problem here is the difficulty in making

frequent calibrations of the couple. If, as is normally to be expected, heat is being conducted away from the junction, an error from this effect will result in an enthalpy that is too high. This error is equivalent to associating the net enthalpy of the sample with a furnace temperature that is too low, and in

this sense the same effect in the empty-container run affords no compensation.

The furnace of Figure 2 has its thermocouple tubes inserted directly into the

thick inner wall of silver. A possible source of error in thermocouple readings may arise if there is electrical leakage from the heaters. The heaters are usually operated with

a.c. to minimize this, but such errors might arise from some rectifying

effect in the insulator materials. Momentary shutting off of the furnace

power is the standard technique for testing this source of error. Other

sources of error are contamination through container leakage and contamination from impurities in the insulating inlet tubes. When differential thermocouples are used, leads to the outside should

be of platinum rather than platinum-rhodium to avoid changes of composition arising from passage through regions of large temperature gradients.

B. Use of Other Temperature-Measuring Instruments

Even at the lowest furnace temperatures, the error in temperature measure- ment with a thermocouple may easily be as much as 0-1 °C. The platinum

resistance thermometer defines the International Practical Temperature

Scale up to 630-5°C and, because an accuracy between 0-01° and 0-1 °C is not difficult to obtain with it, may be substituted in this temperature range.

If the thermometer uses mica for insulation, as has been customary in the

past, it cannot be used for higher temperatures. The thermometer must be

encased in some material which does not soften at the highest temperatures

of use and at the same time allows a snug fit inside a solid part of the furnace

so that conduction along the leads is not a source of appreciable error. Such a mica-insulated thermometer, encased in 90 per cent Pt-10 per cent Rh, has been used in the silver-core furnace at the U.S. National Bureau

of Standards6 . This thermometer had an ice-point resistance of about the

193-305
conventional 250,, which is better than thermometers of much lower

resistance that have been constructed. Periodic reading of the ice-point value,

particularly after the thermometer has been to its highest temperatures, is highly desirable to detect the need for recalibration. If the resistance element

becomes stretched, readings at all temperatures should be displaced by the same percentage as at the ice point. However, if other changes occur,

e.g. through contamination of the platinum, the readings at all temperatures

may tend to be changed by more nearly the same amounts as at the ice point.

If a platinum resistance thermometer and thermocouple are both used

in the furnace, it becomes possible not only to calibrate the thermocouple

by the thermometer (up to 630°C) or to compare their independent calibrations, but also to compare them regularly as a means of detecting any large,

otherwise unsuspected, change in the calibration of either measuring

instrument. Compared with a thermocouple, a platinum resistance thermometer has the disadvantages of slower response to temperature changes

(offset by the temperature sluggishness of a massive core), and difficulty in construction, particularly in mounting and insulating the long fine wire.

The optical pyrometer is usually used to measure furnace temperatures

above the range of Pt-Rh thermocouples. It affords less precision than the Pt versus 90 Pt-10 Rh thermocouple, but has the advantage that it defines the International Practical Temperature Scale above 1063°G.

3. The sample in the furnace

A. The Container

( 1

) Choice of Material. The choice of a suitable container material is usually not difficult at lower temperatures, but it well may be the greatest single factor hindering the extension of data to higher temperatures. Important

considerations for container materials are mechanical strength, melting

point, emissivity, reactivity, and reproducibility oftheir thermodynamic states. The most common factor limiting the choice of a suitable container

material is reactivity with the sample, through either chemical reaction or

miscibility. If the container is exposed to an oxidizing atmosphere, this is also a factor. A useful generalization is that a metallic sample is more likely to be inert to a non-metallic container and vice versa. Since reactivity often

varies greatly with temperature, a calculation or estimation of the free energy changes of all possible reactions is often useful. Platinum-rhodium

(10 or 20 per cent) most generally satisfies the requirements for a metallic

container to about 1500°C. Gold and silver have similar advantages below

their melting points (1063° and 962 °C). The high purity and reproducible

state attainable with these metals allow container replacement with no

appreciable change in enthalpies. If a non-metallic container is needed

silica glass has frequently been used. Devitrification to cristobalite above

1300°C limits its use to about 1450°C.

Measurements above 1500°C are sparse, so that container information

is also lacking. Tantalum has been used to 2600 °C and tungsten to 2500 °C. Graphite, surrounded by a shell of metal to improve the radiation characteristics or to afford an extra seal against possible escape of the sample, could

sometimes be used. It must be recognized that in many cases a high container

enthalpy will have to be tolerated. 194-306
In the absence of any suitable container material, the problem has been

solved by using the sample itself in mechanically cohesive form. In this case the heat lost in the dropping process must be estimated or else determined

by varying the ratio of mass to the surface exposed. Beryllium oxide was

measured to 2200 °K16 by using a sintered sample of BeO surrounded by a

0-2 mm-thick sheath of molybdenum metal which protected the sample from

excessive heat loss and provided a hollow for temperature measurement.

Many laboratories have adopted transition-metal or base-metal containers

for use to moderately high temperatures. The ready availability and workability of these metals and alloys have made them a logical choice. However,

it is wise to avoid the use of alloys that undergo transitions during cooling.

If the degree of transformation and the consequent heat evolved are the same in measurements when empty and when full, the transition cannot

cause any error. However, with a full container the slower rate of cooling

can result in the evolution of more of the heat of transition. The net heat

attributed to the sample is consequently too high. Ginnings8 has critically

examined three sets of drop calorimetry data involving containers of Nichrome V (80 Ni-20 Cr) and stainless steel, types 430 and 446, all of which

undergo transitions between 500° and 700°C. He detected abrupt increases

in the enthalpy-temperature functions derived for the samples from the measurements and showed that, by attributing the effect to the above cause, the data above the transition temperature became much smoother. The

enthalpy correction in these cases ranged from 0-05-1-8 cal/g of sample

and lowered the calculated heat capacities by 0-3 to several per cent.

(2) Container Design; Enclosing the Sample. The container is usually cylindrical and has a capacity of the order of 10 cm3 . The capacity is determined

primarily by the requirements of the receiving medium after the drop. The

wall thickness of metal containers is usually 0-2-0-3 mm, but a thicker wall

is needed for non-metallic containers.

Five designs of sample containers are shown in Figure 3. Figure 3(a) shows

a single cylinder with snug-fitting end caps. When made of a base metal,

the edges can be sealed by induction welding if gas-tightness is needed, with

the sample remaining cold and surrounded by any desired gas. If the container is of noble metal (Pt-Rh, Au, or Ag) the edges can be welded with a gas-oxygen torch. Figure 3(b) shows a variation used by the U.S. Bureau

of Mines in which the top is connected to a narrow neck. After the sample

has been introduced, the container may be evacuated and filled with helium

gas. The neck may be pinched shut near the top and sealed gas-tight by

gas-oxygen welding. A container sealed in this manner will usually remain

so to 1500°C If volatility during welding is a problem, the neck can be

sealed shut by gold soldering; this, of course, limits the measurements to temperatures below the melting point of gold. In extreme cases of volatility,

placing the container in a shallow dish of water keeps the temperature down

during the soldering process. Figures 3(c) and 3(d) show two containers closed by hard metal cones

against gold gaskets. These have been used extensively at the U.S. National

Bureau of Standards, container in Figure 3(c) being of Nichrome V, and

container in Figure 3(d) being of Monel for measuring hydrocarbons up to 20 atm vapor pressure. The threads of the screw cap are pre-oxidized to 195-307
1cm 1 cm 1 cm 1cm 1cm

Figure 3. Designs of sample containers

a, Of base or noble metal and with welded end-caps

b, Of 90% Pt-10% Rh, sealed by welding or soldering

c, Of Nichrome V (80% Ni-20% Cr), sealed by a gold gasket

d, Of Monel, sealed by a gold gasket D (for volatile liquids)~(filling device : A, screw driver ; B, filling tube ; C, tin gasket)

e, Of silica glass, sealed by Welding

prevent sticking by self-welding at high temperatures. Such mechanical

closure is convenient, but gas-tight seals are difficult to maintain.

Figure 3(e) shows a type of silica glass container. Upon filling, the tube

is attached to a vacuum pump and "pulled off" with a hydrogen-oxygen

torch close to the body of the container, retaining the vacuum inside. Accurate knowledge of the masses of sample and container materials

is especially important because the series of runs could have a high inter- consistency that would not reveal large constant or systematic errors in mass. A simple test for a gas leak in the container is to pump around it, then surround it with air one time and helium (or hydrogen) another; with a few cubic centimeters of gas space inside, the difference in weight when

there is a leak is easily detectable.

B. Suspending and Dropping the Sample

(1) Suspension and Dropping Mechanisms. The sample is suspended in the furnace by means of a suitable wire, the kind and diameter of which depend

upon the temperature and the load. Platinum-rhodium (10 or 20 per cent)

has commonly been used up to 1500°C. Diameters range between 0-1 mm and

0-4 mm. Tungsten and tantalum have been used at higher temperatures.

Southard33 and many later investigators left the suspension wire attached

to the container as it fell into the calorimeter, enabling easy return of the

sample to the furnace. The enthalpy of the wire is assumed to cancel out

in the measurements of the container when full and when empty. The other

common procedure is to melt or cut the wire. One investigator used a magnetic release 12 . Another had an arrangement whereby the wire was made to slip off the container4. 196-308
The presence of two or three thin circular disks of bright platinum attached

to the suspension wire just above the sample will reduce radiation losses out

of the top of the furnace. In the furnace shown in Figure 2 such shields are more important in preventing serious heat losses by convection from the hot sample out the calorimeter10

, because there is only one gate and it must be outside the calorimeter proper to dissipate radiation from the fur- nace. However, in the furnace shown in Figure 1 the lower gate is inside the calorimeter and therefore prevents such losses of heat from the sample.

If the sample falls unattached into the calorimeter, the impact with the

calorimeter may be cushioned by falling on to a deformable body. Southard's

procedure of leaving the entire suspension wire attached includes the use of a heavy metal plunger which, attached to the suspension wire, falls through

a vertical tube above the furnace. Through the use of holes in the tube there

is nearly free fall until the plunger reaches a position corresponding to the

point where the sample has entered the calorimeter, when it is slowed by an

air cushion. The air escapes through a small hole in the tube near the bottom

of the plunger travel. The entire fall (including deceleration) takes less than

0-5 sec. To minimize stretching of the suspension wire, Douglas and Payne2 arranged for the container to decelerate uniformly at the end of the fall by

stretching a pre-set spring that had a stop at the end of the fall. The addition of weights to the plunger when the empty container is used

(to keep the total falling mass constant) will help to prevent a systematic

error between the full and empty experiments. It is more important to minimize friction within the plunger tube in order to approach as nearly

as possible the acceleration of free fall. Ginnings and Corruccini1

"0 have

estimated that in free fall at 900 °G, a typical container with sample would

lose not more than one calorie more than the empty container.

(2) Time in the Furnace. The length of time that the sample is in the furnace

is important and varies with the conductivity and size of the sample.

A simple test for temperature equilibrium is to compare several experiments

with different times in the furnace and then to select a time which is clearly

adequate. Under conditions such that the sample is heated mainly by

conduction, it may be shown that approximately

k = //logio[^o - ?)] (1)

in which q is the heat found with time t in the furnace, qo is the heat when

the time is adequate for reaching virtual equilibrium, and & is a constant

representing the time for the temperature difference between the furnace

and sample to be reduced to 10 per cent of the original value. A time in the furnace can then be adopted of at least 4k, since according to equation

(1) this time brings heat transfer to the sample to within 0-01 per cent of

completion. Actually, the contribution of radiation to the heating of the

sample increases rapidly with temperature, with the result that the use of

equation (1) gives an upper limit to the time required in the furnace at higher temperatures.

Additional factors, such as proximity to temperatures of melting, transition, or other complex structural changes, may make equation (1) unsuitable.

197-309
III. The Calorimeter

1. The isothermal calorimeter

An isothermal calorimeter absorbs or evolves heat without a change in temperature, and the amount of heat is measured by an accurately measurable change in some quantity such as volume. Although calorimeters

involving vaporization are more sensitive, those involving fusion (particularly

of ice) have been more commonly used in drop calorimetry. If the volume

change is determined from the mass of displaced mercury, the ratio of heat

absorbed to the mass of mercury (K, the calibration factor of the calorimeter)

is given by

K = AHmlW ~ v)dM (2)

in which AHm is the enthalpy of fusion of the melting substance per unit mass, v' and v are its specific volumes in the less and more dense states respectively, and du is the density of mercury (all at the calorimeter

temperature).

Compared with other calorimeters, the isothermal type has certain

advantages and disadvantages well exemplified by the ice calorimeter. Its calibration factor is a universal constant, no temperature or electrical measurements are required in its operation, and when surrounded by an

ice bath the heat leak can be made very small and quite constant. However,

such a calorimeter is restricted to use at a fixed temperature and must

be completely leak-free and so rigid that its volume capacity is extremely

constant. The isothermal type of calorimeter is not inherently more precise nor more accurate than the best of the other types, and its construction

for accurate work requires a fair amount of time and care ; but once properly

built, it can yield measurements rapidly and accurately by relatively simple

operation. In this chapter detailed discussion of the isothermal calorimeter will be

limited to the ice calorimeter. Isothermal calorimeters employing organic

liquids in place of water have also been used. The diphenylether calorimeter,

which has been applied to the determination of the enthalpy of metals14 as well as in reaction calorimetry, differs from the ice calorimeter principally

in operating at a higher temperature (26-87 °C), expanding during absorption of heat, and being over three times as sensitive.

A. Design of the Ice Calorimeter

A cross-sectional diagram of an ice calorimeter which has been in use in high-temperature drop calorimetry at the U.S. National Bureau of Standards

for many years6 is shown in the bottom half of Figure 2. The calorimeter

"well", A, which, receives the sample from the furnace, is constructed of some low-thermal-conductivity metal such as Nichrome, with a wall thick- ness of approximately 0-25 mm. (The slight taper in the tube shown in

Figure 2 is really unnecessary.) The hot sample comes to rest near the bottom

of the well, and conduction of unmeasured heat out of the well is negligible.

Dry gas (He) flows slowly up the well at all times to keep out moisture, and the

top ofthe well is stoppered loosely when not attached and sealed to the furnace. 198-310
The well is really in two sections joined by a gate, G, which is opened briefly to admit the sample but otherwise shields the calorimeter from radiation

from the hot furnace. The gate is a tinned copper disk with a hole and a

wide-angle slot which moves the sample and its suspension wire to the side of the well when the gate is closed after dropping in the sample.

Around the bottom end of the calorimeter well are two coaxial cylindrical

vessels, P, the inner one enclosing the "calorimeter proper" and the outer one constituting the calorimeter jacket. These vessels are commonly of

Pyrex glass to permit visual observation as ice is being frozen ; however, to reduce somewhat the heat transfer by radiation between them, some

experimenters have silvered the surfaces except for a narrow vertical strip.

The two glass vessels are attached at their tops to metal "caps". At the

U.S. National Bureau of Standards the outside top of each glass vessel was

first ground to true roundness, and the seal to the metal was then made

with a thin intervening layer of Apiezon W wax. If the wax layer is too

thick, the calorimeter may sag or fall apart when allowed to warm up, but

the thickness of the hard wax must be several times the difference in shrinkage of the glass and the metal when cooled. In one case2

, the wax

gap was successfully reduced to 0-15 mm by using a low-expansion iron alloy called "Therlo" (29 per cent Ni, 17 per cent Co, 0-3 per cent Mn), which,

however, must be protected against corrosion. Some experimenters have

replaced the wax joints by less fragile seals. Leake and Turkdogan22 interposed a winding of string impregnated with Araldite synthetic resin,

with compression by a screw collar outside the metal flange. Glass-to-metal

seals28 and O-rings have also been used.

Figure 2 shows a series of horizontal copper disks or vanes, F, which

provide good heat paths inside the calorimeter vessel. These disks are conveniently separated by short metal sleeves. In soldering this assembly

to the well and subsequently tinning or silver-plating the surfaces to render

them inert to water, it is believed desirable to avoid all narrow crevices

which might be filled to an irreproducible extent by the water in the calori- meter.

Several experimenters have provided the top metal cap of the calorimeter

vessel with a filling tube to introduce the water or replace it. Such a tube

(necessarily closed at the top) entails the danger that during the freezing

of an ice "mantle", /, the water in it may freeze solid at the level of the cap

and burst the tube owing to the expansion accompanying freezing. The use of only one opening to the outside (the "mercury inlet tube"), which

normally is completely filled with mercury, obviates this danger. This inlet tube connects the mercury pool, M, in the calorimeter with the mercury

accounting system (C, B, V and R) outside. The center portion, T, of this tube, wound around the outside of the outer metal cap, has preferably a

capacity for as much ice-cooled mercury (perhaps 10 cm3

) as will ever

enter the calorimeter in a single run. The ends of the tube, however, should

be of smaller bore, partly to minimize the effect of varying room temperature on the volume of the mercury outside the ice bath. Since solder which

would dissolve in the mercury must be avoided, one can use a single tube

and draw down its ends. The mercury-accounting system has two glass capillary branches, one 199-311
leading through a valve, V, to a weighed beaker of mercury, B, and the other (a capillary, C, of 0-6 mm bore which is preferably calibrated after assembly) being provided with a scale for observing small volume changes

when the valve is closed. The capillary is sealed to a mercury reservoir, R,

above. For the valve, a hard-steel needle seating precisely on soft steel gives

satisfactory closure, but a rotationless stem and a softer seat (platinum or Kel-F) may.be preferable2

. Oriani and Murphy'28 substituted a precisionbore glass stopcock. The capacity of the valve must be small and reproducible

because one cubic millimeter of mercury is equivalent to almost one calorie of heat. The calorimeter heat leak can be made so small that it does not require

frequent or accurately timed readings. The scale for the capillary outside

the calorimeter is located some 20 cm above the mercury level inside the calorimeter so that the pressure head on the water in the calorimeter lowers

its freezing point to approximately that of the air-saturated water jn the

ice bath outside, the heat leak therefore being conveniently small. Some

investigators have evacuated the jacket space of the ice calorimeter to reduce

heat leak. However, keeping the space filled with a dry gas (such as CO2)

at atmospheric pressure has the advantages of decreasing the net downward

force on the inside (calorimeter) vessel and of making the volume capacity

of the latter nearly independent of changes in atmospheric pressure. In designing rigid mechanical supports for the calorimeter (not shown in Figure 2), some compromise must be made between low flexibility and lowconduction heat paths from the room to the calorimeter. It is also wise to provide sufficient adjustability to facilitate making the calorimeter well and

the furnace core coaxial and strictly vertical. Although modern techniques of thermoregulation permit control of the

temperature of a bath to ;t0-001

o C, a simple ice bath, E, accomplishes the same result with no necessary temperature fluctuations and no instrumentation. If wax seals are present, it is convenient to replace the ice bath by

circulated cold water during idle periods, but such a bath is likely to be

inadequate to preserve any ice mantle present in the calorimeter.

B. Assembly

The two glass vessels are attached and tested for the slightest leak; a helium leak detector is convenient. Pure gas-free water, W, which must

be kept in a closed system to prevent absorption of air, is then allowed to

fill, by gravity, through the mercury inlet tube if no special filling tube

has been incorporated, the dry and thoroughly evacuated inner glass vessel. Unless freezing is* begun immediately, some mercury is then drawn into the reservoir to seal the calorimeter water from air. A suitable amount of mercury is next substituted for an equal volume

of water in the calorimeter by alternately freezing ice to expel water and

melting the ice to draw in mercury in its place. A closedrbottom tube

inserted into the calorimeter well can serve to hold crushed 'Dry Ice' (solid

CO2) to freeze an ice mantle or to contain a stream of warm water to melt it. When the mercury level inside the calorimeter is above the bottom of the mercury inlet tube, one more ice mantle must be frozen, and this must be

large enough to expel a combined volume of water and mercury equal to 200-312
the inlet-tube capacity plus the largest amount (30 cm3 or more for the

calorimeter shown in Figure 2) that will be expelled in freezing any future

ice mantle. Owing to a lens effect, the ice mantle will soon appear to occupy

the entire cross section inside, even when it is far from doing so, and an

estimate of the total volume (and hence average diameter) of the ice present

is far more reliably provided by the total volume of mercury that has been

expelled.

High purity of the water inside the calorimeter is essential for calorimetric

accuracy for two reasons. First, any dissolved gas forced out of solution

by freezing would tend to redissolve slowly and in so doing vitiate the accurate volume determinations. Second, if the water is impure the calorimeter will absorb, without measuring, heat of the order of a calorie for every 0-001 °C

that the calorimeter temperature rises as the ice melts. It is believed possible,

however, to remove as much as 99-9 per cent of the dissolved air by a single

fractional distillation of the water, and tests of electrical conductivity can

be used to detect electrolytic solutes. The mercury used should be of very

high purity. As long as the mercury is kept out of contact with metals which

it dissolves, it can be separated from surface impurities by the usual process of fractional filtering and can be reused repeatedly in the calorimeter.

C. Calibration Factor

The calibration factor used for the ice calorimeter should not be a value

calculated by substitution into equation (2), but one determined by direct

electrical measurement. Nevertheless, the same calibration factor should be

applicable to all precise ice calorimeters. The following electricallydetermined values are "ideal" in the sense that they have been corrected

to the basis of no pressure change through a change in the mercury level inside the calorimeter when heat is absorbed.

Ginnings and Corruccini9

, in an extensive investigation of optimum

conditions, found 270-42 ± 0-06 abs. J/g Hg; and later Ginnings, Douglas,

and Ball11

, using an improved ice calorimeter and more favorable

conditions, found from about 100 determinations a mean value which, with

a slight correction6

, is 270-48 i 0-03 abs. J/g Hg. (The tolerances stated are estimates of absolute accuracy.) Leake and Turkdogan22 later obtained a value of 270-54 abs. J/g Hg, with a standard deviation of ± 0-17. These

values agree within their uncertainties, but the value of Ginnings, Douglas,

and Ball is believed to be the most reliable.

D. General Procedure of Operation

For heat measurements, the first step is to freeze an ice mantle. There i s usually more or less supercooling, so that the first ice appears suddenly,

and may branch out so as to appear to fill the calorimeter. For precise

calorimetry it is recommended that most of this initial ice be melted. A thin

layer of ice in the top region of the calorimeter is needed to trap small

amounts of heat that might otherwise escape. If the calorimeter is to be

operated the same day, a very small layer of ice on all the metal surfaces should be deliberately melted first. The inside of the well is then wiped dry

and the entire ice bath is replenished (to the level, L, in Figure 2). Since

ice-water interfaces in the bath must be kept close to the calorimeter,

201-313
freshly ground clear ice is used, and the interstices are filled with pure

water. When the heat leak becomes "normal" and steady (usually within

2 h), enthalpy measurements may begin.

It is believed that ice mantles may be used in accurate heat measurements

up to several days after they are frozen, provided the melting of ice at the

top of the ice bath during periods of standing (especially overnight) has not allowed much of the upper, protective part of the ice mantle to melt. To

maintain a constant heat leak when the calorimeter is in actual operation,

it sometimes proves necessary to pack occasionally a little fresh ice in close contact with the emerging calorimeter well. If the ice bath is well insulated

(Styrofoam of a few cm thickness serves excellently), one packing of ice in the bath should be sufficient for 12 h or so if the top few cm of ice are replenished often enough. Once an ice mantle is partly melted, it is considered

mechanically safer to melt all the ice attached to the inside calorimeter

surfaces before freezing a new ice mantle.

When the beaker of mercury is removed from the submerged tip, the

mercury in the latter should not recede owing to the presence of air in the valve. If the packing of the stem in the mercury valve is not airtight, it may be necessary to replace the air in the valve with mercury daily. Keeping

the inside surfaces of the glass capillary and mercury reservoir clean may

prove troublesome, but a few mm of water above the mercury meniscus

helps to maintain its proper shape. Oriani and Murphy28 used a precisionground glass taper-joint on the capillary to permit easy removal for cleaning.

The top part of the mercury in the capillary, where foreign particles tend

to accumulate, may be periodically removed by suction. Before each

reading of the mercury meniscus, it is advisable to apply enough pressure

to the reservoir to depress the mensicus slightly (about 1 mm) so that it will

rise to a reproducible level. To allow mercury from the weighed beaker to enter the calorimeter in a heat measurement, the valve may simply be opened and checked against

possible clogging. However, at first, some samples deliver heat to the

calorimeter so rapidly that the meniscus would fall below the capillary and

allow air to enter the calorimeter unless the pressure in the reservoir were

first lowered sufficiently. An alternative procedure is to draw more than

enough mercury for the experiment from the weighed beaker into the

reservoir and then close the valve. (One of the important precautions in using the ice calorimeter is to avoid introducing heat to the well, even from

an object at room temperature, unless the inlet tube is connected to a supply

of mercury in the accounting system.) The gate of the calorimeter is then

opened long enough to admit the sample.

E. A Typical Experiment

The data and calculations involved in a typical enthalpy measurement

with an ice calorimeter are given in Table 1 and Figure 4. Examples of

calorimeter misbehavior and numerous small corrections are introduced

to show how they are handled. In this example, a sample of aluminum oxide in a 90%Pt-10%Rh

container was measured. (The empty container, also with air sealed in at 600°C and 1 atm, had already been measured in separate runs.) In Figure 4 202-314
Table 1. Data and calculations for a typical drop calorimetry experiment with a platinum

resistance thermometer and ice calorimeter

Sample ("AI2O3") Furnace Temperature

weight

buoyancy correction 0-14% Si02 by analysis

16-8299 g +0-0026 -0-0236

Time Thermometer ohms

10:55 77-9094

10-57 77-9083

11:01 77-9078

mass, pure AJ2O3 16-8089 g Mean: 77-9085 (found) -77-8733 ( =600°C;

0-0352 d#/dr= 0-0802 Q/deg at 600°C

600 + 0-0352/0-0802 =600-44 °C

(sample temperature)

Heat measurement f 126-9382 g (weight of beaker + Hg before drop) —74-0812 (weight of beaker + Hg after drop) — 13-6333 (corrected mass of Hg, empty container, 600-44°C) —0-0027 [buoyancy correction for net Hg (sample + container)] +0-0069 [offset correction, g Hg (see Figure 4)] -0-0006 (correction for 0-0021 g Pt - 10% Rh extra with sample, g Hg)f +0-0035 (correction for air, 600°C and 1 atm, displaced by sample, g Hg)f —0-0524 (correction for SiC>2 in sample, g Hg)f

—0-0324 (correction to exactly 600°C, g Hg)f

39-1460 g (corrected mass of Hg for sample at 600°C)

Enthalpy calculation

(K600°C — Ho°Cj (final, pure AJ2O3) = (39-1460) (270-48 + 0-01t)/16-8089. = 629-94 abs J/g

(-M-1840 = 150-56 defined cal/g)

tComputed from, reference 17. ^Calculated correction for rise of mercury level in this calorimeter.

the mercury capillary readings taken when the valve was closed are plotted

against time, with a new line through the points whenever the mercury

valve was opened and the capillary meniscus reset. (The initial abnormal

steepness was traced to moisture in the well that had to be removed.)

The temperature of the furnace was read frequently, just before the drop,

with a platinum resistance thermometer. The sample had too much thermal

inertia to follow the small short-time drift indicated by the three readings in Table 1, so the average was taken. Eight minutes after the sample was dropped, the mercury valve was closed

and the meniscus read, but the negative slopes up to 11 :30 suggested that the sample was still evolving heat. The decreased slope after 12:00 was

traced to a failure to keep the ice bath well packed on top, and illustrates the error that would have resulted had this later part of the graph been

extrapolated back to the time of the drop. The "reset" correction was computed from an empirical calibration factor of 6-3 mg Hg/scale mm,

and was subtracted algebraically from the loss of mercury in the beaker.

To show readily their importance relative to the precision of duplicate

203-315
9-30 10 00 10 30 1100 Clock time

11 30 12 00 12 30

Figure 4. Ice-calorimeter heat leak and reset correction in a typical experiment

A, Calorimeter "well" wet

B, Gas flow through well reduced

C, Normal heat-leak rate before drop D, Time of sample drop

E, Sample not at thermal equilibrium with calorimeter yet

F, Valve opened and capillary meniscus reset G, Near-normal heat-leak after drop

H, Ice-bath packing deficient

/, Reset correction = —1-1 mm.

experiments, which was of the order of 5 mg of mercury, it was convenient

to express the corrections in terms of mass of mercury.

In applying the correction for the impurity (Si02), it was assumed on

the basis of the high-temperature preparation of the sample that the silica was present in the form of an aluminum silicate, and the correction was

accordingly computed by subtracting from the enthalpy17 of AloSiOs that of an equivalent amount of AI0O3.

F. Tests for Accuracy

Overall checks of the accuracy of a particular ice calorimeter used in high-temperature drop calorimetry are afforded by comparing enthalpy

measurements on a suitable material with the best published values. Highly

pure C1-AI2O3 (corundum) is currently considered the best single material

for comparisons up to above 1500°C; the published values have been

referenced and reviewed recently by Kelley17

, and more recent values by

Hoch and Johnston13 (up to 2000°C) are probably the most accurate

available at the highest temperatures. However, the use of such differences

to establish an empirical calibration of a new apparatus is not recommended

in work of high accuracy.

Several comparisons of enthalpy changes obtained by precise drop and

adiabatic calorimetry have been made at the U.S. National Bureau of

Standards. Values for water over the range 0-250°C agreed within an 204-316
average of 0-05 per cent by the two methods6

, whereas the results for aluminum oxide over the range 25-1 07 °C were about 0-2 per cent higher

by the drop method than by low- and high-temperature adiabatic calori- meters6 . (The two adiabatic calorimeters agreed with each other to 0-01 per cent on the average35

.) At these relatively low temperatures the adiabatic

calorimeters were believed to be several times as accurate as the drop method

apparatus. At somewhat higher temperatures the precision of adiabatic

calorimetry decreases considerably because of increased radiation effects, and for this reason the two methods were believed to give comparable

accuracy at these higher temperatures; however, for the range 242-41 6 °C

the difference found for aluminum oxide averaged only 0-05 per cent35 . At still higher temperatures, the drop method is the more accurate.

G. Hunting Causes of Trouble

The possible causes behind a perplexing symptom of trouble are often numerous. If the cause is likely to be a single one, it is economical to eliminate

from initial consideration those causes which can produce effects only of the opposite sign or of a different order of magnitude from that observed. If the only symptom is unsatisfactory precision or accuracy of the enthalpy values,

it may not be immediately clear whether the sample, the furnace, or the calorimeter is responsible. Errors arising from the sample and the furnace

are discussed elsewhere in this chapter.

When the trouble is in the ice calorimeter itself, one source of error and

poor precision is the melting of a hole in the ice mantle. This allows un- measured heat to escape, but fortunately, such a hole can usually be observed

visually, or at least it is usually manifest by an abnormally slow equilibration

after the drop. (Occasionally two successive runs have relatively large

errors of comparable magnitude but opposite sign, presumably because of

a slight irreproducible collapse of the calorimeter like that of the bottom of an oil can.)

A large positive or negative heat-leak rate of the ice calorimeter, apart

from its indication of a condition which is likely to be highly variable, is too great to be followed accurately. If there is apparently a large heat leak into the calorimeter (falling meniscus), there may be a hole in the ice mantle,

the ice bath may need more careful packing, further time may be required

for the calorimeter to equilibrate with respect to heat and volume changes,

or there may be air bubbles in the calorimeter which are slowly dissolving

in the water. (In the last case the compressibility of the calorimeter may be

found to have increased considerably.) On the other hand, if there is apparently a large heat leak out of the calorimeter (rising meniscus), the

calorimeter well may be wet, or so large an ice mantle may have been frozen

that some water has replaced mercury in the inlet tube (causing an abnormally high calorimeter temperature).

There are other possible causes of an apparently abnormal heat leak. Fluid leaks of the calorimeter deserve special mention. If water is leaking out

of the top of the inner glass vessel, this will be visible in time but will immediately cause a falling (or more rapidly falling) mercury meniscus.

On the other hand, if there is leakage at a level higher than the meniscus,

fluid will be entering the calorimeter and the meniscus will tend to rise. 205-317
Fluid leaks may be verified by standard procedures. A time-consuming

procedure is to follow the meniscus readings of a thoroughly temperaturesteady ice-free calorimeter. A more rapid method involves brief evacuation

above the mercury meniscus (when the mercury column will break), but

prolonged evacuation may lead to volume hysteresis which simulates a

fluid leak.

2. The isothermal-jacket, block-type calorimeter

The isothermal-jacket, block-type calorimeter absorbs or evolves heat

with a change of temperature, the change usually not exceeding 4-5°.

Although block calorimeters have been designed to operate adiabatically23

, the usual type employs isothermal surroundings. The following discussion

is limited to a model of this type.

A. Design and Construction

The block calorimeter shown in Figure 1 is the one designed by Southard33

, and is being used at present by the U.S. Bureau of Mines. It is essentially a cylindrical block of copper, L, 12*6 cm in diameter and 20-3 cm high.

The mass is large enough that the largest heat absorption does not cause a temperature rise of greater than about 5°. Aluminum blocks have been

used successfully in place of copper. The block shown is gold-plated and

rests on plastic knife-edges that are glued to the bottom of the surrounding

jacket. The interior surface of the jacket is also gold-plated and both jacket

and block are kept polished to minimize the heat interchange between them.

A brass tube (2-5 cm diameter) through which the sample drops, connects the jacket to the furnace. The top of the jacket is removable and is flange-connected to the lower part with machine screws and a Tygon

gasket. The jacket and calorimeter are immersed to level R in a stirred oil bath maintained at 29-70 i 0-005 °C. It is more convenient to maintain

the temperature of a bath by heating than by cooling or a combination of

the two; thus, if room temperature conditions are such, the bath may be more conveniently maintained at a reference temperature higher than the standard temperature of 25 °C. The receiving "well", 0, is a removable, tapered copper plug bearing a

100£? manganin wire heater, P, which is used in the electrical calibration of

the heat capacity of the calorimeter. The well is covered by a circular copper

gate, M, about 2 cm thick. The gate (solid, except for a 2-5 cm hole) is closed except for the brief interval necessary for dropping the capsule.

The bottom surface is machined to fit into a similarly machined recess in the block itself, thus providing good thermal contact and guarding against

heat losses by convection. The gate rotates on a shaft eccentric with the center line of the receiving well and is operated manually. The shaft is also connected to a similar, but hollow, gate located just under the furnace. This

gate is cooled by a slow stream of water, preventing the intrusion of heat into the calorimeter from the furnace. Both gates have a thin slot of the proper

radius to allow the suspension wire to pass through when the gate is closing.

A slow stream of CO2 (about 50 cm3 /min) is introduced at the bottom

of the jacket and flows continually around the calorimeter and through

the furnace. The procedure prevents condensation of atmospheric moisture

206-318
on the calorimeter and furnace refractory. It also maintains an oxidizing

atmosphere around the furnace thermocouple, which is located within the

furnace core. The heat exchange rates between the block and jacket are reduced by the CO2 to about 60 per cent of those in air. This rate is about

0-002 °/min for a temperature difference of one degree between the block

and the jacket and is reproducible to about 1 per cent. There is a slight

departure from this figure for large temperature rises. This variation is taken

into account in the calculations. The calorimeter resistance thermometer, wound on recess N, is of the transposed bridge type described by Maier25 . The thermometer is wound

so as to cover about one-half of the outer surface of the block and is coated

with Bakelite varnish. The winding is then covered by a tapered copper

sleeve that makes a driving fit on to the similarly tapered block. It consists of four windings, two of copper and two of manganin wire alternately

arranged in the bridge. The two copper coils are wound together in one

operation, as are the two manganin coils. The current passing through the thermometer is then exactly divided at all temperatures and the bridge is in balance at only one temperature. The four windings are approximately

2101? each and have a balance-point at 20-8°C.

The use of this kind of thermometer reduces the number of decades of a

potentiometer—in this case three—necessary for temperature measurements,

and provides greater temperature sensitivity than a single winding. In this particular case the temperature coefficient is 410 /xV/deg with a current of

1 mA. The use of a Leeds and Northrup White lOODOO /xV potentiometer

with a high-sensitivity galvanometer gives a precision of 0-03 ;uV or about

0-0001 °C. Heat is generated by the thermometer at 0-003 cal/min, which is a negligible quantity. (If a singly wound resistance thermometer of either platinum or copper is used, a bridge such as the Leeds and Northrup G-2

type Mueller bridge should be used for comparable precision.) The voltage

drop across the thermometer is 3860 /xV at 30-00 °C. The heat capacity

of the block is 3.691 defined calories per microvolt change in the

thermometer. There is a small heat capacity change of the block with

temperature.

B. Additional Measuring Equipment

The same potentiometer and galvanometer are used in the electrical calibration of the calorimeter and in measuring the resistance of the manganin

heater. Two standard resistances are used, both calibrated by the U.S.

National Bureau of Standards. A 0-1 Q resistance is used in the energy- measuring circuit, and a 100.Q resistance is used in determining, and in periodically checking, the resistance of the manganin heater. The standard

cell used with the potentiometer is checked periodically against several standard cells used only for this purpose. The potentiometer working cells and the cell for supplying the thermometer current are 200 ampere-hour lead cells of the charge-retaining type.

The energy source for heating the block is composed of a battery of 23

Edison cells with taps to use any number. Experience has shown that the lead cells and Edison cells are equally suited to any of these three uses. Energy input is made by using a stop watch which is checked at regular

207-319
/intervals against a standard chronometer. If electrical timing is used, care should be taken to see that the line frequency is maintained at 60 cycles;

otherwise a proper correction must be applied. Time for attainment of

thermal equilibrium by the calorimeter is around 10 min for a calibration

and 10-60 min for a calorimetric measurement, depending mainly upon

the thermal conductivity of the sample.

C. A Typical Experiment

A typical experiment will serve to illustrate the method of operation of the calorimeter and the calculations involved. During the time that the container

and contents are coming to thermal equilibrium in the furnace, the block

is set at some desired temperature. This is conveniently done with dry ice and the heater used in the calibration measurements. During the last 20 min or

so preceding the drop, the temperature of the calorimeter is read at two- minute intervals and the furnace temperature is checked for constancy.

The gates are then momentarily opened and the plunger falls, dropping the sample into the calorimeter. This operation takes about 2 sec and correction

is made for the radiation into the calorimeter from the furnace. (This heat

gain is negligible below 750 °C and does not exceed 0-1 per cent at higher

temperatures.) During the time that the calorimeter is heated, its temperature

is observed, first at one-minute intervals and then at longer intervals, until equilibrium is established. Finally, readings are taken again at two-minute

intervals. Table 2 gives the record of a typical experiment.

The sample temperature in the furnace is given by the thermocouple

reading at 23 min and 23-5 min after the start of the experiment—just prior

to dropping the capsule. The constant resistance thermometer current of

1000 fxA is checked several times during the warming and cooling rate periods.

Adjustment is made with a resistance box connected in series with the thermometer to provide constancy to i 0-01 fiA. During the equilibration period

the change of current is more rapid, necessitating a significant adjustment

before the final equilibrium cooling period.

Correction for heat interchange of the block with the thermostat is made

with the equation R = dT/dt = —0-002027 ( T — 3734). In this equation,

dT/dt is the measured rate in microvolts per minute, —0-002027 is Newton's

constant, T is the calorimeter temperature in microvolts, and 3734 is the temperature, also in microvolts, at which the heat interchange rate is zero. The magnitude of Newton's constant depends mainly upon the heat capacity

of the block, the thermal conductivity of the gas and metal leads between the block and jacket, the exposed area of the block or jacket, and the distance

between them.

The remaining calculations of Table 2 are for the most part self-explanatory.

The conversion from microvolts to joules is made by using the heat capacity

of the calorimeter (15-445 J//xV) as determined by separate calibration

measurement. The conversion from electrical units to defined calories is made by using the relation 1 cal = 4-1840 J. The heat value of the experiment is corrected from the equilibrium temperature (3823 juV) to 30°C

(3860 pV) by using 1 °C = 410 /xV. The heat capacity value of 1-23 cal/deg.

for the container and contents is taken from Kelley and King18 . The enthalpy

of the container was obtained from a separate series of measurements. The

208-320
Table 2. Data and calculations for a typical drop-calorimetry experiment with a thermocouple

and copper block calorimeter (Sample, La2Q3)

Thermostat temperature Wt. of La203 (corrected to vacuum)

Wt. of Pt-10% Rh container (corrected to vacuum)

Time in furnace (at temperature) before start of experiment

Resistance thermometer maintained at

29-70 ± 0-005°C

10-4440 g

10-9640 g

1 h

1000 ± 0-01 ^amp

Record of Experiment

Time Tor RT e.m.j.\ Time Tor RT e.m.f.Time Resistance thermometer (min) (min) 0*V) (min) e.m.f. ( MV)

0 9976 (T) 22 3443-78: (RT) 38 3822 § 2 3431-75+(RT)

3432-93+ (RT)

3434-04J. (RT)

23 9980 (T) 42 (3823-21 )%

4 23-5 9980 (T) 44 3822 -87«~ 6 24 (3444-98) *(RT) 46 3822-5217 8 3435-39: (RT)

3436-57: (RT)

3437-78: (RT)

3439-07: (RT)

24-5 3613§(RT) 48 3822-151" 10 25 3685 §(RT) 50 3821 -8 l r

12 26 3749 §(RT) 52 3821-481"

14 27 3781 §(RT) 54 3821-15T

16 3440- 19:(RT)

3441 - 36: (RT)

3442-55URT)

28 3799 §(RT) 56 3820-751: 18 30 3814§(RT) 58 3820-40«~ 20 34 3821 §(RT) 60 3820-021; 62 3819-681:

Calculations

Temperature of container and contents in furnace (9980/nV) 1308-5°K

Final resistance thermometer e.m.f. 3823-2

1

Initial resistance thermometer e.m.f. 3444-98/xY

Thermometer rise 378-23fiY

Correction for time gates were open —0-20/j.Y Correction for heat interchange with thermostat, by using e.m.f. vs. time plot for equilibration period, as indicated below 2-27^iV

Time interval Resistance thermometer Heat interchange Correction (min) e.m.f. ( MV) rate (/iV/min) (/*V)

24-24-5 3542 0-390 0-195 24-5-25 3652 0-167 0-084 25-26 3720 0-029 0-029 26-27 3766 - 0-064 - 0-064 27-28 3790 - 0113 - 0-113 28-30 3807 - 0-147 - 0-294 30-34 3818 - 0-170 - 0-680 34-42 3822 - 0-178 - 1-424

Total - 2-27

Corrected temperature rise

, . (380-30 x 15-445) Conversion to calories — — . 4-1840

[(3860 - 3823)1-23] 410 Enthalpy of empty container Net enthalpy of La2C>3

(984-14 x 325-82) 10-4440

Correction to 25°C (5 x 25-9) Final value, La2C>3 (Hi308-5 — H2P8.15)

Correction to 30-00°C

Enthalpy per mole

380-30)uV

1403-86 cal - 0-11 cal - 419-61 cal 984-14 cal

30 700 cal

130 cal 30 830 cal/mole

*Drop Capsule fT = Thermocouple, RT = Resistance thermometer

X Warming rate, = 0-601 /xV/min

§Period of equilibration ifCooling rate, R2 = — 0-176 ftV/min

M

209-321
final correction of the La2C>3 enthalpy from 30 °C to 25 °C utilizes the room

temperature heat capacity data of Kelley and King18 . If this datum is not

available from some compilation such as the one cited, the measured enthalpy

data must be extrapolated. Very little error results from this procedure.

D. Calibration Factor

The calibration factor of the block calorimeter described here has remained

substantially unchanged for several years. A single calibration is made for each substance, and its constancy serves as an overall check on the precision

measuring equipment.

A block calibration experiment is conducted in the same manner as the run, except that measured electrical energy is supplied in place of the heat

from the container. This heat is supplied through the calibrated manganin

heater coil, P, surrounding the receiving well. The current passing through

the heater is measured on the White potentiometer by measuring the

voltage drop across a standard resistor (0-\Q) in series with the heater. These readings are made alternately with those of the resistance thermometer. A substitute external resistance of the same magnitude as the heater

is used to "exercise" the energy battery for about an hour before introducing

energy into the block. This procedure provides a total change in current during a calibration of about 0-03 per cent, so that the current values may be

averaged to determine the energy input. In case a precision bridge is used

to measure temperature, a less precise potentiometer such as the Leeds

and Northrup type K-3 is entirely suitable for the measurement of the energy

of calibration. As can be seen from the sample experiment, there is no need to convert from microvolts to degrees. Calibrations are calculated in terms of joules

per microvolt and applied to the experiment in that form.

IV. Treatment of the Data

1. Correcting to standard conditions

A. Correction to a Basis of a Pure Sample

Frequently a sample contains from several tenths to several per cent of

impurities. The thermal behavior of these impurities can be the source of

significant error if ignored. A spectrographic analysis will identify and

estimate the orders of magnitude of the elements of these impurities if they

are different from those of the main sample. An X-ray diffraction analysis

will show the crystal form and indicate impurities, including uncombined

compound constituents, usually to the extent of about 1 per cent or more.

Microscopic examination also is an aid in determining the presence of an

impurity phase, particularly amorphous content if this possibility exists. In most cases a quantitative chemical analysis is highly desirable to determine

the chemical composition with certainty.

(1) Correctingfor Insoluble Impurities. For all impurities which are completely

immiscible with the sample the thermal corrections are strictly additive.

Sometimes such an impurity will melt or undergo transition in the measured

range. Proper enthalpy correction removes the resulting apparent discontinuity of enthalpy of the main sample. At high temperatures substances

210-322
usually become more miscible, so that a misjudgement based on assumed

immiscibility may result in significant error. This consideration stresses the need for taking pains to secure samples of high purity.

Some compilation such as that of Kelley17 is useful in computing corrections for insoluble impurities.

(2) Correcting for Soluble Impurities. Enthalpy corrections for impurities that are wholly or partly in solution in the main substance are almost never

strictly additive. There is a variety of combinations which can occur regarding the states of the impurity and the main sample, as well as the solubility

of the impurity at the two temperature extremes of the measurement.

Corrections for the heat effects involved are often relatively small and

frequently neglected, because they are difficult even to estimate. The heat

corrections are most important when the impurity is in liquid solution only

at the upper temperature. If no heat-of-solution data are available, a good

approximation is to apply a correction based on the heat of fusion of the impurity at its melting point. Othei cases are estimated by treating the

impurity as though it were insoluble. If the correction needs to be refined,

special information is required, i.e., information that provides the degree

of solubility at the two temperatures of the measurement and the accompanying heat effects. When impurities are dissolved in a sample that melts in the range of

measurements, they cause a lowering of the melting point often called "pre-melting". This subject is discussed at some length in other chapters

of this volume. If the amount of dissolved impurities is low, the solution may

be considered ideal. In this case the enthalpy correction is approximately

AHcorT - -N2RT Tm/(Tm - T), (3)

in which N2 is the total mole fraction of impurities, R is the gas constant,

T is the absolute temperature in question, and Tm is the melting point of

the pure sample. If the solution is not ideal so that equation (3) is not

applicable, or if the analysis for the proportion of impurities cannot be

relied on, the value of N2 in equation (3) is better determined empirically

as the value that will give corrections to make the enthalpy-temperature

relation the most plausible one. This matter of judgement often introduces considerable uncertainty in the corrections and the resulting corrected heat of fusion, even for samples

as pure as 99-5 per cent. A sensitive way to examine the results for pre-melting

effects is to plot mean heat capacities for successive intervals of furnace

temperature and then to look for excessive upturn in the curve below the melting point. The heat capacity-temperature curves of some pure solids show an upward turn as the melting point is approached. This upward

curvature can be attributed to lattice vacancies or anharmonic vibrations,

but this effect is more gradual than that due to pre-melting. If the empirical

application of equation (3) leads to a curve which shows a heat capacity

decreasing with temperature, the value chosen for N2 is too great.

B. Correcting for Vaporization Inside the Container; Correcting

to a Different Pressure

If even a small fraction of the sample or one of its components vaporizes

211-323
inside the sample container in the temperature range of the measurements,

the heat involved in the vaporization process may be an appreciable fraction

of the total heat measured, and correction for it is usually desired. If the necessary subsidiary information is available, the total correction can be

computed from an exact thermodynamic relation given by Osborne29 .

[mH]\ = [g]i + [PV]\ — [(V — mv) L/(v' - v)]\. (4) In equation (4) the superscript 2 and the subscript 1 indicate the value

of the bracketed quantity at the higher temperature less that at the lower

temperature; m is the total mass of sample, including the vapor; H is the enthalpy, per unit mass, of the condensed phase (solid or liquid) at pressure

P, which is its vapor pressure; [q]j is the heat evolved by the sample (after

correction for the container and its parts) ; V is the inside volume of the

container; L is the heat of vaporization (or sublimation, if solid) per unit mass at the temperature in question; and v and v are the volume per unit mass of the vapor and condensed phase, respectively. It is usually more

convenient to make a substitution in equation (4) from the exact Clapeyron

equation, to obtain

[mH]\ = [q]\ + [PV]\ - [{V - mv) TdP/dT]j. (5)

If the vapor pressure and its temperature coefficient are known with

sufficient accuracy (which must be high if P and consequently dP/dT are

large), it is sufficient to apply equation (5) to measurements on a single

sample, with the precaution to minimize the gas space ( V — mv) (after due

allowance for thermal expansion of the sample) in order to minimize the

last correction term. However, an alternative procedure is available if the vapor pressure data are not sufficiently reliable. The most uncertain

quantity in equation (5) can be eliminated by making heat measurements on both a "high" and a "low" filling of the container and applying the equation to each. Sufficient sample must be used in the "low filling"

experiments to ensure that not all the condensed phase is evaporated.

As an example, Douglas et al. 1 measured the enthalpy (relative to 0°C) of

n-heptane at 250 °C, at which temperature the vapor pressure is about

21 atm, using "high" and "low" fillings in which the liquid occupied 83

per cent and 27 per cent of the container, respectively. Although in the case of the "low" filling experiments the net correction calculated from equation

(5) amounted to about 12 per cent of the total heat measured (the correction was far smaller for the "high" filling), the two separately corrected liquid

enthalpies differed by only 0-1 per cent. Each value was the mean from several duplicate experiments.

If the pressure on the sample varies with temperature either because of a

rapidly changing vapor pressure or because inert gas is sealed in at some

temperature and pressure, it may be desirable to correct the enthalpy increment for the condensed sample, calculated from equation (4) or (5), to the

basis of a given fixed pressure, such as a standard state of 1 atm. The correction may be computed for both terminal temperatures from the exact thermodynamic relation

{8HldP) T = V — T(dV\dT)-p (6) 212-324
in which V and H apply to the same quantity of sample. For large pressure

differences, equation (6) requires integration if the thermal expansion data

are accurate enough to justify it. For a change of pressure of only a few

atmospheres, however, the correction is very small (less than 0-1 per cent).

The calculation of Cy from Cp, which are thermodynamically related by

CP - CV = a

2 F77/S (7)

in which a is the volume coefficient of thermal expansion and jS is the

compressibility, is a special case of correction to different pressures.

2. Smoothing and representing enthalpy values

Measurements of relative enthalpies over a range of temperature may be

presented by graph, equation, or tabulation.

A. Graphing

Although graphing is not generally considered to be a satisfactory way

to represent the final data, it is a good aid in smoothing the data and

finding a suitable form of empirical equation or its coefficients. For these purposes it is not suitable to graph the enthalpy data directly; instead,

functions of enthalpy are plotted. These function plots must be sensitive enough to show deviations from smooth continuity which are within the

precision attained by the measuring technique.

Generally, some form of heat capacity function is most convenient for plotting the measured data. This procedure not only provides a good basis

for smoothing the data, but also shows continuity with any existing lowtemperature heat capacity data directly and provides a precise means of

comparison with other work.

The heat capacity curve derived from the smoothed enthalpy data is often plotted together with unsmoothed heat capacity values corresponding

to mean heat capacities given directly by AH/A T for pairs of successive

furnace temperatures. If the heat capacity does not vary linearly with

temperature, a curvature correction is needed to convert mean values to true heat capacities; the curvature correction is given by the infinite series according to Osborne et al. 30 c - (q/AT) = - (32c/ar2)(jr)2/24 - (a«c/a r4)(/jr) 4 /i920 - . . . (8)

in which C is the true heat capacity, q is the heat interval for the sample

over the temperature interval A T, and C and its derivatives apply at the mean temperature of this interval. Even for a temperature interval as large

as 100°C, the first term of the right-hand side of equation (8) is normally only a very small fraction of the total heat capacity and the remaining terms are completely negligible. If this is not true because the curvature is unusually

great, measurements should be made at one or more intervening temperatures. If the enthalpy-temperature relation is represented analytically, it is convenient to compute the derivatives in equation (8) from that relation. If the heat q is that for the sample at constant pressure, q may be replaced

by AH and C by Cp.

Another method is to plot the quotients of the individual enthalpies

213-325
divided by the corresponding temperature intervals of the measurements.

The value of the ordinate is the mean heat capacity between the furnace

temperature and the standard reference temperature. Thus if 298 °K

is the reference temperature, the ordinate of this curve at 298°K is the

true heat capacity at this temperature. Any existing low-temperature data can easily be calculated in this form to show continuity with these data. This comparison is important, because almost always the low-temperature

heat capacity data are more accurate than the high-temperature data.

If (Hi — H29s)l(T — 298) is the mean heat capacity as defined here, then

the true heat capacity is given by the relation

CP = (HT - H2 »s)l(T- 298)

+ {T - 298)d [(HT - H29a)l(T- 298)] /dr. (9)

(1) Choice and Treatment of Measurements. In the process of smoothing data, the choice of the number of measurements over the same temperature inter- val requires some decision as to how such duplicates will be handled. It is the usual practice to repeat measurements for which agreement is unsatisfactory. This raises the question as to which individual measurements to discard, and of those remaining, which will receive the most weight. Statisti- cal methods have been developed to show when a single measurement can

be discarded objectively. Most of these methods depend upon the assumption

that the probability of encountering a single measurement with such a large

deviation from the mean is small. This mean can be considered as the mean

value of several duplicate experiments or as a smooth curve such as the heat

capacity curves discussed. Of the measurements remaining for each temperature range, it is a good procedure to treat them equally in getting the mean value, and then to treat these mean values equally in deriving smooth

values or an empirical equation to represent them. Additional measurements

for any one temperature range should be chosen primarily so as to give

statistical precision to the mean value of enthalpy or its derivatives. However, the existence of systematic errors usually makes a large number of

repetitive experiments of limited value.

B. Representation by Equations

(1) Theoretical and Semi-Theoretical Equations. For the crystalline state, the Debye treatment for intermolecular vibrations is often coupled with the Einstein treatment for intramolecular vibrations. This procedure has given a representation of the Cy-temperature curve so closely approximated by

experimental results for many substances as to be useful, especially at low

temperatures for which the difference between Cp and Cy is generally small. However, the limiting value (3R) of the Debye and Einstein functions is generally exceeded over the high-temperature range. In this case calculations

of heat capacities are so complicated by such factors as anharmonic vibrations, electronic heat capacity, and the difference between Cp and Cy that such calculations are seldom made.

(2) Empirical Equations. Empirical equations for enthalpy may necessitate more labor in obtaining values at odd temperatures than from tables, and

214-326
they are usually less precise than the smooth values given in tables; but they

have the advantage of affording an easy means of deriving related thermodynamic properties such as heat capacity and entropy increments. In addition, if the form of the enthalpy equation is the standard one suggested by

Maier and Kelley26

, the constants in the calculation of chemical reactions

may be expeditiously combined. This equation is HT - //298-15 = aT + bT* + cT-* + d (10)

A procedure for evaluating the constants of this equation was given by

Shomate31

. If the heat capacity at 298-1 5 °K was accurately known from

low-temperature calorimetry, Shomate used the following equations

Cp,298-15 = a + 596-306 - e/(298-15)2 (11)

0 = 298-15a + (298-15)2£ + c/298-15 + d (12)

[(HT - #298-15) - CP,298.i5 (T - 298-15)] Tj{T - 298-15)2 = bT + c/(298-15)2 (13)

The function on the left side of equation (13) is evaluated for each measured

high-temperature enthalpy value (or for evenly spaced, smooth-cmve

values), and the results are plotted against T. The slope and intercept of

what is judged to be the best straight line give values for b and c respectively.

If c is nearly zero, the line is sometimes drawn to make it exactly so. The other

constants are then supplied by equations (11) and (12). If the substance has a melting point or transition in the measured temperature range, the same

procedure can be applied above and below the temperature of discontinuity.

Otherwise, four simultaneous equations are used to determine the constants. Frequently the equation form can be simplified above a temperature of

discontinuity. This is particularly true if the discontinuity is above about

600°K.

The general adoption of equation (10) for all substances has the advantage of fitting data reasonably well while minimizing the number of terms. In addition, the error in using the equation to extrapolate the data to higher

temperatures, while generally considerable, is often less than with many

other forms of equation. However, there are the disadvantages that in many

cases this equation form does not fit the precise data at all temperatures

within the precision of the measurements or does not give weight to the

temperature derivative of Cp at 298-1 5 °K indicated by precise lowtemperature calorimetry.

A better fit of an equation to the data may be obtained for many specific cases by choosing a different temperature function with the same or a greater

number of constants. The number of constants should not be increased to the extent that implausible points of inflexion appear. The labor of fitting coefficients of an empirical equation by the least squares method is greatly

reduced by the present-day availability of high-speed electronic computers

and the ability to develop general-use codes, each of which includes any

215-327
desired combination of temperature terms. A least squares method has the

advantage of mathematical objectivity, but loss is encountered through the

difficulty of selecting the temperature range of "best fit". Unless an equation is found which fits the enthalpy measurements within

their precision at all temperatures, tabular values should be used for the

most precise calculations.

C. Treatment of Fusions and Transitions

After correcting for any pre-melting, the enthalpy of a pure substance as a function of temperature is extrapolated to the melting point for both the

solid and the liquid. If the enthalpies of both the solid and the liquid are expressed relative to the same state at the same temperature, the difference

is the heat of fusion. The accuracy of the heat of fusion so obtained will depend upon the uncertainties of these extrapolations, the correction for "pre-melting", and the melting point. Since the heat capacities of the solid and liquid are not too far different at the melting point, an error of several degrees in the melting point has little effect on the resulting heat of fusion. Unless the melting point is already known, it may be determined directly

in the furnace by the cooling curve method, or by using the enthalpy data

as a basis. In the latter case the melting point is taken as the lowest temperature at which the enthalpy measurement of the pure material falls on the

liquid curve.

Solid-solid transitions are classed as first and second order according

to whether, at equilibrium, they are abrupt and isothermal or gradual over

a range of temperature. A first order transition is sometimes so sluggish that

it is difficult to distinguish between the two types by drop calorimetry. These

cases are spread out as an enhanced heat capacity. Sluggish heats of transi- tion may sometimes be assigned arbitrarily as isothermal transitions for convenience in deriving the empirical equations. In any case, if the range

of interest is above the range of transition, the enthalpies will be unaffected

by the interpretation of the transition range, and the entropy calculations are likely to suffer little error. In efforts to measure enthalpies of substances

in the neighborhood of either transition points or melting points, it may be

necessary to greatly increase the length of time in the furnace. Also it is sometimes necessary to "overshoot" the temperature of transformation and

then lower the temperature in order to increase the rate of transformation.

If a latent heat of transition is quite small, its existence may be hard to detect. An enthalpy-function plot such as the AHjATvsT plot mentioned

earlier is of considerable value in detecting and defining them. Shomate32 describes another type of plot used for this purpose; it is based on equation

(13).

3. Derivation of other thermodynamic properties from relative

enthalpy

The following common thermodynamic functions can be readily derived

by the indicated mathematical operations on the enthalpy equation; the

values are those at temperature T unless otherwise indicated

CP

° = [d(H° - //°298.15)/8r] P (14)

216-328
S° = J (C?°[T)dT+ ST

.°

T' (15)

- (G° - i/°298.15)/r = S° ~ (H° - H°29S.15)/T. (16)

Sometimes (i/°298-i5 — H°o) is known from low-temperature calorimetry;

in such cases the enthalpy and free-energy functions are often expressed

relative to 0° instead of 298- 15 °K. For high-temperature thermodynamic

applications, however, it is much more important to be able to substitute into

equation (15) an accurate value of the integration constant Sr

,° (at some temperature T' within the range of the high-temperature enthalpy measurements). In this case, equation (16) will yield free-energy functions, the use of which predicts equilibrium relations at high temperatures without the

need for their direct measurement. A value for .S 0298-i5 is often available from

low-temperature calorimetry on the substance in question and assumption

of the Third Law of Thermodynamics.

If for some reason the enthalpy is represented only approximately by an

empirical equation, the deviations of the unsmoothed values from the equation may be plotted and an empirical curve drawn through them. A smooth

value of enthalpy at any temperature in the range can then be obtained by

adding algebraically the ordinate of the deviation plot to the value given

by the equation. A value of the heat capacity can also be obtained by adding

the slope of the deviation plot to the temperature derivative of the (approximate) enthalpy equation. A variation for determining heat capacity is given by equation (9). Usually the contribution of the second term is only a

few per cent of the first term, and the error in its graphical determination

thus contributes only a small percentage error to the Cp so evaluated.

Kelley17 describes a correction in the calculation of entropy based on the

standard equation form. The corrections are applied incrementwise every

100°C as g/Tav., in which q is the enthalpy deviation of the equation from

the smooth values for the temperature interval, and T&v. is the mean temperature of the interval.

4. Precision and accuracy

Values derived from drop measurements are often given accompanied by

tolerance figures, but it is sometimes not clear whether precision or estimated

accuracy is meant. In drop calorimetry the systematic errors are the important ones, so that the precision, as calculated by standard statistical procedures, is not as large as the absolute uncertainty of the results. Some

estimate of the systematic error should \be made to combine with the precision in arriving at a value of estimated uncertainty. Examples of experi- menters who have presented such detailed analysis of their errors are Ginnings and Corruccini10

, Furukawa et alfi, and Hoch and Johnston12 . Particular

sources of error are measurement of the temperature of the sample; cali- bration of the calorimeter and other instruments such as standard cells, potentiometers, thermometer bridges, thermocouples, and pyrometers;

the calorimetric measurement, including allowance for heat leak corrections;

sample impurities and mass changes; empty-container measurements; and

217-329
the loss of unmeasured heat by the sample during the drop and in the calori- meter. Some investigators will combine possible errors statistically and then

multiply the result by some arbitrary factor such as two, whereas others will combine possible errors with the signs taken to give the largest overall error. Comparison with work of different laboratories is an aid in error estimation.

The uncertainty of the heat capacity is difficult to estimate. The process of

differentiation of enthalpy may multiply the percentage uncertainty characteristic of the enthalpy by a factor of two to much more if the heat capacity

itself is changing rapidly with temperature. The uncertainty of the derived

entropy may be calculated from the equation

St — ^298-15 = (Ht — #298-15)/ T +

J [(#T -#298.15)/^] dr. (17)

298-15

By substituting in the uncertainties of the enthalpy measurements and inte- grating the second part graphically, the entropy uncertainty may be deter- mined. It is a close approximation to assume the same percentage uncertainty for the entropy increment as for the measured enthalpy increment.

Precise calorimetric data gain maximum value not only when the uncertainties can be estimated and stated, but also when the results are reported

in sufficient detail to permit future corrections to less arbitrary procedures

of data treatment or to more accurate physical constants.

V. References

1 Douglas, T. B., G. T. Furukawa, R. E. McCoskey, and A. F. Ball, /. Res. Natl. Bur. Std., 53, 139 (1954).

2 Douglas, T. B., and W. H. Payne, in S. F. Booth, ed., Natl. Bur. Standards Handbook 77,

Precision Measurement and Calibration, Vol. II, Selected Papers on Heat and Mechanics, U.S.

Govt. Printing Office, Washington, 1961, pp. 241-276.

3 Dworkin, A. S., and M. A. Bredig, /. Phys. Chem. 64, 269 (1960).

4 Ferrier, A., J. Sci. Irtstr. 39, 233 (1962).

5 Fomichev, E. N., V. V. Kandyba, and P. B. Kantor, Izmeritel. Tekhn. 1962, No. 5, 15.

6 Furukawa, G. T., T. B. Douglas, R. E. McCoskey, and D. C. Ginnings, /. Res. Natl. Bur.

Std., 57, 67 (1956).

7 Gilbert, R. A., J. Chem. Eng. Data, 7, 388 (1962).

8 Ginnings. D. C, /. Phys. Chem., 67, 1917 (1963).

9 Ginnings, D. C, and R. J. Corruccini, /. Res. Natl. Bur. Std., 38, 583 (1947).

10 Ginnings, D. C., and R.J. Corruccini, /. Res. Natl. Bur. Std., 38, 593 (1947).

11 Ginnings, D. C, T. B. Douglas, and A. F. Ball, /. Res. Natl. Bur. Std., 45, 23 (1950).

12 Hoch, M., and H. L. Johnston, J. Phys. Chem., 65, 855 (1961).

13 Hoch, M., and H. L.Johnston, /. Phys. Chem., 65, 1184 (1961).

14 Hultgren, R., P. Newcombe, R. L. 6rr, and L. Warner, N.P.L. Symposium No. 9 (1958), Met. Chem., H.M.S.O. (1959), p. 1H.

15 Jewell, R. C, E. G. Knowles, and T. Land, Metal Ind. (London) 87, 217 (1955).

16 Kantor, P. B., R. M. Krasovitskaya, and A. N. Kisel, Fiz. Metal, i Metalloved. 10, No. 6, 835 (1960).

17 Kelley, K. K. "Contributions to the Data on Theoretical Metallurgy. XIII. HighTemperature Heat-Content, Heat Capacity, and Entropy Data for the Elements and

Inorganic Compounds", U.S Bur. Mines Bull. 584 (1960).

18 Kelley. K. K., and E. G. King, "Contributions to the Data on Theoretical Metallurgy. XIV. Entropies of the Elements and Inorganic Compounds", U.S. Bur. Mines Bull. 592 (1961). 218-330
19 Kelley, K. K., B. F. Naylor, and C. H. Shomate, U.S. Bur. Mines Technical Paper, No. 686

(1946).

20 Kirillin, V. A., A. E. Sheindlin, and V. Y. Chekhovskoi, Dokl Akad. Nauk SSSR 135, No. 1, 125 (1960).

21 Kirillin, V. A., A. E. Sheindlin, and V. Y. Chekhovskoi, Dokl. Akad. Nauk SSSR, 139, No. 3, 645 (1961).

22 Leake, L. E., and E. T. Turkdogan, /. Sci. Instr., 31, 447 (1954).

23 Levinson, L. S., Rev. Sci. Instr., 33, 639 (1962).

24 Lucks, C. F., and H. W. Deem. " Thermal Properties of Thirteen Metals", ASTM Special Technical Publication No. 227, American Society for Testing Materials, Philadelphia,

Pa. (1958).

25 Maier, C. G., /. Phys. Chem., 34, 2860 (1930).

26 Maier, C. G., and K. K. Kelley, /. Am. Chem. Soc, 54, 3243 (1932).

27 Olette, M., Compt. rend., 244, 1033 (1957).

28 Oriani, R. A., and W. K Murphy, J. Am. Chem. Soc, 76, 343 (1954).

29 Osborne, N. S., Bur. Std. J. Res. *4, 609 (1930).

30 Osborne, N. S., H. F. Stimson, T. S. Sligh, and C. S. Cragoe, Bur. Standards Sci. Pap., 20, 65 (1925).

31 Shomate, C. H., J. Am. Chem. Soc. 66, 928 (1944).

32 Shomate, C. H. J. Phys. Chem. 58, 368 (1954).

33 Southard, J. C, J. Am. Chem. Soc, 63, 3142 (1941).

34 Wensel, H. T. and W. F. Roeser. In Temperature, Its Measurement and Control in Science and

Industry, Vol. I, American Institute of Physics, Reinhold Publishing Corp., New York,

1941, pp. 284-314.

35 West, E. D., and D. C. Ginnings, J. Res. Natl. Bur. Std., 60, 309 (1958).

36 White, W. P., The Modern Calorimeter. Chemical Catalog Co., New York, 1928.

3 ? White, W. P., J. Am. Chem. Soc, 55, 1047 (1933).

38 Wisely, H. R., Thermocouples for Measurement of High Temperature, Ceramic Age, Newark,

N.J. (1955).

219-331
A Calorimetric Determination of

the Enthalpy of Graphite

from 1200 to 2600°K

E. D. West and S. Ishihara

National Bureau of Standards Washington, D. C.

Abstract

Measurements are reported of the increase in the enthalpy of high-purity graphite between room temperature and 1200 to 2600°K. A new apparatus is de- scribed briefly. Methods of operation are developed

which eliminate some systematic and random errors and are especially advantageous at high temperatures.

The enthalpy data fit the equation

Ht-IU**. ,5=28.90047' - 1.045 > 10" 4 T

2

- 16,126.2 log, 0 77313.15 - 8907.3

where H is in absolute joules per gram atomic weights

and T in degrees Kelvin.

Introduction

Spence [1] has pointed out deficiencies in the data on the heat capacity of graphite. As one of the tests of a preliminary version of a new high-temperature apparatus, we have made measurements of the enthalpy of graphite which overlap the work of McDonald [2] from 1200° K to 1700°K and extend to 2600°K.

Specimen

The specimen was a solid cylinder machined from

a larger piece of grade CCH graphite (National Carbon

Company) density 1.6 g/cm. According to the supplier, this grade is purified by the same treatment used for spectroscopic grades. After machining, it was heated in our furnace at temperatures up to 2700 K for several hours' before measurements were

begun.

The specimen was weighed before and after each

group of experiments at each furnace temperature.

The average observed weight was 2.4023 g and the maximum variation was 0.2 mg. The calculations were nevertheless made with the observed weight for that experiment, so that the data include the random

errors of weighing.

Spectrographic analysis of the sample showed

traces of Al and Si (less than 0.001 per cent and

faint traces of B, Ca, and Mg (l ess tnan 0.0001

per cent).

Apparatus

The apparatus will be described briefly to in- dicate several novel features; a detailed description

will be deferred until improvements indicated by these preliminary measurements have been incor- porated and tested. The apparatus, shown schematically in Fig. 1, consists essentially of a furnace in which the capsule, with or without the sample, is held at a constant temperature and a calorimeter to which it is lifted for measurement of the quantity of heat. The

furnace core is a hollow graphite cylinder heated by

induction. The induction coil has a higher turns density near the ends to produce a greater field and

220-146
FIG. 1 DIAGRAM OF THE APPARATUS FOR ENTHALPY

MEASUREMENTS,

more heat near the ends of the core, in contrast to the usual uniform solenoid which produces the maximum

field at its center. To reduce the power requirement and the accompanying temperature gradient, the graphite core is supported by thin carbon tubes and insulated by suc- cessive layers of carbon black and silicon carbide powder. The furnace operates in about 0.1 atm of purified argon, and can be held at 2500°K with 980W,

including coil losses. It is heated to 2500°k in about an Jiour with 5 kW power input.

The furnace is controlled directly by sensing the temperature of a graphite diaphragm located four inches inside the furnace core with a Leeds and

Northrup automatic optical pyrometer sighted into the bottom of the furnace. The observed temperature of the diaphragm is held constant within ± 0.2°k throughout the experimental range. Two different instruments were used in different phases of this work. The temperature is also observed after each lift with a visual optical pyrometer focussed on the dia- phragm at the bottom of the region which was oc- cupied by the sample. The currents in the pyrometers

are calculated from the voltage across one-ohm

standard resistors measured with a Wenner potentiometer. The automatic pyrometers tend to give a temperature reading a few degrees lower than the

visual pyrometer, indicating a significant temperature gradient in the furnace (or a difference in the calibrations). The calibration for the automatic

optical pyrometer was not appreciably better than

that for the visual pyrometer at the time these measurements were undertaken. The temperature of the latter was therefore taken as more indicative of

the temperature of the capsule without appreciable

sacrifice of the accuracy of the measurements. A

calculation exaggerating the effect of the gradient has been made assuming the temperature of the furnace core is uniformly 5 degrees different from

that of the diaphragm. This calculation shows that the effect on the temperature measurement of the gradient in the graphite core is small compared to other temperature uncertainties discussed below. The heat is measured with an adiabatic calorimeter operating between 30 and 65 C. The calorimeter proper consists of a hollow nickel cylinder sur- rounded by a hollow copper cylinder which is en- closed by thin gold-plated copper shields similar to an earlier calorimeter used in this laboratory [3]. The total heat capacity is about 2400 J/C. The main

heat capacity of the calorimeter is made up of two

coaxial parts which are separated by a 4.8 mm (3/16 in.) annular space except for an annular metallic contact midway along the axis. This construction introduces

a time constant of about a minute, which eases the problem of adiabatic control of the surrounding

shield. This time constant is short compared to the time constant for equilibration between the capsule

and the calorimeter, so that the experiment is not lengthened appreciably. In the upper part of the temperature range corrections are still necessary for shield control deviations, equivalent to 0.1 per cent

of the heat evolved by the full capsule at 2360°K.

After the last alteration of the calorimeter, two

electrical calibration experiments were made of its heat capacity by usual techniques over each five- degree interval. From these data the pooled esti- mate of the standard deviation of the mean over each

interval is 0.01 per cent. The heat capacity and temperature range of the calorimeter limit the number of lift experiments to six per day at low furnace temperature and four per day above 2100°K.

When the capsule is in the calorimeter, the bottom

of the calorimeter is closed by a "shutter" consisting of two gold-plated copper radiation shields which

reflect most of the radiation from the hot capsule back

into the nickel block. These radiation shields have

a large area of thermal contact with the copper block so that any excess heat they absorb from the radiation may be returned to the copper block with only a small thermal head. Located between the furnace and the calorimeter

are a vacuum valve, a sliding support for a prism for

221-147
temperature observations, and a sliding radiation shield, with a slot to accommodate the suspension

wire. 1 his shield reduces the radiation heat transfer when the capsule is in the furnace so that the measurement ol the initial temperature of the calorimeter

tan he made more accurately, and so that the cor- reetion fur radiation into the calorimeter will not depend critically on timing.

I lie sample is lifted Iron) the furnace into the calorimeter by a servo-mechanism which imposes

constant acceleration (or deceleration) on the capsule, avoiding the large forces of the usual jerky

stops. The tension in the suspension wire is thus kept small, an important consideration for small

wires at high temperatures. We have used 800 cm

sec

2 for both acceleration and deceleration. The

time lor the capsule to cross the "cold" region

between the top of the graphite tube in the furnace and the boundary of the calorimeter is 0.16 sec. The period ol acceleration (= 1/2 the lift time) is measured in each experiment with an electronic

counter-timer. This observed time did not vary more than 1 ins from 312 ms.

1 he capsule is machined from grade AUG graphite.

It is 1 cm long and I cm in diameter with a 1.5 mm

wall. It is fitted with a screw cap having a tantalum

wire hook for attaching to the suspension wire. The

capsule wall thickness is calculated from the thermal

diffusivity of graphite to give no cooling of the inner wall during the short exposure time in the "cold"

region. This technique has the advantage that the presence of the sample cannot increase the heat loss during the lift by maintaining the outer surface at a higher average temperature than in the corresponding

empty capsule experiment. As a check on the apparatus, we determined the enthalpy of a solid cylinder of single crystal sapphire

(A1 2 0 3

) at 1179. 2°k which is in the temperature range of earlier National Liureau of Standards measurements with another apparatus. The average result

of three measurements each on the empty and full capsule is //, 179 . 2 - //3 ,3., 5 = 99134 J/mole, about 0.14 per cent below the data of Furukawa, el al. [4], as corrected by Cinnings [5]. 'I his agreement is well

within the estimated maximum uncertainty of 3 to 4 K

in the calibration of the pyrometer.

Method of Operation

The experiments are carried out so that a day's work provides all the data required for calculating the enthalpy at one furnace temperature. Four to six experiments are carried out in a day — two or three each on the empty and full capsule. This method of operation has several advantages over the more usual

practice ot making one series of measurements on the empty capsule and another series on the full capsule.

An important practical advantage is that subsequent

minor disasters, such as breaking a suspension wire

or chipping the capsule, do not affect the validity of results for other days. This method also eliminates

the systematic error due to the slow changes in the emittance of the surface of the capsule between two

series of measurements with the empty and full capsule and the corresponding change in the radiative heat loss in the lift. Often, no estimate is made of

this error, presumably because other uncertainties are

relatively large, but in one case the error was esti- mated to be less than 0.1 per cent in work at 1200°K

[4]. Without this method of operation, much larger

errors might be expected in our temperature range. From an alternate point of view, it permits the use of

different capsules, different samples and different suspension wires to suit the temperature range. At each furnace temperature the last experiment

duplicates the first — if the first is on the empty

capsule, so is the last. This technique affords the considerable advantage of averaging out most of the effect of gradual changes which occur during the day,

such as changes in the emittance of the capsule or in its weight due to evaporation, or changes in temperature gradients in the furnace. The latter were found

to be significant at the higher temperatures where a

large furnace power was used in a one-hour heat-up

period before stabilizing the furnace with the auto- matic control. Although the first experiment is made three hours

after the heat-up period, the gradient continues to de- crease somewhat during the day. Making the first and

last experiments on the empty capsule for example,

will partially compensate for the effects of the change

in gradient when the observations are averaged.

The experimental procedure is designed so that the small amount of radiation from the furnace to the calorimeter is the same for all experiments at

the same furnace temperature. This procedure makes

it unnecessary to measure the radiation to the calorimeter under the various conditions of shielding and temperature.

To start an experiment, the calorimeter heat leak

rate is observed for ten minutes with the shutter closed and with the vacuum valve and the prism

blocking radiation from the furnace. (Either the valve

or the prism is sufficient to block the radiation.) The

prism is removed, the capsule lowered to a position

just above the vacuum valve and the slotted shield

is positioned around the suspension wire. The

vacuum valve is then opened and the capsule lowered

slowly into the furnace so as not to disturb its temperature control. After about 15 minutes, the initial calorimeter temperature is observed. The subsequent

operations are in a timed sequence starting 85 sec

after the temperature measurements and requiring 10 sec to complete: the slotted shield is removed,

222-
the lift mechanism is actuated, the shutter closed and the prism moved into position for temperature measurements. The time the capsule is in the furnace

is adequate as shown by the experiments on aluminum

oxide near 1200°k, where radiation is least and the time constant therefore longest. Data taken after 15 and 20 minutes in the furnace were not significantly

different at this temperature.

The temperature is then observed with the visual pyrometer, usually eight readings by two observers. The final calorimeter temperature is taken when its rate of change is constant, about 25 min after the

lift for the empty and 35 min for the full capsule. In the experiments with aluminum oxide, the equilibration time was 50 min, reflecting the higher heat capacity at the calorimeter temperature and the correspondingly longer time constant for equilibration.

Results

1 he experimental results are shown in Table I. The heat delivered to the calorimeter has been cor- rected to a calorimeter temperature of 313.15°K and

to the average observed furnace temperature, using

the integral of the heat capacities over the small temperature intervals. Ihe validity of these corrections depends on the following argument: the heat Q delivered to the calorimeter is equal to the enthalpy of the capsule

(and contents) at the furnace temperature, Hp , de- creased by the enthalpy at the calorimeter temperature, He, and by the heat loss Ql during the lift, and

increased by the heat QR radiated from the furnace between the time of the initial calorimeter temperature measurement and blocking the radiation with the shutter and prism. In our experiments the Q' s as

defined are always positive quantities. The differ- ence in the heat delivered to the calorimeter for two

experiments is given by

Qi-Qt = HFi-lIci-QLi+QRi-HFt + fIc*+ Qlz-Qrz-

(1)

If the temperatures of the furnace differ by only a few

degrees, then, since Ql and Qr are already small,

the differences QLi - QLz and - Qr z can be

neglected. The right-hand side of (1) then reduces

to (//p, — Hp2 ) — (Hqi — Hqz) which can be computed

from heat capacities and weights of materials in the capsule and specimen. The remaining differences are

the random errors of the experiment. Corrections at the calorimeter temperature range

up to 0.6 per cent of the observed heat. Corrections

for small variations in the observed furnace temperature do not exceed 0.1 per cent of the observed heat. To some extent, they reflect random errors in the visual pyrometry. The corrections are so small that

the effect of uncertainties in the heat capacity data used in making them [6] -[8] is negligible.

The enthalpy may be represented by the following

equation for the range 1200 to 2600°K:

#7—#298.15 = 28.90047" - 1.045 x 10' 4 T

2

- 16,126.25 lo gl0 31 ^ 15

' - 8907.3 (2)

where H is in absolute Joules per gram atomic weight

and T in degree Kelvin. The heat capacity is given

by

Cp = 28.9004 - 2.090 x

10"

4 T - 7003.54/ T. (3)

Eq. (2) was obtained by a least squares fit of the en- thalpies in Table I. Per cent differences between

these observed values and those calculated from the equation are shown just below the observed values. Above 2200°K, where the effect of the temperature

gradient in the furnace is greatest, the order of taking

the data alternated — empty capsule first at 2263 and 2462 and full capsule first at 2364 and 2576 C - in order to exaggerate the effect of the change in gradient. The data at 2034 C, lacking the final empty

capsule data, would be expected to lie above the smooth curve. Data at 2576 C, also incomplete,

would be expected to lie below the smooth curve be- cause the first experiment was made with the full capsule. These two sets of data were not used in computi ng (2). The estimated standard error for the enthalpy

calculated from (2) is not more than 0.14 per cent. Systematic errors in measuring the furnace temperature are estimated to be not more than 0.3 per cent due to the pyrometer calibration and not more than 0.4

per cent due to the difference between the observed

temperature and the average temperature of the capsule.

Discussion

In the case of carbon, two questions must be con- sidered in a presentation of the thermodynamic properties of the standard state: 1) Are the data sufficiently accurate in themselves? 2) Do they refer to a standard crystalline form of carbon? Enthalpy differences calculated from (2) lie consistently about 0.7 per cent below the smooth data of McDonald for spectroscopic grade SPK graphite

(density 1.9). They agree with recent reviews of older data, maximum deviations being 1 per cent be- low Dergazarian, el al. [8] at 1200°K and 0.7 per cent above Evans [7"| at 2500°K. The heat capacity data derived from (3) are well within the scatter of the observations and the estimated accuracy of Rasor and

223-149
McClelland [9] in the range 1500-2600°K. Since the older experimental work includes measurements on

natural graphite, this consensus supports reasonable confidence that the enthalpy and heat capacity

are known to a few per cent from ambient to 2600°K.

Regarding the second question, there is experi- mental evidence to indicate differences in the heat capacity of different graphites. DeSorbo [10] reports enthalpies at 298.15°K for Ceylon natural graphite and an Acheson graphite which differ by 88 J/gfw, almost twice the tolerance on the heat of formation of C02 set by Rossini and Jessup [11] in their paper recommending graphite as the standard state for carbon. The corresponding difference in heat capacity might be expected to extend at least to somewhat

higher temperatures. There are obvious systematic

trends amounting to several per cent in the high temperature data for the four samples of Rasor and

McClelland, but they state that these differences are

not significant. The difference between our measurements and those of McDonald on A1

2 03 near 1200°K is about 0.3 per cent. Taking this to repre- sent the systematic difference between the two methods, we have 0.5 per cent difference between

smoothed values at 1200°K to ascribe to random

errors of measurement or to a difference in the samples. Considering our standard error of 0.14 per

cent and a slightly larger value for McDonald's data,

the 0.5 per cent difference is too large to claim no

significant difference in samples, but too small to be reasonably sure of a significant difference.

TABLE I EXPERIMENTAL DATA FOR GRAPHITE*

Fu rna ce Heat to H"T-H 313.15 Furnace Heat to H"[~-H 313.15 Temp eratu re Ca lo ri meter and % Temperature Calorimeter and %

and Date at 313. 15°K a bov e Eq . (2) and Date at 313.15°K above E q. (2)

4148 3 J i joo't j/grw 8544.1 J 33397 J/afw

4148.6 8559.7

1191.3 7327.5

0.00 1920.2 15248.7

+ 0.09 7-2-64 7325.6

7329.6

4152.0

7-1-64 15234.1 15245.5 8578.2

4682.3 17957 931 1.4 36269

468 1.0 9323.0

1281.4

6-23-64

8277.2

8271.9 8277.7 4684.9

+ 0.02 2034.2

6-12-64

16576.7 16574.0 16571.6

10210

+ 0.16

40198

5974.0 23051 2191.2 18259

+ 0.10 5975.4 7-15-64 18246

1498.2 10593.3

-0.04 10207

6-25-64 10582.2

10591.4 10605 41989

5980.6 2263.2 19031

+ 0.02 7-17-64 19040 6950.7 26927 10663

1659.7 12349.2 12352.3 -0.12 20087 44398

6-30-64 6968.4 6970.3

7280.3 28231

2364.7

7-20-64 11247

1 1249 20176

-0.36

1710.9 6-19-64

7290.4 1 1872 47138

12935.0

12935.8 7289.3

+ 0.08 2462.1 7-27-64

2576.4

7-29-64

21300

21339

11906

22652

12677

+ 0.21

49869

-0.19

* At. wt. 12.01115

224-150
Acknowledgment

The authors are grateful to Mrs. E. K. Hubbard of the National Bureau of Standards Spectrochemical Analysis Section for the analytical work on the graphite spec imen.

References

[l] G. B. Spence, Technical Report WADD-TR-6 1-72, Vol. XLI to the Air Force Materials Lab., Wright-Patterson

AFB, Ohio, 1963.

[2] R. A. McDonald, private communication. Smoothed

data are given by H. Prophet and D. R. Stu 11, /. Chem.

Eng. Data, Vol. 8, 1963, p. 78.

[3] E. D. West and D. C. Ginnings, /. Res. Natl. Bur.

Stds., Vol. 60, 1958, p. 309,

[4] G. T. Furukawa, T. B. Douglas, R. E. McCoskey,

and D. C. Ginnings, J. Res. Natl. Bur. Stds.. Vol. 57, 1956, p. 67.

[5] 1). C. Ginnings, /. Phys. Chem.. Vol. 67, 1963

p. 1917.

[6] G. T. Furukawa and M. A. Krivanek, to be published.

[7] tt. H. Evans, private communication.

[8] T. E. Derg azarian, N. J. Dumont, L. A. duPlessis,

W. E. Hatton, S. Levine, F. L. Oetting, H. Prophet, G. C. Sinke, D. R. Stu 11, and C. J. Thompson, "JANAF Interim Thermochemical Tables," The Dow Chemical Co., Midland,

Michigan; March 31, 1961.

[9] N. S. Rasor and J. D. McClelland, /. Phys. Chem.

Solids, Vol. 15, 1960, p. 17; Wright Air Development

Command Tech. Report 56-400, 1956.

[10] W. De Sorbo and W. W. Tyler, J. Chem. Phys.,

Vol. 21, 1953, p. 1660. W. De Sorbo, J. Amer. Chem. Soc., Vol. 77, 1955, p. 4713.

[ill E. D. Rossini and R. S. Jessup, /. Res. Natl. Bur.

Stds., Vol. 21, 1938, p. 491.

Reprinted from "Advances in Thermophysical

Properties at Extreme Temperatures and Pres- sures," 1965, The American Society of Mechanical Engineers, 345 East 47th Street, New York,

N. Y. 10017.

225-151
Dynamic Measurement of Heat Capacity and Other Thermal Properties of Electrical Conductors At High

Temperatures

A. Cezairliyan and C. W. Beckett Most measurements of heat capacity at high

temperatures (above 1000 K) use the "drop

method" in which the specimen is heated in a furnace to a known temperature and then dropped

into a calorimeter near room temperature which

measures the heat given up (enthalpy) by the

specimen as the latter cools to the ambient

temperature. A series of such experiments yields

the relative enthalpy of the specimen from which

heat capacity can be derived.

When this technique is extended to very high

temperatures (above 2000 K) many problems

are created as the result of increased heat transfer,

chemical reactions, evaporation, diffusion, mechanical strength, etc., which limit the application

of the method. Consequently, it has become neces- sary to develop a dynamic method which allows

the heating of the specimen and the measurement

of the pertinent quantities in a time so short the

contribution of most of the phenomena, which

limit the application of the conventional methods

to very high temperatures, become negligible.

In dynamic measurements of heat capacity,

the tubular specimen (electrical conductor) is heated from room temperature to near its meltingpoint by a single heavy-current pulse of subsecond duration (heating rate is approximately

10 °K/ms). During this period, current flowing

through the specimen, voltage drop across the

specimen, and its temperature are measured at

0.4 ms intervals. The measurement of current is achieved by measuring the potential difference across a standard resistance placed in series with

the specimen. Temperature measurements are made with a high-speed photoelectric pyrometer,

which permits 1200 evaluations of the specimen

temperature per second. A small hole drilled in

the wall of the tubular specimen provides blackbody conditions. A bank of heavy-duty batteries

constitutes the pulse-power source. Dynamic recording of the pertinent variables

is made with a high-speed digital data acquisition

system which has a full-scale resolution of one

part in 8000. The recording system consists of a

multiplexer, analog-to-digital converter, a core memory, together with control and interfacing

equipment. The output of the system consists

of a teletypewriter which is connected to a timesharing computer. Thus, the recording system

allows the automatic digitization and storage of data during the dynamic experiment, and their

computerized processing after the experiment.

The method described above provides considerable versatility in the measurements and the

computational techniques. Heat capacity and

electrical resistivity are calculated from data

obtained during the heating period. Because of the short duration of the experiments, the only

significant heat loss is that due to thermal radiation, which in most cases is less than five percent

of the input power. Data taken during the initial free cooling period enables one to compute hemispherical total emittance and thus apply a cor- rection to heat capacity. By conducting separate

dynamic experiments—where the pyrometer is aimed at the outer surface of the specimen instead

of the hole—one can obtain sufficient data to compute normal spectral emittance. Melting

point of the specimen can be determined by

allowing the heavy pulse current to flow until the

specimen undergoes partial melting.

Preliminary results on molybdenum in the

range 1800-2800 K yield standard deviations of

0.3, 0.1, and 2 percent for the precision of heat

capacity, electrical resistivity, and hemispherical

total emittance, respectively. It is believed that

the accuracies of these measurements are comparable or better than the accuracies of other

measurements of these properties at high

temperatures.

Manuscripts related to the construction and

operation of the various components of the

dynamic measurements system, and the final results on molybdenum are in preparation.

226
The Vapor Pressure, Vapor Dimerization, and Heat of Sublimation

of Aluminum Fluoride, Using the Entrainment Method1

by Ralph F. Krause, Jr., and Thomas B. Douglas

National Bureau of Standards, Washington, D. C. 20284 (Received May 1, 1967)

The vapor pressure P of anhydrous aluminum fluoride was measured at eight temperatures

between 1194 and 1258°K by an entrainment method. The standard deviation of P from

a least-square fit was 0.15%, and possible systematic errors of 0.5% in P and 1° in f

were estimated. Smoothed values of P and dP/dT at 1225°K were determined. Considering P as the sum of the ideal monomeric and twice the dimeric vapor pressure, the

other two thermodynamic properties necessary to define (1) AlF3 (c) ^± AlF3 (g) and (2) 2AlF3 (g) ^ Al2F6 (g) were taken as (a) A*S°(1), derived from published spectroscopic and

crystalline heat capacity data, and (b) 2AH°(l) + A#°(2), reported in a recent mass

spectrometric study. The derived results at 1225°K along with their estimated uncertainties were A#°(l) = 67.0 ± 0.4 kcal, A£°(l) = 43.0 ± 0.4 eu, and A(?°(2) = -7 ±

1 kcal.

Introduction

As part of a program of research to determine ac- curately the thermodynamic properties of substances

that are important to high-temperature applications

like chemical propulsion, a new apparatus was constructed to apply the entrainment method for measuring

equilibria between solid and vapor. The high stability

of anhydrous aluminum fluoride A1F3 and the ease of obtaining a sample of fairly high purity made it suitable

for precise measurements. Also, interpretation of current work in this laboratory on subliming A1F3 in the presence of A1CL vapor demands precise data

for AIF3. Even though several investigators2-13 had measured

the vapor pressure of A1F3 , predominantly from 890 to 1100°K or from 1370 to 1570°K, most of their results were too imprecise to contribute to an evaluation of the

composition of the saturated vapor. Each had derived a AH° for

AlF3 (c) AlF3 (g) (1)

by assuming the vapor to be completely monomeric.

A mass spectrometric study by Porter and Zeller 14 indicated that the saturated vapor at 1000° K sustains

perceptible dimerization

2AlF3 (g)

^

Al2F6 (g) (2)

Also, the mole fraction of dimer in the saturated vapor

increases with temperature because a mass spectrometric study by Buchler15 showed that AH° of reaction 1

is less than that for

2AlF3 (c) —^ Al2F6 (g) (3)

If each of the preceding vapor pressure measurements

were considered to reflect the presence of both the monomer and the dimer, a corrected AH° of reaction

1 could be shown to be less than a second-law value,

derived by assuming the vapor to be completely monomeric, and greater than a corresponding third-law

value; moreover, the difference between these uncorrected second- or third-law values and the true ones would increase with temperature. Nevertheless, an

inspection of all of these uncorrected values showed

no such trend, but rather a scattering.

(1) This work was supported by the Advanced Research Projects

Agency under Order No. 20 and by the Air Force Office of Scientific Research under Contract No. ISSA-65-8.

(2) W. Olbrich, Dissertation, Technische Hochschule, Breslau, 1928.

(3) O. Ruff and L. LeBoucher, Z. Anorg. Allgem. Chem., 219, 376

(1934).

(4) I. I. Naryshkin, Zh. Fiz. Khim., 13, 528 (1939).

(5) P. Gross, C. S. Campbell, P. J. C. Kent, and D. L. Levi, Discussions Faraday Soc, 4, 206 (1948).

(6) W. P. Witt, Thesis, Oxford University, Cambridge, 1959.

(7) W. P. Witt and R. F. Barrow, Trans. Faraday Soc, 55, 730

(1959).

(8) A. M. Evseev, G. V. Pozharskaya, A. N. Nesmeyanov, and Ya. I. Gerasimov, Zh. Neorg. Khim., 4, 2196 (1959).

(9) M. M. Vetyukov, M. L. Blyushtein, and V. P. Poddymov, Izv. Vysshikh Uchebn. Zavedenii, Tsvetn. Met., 2, 126 (1959).

(10) D. L. Hildenbrand and L. P. Theard, Aeronutronic Report No.

U-1274, Newport Beach, Calif., June 1961.

(11) D. L. Hildenbrand and N. D. Potter, personal communication,

1964.

(12) P. E. Blackburn, Arthur D. Little Report, Cambridge, Mass., May 1965.

(13) H. C. Ko, M. A. Greenbaum, J. A. Blauer, and M. Farber,

/. Phys. Chem., 69, 2311 (1965).

(14) R. F. Porter and E. E. Zeller, J. Chem. Phys., 33, 858 (1960).

(15) A. Buchler, Arthur D. Little Report, Cambridge, Mass., Sept

1962. 227-475
17 16 15 -^20 cm

12 •56cm

Figure 1. Diagram of entrainment tubes in the cylindrical furnace: (1) nickel core, (2) Pt-20% Rh main heater,

(3) cross-sectional center, (4) alumina tubes, (5) insulation, (6) an end heater, (7) Teflon gaskets,

(8) argon input, (9) argon output, (10) Pt-10% Rh composite tube, (11) Pt-20% Rh housing, (12) perforated

disks, (13) condenser, (14) capillary tube, (15) alumina sled, (16) sample boats, (17) vapor cell, (18) detachable

entrance cap, and (19) longitudinal axis. Note that vertical and horizontal scales differ.

The aim of this paper is to show how far the use of our precise sublimation data can go toward defining

the thermodynamic properties of sublimation and di- merization of A1F3 at temperatures where the vapor

pressure is appreciable.

Entrainment Method

The entrainment method used in this work involved

the flowing of argon gas through a high-temperature

vapor cell, holding a sample of anhydrous A1F3 . The

sublimed sample was condensed downstream, while the

carrier gas was collected in a tank. Saturation was

closely approximated by using an appropriate geometry

of the vapor cell and flow of the gas mixture.

The vapor cell and condenser were separate sections

of the same Pt-10% Rh composite tube as shown in Figure 1. The detachable cap prevented accidental

spilling of the sample from the cell. The exit of the

cell was connected to the condenser by a capillary tube

of 5-cm length and 1-mm i.d. The application of Merten's16 diffusion study to this system indicated

negligible diffusion of the sample vapor through the

capillary tube at the gas flows employed in this work.

The crystalline sample of anhydrous A1F3 had been

sublimed preliminarily at 1050° in a nickel retort. A

spectrographs analysis reported 0.01 to 0.1% Mg;

0.001 to 0.01% Ca, Cu, Fe, Mn, Ni, and Si; and 10"4

to 10 _3% Cr and V. Triplicate chemical analyses

reported from 67.61 to 68.00% F and from 32.13 to 32.17% Al, compared to the theoretical value of 32.130% Al. The mass of sublimed sample, roughly

200 mg, was taken as the mean of the condenser gain

and the sample loss. The sample loss was the weight

change of the loaded boats minus 11-16 mg of the

weighed sample accidentally spilled in the cell. Since

the sample loss was observed to be less than 0.2 mg

for several experiments at zero gas flow, no correction

for diffusion or distillation of the sample was warranted. While the condenser gain was consistently

less than the above mean by an average 0.3%, apparently due to a weight loss of the composite tube itself, this difference was near the weighing uncertainty of this 137-g tube. Preliminary to the argon flow, the atmosphere of air which was held in the vapor cell prior to its installation

in the furnace was reduced to 10-4

torr while the vapor

cell was being heated to 500°. Next, 99.996% pure

argon, dried by anhydrous Mg(C104 ) 2 , was carefully

introduced into the flow path until its pressure was

equal to barometric pressure. Finally, after the vapor

cell was heated to its operational temperature, an

additional 3-4 hr at zero gas flow was required to attain a steady temperature. The total pressure of the gas mixture in the vapor cell was taken as 'the time average

of the continuously recorded barometric pressure

plus a head pressure of 0.6-1.2 torr. The volume of argon was measured with an accuracy of 10 ml by a

calibrated gasometer which was immersed in a highvacuum-pump oil saturated with argon and whose

displacement of 14-28 1. was corrected for differences

in the initial and final barometric pressure and room

temperature.

Vapor Cell Temperature

Usually being the greatest single source of error

in vapor pressure measurements, the temperature of

(16) U. Merten, J. Phys. Chem., 63, 443 (1959). 228-476
the vapor cell was measured with special care, 17 using

Pt—Pt-10% Rh thermocouples. As shown in Figure 1, a nickel core in an atmosphere of nitrogen

served to reduce any temperature gradient in the vapor

cell, which was centered within an alumina tube of a wire-wound resistance furnace. Three thermocouples

were inserted longitudinally into the walls of the nickel

core; two had fixed differential junctions and the third

had variable immersion to observe the temperature

profile. A fourth was inserted along the furnace axis with its junction in the well near the vapor-cell entrance. A fifth was placed aside to check periodically

the stability of the others. The thermocouples w

T ere calibrated by the NBS temperature section to an

accuracy of ±0.5° at 1000°.

Some preliminary experiments showed that if the

temperature gradient were negative in the direction of the gas flow through the vapor cell, the sample vapor

would condense prematurely and plug the capillary

tube. To prevent this deposit, each of three heaters was adjusted manually by an autotransformer to give

the same temperature at the entrance and exit of the

vapor cell and at the exit of the capillary tube. In- stead of a zero-temperature gradient, however, a steady

profile was observed to decrease about 2° for the

first 5 cm along the length of the vapor cell, to increase

linearly about 2° for the remaining 15 cm of the

cell, and to be close to zero through the capillary

tube. Besides, the axis temperature was observed to be 0.05-0.3° lower than that in the nickel core

at the same cross section. The temperature of an experiment was taken as the

time average of the vapor-cell exit, the temperature of which drifted 1 or 2° during an 8-16-hr flow. An

automatic recorder registered continuously the thermocouple emf relative to that of a Diesselhorst potentiometer with a precision equivalent to 0.05°. A possible systematic error of 1° in T was estimated and

was considered to be nearly constant over the entire

range of our measured temperatures.

Test for Saturation

Since diffusion of the sample vapor through the

capillary tube was shown to be negligible, a test

for saturation would be the linearity, extrapolated

through the origin, of the flow of sample mass

q vs. the average flow, v, of the gas mixture at a given cell temperature. When v was varied

by a factor of 2, this test was satisfied, within ac- cidental error, as shown by the very close agreement

of each of the four successive pairs in the sixth column

of Table I. Another test for the degree of saturation was applied by considering the mass of sample lost in each of two successive boats in the vapor cell with a temperature

gradient. The ratio of the weight loss of the second

boat to that of the first was observed as 0.03 ± 0.005

for v near 120 ml/min and 0.04 ± 0.005 for v near 60

ml/min; the uncertainty resulted from accidently

spilling some sample from either boat for each assembly.

The partial pressure p of the sample was assumed to increase with the distance x beyond the start of the

first boat at a given v according to dp/dx = k(P - p) + AD(d2 p/dx*)/v (4) where k is a constant, P is the vapor pressure at x, A

is the cross-sectional area, and D is the interdiffusion

coefficient of the gas mixture. If there were no

temperature gradient and p were zero at zero x, inte- gration of eq 4 would yield a degree of unsaturation at the exit of the vapor cell less than 0.1%. Since we

observed a temperature gradient b = dT/dx, P was

assumed to be represented by

P = P0 (l + hex) (5) where P0 is the vapor pressure at x = 0 and c = dP/

PdT. Assuming the observed b and c, integration of eq 4 combined, with eq 5 yielded a degree of unsaturation less than 0.4%.

Preliminary Assumption

If the sample vapor under the conditions of this work were assumed to be wholly monomeric and ideal,

the vapor pressure P could be calculated from

P = PT/(1 + (nM/w)) (6)

in which PT is the total gas pressure, n is the number of moles of collected argon, w is the mass of sublimed A1F3 , and M is the molecular weight of its monomer. The

resulting P's at eight independently measured temperatures are tabulated in Table I. Second-law values of A#°(l) 18 and A£°(l), which

are listed in Table I, were determined by a least- square fit of our entrainment data with

R InP = AS°(1) - (A#°(l)/T) +

AC'p °[ln (T/T') + (T'/T) - 1] (7)

in which the published value of ACP

° = -2.67PatT' =

1225°K was assumed constant over our temperature

range. Such a fit gave standard deviations of 0.15% in P, 0.07 kcal in A#°(l), and 0.06 eu in A£°(l). A possible systematic error of 1° in T would give an additional 0.01 kcal in A#°(l) and 0.05 eu in A*S°(1).

A third-law value of A#°(l) at T = 1225°K was

determined for each vapor pressure measurement ac- cording to A#°(l) = T[( — (AG° - AH°T,)/T) - PlnP] (8) whose mean AH°(1) and deviations from this mean

(17) W. F. Roeser and H. T. Wensel, J. Res. Nat. Bur. Stand., 14, 247

(1935).

(18) Hereafter, a specific reaction will be indicated by the number

in parentheses, and 1 cal = 4.1840 joules. 229-477
Table I : Preliminary Results for Reaction 1 by Assuming Wholly Monomeric Vapor

T, 3obsd, "obsd. P, (P - Pcalcd)/Pcalcd, %

No." °K mg/min ml/min matm II law III law

1 1194.0 0.1441 112.1 1.500 0.07 — 1.8

2 1194.7 0.0781 59.90 1.523 -0. 10 — 1.9

3 1212.1 0.2385 122.5 2.311 0.11 -0.6

4 1217.5 0.1342 61.00 2.619 0.00 -0.4

5 1236.9 0.3875 115.1 4.070 -0.3 0.4

<> lOOQ Q IZoo .

O

01 . 00 q Qin 6. oIU u . uy 0.6

7 1252.5 0.5869 124.3 5.778 0.08 1.7 8 1257.5 0.3226 62.23 6.441 0.03 1.9

1225

/Aff°(l) = 68.49 ± 0. l

b 66.73 ± 0.4 kcal \AS°(1) = 44.44 ± 0.

1

6 43.0 ± 0.4 eu

c

Chronological sequence: 3, 7, 5, 1, 4, 8, 6, and 2.

6 This uncertainty was taken to be the sum of the random and possible syst

atic errors.

c See ref 19, 20, and 24.

are listed in Table I. Each -(AG° - LH°T.)fiT, the

third-law A*S°(1), and ACP

° of eq 7 were evaluated

from the literature which is discussed in the next section. A comparison of the preceding second- and third-law

values reveals that our entrainment data appear incompatible with this preliminary assumption. The secondlaw AH°(1) in Table I is appreciably greater than the mean third-law AH°(l). Neither the experimental

uncertainty of the entrainment data nor a reasonable

estimate of the uncertainty of the third-law A*S°(1)

appears sufficient to overlap these discrepant values. Incidentally, the third-law values exhibit the characteristic temperature trend which is consistent with the

concept of dimerization as shown by the two previously

mentioned mass spectrometric studies. Although its magnitude has doubtful significance, the trend itself reflects the precision of our work.

Entropy of Sublimation

Of course, a possible cause for the trend and dis- crepancy of the preliminary assumption might be the

third-law value of AS°(1). More importantly,

however, its value and uncertainty were examined

closely to evaluate the extent of dimerization whose

reliability would depend upon the accuracy of A*S°(1)

despite the relatively high reliability that we believe our entrainment data have. Since AS°(1) was last evaluated for the JANAF tables, 19 more re- cent studies led us to make two revisions. The first revision is that suggested by Douglas and

Ditmars, 20 who measured the relative enthalpy of the

crystal from 273 to 1173°K. Their work is in good

agreement with a similar measurement by O'Brien

and Kelley21 and invalidates Frank's22 adjustment of the latter's temperature scale. The assumed uncertainty in the entropy of the crystal arises from esti- mated uncertainties of 0.08 eu/mol from the hightemperature enthalpy measurements and of 0.08 eu/

mol from King's23 measurement of the low-temperature heat capacity.

The second revision is that suggested by Snelson's24 infrared spectrum of A1F3 by matrix isolation which

is considered by most spectroscopists to yield more

precise locations of band centers than a direct hightemperature technique. Both Buchler25 and McCory,

et al., 26 performed the latter, which was a basis of the

latest JANAF table. 19 Snelson observed spectra of saturated AIF3 vapor in matrices of neon, argon, and

krypton down to 200 cm-1 and assigned the strong

absorption features to the three infrared-active fre- quencies of the AIF3 molecule, which has a planar configuration of D3h symmetry, analogous to BF3. His

assignment of the two doubly degenerate frequencies was confirmed by the matrix environment appearing

to remove the degeneracy of these modes. Weaker

absorption features of the saturated vapor were at- tributed to the dimer molecule A12F6 ; the spectrum

of the superheated vapor gave further support to this assignment, since only the strong absorption features

remained. Another matrix spectrum reported by

Linevsky27 is in good agreement with Snelson's observed spectra, but Snelson noted that frequency

shifts in his three matrices showed a regular trend. Following the procedure described in an earlier paper, 28 he estimated the gas-phase frequencies from the values

(19) D. R. Stull, et al., "JANAF Thermochemical Tables," Dow

Chemical Co., Midland, Mich., 1965.

(20) T. B. Douglas and D. A. Ditmars, J. Res. Nat. Bur. Stand., 71A

185 (1967).

(21) C. J. O'Brien and K. K. Kelley, J. Am. Chem. Soc, 79, 5616

(1957).

(22) W. B. Frank, J. Phys. Chem., 65, 2081 (1961).

(23) E. G. King, J. Am. Chem. Soc, 79, 2056 (1957).

(24) A. Snelson, J. Phys. Chem., 71, 3202 (1967).

(25) A. Btlchler, Arthur D. Little Report, Cambridge, Mass., June

1962.

(26) L. D. McCory, R. C. Paule, and J. L. Margrave, J. Phys.

Chem., 67, 1086 (1963).

(27) M. J. Linevsky, Space Science Laboratory Report, Philadelphia,

Pa., Nov 1964.

(28) A. Snelson, /. Phys. Chem., 70, 3208 (1966) 230-478
ne ooserved m the neon matrix to be i> 2 = 300,

v% = 965, and v4 = 270 cm-1 with a probable accuracy

of 10 cm-1

. Using the formulas given by Herzberg, 29

v\ was calculated to be 660 cm-1. If the uncertainties

of these assignments were all added in the same di- rection, this would contribute 0.3 eu/mol to the en- tropy of the monomeric gas established by applying

the harmonic-oscillator, rigid-rotor approximation to the published spectroscopic data. Two other sources of uncertainty were considered.

First, an electron-diffraction study of A1F3 by Akishin,

et al., 30 was considered to have an uncertainty of 0.03 A

in the Al-F bond distance which would contribute

0.1 eu/mol to the entropy of the gas. Second, we

attempted to realize an error due to the neglect of anharmonicity and stretching. The formula derived

by Mayer and Mayer31 for diatomic molecules gives +0.1

eu correction to A1F at 1000°K. Assuming comparable

anharmonicity and stretching for A1F3 gave us a rough

estimate of +0.2 eu, which may be several times larger

than a true correction.

Applying the previous revisions to the JANAF19 value at 1225°K yielded AS°(1) = 43.0 ± 0.4 eu.

32 Incidentally, the second-law value of AS°(1), derived from our entrainment data by assuming the dimer

content of the saturated vapor to be zero, set an upper

limit which is 1.5 eu higher than the above adopted

value.

Correction for Dimerization

The previously mentioned mass spectrometric studies14 - 15 and the infrared spectra by matrix isolation, 24 ' 27 besides the results of our preliminary as- sumption, indicate that the saturated vapor of A1F3 can be interpreted by taking into account the occurrence of some dimerization.

Two of the four thermodynamic properties necessary

to define reactions 1 and 2 at 1225°K, near the midpoint of our observed temperature range, were derived solely from our entrainment data. They are the

smoothed values P = (3.115 + 0.0720 lO"3 atm and

dP/dT = (7.154 + 0.165010-5 atm/deg derived

from the least-square fit with eq 7, as discussed previously. The parameter t = TtTue — Tohsd was intro- duced to reflect the effects of a possible systematic error

in our temperature measurements on P and dP/dT. A

value of t = 1° corresponds to an error in P of 2.3%, which makes a possible systematic error of 0.5% in P from eq 6 negligible. Having to look

elsewhere for the other two properties, we chose

AS°(1), discussed earlier, and Ai?°(3).»

Since P was determined by the monomeric vapor

assumption of eq 6, its resolution into the partial pressures of monomer and dimer is approximated very

closely by

where Pm and Pd are assumed to be related to properties of reactions 1 and 3, respectively, by

Pi = exp[(AS°/R) - (AH°/RT)} (10)

The relationship among reactions 1, 2, and 3 is obviously

exemplified by

A#°(3) = 2A#°(1) + AH°(2) (11)

To make temperature conversions of AH°(2) and

AS° (2) between 1000 and 1225°K, ACP

° (2) was assumed

as 2R from the equipartitional heat capacities of the

gas species involved. Combining eq 9, 10, and 11 allows P and dP/dT to be expressed as functions of A£°(l), AH°(1), A<3°(2), and A#°(3) at 1225°K.

Pm + 2Pd (9)

84 86 88

2 AH°(i ) + AH°i2) in kcal at 1000 °K Figure 2. Hypothetical values of (a) AH°(1) and

(b) AG°(2) calculated from P and dP/dT of this work and

selected values of AS°(1) and 2AH°(1) + AH°(2) for reactions (1) AlF3 (c) = AlF3(g) and (2) 2AlF3 (g) =

AU^Vg). A possible systematic error of 1° in our observed T would contribute 0.05 kcal to A#°(l) and A(?°(2). The superscript c in part a refers the reader to

ref 19, 20, and 24, and the d at the bottom

of part b, to ref 15.

(29) G. Herzberg, "Infrared and Raman Spectra of Polyatomic

Molecules," D. Van Nostrand Co., Inc., New York, N. Y., 1945, p

177.

(30) P. A. Akishin, N. G. Rambidi, and E. Zasorin, Kristallografiya,

4, 186 (1959).

(31) J. E. Mayer and M. G. Mayer, "Statistical Mechanics," John

Wiley and Sons, Inc., New York, N. Y., 1940, p 165.

(32) This uncertainty was taken to be the root of the sum of the

several independent uncertainties squared.

231-479
70

8 69

< 68

A ®

--fir © Q0 <£> 00 -

V 7 V

y ' j o 1200

T CK)

1300

Figure 3. Third-law values of AH°(1) for AlF3 (c) = AlF3 (g) from several vapor pressure measurements corrected for dimerization: Olbrich, 2 •; Ruff and LeBoucher,3 V; Witt,6 ; Evseev, et aZ.,8 ; Hildenbrand and Theard, 10 ; Blackburn, 12 A; and this work, O. Hildenbrand and Potter 11 reported 108 other values from 949 to 1128°K, which gave a 0.2-kcal standard

deviation and whose mean Aff°(l) = 67.5 kcal. Note that AH°(l) was derived using AS°(1) = 43.0 eu at 1000°K.

In this way, we generated hypothetical values of A#°(l) and AG°(2), calculated from P and dP/dT

of this work and selected values of AS°(1) and

Ai/°(3). An iterative method was used with a digital

computer programed in basic. 33

Derived Values

Figure 2 indicates values of AH°(1) and A6'°(2)

which are simultaneously in agreement with our

precise entrainment data and reasonable choices of AS°(1) and A#°(3) of eq 11. Note that a A#°(l)

which is associated with a given A5°(l) is nearly constant over a reasonable range of AH°(3).

In view of our adopted value of AS°(1) and Buchler's 15 AH° (3), the foregoing analysis leads us to AH°(1) = 67.0 ± 0.4 32 kcal and AG°(2) = -7 ± l

32

kcal at 1225°K. The effects on these values of small

errors in the data used to derive them are shown explicitly by

A#°(l) = 66.95 + 1.1s - 0.01/i + 0.05< (12)

A(?°(2) = -6.9 + 2s + O.lh + 0.05t (13)

where s, h, and t represent any variations from the

values that we have assumed for A<S°(1), A#°(3), and

our observed T, respectively.

The above values derived from this work are given

in Table II to compare with several values resulting

from previously published investigations. Although

Porter and Zeller 14 reported a value of AH°(2) which

depends upon A*S°(2) assumed by analogy with other

halides, their measurement of Pd/Pm may be repre- sented independently of this assumption by

232-

AG°(1) + AG°(2) = -RT In (Pd/Pm) (14)

Our evaluation of the extent of dimerization implicit

in our entrainment data substantiates Porter and

Zeller's mass spectrometric measurement.

The precision of our entrainment data is demonstrated by its comparison with that of some other

investigations. 2 ' 3 ' 6,8,10-12 After each reported vapor

pressure was corrected for dimerization, AH°(1) at 1000° K was calculated by eq 8 and plotted in Figure 3

at the temperature of its measurement. The consistency of our points contrasts with the scattering of most of the others. Only the results of Witt6 agree

rather closely with ours, except for a systematic dis- crepancy equivalent to about 1° in measuring temperature. Although his data have a precision similar

to ours, they could do much less toward evaluating

dimerization, whose extent is much smaller over his temperature range than ours. We found the mole per

cent of dimer in the saturated vapor to be 4.6 ±1.4

at 1225°K while Porter and Zeller 14 reported it to be

near 1 at 1000°K.

There are numerous other substances besides alu- minum fluoride for which the status of the data available

for evaluating the thermodynamics of evaporation and

vapor association is similar. Invariably, the various

types of data are related complexly, and hence in- consistencies among them are not easy to evaluate.

We believe that such parametric plots as Figure 2

offer perhaps the clearest and most objective means of

(33) J. G. Kemeny and T. E. Kurtz, "basic," Dartmouth College, Hanover, N. ft., 1965. 480
Table II : Thermodynamic Values for Reactions 1 and 2

T, Previous This °K Property work work"

| AH°(1), kcal 67.0 ± 0 4

1225< AS°(1), eu 43.0 ± 0 4»

{ A<?°(2), kcal -7 ± 1

2Afl°(l) + A/J°(2), kcal 85 a ± 3 1 Aff°(l), kcal 67. 3 ±3 • 68. 1 ± 0 4 1000 Afl°(2), kcal -48 ±4 ~\ -50 ± 3 AS°(2), eu -32 ± 3 >d -35 ± 3 AG°(1) + AG°(2), kcal 8.6 ±0.67 9 ± 1

" Derived by assuming 2A#°(1) + AH°(2) = 86 kcal at 1000°K. " References 19, 20, and 24.

c Reference 15. " Reference 14. See eq 14 for conversion of observed Pd/Pm, the uncertainty of which was taken to be twice its standard error.

establishing what the inconsistencies are, how sensi- tive they are to errors in the various types of data,

and whether there are one or more sets of fundamental

thermodynamic quantities which appear to fit all the

available data within the respective experimental

reliabilities.

Acknowledgments. The initial development of the

entrainment apparatus was carried out by A. Q. Victor.

We thank E. J. Maienthal and R. A. Paulson for their

chemical analyses of the sample and appreciate the

helpful advice of D. R. Lide, Jr., and S. Abramowitz in evaluating the spectroscopic data. George Long, of the Aluminum Company of America, kindly supplied

the sample.

(Reprinted from the Journal of Physical Chemistry, 72, 475 (19U8).]

233-481

5. Reaction Calorimetry

Paper Page

5.1. Precise measurement of heat of combustion with a bomb calorimeter.

Jessup, K. S., Nat. Bur. Stand. (U.S.) Monograph 7, (Feb. 1960).

Key words: Techniques in bomb calorimetry 237

5.2. Heat of isomerization of the two butadienes.

Prosen, E. J., Maron, F. W., and Rossini, F. D., J. Res. Nat. Bur.

Stand. (U.S.) 42, No. 3, 269-277 (Mar. 1949).

Key words: Bomb calorimetry 262

5.3. Heats of formation of diborane and pentaborane.

Prosen, E. J., Johnson, W. H., and Pergiel, F. Y., J. Res. Nat. Bur.

Stand. (U.S.) 61, No. 1, 247-250 (Oct. 1958).

Key words: Heats of formation 271

5.4. Studies in bomb calorimetry. A new determination of the energy of combustion of benzoic acid in terms of electrical units.

Churnes, K. L., and Armstrong, G. T., J. Res. Nat. Bur. Stand.

(U.S.) 72A, (Phys. and Chem.) No. 5, 453-465 (Sep.-Oct. 1968).

Key words: Errors in bomb calorimetry; techniques in bomb

calorimetry; benzoic acid standard • 275

5.5. Constant pressure flame calorimetry with fluorine. II. The heat of formation of oxygen difluoride.

King, R. C. and Armstrong, G. T., J. Res. Nat. Bur. Stand. (U.S.)

72A, (Phys. and Chem.) No. 2, 113-131 (Mar.-Apr. 1968).

Key words: Flame calorimetry; flow combustion calorimetry;

fluorine calorimetry 288

235

UNITED STATES DEPARTMENT OF COMMERCE . Frederick H. Mueller, Secretary NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Precise Measurement of Heat of Combustion

With a Bomb Calorimeter

R. S. Jessup

National Bureau of Standards Monograph 7

Issued February 26, 1960

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington 25, D.C. - Price 25 cents

237-1
Contents

Page

1. Introduction 1 1.1. Definitions of terms 1

a. Heat units 1 b. Heats of combustion 2

2. General discussion of bomb-calorimetric measure- ments 2

3. Factors affecting accuracy in bomb-calorimetric measurements 3

3.1. Undesirable side reactions 3

a. Incomplete combustion 3

b. Oxidation of crucible and fittings 4

c. Reaction of acids with bomb material- 4

d. Combustible impurities in oxygen 4

3.2. Experimental techniques of individual measurements* 4

a. Weight of sample of combustible 4

b. Weight of calorimeter plus water 5

c. Temperature measurements 6

d. Firing energy 9

e. Materials in bomb 9

f. Acids formed in combustion 9

4. Summarized directions for a bomb-calorimetric ex- periment 10

4.1. Preliminary adjustment of apparatus 10

4.2. Preparation and weighing of sample of benzoic acid 10

4.3. Preparation of bomb 10

4.4. ' Weighing of calorimeter plus water 10

4.5. Assembly of calorimeter 10

4.6. Adjustment of initial temperature of calo- rimeter 11

4.7. Observation of temperature and ignition

of sample 11

4.8. Analysis of contents of bomb 11

4.2. a. Preparation and weighing of sample of

fuel 11

Page

4. Summarized directions for a bomb-calorimetric ex- periment—Continued

4.3. a. Preparation of bomb 11

4.6. a. Adjustment of initial temperature of calorimeter 11

4.8. a. Analysis of contents of bomb' - 12

5. Calculation of results 12

5.1. Calibration experiment 12

a. Heat of combustion of benzoic acid 12

b. Correction terms ci and c2 13

c. Corrected temperature rise 13

d. Example illustrating the calculations E and Es 14

5.2. Calculation of heat of combustion 15

a. Energy equivalent of calorimeter as used 15

b. Corrected temperature rise 15

c. Corrections C\, ty, Cz 15

d. Calculation of Q v (gross) 15

e. Calculation of Qp (net) 16

6. References 16

7. Appendix 17

7.1. Apparatus 17

a. Bridge 17

b. Thermometer 18

c. Galvanometer 18

d. Bomb 18

e. Calorimeter and jacket 19

f. Balance for weighing samples 20

g. Balance for weighing calorimeter 20

h. Oxygen purifier 20

i. Laboratory table for bridge 21

j. Pressure gage 21

7.2. Glass sample bulbs 21

238-11
Precise Measurement of Heat of Combustion

With a Bomb Calorimeter 1

R. S. Jessup

This Monograph gives detailed descriptions of apparatus and methods which are used

at the National Bureau of Standards for precise determinations of heats of combustion

of liquid hydrocarbon fuels. Numerical examples are given of methods of calculating

results of measurements from observed data. The technique of making and filling glass bulbs to contain samples of volatile liquid fuels is described. The accuracy of the methods described is about 0.1 percent. This is intermediate

between the accuracy of 0.01 or 0.02 percent attained in certain measurements on pure compounds, and the accuracy of several tenths of one percent obtainable with published

standard procedures for measurements on fuels.

1. Introduction

Standard methods of moderate precision for bomb-calorimetric measurement of heats of combustion of solid and liquid fuels are published by

the American Society for Testing Materials [1,2].

2 These methods can be used to measure heat of

combustion with an accuracy of several tenths

of one percent. Apparatus and methods for measurements of heat of combustion with an

accuracy of 0.0.1 or 0.02 percent have been

described in the literature [3]. The attainment

of such accuracy involves the use of rather

laborious and time-consuming procedures. In some applications of fuels the heat of combustion

is required with an accuracy of approximately 0.1 percent, which is probably not attainable with the

standard methods referred to [1, 2], but can be

attained with less expenditure of time and effort than is required in the most precise measurements.

This Monograph describes methods and apparatus used at the National Bureau of Standards in connection with several series of investigations of

heats of combustion of aircraft fuels [4, 5, 6, 7]. The restrictions of the treatment to a particular

set of apparatus, and a particular experimental

procedure involves some loss of generality, but

this is not believed to be serious. Most precise

measurements of heats of combustion of materials

containing essentially only the elements carbon,

hydrogen, nitrogen, and oxygen have been made in

apparatus of similar design, to which the same

procedures are applicable. Descriptions of other

equally satisfactory apparatus for this purpose

will be found in reference [3] and the references

there cited. There will also be found in some

of these references descriptions of apparatus and

procedures suitable for measurements on materials

containing considerable amounts of such elements

as sulfur and halogens. The apparatus and

methods described in this Monograph are not

suitable for measurements on such materials.

Although the apparatus described in this Monograph is suitable for measurement of heat

1 The preparation of this Monograph was supported in part by the Air Force Ballistic Missiles Division, Air Research and Development Command, U.S. Air Force.

2 Figures in brackets indicate the literature references on page 16.

of combustion with an accuracy of 0.01 or 0.02

percent, the procedure in measurements on fuels is such that a considerable saving in time was

achieved at the cost of a somewhat lower precision.

This lower precision resulted from several factors

as follows:

(1) As a rule only two experiments were made

on each fuel, as compared with six or more experiments where the highest possible accuracy is desired; (2) an approximate method was used to obtain the corrected temperature rise of the calorimeter, i.e., the temperature rise corrected for heat

of stirring and heat transfer between calorimeter

and surroundings; (3) because some liquid fuels are quite volatile there may be an appreciable loss of lighter components in handling. In spite of

these effects the results of measurements even on

the most volatile fuels (gasolines) are, in general,

precise to about 0.05 percent. The results contain

a nearly constant systematic error of approximately 0.03 percent (for hydrocarbon fuels) due

to neglect of the Washburn correction [18] which

takes account of the difference between heats of

combustion in oxygen under a pressure of about

30 atm and at a pressure of 1 atm.

(If desired, this error can be approximately corrected, in the case of hydrocarbon fuels only, by

reducing the observed heat of combustion by 0.03

percent.)

In other respects the methods described are applicable in measurements of the highest precision, and may serve as a useful guide to persons

interested in such measurements.

1.1. Definitions of Terms

a. Heat Units

The heat units used in connection with measure- ments of heats of combustion of fuels are the IT

calorie 3 and the Btu. These units are here

defined as follows:

3 IT calorie is an abbreviation for International Steam Tables calorie. This calorie was adopted by the International Steam Table Conference

held in London in July 1929 [12], and is in fairly general use in engineering

practice both in this country and abroad.

239-1
1 IT calorie =4.1868 absolute joules

1 Btu= 1055.07 absolute joules.

The definition of the Btu was obtained from that

of the IT calorie by means of the relations

1 pound (avoirdupois) =453.5924 grams

1 IT calorie per gram=1.8 Btu per pound.

b. Heats of Combustion

The quantity directly measured in a bombcalorimetric experiment is generally referred to as the "total (or gross) heat of combustion at constant volume"; this quantity is represented by the

symbol Qv (gross) in this Monograph. A precise

definition of this term requires a specification of

the initial states of the reactants (oxygen and fuel)

and of the final states of the products of combustion. For most purposes the following definition

is sufficient: The total (or gross) heat oj combustion

at constant volume of a liquid or solid fuel containing

only the elements carbon, hydrogen, oxygen, nitrogen

and sulfur is the quantity of heat liberated when unit

weight of the fuel is burned in oxygen in an enclosure

of constant volume, the products of combustion being

gaseous C02 , N2 , and S02 and liquid H2 0, with the

initial temperature of fuel and oxygen and the Anal

temperature of the products of combustion at 25° C. Although the total heat of combustion is the

quantity directly measured in a bomb-calorimetric

experiment, the quantity required in many practical applications is the "net heat of combustion

at constant pressure." This quantity is designated by the symbol Qp (net), and may be defined

as follows: The net heat of combustion at constant pressure of a liquid or solid fuel containing only the elements carbon, hydrogen, oxygen, nitrogen, and

sulfur is the quantity of heat liberated when unit

weight of the fuel is burned in oxygen (or air) at a

constant pressure of one atmosphere, the products of

combustion being C02 , N2 , S02) and H2 0, all in the gaseous state, with the initial temperature offuel and

oxygen and the Anal temperature of products of

combustion at 25° C. For the most fuels to which these definitions

apply the elements oxygen, nitrogen, and sulfur

will be minor constituents if present at all. The

methods described in this Monograph are not

suitable for accurate measurements on materials

containing more than about 2 percent sulfur.

2. General Discussion of Bomb-Calorimetric Measurements

A bomb calorimeter consists essentially of a

calorimeter vessel containing a measured amount

of water, in which are immersed (1) a thermometer

for measuring the temperature of the water, (2) a

stirring device for maintaining the water at a uniform, and therefore definitely measurable

temperature, and (3) a "bomb" of constant volume

in which combustible materials can be burned in oxygen under pressure. In order to control heat

transfer between the calorimeter and its environment ("thermal leakage") the calorimeter vessel

is enclosed by a "jacket" which is separated from

the vessel by an air space about 1 cm thick, and

which for a majority of precise calorimeters, is kept at constant temperature by means of a thermostat.

A schematic diagram of a bomb calorimeter and

its jacket is shown in figure 1. The calorimeter

vessel is made in the form shown in order to

facilitate stirring of the calorimetric liquid. The

effectiveness of a screw propeller stirrer is greatly

increased by enclosing it in a tube which extends

from near the top to near the bottom of the

calorimeter vessel. Putting the tube outside of the main part of the calorimeter vessel, as shown

in figure 1(b), reduces the total volume of the

calorimeter necessary for a bomb of given size. In principle, a measurement of the heat of

combustion of a given material consists in comparing the corrected temperature rise of the

calorimeter in an experiment in which a known

quantity of energy is supplied to it, with that

produced in another experiment by combustion

(a) Figure 1. Schematic diagram of a bomb calorimeter.

(a) Assembled calorimeter with jacket: B, bomb; C, calorimeter vessel;

J. jacket wall; P, resistance thermometer; FL, firing leads; CS, calorimeter

stirrer; JS, jacket stirrer; TV, tube to thermostat valve; H, jacket heater; TB, thermostat bulb; and TH, tubular housing, (b) Top view of calorimeter

vessel OL, opening for firing lead; and OT, opening for thermometer, (c) Firing lead through jacket T, tube; R, rod; and W, washers, (d) Firing lead

to calorimeter vessel CL, clip.

in the bomb of a weighed sample of the given

material. The temperature rise in both experiments should be as nearly as possible over the same

temperature range from a standard initial temperature to a standard final temperature. This

method of using the corrected temperature rise of the calorimeter to compare an unknown with a known quantity of energy eliminates some of the

systematic errors of calorimetric measurements,

in particular those associated with uncertainty

as to the exact location of the boundary of the

240-2
calorimeter, and those associated with various

kinds of lag, by virtue of which different parts

of the calorimeter are at different temperatures

when the temperature is changing.

Experiments to determine the corrected temperature rise of the calorimeter when a known

quantity of energy is supplied to it are generally

called calibration experiments, and the mean

result of a series of such experiments expressed as energy supplied per unit of corrected temperature

rise is called the "energy equivalent" of the

calorimeter. The product of the energy equivalent and the corrected temperature rise of the

calorimeter in an experiment in which a material

of unknown heat of combustion is burned in the

bomb gives the energy liberated in the combustion reaction plus any side reactions which may

occur. Calibration experiments are conveniently carried

out by burning in the bomb weighed samples of a standard material, such as benzoic acid (NBS

Standard Sample 39), the reat of combustion of which is accurately known. If the calorimeter is

to be used for measurements of heats of combustion of volatile liquids, such as gasolines, it is desirable to supplement the calibration experiments

with benzoic acid by making a series of measure- ments on NBS Standard Sample 217 of 2,2.4-

trimethylpentane, which is a volatile liquid with a

certified value for its heat of combustion. The

difference between the measured and certified values of heat of combustion will give an overall

check on the accuracy of the measurements, and in particular, on the effectiveness of precautions

taken to eliminate effects of volatility.

Since a measurement of heat of combustion in- volves the comparison of two nearly equal changes

in temperature covering the range from a standard

initial temperature to a standard final temperature,

the temperature scale used in the measurement is not important. Thus temperatures can be ex- pressed in terms of the resistance in ohms of a

given platinum resistance thermometer with the

energy equivalent of the calorimeter in calories

per ohm, or in Celsius degrees with the energy

equivalent in calories per degree.

3. Factors Affecting Accuracy in Bomb-Calorimetric Measurements

The overall error in the result of a bombcalorimetric measurement is the algebraic sum of

individual errors contributed by various factors. Some of the individual errors may be positive and

others negative, so that to some extent they may

be expected to cancel. However, the extent to which cancellation ma}' take place is uncertain,

and may vary from one experiment to another, so that the percentage contribution of each individual

error should be kept well below the permissible

overall error of the determination. In the present

Monograph the permissible difference between duplicate determinations is taken as 0.05 percent. In

order to attain this precision, the error contributed

by each of the various independent factors should

be kept below 0.01 percent so far as possible.

The factors which may affect the accuracy of a bomb-calorimetric determination may be divided

roughly into two classes, (1) side reactions which

may take place in the bomb, the effect of which

cannot be readily evaluated, and (2) the experimental techniques used in making the various

individual measurements. These two classes of factors are discussed in sections 3.1 and 3.2,

respectively.

3.1. Undesirable Side Reactions

These include (a) formation of carbon monoxide,

carbon, or other products of incomplete combustion of the samples; (b) oxidation of the crucible

in which combustion of the fuel sample takes place, or oxidation of other parts of bomb or fittings;

(c) reaction of acids formed in combustion with

the material of the bomb; (d) oxidation of combustible impurities such as hydrogen or hydrocarbon gases in the oxygen used.

a. Incomplete Combustion

In tests of volatile liquid fuels which must be

enclosed in glass bulbs to prevent loss by evaporation, incomplete combustion sometimes occurs as a result of breakage of the bulb before ignition of

the sample. In such cases large amounts of

carbon will usually be formed, and the results of such tests should be discarded. Normally a bulb containing a volatile liquid sample does not

break before ignition of the sample, and in such

cases there is generally little or no evidence of

incomplete combustion. It occasionally happens

that globules of glass remaining in the crucible

after combustion are gray or black in color. This

may be due to metal oxides formed in combustion

of the fuse wire, or to inclusion of a small amount

of carbon in the glass while it is molten. Determinations of carbon dioxide in the products of

combustion of pure liquid hydrocarbons which

were enclosed in soft glass bulbs indicate that the

amount of carbon in such glass globules does not

exceed 0.01 percent of the carbon in the sample.

Incomplete combustion of solid materials, such

as benzoic acid, is very likely to occur if these

materials are placed in the crucible in powdered

form. For this reason, such materials should be

compressed into pellets. For samples of nonvolatile liquid fuels which are not enclosed in

glass bulbs, and for pelleted samples of benzoic

acid, incomplete combustion almost never occurs

in apparatus such as that described in the

appendix.

241-3
b. Oxidation of Crucible and Fittings

Oxidation of the crucible and its support and

other fittings exposed to the direct action of the

flame can be avoided by using platinum crucibles

and fittings (see appendix).

c. Reaction of Acids witb Bomb Material

Reaction of acids formed in combustion with

the material of the bomb can be made negligible

by the use of suitable corrosion-resistant material

for the bomb. The bomb described in the appendix has been found satisfactory in this respect.

Bombs provided with gald or platinum linings

have also been found to be satisfactory.

d. Combustible Impurities in Oxygen

Combustible impurities in the oxygen used may

introduce very serious errors into the results of

bomb-calorimetric measurements. Oxygen pre- pared by electrolysis of water may contain enough

hydrogen to cause errors of 1 percent or more. The possibility of error from this source is eliminated by passing the oxygen over copper oxide

at 500° C before admitting it to the bomb (see

appendix).

3.2. Experimental Techniques of Individual

Measurements

The most important of the individual measure- ments which go to make up a bomb calorimetric

determination include measurements of (a) the

weight of the sample of combustible; (b) the

weight of the calorimeter plus water; and (c) the

temperature rise of the calorimeter, including

correction for thermal leakage and beat of stirring.

A given percentage error in any one of these

measurements introduces an equal percentage

error into the final result of the experiment. Other

individual measurements which determine rela- tively small correction terms and which can be

easily made with the necessary precision include

measurements of (d) the quantity of energy used

to fire the charge of combustible; (e) the amounts

of oxygen and other materials in the bomb; and

(f) the amounts of nitric and sulfuric acid formed

in the combustion reaction.

a. Weight of Sample of Combustible

The sample of combustible (0.8 to 1.5 g) is weighed with a precision of about 0.02 mg using an undamped semimicro balance with a keyboard

arrangement for adding and removing the smaller

weights (see appendix). Calibrated high grade

(class M) weights are used, and the corrections

to the weights given on the calibration certificate are applied in determining the weight of the

sample. If weighings are made in the ordinary manner with weights and object weighed on

opposite pans of the balance, the balance should

be tested to determine whether the balance arms

are of equal length. If the arms are found to

differ in length by a significant amount a correction

for this difference will be necessary.

The necessity for such a correction can be

eliminated by using the method of weighing by

substitution. This consists in placing on the left- hand pan a fixed weight or "tare," somewhat

greater in weight than the heaviest object to be

weighed, then placing the object to be

weighed on the right-hand pan together with

.sufficient weights, including rider adjustment, to balance against the tare. The object beingweighed is then removed and weights and rider

again adjusted to obtain balance. The difference

in the weights required in the two cases is the

desired weight of the object. In addition to eliminating the effect of any difference in length

of the balance arms, this method also eliminates

any change in sensitivity with load, since the load

is constant. The following description of the

procedure is for this method of weighing by

substitution.

Each half of the balance beam from the center

knife edge to the outer knife edge is graduated in

100 equal divisions, so that if a 1 mg rider were

used a change in position of the rider by one

division on the scale would correspond to a change

in weight of 0.01 mg. However, it may be inconvenient to use such a small rider because of the

likelihood of its being deformed or lost. Instead, a 10 mg rider may be used so that one division on

the scale corresponds to 0.1 mg in weight, and

hundredths of a milligram obtained from the

deflection of the pointer, as described below.

Weighings are normally made with the weights

to the nearest milligram on the right-hand pan of

the balance, and the 10 mg rider so placed (between 0 and +10 divisions on the beam scale)

that the tare weight on the left-hand pan is balanced to the nearest 0.1 mg. The equilibrium

position of the pointer with reference to the zero

of the index scale is then determined by observing

the turning points of the pointer in an odd number

of swings (3 or 5). The procedure in using the balance will be

illustrated by an example of the weighing of a sample of benzoic acid. All weighings are made

after time has been allowed for temperature

equilibrium to be established, and for air currents

set up when the balance case was open to die out. To determine when equilibrium has been established, the apparent weight is observed from time

to time until no change has been observed during

a period of about 10 min.

The following observations were made in determining the weight of a pellet of benzoic acid, the

first set of observations were made with the empty

crucible, and the second with the crucible containing the pellet:

242-4
Crucible empty:

Weights 12. 493 g Turning points of swings:

Rider 0. 0002 -2. 6 2. 0 Pointer deflection X2, -0.55X0.07 X 10-3. - . 00004 -2. 5

Total weights 12. 49316 -2. 55 2. 0 2X pointer deflection = —0.55

Crucible plus pellet: Weights 10. 971 Turning points of swings:

Rider 0.0003 -2.3 2.6

Pointer deflection X2, 0.45 X 0.07 X 10- 3. 00003 -2. 0

Total weights 10.97133 -2.15 2.6

2 X pointer deflection = +0.45

Observed weight of pellet 1. 52183

Weight correction a + . 00005

Corrected weight of pellet 1. 52188

» The weight correction is the algebraic sum of the certificate corrections to the individual weights used with the empty crucible minus the algebraic sum of the corrections to the weights used with crucible plus peUet.

In the above example the weight corresponding

to the pointer deflection from the zero of the

index scale was obtained by multiplying twice

the average deflection (in divisions on the scale)

by one-half of the sensitivity reciprocal of the

balance, in this case 0.07 = 1/2X0.14 mg per scale

division. (The same result would be obtained, of course, if the average deflection were multiplied by

the sensitivity reciprocal, e.g., for the first weighing of the above example the average pointer

deflection = —0.28 and —0.28X0.14= —0.04 mg).

The same procedure is followed, for example,

in weighing a sample of a volatile liquid which

must be enclosed in a glass bulb to prevent loss by evaporation, except in this case it is not nec- essary to include the crucible in either weighing.

The empty bulb is first weighed against the tare, and then the filled bulb together with glass re- moved in sealing is weighed against the tare. It should be emphasized that the balancing weight

against the tare with only the weights on the righthand pan should be determined in weighing both

the empty bulb and the filled bulb. The use of a

fixed value for the balancing weight against the

tare with only the weights on the right-hand pan

would introduce errors if the rest point of the bal- ance changes between the times of weighing the

empty and filled bulbs. This is likely to occur if a considerable length of time elapses between the

weighings with the bulb empty and filled. The use

of a fixed value for the balancing weight with the

empty crucible on the right-hand pan is ruled out

by the fact that the crucible is subject to changes

in weight in use.

b. Weight of Calorimeter Plus Water

The calorimeter plus water (3,700 g total

weight) 4 is weighed on a magnetically damped

balance having a capacity of 5 kg and a sensitivity

of 0.5 mg (see appendix). The procedure in this weighing is as follows: The ^calorimeter is filled with approximately the desired quantity of water,

the temperature of which is adjusted to a value

such that after assembly of the calorimeter its temperature will be a few tenths of a degree

4 The weight should correspond to an amount of water in the calorimeter such that when the bomb is Immersed in the water the calorimeter cover can be put In place with its lower side in contact with the water.

below the desired initial temperature in the

experiment. The choice of the temperature to which the water is to be brought before weighing

will depend upon a number of factors, including room temperature, the desired initial temperature

in the calorimetric experiment, and the relative

heat capacities of calorimeter vessel, water, and

bomb. No definite rule can be given for this

choice, but the operator will learn by experience

how to select the proper temperature under the

conditions of his particular laboratory and apparatus.

After adjustment of the temperature the calorimeter is placed on one pan of the balance with

the desired weights (see footnote 4) on the other.

The amount of water in the calorimeter is adjusted

so that the total weight of calorimeter plus water

exceeds slightly that of the weights on the opposite

balance pan, and the balance case is closed.

Because of evaporation of water the weight of

calorimeter plus water decreases slowly, and the

pointer on the balance gradually moves toward

the zero of the index scale. When the pointer

reaches the scale zero the balance beam is arrested,

the case is opened, and the calorimeter is removed

from the balance and placed in position in its jacket preparatory to making a calorimetric

experiment.

It is not feasible in weighing the calorimeter to wait for it to come to temperature equilibrium

with the air, partly because this would require a very long time and partly because the desired

initial temperature in the calorimetric experiment

will usually differ from room temperature. Any

difference in temperature between calorimeter

and the air in the balance case will cause convection currents which will affect the observed

weight. The effect of this will partially cancel

if the difference between the temperature of calorimeter and the air in the balance case when the

calorimeter is weighed is the same in all experiments, including both calibration experiments and

measurements of heat of combustion.

The change in. weight of the water in the

calorimeter due to evaporation after weighing will affect the energy equivalent of the calorimeter,

but the effect of this is small and will cancel if the

243-5
procedure in placing the calorimeter in its jacket

and completing the assembly of the system is carried out in the same manner and in the same

length of time in the calibration experiments as

in measurements of heat of combustion.

In addition to the water in the calorimeter

vessel, 1 cm3 of water is placed in the previously

dried bomb before each experiment to insure that

the space in the bomb is saturated with water

vapor at the beginning of the experiment as well as at the end, when water formed in combustion

will be present in any case. This water is introduced into the bomb by means of a buret or pipet accurate to about 0.01 cm3

, immediately

before introducing the sample of combustible.

c. Temperature Measurements

The temperature rise of the calorimeter in a combustion experiment is approximately 3° C,

and must be measured with an accuracy of 0.0003°

if the error in temperature measurement is to contribute not more than 0.01 percent to the

result of the calorimetric experiment. Measurements of temperature differences with this precision can be made conveniently with a suitable

25 ohm platinum resistance thermometer, and

a Mueller bridge of the tvpe commonlv designated

as G-2.

In precise measurements of temperature with a

resistance thermometer it is customary to eliminate the resistance of the thermometer leads

completely by making two resistance readings,

with the commutator set first in the N position

and then in the R position. In bomb calorimetric

measurements where only a small temperature

difference is to be measured and where time for making the temperature measurements is limited,

it is permissible to omit changing the commutator

setting. However, if this procedure is followed it

is very important that all measurements in all ex- periments be made with the same commutator

setting, since the change in observed resistance per

degree change in temperature may be different for the N and R positions of the commutator. The

possibility of error due to change in the commutator setting may be eliminated by permanently

disconnecting one of the current leads (c or t) of

the thermometer from the bridge. The thermometer is then effectively a 3-lead thermometer

and the bridge can be operated with only one

setting of the commutator.

It is also important that the thermometer be

immersed to the same depth in all experiments, so that its contribution to the energy equivalent of

the calorimeter will be the same in all experiments,

and so that the temperature distribution along the

leads will be the same. The observations of the temperature of the

calorimeter in a bomb-calorimetric experiment

must be made in such a manner as to provide data

from which can be derived a value for the temperature rise corrected for thermal leakage and heat

of stirring. The following procedure is for a

calorimeter with the jacket maintained constant

at a standard temperature.5 Temperatures of the calorimeter are measured

at definite times during three periods: (1) An initial period of 6 to 10 min during which the temperature change results solely from thermal

leakage and heat of stirring; (2) a middle period

of about 12 min, at the beginning of which the

charge in the bomb is fired, and during which the

temperature change is due partly to thermal

leakage and heat of stirring but mostly to the

heat liberated by the combustion reaction in the

bomb —this period continues until the rate of

change of temperature has become constant; and

(3) a final period of 10 min or more, during which

the temperature change is again due solely to thermal leakage and heat of stirring. It is desirable to choose the initial temperature of the

calorimeter so that its final temperature will be

slightly below that of the jacket. This reduces

the total thermal leakage during the middle period

and eliminates heat transfer by evaporation of

water from the calorimeter and condensation on

the jacket wall which would occur if the temperature of the calorimeter exceeded that of the jacket.

During the initial and final periods the resistance

of the thermometer should be measured with the

highest possible accuracy, since the overall accu- racy of the determination depends directly upon

the accuracy of these temperature measurements.

During the middle period, because of the very

rapid rate of temperature rise, it is not possible

to make readings as accurately as during the initial and final periods, but this is not important because

the readings of the middle period are used only for calculating the relatively small correction for thermal leakage and heat of stirring.

With a G-2 bridge and a thermometer having

a resistance of approximately 25.5 ohms at 0°C, one step in the last dial of the bridge (0.0001

ohm) corresponds to approximately 0.001 °C in temperature. Readings of the bridge are made to the nearest 0.00001 ohm (0.0001°) by interpolating between two adjacent settings of the last

dial of the bridge. This interpolation is accomplished by observing the deflection of the galvanometer as follows: The galvanometer is located

about 2 meters from a ground glass scale graduated

in millimeters, which is so placed as to be conveniently observable by the operator of the bridge.

In front of the galvanometer mirror is placed a

lens of such focal length that the reflected image

of the vertical filament of a light source is focused on the ground-glass scale. 6 The bridge current is adjusted so that with constant thermometer

resistance a change of 0.001 ohm in the bridge

5 The NBS calorimeter is located in an air-conditioned laboratory, the temperature of which is maintained at about 25° C. The jacket temperature is always maintained constant at 28° C and the calorimetric experiments

cover the range from 25° to 28° C. If room temperature is not controlled the standard temperature of the jacket should be taken high enough so that it will be above room temperature at all seasons. A jacket temperature below

that of the room is undesirable as it may result in the condensation of water on the calorimeter, the initial temperature of which is 3° C below that of the

jacket.

« Lamryand scale devices for indicating galvanometer deflection are available commercially, and are as satisfactory as the device described here. 244-6
setting causes a galvanometer deflection corre- sponding to a 2.5 cm displacement 7 of the filament

image on the scale. This is equivalent to a dis- placement of 2.5 mm per step in the last dial of

the bridge, i.e., to 2.5 mm per millidegree. This

sensitivity is doubled by reversing the current through the bridge and observing the resulting

change in position of the filament image. The

sensitivity is such that when the bridge current

is reversed a displacement of the filament image

by 0.5 mm corresponds to 0.00001 ohm (0.0001°).

Reading the bridge by observing the deflection of the galvanometer when the bridge current is reversed not only increases the sensitivity but

also reduces the effect of changes in the galvanometer zero. The reversal of the bridge current

is conveniently made by means of a double-pole

double-throw toggle switch connected in the

battery circuit. The above discussion of the deflection of the

galvanometer when the bridge current is reversed

tacitly assumes that the resistance of the thermometer remains constant during this operation.

In an actual calorimetric experiment the resist- ance of the thermometer is usually changing

with time; in the initial period for example the

resistance of the thermometer is increasing at a

rate of approximately 0.0007 ohm/min. (0.007°

C/min). During this period readings are made

once per minute in such a manner as to give

the resistance of the thermometer to the nearest 0.00001 ohm at intervals of exactly 1 min.

These readings are made as follows: The

switch for reversing the bridge current is thrown

in the direction such that as the temperature of

the calorimeter rises the image of the filament of

the galvanometer light source moves toward

the observer's right. The bridge dials are adjusted occasionally so as to keep the filament

image slightly to the left of its zero position.

The time is observed by means of a stop watch,

or preferably by means of a combination of stop

watch and audible second signals from a standard

clock. The position of the filament image is observed to the nearest 0.5 mm at a time 4 sec before the even minute and the reversing switch

is thrown immediately. The position of the

image is observed again at 4 sec after the even minute 8 and the switch is then thrown back to

its original position in preparation for later readings. If the second position of the filament

image is exactly the same as the first, then the

galvanometer deflection on the even minute was

zero, and the reading of the bridge is correct with

zero in the next place after the reading of the

' With the particular combination of bridge, thermometer, galvanometer, and galvanometer to scale distance used, the bridge current of 6.8 ma (thermometer current of 3.4 ma) gives the sensitivity indicated. Much higher bridge current is undesirable because of the increased heating of the thermometer and the consequent increased variation of thermometer resistance with

slight variations in bridge current. A 6-volt low-discharge storage battery

is a convenient source of bridge current.

» The time which should elapse between the two observations of the galva- nometer deflection depends upon the free period of the galvanometer. The

reading time of an underdamped galvanometer with a relative damping

constant of 0.8 or 0.9 is roughly equal to the free period [19].

last dial. If the second position of the filament

image is x mm to the left (or right) of the

original reading, then the reading of the bridge

should be increased (or decreased) by 0.00002cc

ohm to obtain the reading corresponding to the even minute. For example, if the reading

of the bridge is 27.3956 ohms and the upper

and lower arrows in figure 2(a) represent the

initial and final positions, respectively, of the

filament image, then the corrected reading of

the bridge at the even minute would be 27.39563

ohms. On the other hand the situation repre- sented in figure 2(b) for the same setting of the

bridge dials woidd correspond to a corrected

bridge reading of 27.39556 ohms.

(a) (b)

Figure 2. Diagram to illustrate use of galvanometer deflec- tions in reading bridge.

With a little practice an observer can learn to anticipate each bridge reading fairly closely after the first one or two of a series, and to preset the

bridge dials for each subsequent reading so that

the change in galvanometer deflection upon re- versal of the current will not exceed 2.5 mm

(0.00005 ohm or 0.0005° C).

As a result of the preliminary adjustment of the

temperature of the water in the calorimeter before

weighing it as described in section 3.2.b., it is to be expected that after assembling the calorimeter

the temperature will be a few tenths of a degree

below the desired initial temperature. The temperature should then be raised to about 0.05°

(0.005 ohm) below the temperature at which the

initial period is to start, and allowed to drift up

to this temperature as a result of thermal leakage

and heat of stirring. The observations of the

initial period are then made as described above.

The heating of the calorimeter to 0.05° below

the starting temperature is most conveniently done

by means of an electric heater which is a permanent part of the calorimeter system. Another

method which is frequently used is to place a heated brass rod (}{ in. X 2 in.) on top of the

calorimeter cover. The rod is inserted through a

hole in the jacket cover which is normally closed

by a brass plug. Care is taken to avoid having

the heated rod come in contact with the jacket and

thereby upset the control of its temperature.

245-7
The above instructions may be illustrated by an

example. The calorimeter temperature before

weighing was adjusted to a value such that after

assembly of the calorimeter the thermometer reading was 20.5 +7.420 ohms.9 By means of the

heated rod referred to above, the temperature was

raised until the reading of the bridge was 20.5 +

7.465 ohms. The rod was then removed, the plug

replaced in the hole in the jacket, and the calorimeter temperature allowed to drift upward until

the bridge reading was 20.5 + 7.4701 ohms when

the readings of the initial period were begun.

These are made once per minute as indicated

previously.

Immediately after the observations of the initial period are completed the charge of combustible in the bomb is ignited by means of an electric fuse,

the sensitivity of the galvanometer is reduced by

reducing the bridge current to about one-third of

its original value, and the observations of the

middle period are begun. These must be made so rapidly that there is no time for reversing the

bridge current for each observation. The observations are made by setting the bridge dials

successively at certain predetermined readings and

observing the times at which the galvanometer deflection becomes zero. After about 3 min the

rate of temperature rise has decreased to such an

extent that the bridge current can be increased to

its original value and the precise readings of resist- ance each minute are resumed. These precise

readings are continued until the rate of temperature change has been constant for at least 10 min.

The observations made after the rate of temperature change has become constant constitute those

of the final period.

Table 1. Observations of time and thermometer resistance during a bomb-calorimetric experiment

Time

minutes

Resistance minus

27.5 ohms

Difference X 105 Time

minutes

Resistance minus

27.5 ohms

Difference X 10'

0

12

34

5

66.528

6.621

6. 682

6. 754

6. 820 6.894 6.970

7. 066

7, 170

7. 320

7. 399

7. 496

0. 47015

. 47078 .47142

. 47206

63

6464

128 (64) lai

(64) 63

7. 614

7. 747 7.922

9

10

111213

1415

16

1718

1920

212223

24

25

26

2728

0. 7000 .7100

. 7200

. 75050

. 75920

. 76270

. 76410

. 76470

. 76499

. 76515

. 76525

.76534

. 76540

. 76546

. 76553

. 76560

. 76566

870

350

140

60

29

16

10

96

6

76

20 (7)

(6) (7) 6

7

. 47334

. 47397

.4900

. 5100 .5300

.5500

.5700

.5900 .6100

.6300 .6500

. 0700

. 6800

.6900

. 76586

. 76592

. 76599

. 76606

» The bridge has a 20.5-ohm coil in addition to the 10-, 20-, 30-ohm coils, etc., in the lOxlO-ohm decade (see appendix).

Bridge readings made during the course of a

typical bomb calorimetric experiment are given in

table 1, and are shown graphically in figure 3. The values given for resistance represent the observed resistance of the thermometer minus 27.5

ohms. The initial period extends from t=Q to

/ = 6 min, the middle period from t—Q to t—lS

min, and the final period from t=18 to t=2S min.

The constancy of the differences between consecutive readings in the initial and final periods is an

indication that the system has attained a steady

state. This is a necessary condition for the applicability of the method given in section 5 for calculating the corrected temperature rise.

I I | | I I 0 5 10 15 20 25 30

TIME, MINUTES Figure 3. Bridge readings versus time in a bomb calori- metric experiment.

In the particular experiment illustrated in table

1 and figure 3 the time readings during that part

of the middle period from f=6 to t =9 min were made by means of an electric timer which prints

the time at which the operator presses a button

when he observes the galvanometer deflection to pass through zero. This instrument is a con- venience and would be an important part of the

equipment in measurements of extremely high

precision. It is not a necessary part of the apparatus for measurements of the precision aimed at

in the procedures described in this Monograph. For

such precision it is also not necessary to obtain

as many readings in the middle period. It is sufficient to make three or four measurements in the range from 55 to 70 percent of the total temperature rise, and to read the time to the nearest second (or the nearest 0.01 min) by means of a

stopwatch.

246-8
The corrected temperature rise for the experiment illustrated in table 1 and figure 3 is calculated in section 5.

d. Firing Energy

The quantity of energy used to fire the charge

is the sum of the electric energy used to ignite the

fuse plus the heat of combustion of the amount

of fuse wire burned. The current for igniting the

fuse is obtained from a small transformer with a secondary voltage of about 10. The total firing

energy can be determined in a series of blank ex- periments in which only the fuse wire is burned.

In such experiments the temperature rise of the

calorimeter is very small, and the initial temperature of the calorimeter should be very near that

of the jacket. The rate of change of temperature

in the initial and final periods will then be small,

and the correction for thermal leakage will also be small.

When a 2-cm length of fuse wire is used in the manner described in the appendix it has been

found that if the wire is burned completely 10 the

firing energy is constant and equal to 5.2 cal. No

appreciable error will result from using this value

in any case where the same type of fuse is used,

i.e., a 2-cm length of Parr fuse wire wound into a

helix and attached to platinum leads. The firing

energy in this case is only 0.05 percent of the en- ergy normally produced in a combustion experiment, and any error in the value 5.2 cal will largely

cancel if this same value is used for both calibration experiments and measurements of heats of

combustion, and if the temperature rise is about

the same in the two kinds of experiment.

The most serious error likely to be encountered

in accounting for the firing energy is that which

may result from a short-circuit between the firing

electrode and the bomb, either because of failure of the insulation around the electrode or because

of moisture getting into the mica insulation inside

of the bomb. This mica normally is wet by the

acid solution formed in combustion and by the

water introduced in washing the interior of the

bomb after each experiment. It should be dried

thoroughly before each experiment, and the insulation should be tested before attaching the fuse

to its platinum leads. An insulation resistance of

less than 10 9 ohms usually indicates either moisture in the insulation or some other failure of the

insulating material which needs to be corrected.

A "megger" or volt-ohmeter or other similar in- strument may be used for testing the insulation

resistance.

10 Combustion of the fuse wire may not be complete in all blank experi- ments to determine the firing energy, although it is practically always complete when a sample of fuel is burned in the bomb. Blank experiments in which combustion of the fuse wire is incomplete should be rejected, or else a correction for the unburned wire should be applied.

e. Materials in Bomb

A calibration of the calorimeter yields a value

for the energy equivalent E of the system as ac- tually used, consisting of calorimeter vessel, stirrer,

water, thermometer, bomb, and contents of the

bomb at the beginning of the experiment. The

calorimeter vessel, stirrer, mass of water, thermometer, and bomb will ordinarily be unchanged

from one experiment to another, and the crucible

and amount of water placed in the bomb will also be constant. However, the mass of the platinum

leads to the fuse, the mass of oxygen, and the mass and kind of combustible material may change

from one experiment to another. The heat ca- pacity of the largest amount of platinum wire in the bomb amounts to only 0.00] percenl of the

total energy equivalent of the system, so that

variations in the amount of platinum wire are entirely negligible. The mass of oxygen in the

bomb is inversely proportional to absolute temperature and directly proportional to absolute

pressure. The temperature is measured to about

0.5° C at the time the oxygen is admitted to the

bomb, by means of a mercurial thermometer with

its bulb near the bomb. The pressure of the

oxygen (about 30 atm=450 psi) is measured to the

nearest 0.1 atm (1.5 psi) by means of a calibrated

Bourdon gage. The values of the energy equivalent E obtained

in calibration experiments are reduced to the

energy equivalent Es of a standard calorimeter

system consisting of the calorimeter vessel with

cover, the standard mass of water, stirrer, thermometer, and bomb containing 1 ml of water,

the crucible, and oxygen under an absolute

pressure of 30.0 atm at 28.0° C but no combustible material. In a measurement of heat of

combustion the energy equivalent Es of the

standard calorimeter system is corrected for any

excess of the oxygen pressure at 28° C over 30

atm and for the heat capacity of the charge of

combustible.

The reduction of the observed E to the corre- sponding value of Es , and vice versa, is discussed

in section 5 on calculation of results.

f. Acids Formed in Combustion

Nitric acid is normally formed in the combustion reaction from nitrogen either in the fuel sample itself or present as an impurity in the

oxygen. If sulfur is present in the fuel, oxides of

sulfur will be formed. These are entirely con- verted to sulfuric acid if nitric acid is also formed.

For this reason, if the fuel is known or suspected

to contain a significant amount of sulfur, the air

initially present in the bomb should not be flushed

out with oxygen at the time oxygen is admitted

to the bomb. The sulfur will then be all con- verted to aqueous sulfuric acid, and therefore to a determinate final state. The total acid formed in combustion is deter247-9
mined by washing the inner surface of the bomb

with distilled water and titrating the washings

against 0.1 N sodium hydroxide, using methyl

orange as the indicator.

If both nitric and sulfuric acids are formed the

total acid is determined by titration as before,

and the sulfur is determined by analyzing the

bomb washings after titration, using the procedure

described in ASTM Designation D129-58 [14]. The correction for nitric acid is 14.0 kcal/mole of

acid formed. If sulfur is present in the fuel the

total acid is corrected for as if it were all nitric acid, and an additional correction of 1 ,400 cal/g

of sulfur is applied.

4. Summarized Directions for a Bomb-Calorimetric Experiment

Summarized directions will now be given for carrying out a bomb-calorimetric experiment with

benzoic acid to determine the energy equivalent

of the calorimeter. Following these directions

there will be a brief discussion of the differences

in procedure in an experiment to determine the

heat of combustion of a fuel.

4.1. Preliminary Adjustment of Apparatus

Observe the temperature of the oxygen purifier

and if necessary bring its temperature to 500° C.

(Caution: The temperature and oxygen pressure

should never be allowed to exceed values consist- ent with safety with respect to the possibility of

explosive failure of the purifier. The manufacturer's recommendations regarding safety precautions should be adhered to rigidly.) Add water, if necessary, to fill the calorimeter jacket bath, bring

its temperature to the desired standard value and

put the thermostat into operation (see sec. 3.2.c).

4.2. Preparation and Weighing of Sample of

Benzoic Acid

Weigh out approximately an amount of benzoic

acid somewhat in excess of 1.52 g

11 and compress

it into a pellet. Weigh the pellet on a balance

sensitive to about 0.01 g and adjust the weight, if necessary, to 1.52 ±0.01 g (see footnote 11) by

scraping the pellet. Carefully remove any powdered benzoic acid from the pellet by brushing.

Weigh the crucible on the semimicro balance,

first empty and then after placing the pellet of

benzoic acid into it, following the procedure

described in section 3. 2. a.

4.3. Preparation of Bomb

Test insulation resistance. If less than 106 ohms, dry mica or replace cone insulator.

Attach fuse wire to platinum leads as described

in the appendix. 12 Measure 1.00 cm3 of distilled water into the bomb by means of a buret or pipet.

Attach the crucible to its support in such a manner

that the fuse is nearly touching the pellet of benzoic

acid and assemble the bomb. Connect the bomb

11 The standard mass of benzoic acid should be such as to give a temperature rise of approximately 3° C. The mass used should be within 0.01 g of the standard mass.

12 It may be convenient to do this while waiting for the attainment of temperature equilibrium in the balance case in connection with weighing the sample of combustible.

to the oxygen cylinder through the purifier and

admit oxygen to a pressure of approximately 30

atm. The oxygen should be admitted slowly so as not to cool the copper oxide in the oxygen purifier

below the temperature at which it will oxidize

combustible impurities in the oxygen. Close the

valve in the oxygen line and open the needle valve on the bomb, allowing the oxygen to escape until

the pressure is reduced to atmospheric. This

procedure removes about 97 percent of the nitrogen

in the air initially in the bomb. Refill the bomb to the pressure of approximately 30 atm, read and

record the temperature and pressure, and discon- nect the bomb from the oxygen tank. Attach the

binding post (fig. 6(b)) Math the lead wire to the

terminal nut on the bomb.

4.4. Weighing of Calorimeter Plus Water

Fill the calorimeter with water, adjust temperature of water, and weigh calorimeter plus water as described in section 3.2.b.

4.5. Assembly of Calorimeter

Immediately after the calorimeter is weighed

carry it to the jacket and place it in its proper

position in the jacket space. Place the bomb in the calorimeter, 13 put the calorimeter cover in place and press it down until its lower surface is in

contact with the water. These operations should

be performed rapidly and as nearly as possible in the same manner and in the same length of time in

all experiments. Complete the firing circuit by

connecting the lead to the bomb electrode to the

binding post provided for this purpose (fig. l.(c))

and connect the other lead (already attached to the other binding post) to the calorimeter vessel

by means of the clip shown in figure l.(d) (see

appendix). Close the jacket cover and connect

the calorimeter stirrer to its driving shaft. Measure the jacket temperature to 0.001° C (0.0001

ohm) by means of the bridge and resistance thermometer, then remove the thermometer from the

jacket bath, dry it, and put it in place in the

calorimeter.

13 The bomb should be lowered into the calorimeter without touching the water with the fingers. This can be done by using some sort of hook on which

the bomb can be hung and which can be removed after the bomb is in place. A hook made of a piece of brass or nichrome rod about Me in. in diameter and

bent into the form shown in fig. 6(f) has been found satisfactory for this pur- pose with the Parr bomb. The hooked ends of the rod are inserted into holes on opposite sides of the screw cap of the bomb, and are easily removed after the bomb is in place. The amount of water whiclnadheres to the hook when

it is withdrawn from the calorimeter is negligible. 248-10
4.6. Adjustment of Initial Temperature of

Calorimeter

Adjust the calorimeter temperature to 0.05°

(0.005 ohm) below the starting temperature of the

initial period, and allow it to drift up to the start- ing temperature as described in section 3.2.c. The starting temperature (in calibration experiments) always has the same value, which is so chosen that the final temperature of the calorimeter after combustion will be at, or preferably a few hundredths of a degree below, the temperature

of the jacket.

4.7. Observation of Temperature and

Ignition of Sample

After the temperature of the calorimeter has

been allowed to drift up to the starting temperature, make and record the readings of time and

temperature of the initial period each minute as described in section 3.2.c. Immediately after the

last reading of the initial period fire the charge by

closing the circuit through the fuse in the bomb.

Observe the ammeter in this circuit when the

charge is fired. The reading of the ammeter

should rise abruptly to about 5 amp and then drop

almost instantly to zero. Failure of the current

to drop immediately indicates a short circuit, and

the charge will probably not be ignited, or if it is ignited the result of the experiment will be in error by an unknown amount because of the excess

electrical energy. If the ignition takes place

normally, make and record the observations of the

middle and final periods as described in section

3.2.C. After the end of the final period remove the

thermometer from the calorimeter, insert it in the

jacket bath and measure the temperature of this

bath to 0.001°. If the temperature control equipment has been operating properly the jacket temperature should remain constant to 0.005° or better

during an experiment.

4.8. Analysis of Contents of Bomb

Remove the bomb from the calorimeter, dry it, open the needle valve and allow the gas to escape

at a rate such as to reduce the pressure to atmospheric in not less than 1 min. Then open the

bomb and examine the interior for unburned

carbon, which would indicate incomplete combustion. If more than a slight trace of unburned

carbon is found the experiment should be rejected.

If no appreciable amount of unburned carbon is found wash all interior surfaces of the bomb with

distilled water and collect the washings quantitatively in a beaker. The quantity of the washings should preferably not exceed 150 ml. Titrate the washings against a 0.1 TV solution of

NaOH using methyl orange as the indicator.

Calculate the correction for nitric acid as described in section 5 on calculation of results.

The procedure in a measurement of heat of

combustion follows the same steps outlined in

paragraphs 4.1 to 4.8, witb certain differences

in individual steps as indicated below.

4. 2. a. Preparation and Weighing of Sample of Fuel

If the material whose heat of combustion is to be

determined is a sufficiently nonvolatile liquid,

weigh the empty crucible by the method of

substitution as described previously, decrease

the weights on the pan with the crucible by

the desired weight of sample, 14 and add the

liquid drop-wise from a pipet until the weights

plus sample plus crucible balance the tare weight on

the opposite pan. Ordinarily this procedure will add more than the desired weight of sample, and

the excess may be removed, for example, by dipping the end of a fine glass capillary into the

liquid. Great care should be taken during the

introduction of the sample into the crucible and

making the final adjustment of the weight to avoid getting any of the sample on the outside

of the crucible. The final weighing of crucible

plus sample is carried out as described in section

3.2.a. If the material whose heat of combustion is to be determined is a volatile liquid, the enclosure

of the sample in a glass bulb (as described in the

appendix) and the determination of its weight

(as described in sec. 3. 2. a.) will ordinarily have

been done prior to the beginning of the calorimetric measurements. It is then only necessary to place the bulb in the crucible before starting the

procedure described in section 4.3. and 4. 3. a.

4. 3. a." Preparation of Bomb

The procedure here is the same as that described

in section 4.3 except that if the sample contains

sulfur the air initially in the bomb is not flushed

out before filling the bomb with oxygen. If the

sample does not contain sulfur the ah should be

flushed out as described in section 4.3 by filling

the bomb with oxygen to 30 atm, allowing the

gas to escape until the pressure is reduced to atmospheric, and then refilling the bomb to 30

atm. Where the sample is enclosed in a glass

bulb, premature breakage of the bulb when the

pressure is first raised to 30 atm can sometimes

be detected by the odor of the fuel in the escaping

gas when the pressure is released.

4. 6. a. Adjustment of Initial Temperature of Calorimeter

In the case of a nonvolatile liquid where the

weight of sample is such as to give a temperature

rise equal to that in a calibration experiment

the adjustment of the initial calorimeter temperature is carried out in the same manner as described

in section 4.6.

m The weight of sample should be such as to give approximately the same

temperature rise of the calorimeter as in the calibration experiments. 249-11
In the case of volatile samples it is difficult to make the glass sample-bulbs sufficiently uniform

in capacity to give the same temperature rise of

the calorimeter in all experiments. Select the

initial temperature for each experiment so that

the mean of the initial and final temperatures of

the calorimeter will be the same as in the calibration experiments.

4.8. a. Analysis of Contents of Bomb

If the sample contains no sulfur follow procedure described in section 4.8. If the sample contains sulfur titrate the bomb washings to determine total acid is described in section 4.8. After

this titration analyze the bomb washings for sulfur

using the procedure described in ASTM Designation D129-58 [14].

5. Calculation of Results

5.1. Calibration Experiment

Calculate a value for the energy equivalent E

from the data of each calibration experiment,

using the following formula:

E=Qc Xms +cx +c2 At

where Qc =heat of combustion of benzoic acid in IT calories per gram under the conditions of the experiment.

ms =weight in air, in grams, of sample of

benzoic acid bmned.

Ci =correction for firing energy, in calories.

c2 =correction for nitric acid, in calories. A£= corrected temperature rise of calori- meter, in degrees Celsius (or ohms).

The value of E will be in calories per unit of the

temperature scale used, e.g., in calories per deg C,

or calories per ohm.

a. Heat of Combustion of Benzoic Acid

The certified value for the heat of combustion

of the present standard sample (39h) of benzoic

acid under the standard conditions of the bomb

process is 6318.3 IT cal/g weight in air. 15 The

standard conditions are: A. The combustion reaction is referred to 25° C.

B. The sample is burned in a bomb of constant

volume in pure oxygen at an initial pressure of

30 atm at 25° C.

C. The number of grams of sample burned is equal to three times the internal volume of the

bomb in liters. D. The number of grams of water placed in the

bomb before combustion is equal to three times

the internal volume of the bomb in liters. If the conditions in the experiment differ from

the standard conditions A, B, C, and D above,

the value of Qc for the heat of combustion of

benzoic acid under the actual conditions of the

experiment will be obtained from the following

approximate equation, which was derived in accordance with the procedure recommended by

Washburn [18]: " The value for the heat of combustion of 1 .nzoic acid is given here in IT

calories per gram weight in air against brass weights, the densities of air, brass, and benzoic acid being taken as 0.00116, 8.4, and 1.320 g/cm3

, respecively.

&=6318.3 ^j+10"6 |^20 (P- 30^+42 (jf-s)

+30(^-3)-45(i -26)]}

where P=initial absolute pressure of oxygen, in atmospheres, at the temperature t, ms =weight of sample, in grams,

Wu,=weight in grams, of water placed in bomb before combustion,

V=internal volume of bomb in liters,

t= temperature to which the combustion

reaction is referred, in degrees C.

The temperature to which the reaction is referred

is here taken as the final temperature of the

calorimeter. The value of the energy equivalent

E obtained from eq (1) is then that of the initial calorimetric system at the mean temperature of

the calorimeter. By the initial calorimetric sys- tem is meant the system before combustion of the

benzoic acid, i.e., it includes the benzoic acid,

water, and oxygen in the bomb before combustion

takes place.

For example let the following data be given:

Volume of bomb,

V =0.380 liter Weight of benzoic

acid, m, =1.522g; ms /F=4.01g/liter

Weight of water

in bomb, mw = l.OOg; 7tt„/F=2.63g/liter

Initial oxygen

pressure =30.8 atm gage at 25.5° C =31.8 atm abs at 298.7° K

Final temperature

of calorimeter, * =28.00° C=301.2° K

Oxygen pressure

at 28.00° C, P=31.8X

301.2

298.7 =32.1 atm absolute

Substituting in eq (2) we obtain

Qc = 6318.3{1 + 10-6 [20(32.1-30) +42(4.01 -3) +

30(2.63-3) -45(28.00-25.00)]} =6317.9 cal/g in air.

250-12
b. Correction Terms Cj and c2 The correction Ci for firing energy is preferably

determined in a series of blank experiments as described in section 3.2.d. The use of the value

Ci=5.2 cal will not lead to a significant error if the fuse is a 2-cm length of Parr fuse wire wound

into a helix and attached to platinum leads. In some cases a greater length (5 cm or more) of fuse wire is attached to electrodes which are located a short distance away from the crucible. In such

cases the fuse may not all burn, and the firing

energy will be different in different experiments

depending upon the length of wire burned. If this procedure is followed, the length of wire

burned in each experiment must be determined

and the correction may be taken as 2.6 XL

calories, where L is the length of wire burned,

in centimeters.

The correction c2 for nitric acid is 14.0 kcal/mole

of nitric acid formed, or 14.0 N cal/cm3 of sodium

hydroxide solution of normality Ar required to neutralize the acid. Thus if 2.4 cm3 of 0.0987 N

sodium hydroxide is required to neutralize the

nitric acid formed, c 2 =2.4X14.0X0.0987 =3.3 cal.

c. Corrected Temperature Rise

The calculation of the corrected change in re- sistance of the thermometer in a bomb calorimetric experiment will be illustrated by carrying out

the calculations for the experiment in which the

data given in table 1 were obtained. As stated

in section 3.2.c. the initial, middle, and final periods in this experiment extend from t=0 to t=Q,

£=6 to t=18, and £=18 to £=28 min, respectively.

The observed change in resistance of the ther- mometer is taken as the difference between the

bridge readings at £=6 and £=18 min, namely,

0.76540 —0.47397 =0.29143 ohm. This difference

is to be corrected for thermal leakage and heat

of stirring. Correct methods for calculating this correction will be found in reference [3] and in a number of the references there cited. For the

accuracy aimed at in this manual it is sufficient to use the following procedure which has been

found empirically to give correct results within

about 0.01 percent of the total resistance change.

We first calculate the average rates of change of

resistance r1 and r2 in the initial and final periods,

respectively. These are seen to be

0.47397-0.47015 0.00382 _ nnnco- . rx — = =0.00063 i ohm mm

6 6 0.76606-0.76540 0.00066 _ nnnncc . r2 = — =———=0.000066 ohm mm.

Next we calculate from the data of the middle

period the time t n at which 63 percent of the observed resistance change has taken place. The re- sistance at t m is given by that at the final reading

of the initial period (at £=6), 0.47397, plus 63 per- cent of the observed resistance change. In other

words

i?m =0.47397+0.63X0.29143 =0.65757 ohm.

Referring to table 1 it is seen that this resistance

is reached at a time intermediate between 7.17

and 7.32 min, and by interpolation we obtain

£„= 7.227 min. The corrected initial and final re- sistances, R{ (corr.) and Rf (corr.), are then obtained by applying corrections to the observed

resistance at £=6 and £=18 min as follows: 18

Ri (corr.)=i?6 (obs)+r1 (tm -6) =0.47397+0.000637 X 1.227 =0.474752

ohm,

Rf (corr.)=i?ls (obs)-r2 (18-£m) =0.76540-0.000066X10.773 =0.764689

ohm.

The change in resistance corrected for thermal

leakage and heat of stirring is then

Rf (corr.)—Ri (corr.) =0.764689 —0.474752 =0.289937 ohm.

Practically the same result would have been obtained if only three readings had been taken during

the period of very rapid temperature rise, say at

i? =0.6300, 0.6600, and 0.6900 ohm.

This result must be corrected for errors in the

bridge coils by applying a correction equal to the

algebraic sum of the certificate corrections to the

coils used in obtaining RiS (obs) less the algebraic

sum of the corrections to the coils used in obtaining

i?6 (obs.). It is evident that it is not necessary in

this calculation of the change in resistance to in- clude corrections to coils which enter into both

i?6 (obs) and R1S (obs). In this case such coils in- clude one of 20.5 ohms and one of 7 ohms. The

bridge correction in the experiment under consideration was +0.000029 ohm, making the cor- rected resistance change AR=0.289966 ohm.

Resistance of the thermometer can be converted

to temperature with the aid of the formula or

tables accompanying the NBS certificate for the

thermometer. It is somewhat more convenient,

however, to compute a table of factors At/AR

which when multiplied by the corrected change in resistance AR will give the desired change in temperature At. Such a table may be calculated as

follows. First the temperatures corresponding to certain given resistances, say 5=27.5000, 27.6000,

. . . - 28.5000. . . , are calculated, using the data in the certificate for the thermometer. These temperatures are then substituted into the formula

At = 1 ^

oQt ioo 10000J

16 Resistances are read to 1 in the fifth decimal. The calculations are carried one place farther to avoid errors from rounding off. " Strictly speaking, eq (3) gives the derivative dtjdR. This is exactly equal

to At/AR for a finite interval AR, provided it is calculated for the mean temperature of the interval. If. as is customary, the value of dtjdR corresponds

to the mean resistance of a finite interval, then dtjdR is not exactly equal to At/AR, but the error is entirely negligible.

251-13
where R0 , a, and 5 are constants given in the cali- bration certificate for the particular thermometer.

The values of R and corresponding values of

At/AR calculated from the above formula are tabulated. The value of At/AR to use in calculating

the corrected temperature rise in a given experiment is that corresponding to the mean of the

corrected initial and final values of R for the

experiment . This value of At/AR is obtained from

the table, by interpolation if necessary. For ex- ample, in the example given above the value of

At/AR used should be that corresponding to the

mean of 27.5 +i?, (corr.) and 27.5 +#/ (corr.) or

27.5 + (0 .47475 -f 0.76469)/2=27.5+0.6197 =28.1197 ohms. 18

It is found that At/AR increases by about 0.03

percent for an increase in temperature of 1 deg C

(0.1 ohm).

It is not necessary, however, to convert re- sistance to temperature. If desired, the re- sistance change can be taken as the measure of

the temperature change, with the energy equivalent E expressed in caloreis per ohm. The

corrected resistance change AR (ohms) in a meas- urement of heat of combustion would then be

multiplied by E (calories per ohm) to give the

energy (calories) produced in the combustion

reaction. One disadvantage of this procedure is that E in calories per ohm changes more for a given change in the mean temperature of the

experiment than does E in calories per degree.

For a typical bomb calorimeter it has been

calculated that the change in the value of E for an increase of one degree (0.1 ohm) in the mean

temperature of the experiment is about +0.03

percent if E is expressed in calories per ohm,

but is less than 0.01 percent if E is expressed in calories per degree. Hence if temperatures are expressed in ohms, then for a precision of 0.01

percent, the mean temperature of the calorimeter

should be kept within about 0.2 degree (0.02

ohm) of some fixed value, or else the value of

Eg in each calibration experiment should be cor- rected to some standard temperature, and the

mean value of Es for this standard temperature

should be corrected to the actual mean temperature of each measurement of heat of combustion.

The greater change with temperature of Es ex- pressed in calories per ohm is due to the fact that

the resistance of the thermometer is not a linear,

function of temperature, i.e., the fact that At/AR

is not constant. A convenient check on the behavior of the

calorimeter and the correctness of the temperature

measurements may be obtained by calculating

the "cooling constant," k, of the calorimeter.

This is defined b}T

R2-R1

where rx and r2 are the average rates of change

of resistance in the initial and final periods,

respectively, and and R2 are the observed

resistances at the mid-points of these periods.

Thus, using the data of table 1 at the beginning

of this section (5.1c):

k=0.000637-0.000066

0.76573 - 0.47206

=0.001944.

This quantity is a constant of the calorimeter

and should remain constant to better than one

percent in different experiments.

d. Example Illustrating the Calculations of E and E,

The calculation of E may be illustrated by air example, using the following data taken from

preceding sections as indicated.

Weight benzoic acid, ms = 1.52188 g (sec. 3.2 a)

Heat of combustion of benzoic acid, Qc =6317.9

cal/g (sec. 5.1. a)

Firing energy (2 cm fuse wire), Ci =5.2 cal (sec. 5.1.b)

Correction for nitric acid, c2 =3.3 cal (sec. 5.1.b)

Corrected resistance change, AR—0.289966 ohm

(sec. 5.1.c)

Corrected temperature change, A£=2.87462 deg

C (At/AR= 9.91364)

Oxygen pressure at 28.0°, P=32.1 atm abs

(sec. 5.1. a)

Substituting the above values in eq (1), the value

of E is found to be

g=1.52188X6317.9+5.2+3.3=331887cal/obm

0.289966

1.52188X6317.9+5.2+3.3

2.87462

=3347.78 cal/deg.

To reduce the above values of E to the cor- responding values of Es , the energy equivalent of

the standard calorimeter sj^stem, it is only neces- sary to subtract the heat capacity of the sample

of benzoic acid, and of the amount of oxygen in excess of that required to fill the bomb to 30 atm

absolute at 28° C, as follows:

cal/° C cal/ohm

Observed value of E.. 3, 347. 78

0. 16 0.44

3, 347. 18

33, 188.

7

1.6

4.4

33, 182.

Heat capacity of excess oxygen= (32.1-30.0) X0.077-- Heat capacity of benzoic acid = 1.522X0.29= Value of E. -

18 Strictly speaking, the corrections to all the coils used should be, applied

In calculating the mean value of the resistance. In many cases, however,

these corrections are too small to be significant in this calculation and may

be neglected.

The factor 0.077 used in calculating the correction for excess oxygen is the increase in heat

capacity (in calories per degree) per atmosphere

252-14
increase in pressure in the bomb used, which has an internal volume of 0.380 liter. For a bomb

of volume V the corresponding factor is 0.077

F/0.380. The factor 0.29 used in correcting for the benzoic acid is the specific heat of benzoic

acid in calories per gram degree Celsius. Both

factors are greater by a factor of 10 if E is in

calories per ohm (for a thermometer having a

resistance of 25.5 ohms at 0° C).

5.2. Calculation of Heat of Combustion

Calculate a value of total (or gross) heat of

combustion at constant volume from the data

of each measurement, using the following formula.

Q, (gross):

EXAt—Ci— c2 —

c

3 (4) where

Q, (gross) =total heat of combustion at constant

volume at the final temperature of

the experiment, in IT calories per

gram.

£=energy equivalent of the calorimeter as used, in IT cal/deg (or IT cal/ohm)

At= corrected temperature rise of calorimeter in degrees (or ohms)

to, =mass of sample, in grams

Ci =firing energy, in calories

c2 =correction for energy of formation of

nitric acid, in calories

c3 =correction for energy of formation of

sulfuric acid, in calories.

a. Energy Equivalent of Calorimeter as Used

The calorimeter as used differs from the standard calorimeter because it contains the sample of

fuel and because, in general, the absolute pressure

of the oxygen at 28° differs from 30.0 atm.

The energy equivalent E of the calorimeter as used

is obtained by adding to the energy equivalent

Es of the standard calorimeter the heat capacity

of the charge of combustible and the heat capacity

of the oxygen in excess of that required to fill the

bomb to 30.0 atm absolute at 28° C. The calculation is illustrated as follows, taking the sample

of combustible as 0.92231 g of gasoline, and the

oxygen pressure at 28.0° as 29.0 atm absolute:

cal/°C cal/ohm

Energy equivalent of standard calorimeter, E,...= Heat capacity of excess oxygen, (29.0-30.0) X0.077- =

Heat capacity of sample, 0.922X0.51 .__ =

3, 347. 18 -.08 +.47

33, 182. 7 -0.8 +4.7

Energy equivalent of calorimeter as used, E= 3, 347. 57 33, 186. 6

The factor 0.51 used in calculating the heat

capacity of the sample is the specific heat of

gasoline 19 at 26.5°C in cal/g°C. The factor

0.077 used in calculating the heat capacity of the

excess oxygen is defined in section 5.1.d. Both

factors are greater by a factor of 10 if E, is in calories per ohm (for a thermometer having a

resistance of 25.5 ohms at 0°C). The heat

capacity of the glass bulb (less than 0.1 g) used

to enclose the sample of gasoline may be neglected.

b. Corrected Temperature Rise

Directions for calculating the corrected temperature rise are given in section 5. I.e. The value

to be used in the example to be given later may

be taken as 0.309617 ohm or 3.06943°C.

c. Corrections c u c2 , c3 The correction cx for firing energy with a 2-cm

length of fuse wire may be taken as 5.2 cal. The

corrections c2 and c3 are calculated as follows:

The correction c2 is calculated as if all the acid

found by titration were nitric acid, as described in section 5.1.b. Thus if it required 14.2 ml of 0.0987 N sodium hydroxide to neutralize the total acid the correction c2 would be given by c2 =

14.2X14.0X0.0987 = 19.6 cal. If the test for sulfur showed 0.0042 g sulfur present in the bomb

washings the correction for sulfuric acid, as given

in section 3.2.f., would be c3 = 1400 X0.0042 = 5.9

cal.

d. Calculation of Qv (gross)

Substituting the values of E in calories per

degree (or calories per ohm), At (or AR), cu c2 , c3, and tos given in sections 5. 2. a., b., and c. into formula (4) yields

Qv (gross):

or

Qv (gross):

3347.57X3.06943-5.2- 19.6-5.9

0.92231

33186.6X0.309617-5.2- 19.6-5.9

0.92231

Both of these expressions yield the value 11107.4

cal/g weight in air for the total (or gross) heat of

combustion of the liquid gasoline at constant

volume. The corresponding value in terms of

engineering units is

Qv (gross) = 11107.4X1.8 = 19993 Btu/lb.

The method of calculation is such that the value

obtained for Qv (gross) is referred to the final temperature of the calorimeter, in this case 28.1° C. The observed value may be reduced to the standard temperature of 25° by means of the

following; formula

18 Taken from NBS Miscellaneous Publication M97 [15] for a gasoline having an API gravity of 70. Values of heat capacity of petroleum products

given in this publication for a temperature of 80° F range from 0.42 to 0.52 for API gravities ranging from 10 to 80. 253-15
Qv (gross, 25° C) = Q, (gross,/ 0 C)+.4(*-25) (5) Where the value of the factor A is given in the

following table. 20

<">„ (gross) A ('v (gross) A

Btu/lb Btu/lb" C lit RlnU lift / IU Ttln llh° C

18,500 0.68 19.600 1. 14

18, 600 .72 19, 700 1. 18 18.700 .76 19, 800 1.22

18, 800 .80 19, 900 1.26

18. 900 .85 20, 000 1.30 19,000 .89 20, 100 1.35

19, 100 .93 20, 200 1.39

19, 200 .97 20, 300 1.43

19, 300 1.01 20, 400 1. 47

19, 400 1.05 20, 500 1. 51

19. 500 1.09 20, 600 1.55

Substituting the value of Qv (gross, 28.1° C) =

19993 Btu/lb and the corresponding value ^4=1.30

from the above table in eq (5) we obtain

Qv (gross, 25° 0= 19993 + 1.30X3.1 =

19997 Btu/lb.

»The valuesof A were calculated using the specific heats of liquid petroleum

fuels, of gaseous oxygen and carbon dioxide, and of liquid water. The masses

of oxygen consumed and of carbon dioxide and water formed in combustion of unit mass of fuel were obtained from an empirical relation between Q, (gross) and hydrogen content. See reference [5]. In general, the change in Q, gross ^Btu/lb) with temperature for any fuel may be calculated from the relation dO, (gross)ldt=K, (reactants)—K, (products). Here K, (reactants) denotes the heat capacity at constant volume of 1 lb

of fuel plus the oxygen consumed in its combustion, and K, (products) denotes the heat capacity of the products of combustion of one pound of fuel, including gaseous carbon dioxide and liquid water. In calculating K, the heat capacities of solids and liquids may be taken as heat capacities at con- stant pressure.

e. Calculation of Q p (net)

If the hydrogen content of the fuel is known the

value of the net heat of combustion, Qp (net, 25°), can be calculated from that for Qc (gross) by

means of the following formula [4]

Qp (net, 25° C) = Q, (gross, 25° C)- (6) 91.23 (%H)

Thus if Q, (gross, 25° C) = 19997 Btu/lb and

(%H) = 13.9, we obtain

Qp (net, 25° C) = 19997-91.23X13.9 =

18729 Btu/lb.

If the hydrogen content of the fuel is not known,

an approximate value for Op (net, 25° C) can be

calculated from the following empirical relation

Qp (net, 25° C) (7) =4310 +0.7195 Q, (gross, 25° C).

Substituting the value Q, (gross, 25° C) = 19997

Btu/lb in this equation we obtain

Qp (net, 25° C)=4310 +0.7195X19997 = 18698 Btu/lb (approximate)

Equation (6) is preferable to eq (7) for calculating

net from gross heat of combustion, since the latter equation is purely empirical. A fairly accurate

value of (%H) is required in eq (6), since an error

of 0.1 in this quantity introduces an error of about

0.05 percent in Qp (net).

6. References

[1] ASTM Method D 240-57T. ASTM Standards 7, 143, (1958).

[2] ASTM Method D 271-58, ASTM Standards, 8, 999 (1958).

[3] F. D. Rossini, Experimental thermochemistry (Inter- science Publishers, New York, N.Y., 1956), and the

references there cited.

[4J R. S. Jessup and C. S. Cragoe, Nat. Advisory Comm.

Aeronaut. Tech. Note No. '996 (1945) (copies not

available)

.

[5] S. Rothberg and R. S. Jessup, Ind. Eng. Chem. 43, 981 (1951).

[6] R. S. Jessup and J. A. Cogliano, ASTM Bull. No. 201

(Oct. 1954).

[7J G. T. Armstrong, R. S. Jessup, and T. W. Mears,

Chem. Eng. Data Ser. 3, 20 (1958).

[8] H. C. Dickinson, Bui. BS 11, 189 (1914) S230.

[9] N. S. Osborne, H. F. Stimson, and T. S. Sligh, Bui. BS 20, 119 (1925) S503.

[10] C. H. Meyers, J. Am. Chem. Soc. 45, 2135 (1923).

[11] T. W. Richards and F. Barry, J. Am. Chem. Soc. 37, 993 (1915).

[12] H. N. Davis, Mech. Eng. 51, 791 (1929).

[13] See for example:

(a) N. Irving Sax, Handbook of dangerous materials (Reinhold Publishing Corp., New York,

N.Y., 1951).

(b) Manufacturing Chemists Association, General

Safety Committee, Guide for safety in the chemical laboratory (D. Van Nostrand and

Co., New York, N.Y., 1954).

(c) National Safety Council, Accident prevention

manual for industrial operations (Chicago,

111., 1951).

(d) National Board of Fire Underwriters, National

electrical code (Chicago, 111., 1940).

[14] ASTM Method D 129-58, ASTM Standards 8, 81 (1955).

[15] C. S. Cragoe, Thermal Properties of Petroleum Products, NBS Misc. Publ. M97 (this paper is out of print but may be found in many public libraries).

[16] E. J. Prosen and F. D. Rossini, J. Research NBS 27,

289 (1941) RP1420.

[17] J. Coops, D. Mulder, J. W. Dienske, and J. Smittenberg, Rec. trav. chim. 66, 153 (1947).

[18] E. W. Washburn, J. Research NBS 10, 525 (1933)

RP546; see also chapters 5 and 6 of reference [3]. [19] F. K. Harris, Electrical measurements, p. 57 (John

Wiley & Sons, Inc., New York, N.Y., 1951).

[20] E. J. Prosen, W. H. Johnson, and Florence Y. Pergiel,

J. Research NBS 62, 43 (1959) RP2927.

254-16
7. Appendix

7.1. Apparatus

The major items of apparatus used in bombcalorimetric measurements on fuels at the National

Bureau of Standards are listed in table 2. On the

basis of prices listed in manufacturers' catalogs at the present time (1959), the estimated total cost

of replacement of the equipment listed is in the

neighborhood of $15,000.

Table 2. Major items cf equipment used in measurement

of heats of combustion of liquid fuels at the National Bureau of Standards

Mueller bridge. Resistance thermometer. Galvanometer.

Calorimeter, jacket, and thermostat. Combustion bomb.

Platinum crucibles and fittings. Balance.

Set of class M weights for above. Heavy duty balance

Set of weights for above. Oxygen purifier. Temperature controller for oxygen

purifier. Laboratory table for bridge. Laboratory bench.

Pellet press. Reducing valve. Julius suspension.

The approximate arrangement of the calorimeter

and accessory apparatus is shown in figure 4. The

reading station R provides support for the lamp L

and ground glass scale S, as well as for some electrical equipment for measurements not covered in

this Monograph. It also contains a convenient

"desk" for use in recording the data of bomb calo- rimetric experiments. The arrangement of the

equipment for purifying oxygen and admitting it to the bomb is shown schematically in figure 5. The arrangements shown in figures 4 and 5 are not necessarily the best under all circumstances.

For example, the bench BE (fig. 4) is considerably

larger than necessary for the calorimeter alone, as part of this table is used for other purposes.

The essential features of the various items of

apparatus are described below. Items not obtainable commercially, and modifications of commercial items are described in considerable detail.

Figure 5. Arrangement of apparatus for admitting oxygen

to bomb.

B, bomb; D, dryer; G, pressure gage; N, needle valve; O, oxygen cylinder; P, oxygen purifier; and R, reducing valve.

a. Bridge

The bridge used is a special Mueller bridge

designed especially for bomb-calorimetric measurements. It is substantially equivalent to the commercially available bridge designated as 67-2. In

addition to the usual 10-, 20-, 30-ohm coils of

the lOXlO-ohm decade this bridge has a 20.5-ohm

coil. Such a coil is useful in bomb-calorimetric

measurements, where the change in resistance of

the thermometer in an experiment is of the order

of 0.3 ohm, since it makes it possible to avoid a change in setting of the dial of the 10Xl-obm

decade which would otherwise be necessary in

certain circumstances. Thus if the initial and

final resistances of the thermometer are 27.8721

L

I i I I I I I I 1 I I 0 1 2 3 4 5 FEET

Figure 4. Arrangement of calorimetric apparatus.

BE, bench; C, calorimeter; BR, bridge; G, galvanometer; L, light source; M, stirring motor; R, reading station; and S, ground glass scale. 255-17
and 28.1806, the corresponding dial settings with

the 20.5-ohm coil would be 20.5 + 7.3721 and

20.5 +7.6806 and the change in dial setting would

involve only the lOXO.l-ohm and lower decades.

If no 20.5-ohm coil were available, it would be

necessaiy to change the dial setting of the 10X1-

ohm decade from 7 to 8 at a time when the temperature of the calorimeter was rising very rapidly.

This would greatly increase the difficulty of following the temperature of the calorimeter during the

period of rapid temperature rise, and might also involve a larger correction to the observed change

in resistance of the thermometer.

b. Thermometer

The platinum resistance thermometer has a

resistance of approximately 25.5 ohms at 0° C.

It is of the strain-free type with coil windings very

close to the wall of the enclosing glass tube. It was purchased under a specified requirement that

the temperature of the coil with a current of 1 ma

flowing through it should not exceed that of the

bath in which the thermometer is immersed by

more than 0.0003° C. Calorimetric resistance

thermometers enclosed in metal sheaths are available commercially. These are less subject to breakage than glass-enclosed thermometers, but

are subject to damage from bending the metal

sheath. Such damage might not be obvious on

casual examination, but could be detected by

periodic determination of the ice point of the

thermometer.

c. Galvanometer

The galvanometer has a sensitivity of about

0.2 juv/mm at 1 m, an external critical damping

resistance of 40 ohms and a period of about 5 sec. The damping resistance used is so chosen that the

galvanometer is slightly underdamped. The galvanometer is protected from air currents and

abrupt changes in temperature by an enclosure

made of cork pipe covering (for 6 in. pipe) about

10 in. in outside diameter. The galvanometer is supported by a Julius suspension, which is very

effective in reducing the effect of vibrations.

d. Bomb

The combustion bomb 21 is made of a corrosionresistant alloy (Hlium). It is provided with a check valve for admitting oxygen and also with a

needle valve for releasing the gases contained in it. It is sealed by a self-sealing neoprene gasket.

The original bomb has been modified by replacing

the three supporting feet furnished with it by new

ones of monel metal about 12 mm in height. This

permits freer circulation of water under the bomb.

The base-metal electrode inside of the bomb,

and the crucible-support rod were cut off leaving

lengths of about 3 cm from the point at which they

enter the lock nuts. To the shortened electrode

2 ' Parr Instrument Company Catalog No. 1101.

was hard soldered a }U in. platinum rod about 3 cm in length. To the shortened crucible-support

rod was hard soldered a 5-cm length of )'% in. o.d. platinum tube having a 0.01 in. wall. The ar- rangement of electrode, crucible support, crucible,

electric fuse and 0.3 mm platinum leads thereto

is shown in figure 6(a) (valves not shown). An

enlarged view of the platinum crucible is shown

at (c) figure 6. The crucible is put in place by

sliding the split tube (%2 in. o.d.) shown at the

right of figure 6(c) over the end of the % in. platinum crucible-support tube referred to above

until the fuse is nearly in contact with the sample

of combustible. The split tube may be deformed

slightly with the fingers to make it fit the )% in. tube tightly enough to be held in place by friction. The length of the crucible-support, and the position of the crucible on this support should be such

that the crucible cannot come in contact with the

water in the bottom of the bomb when the bomb

is assembled. If the crucible should come in

contact with the water, combustion will be in- complete.

(f) Figure 6. Bomb and accessories.

(a) Bomb, showing arrangement of crucible, crucible support, electrode,

etc. (Valves not shown, see fig. 1); (b) Binding post and lead wire; (c) Enlarged view of crucible; (d) Platinum lead flattened at end; (e) Fuse wire

attached to platinum leads; and (f) Hook for handling bomb.

A supply of platinum lead wire is wound around

the electrode and crucible support rods as shown,

and a sufficient amount of this to reach down to the

crucible is unwound for each experiment. The

electric fuse is a 2-cm length of Parr fuse -wire (No. 34 AWG chromel C) which is formed into a

small helix by winding it around a rod about 0.04

in. in diameter. The method of attaching the

fuse to the platinum leads is illustrated at (d) and

(e), figure 6. The ends of the lead wires are first flattened by hammering as shown at (d). The

flattened ends are then bent and the fuse inserted

as shown at (e), after which the turned-up ends

256-18
of the lead wires are hammered down with a small

hammer or squeezed together with pliers to clamp

the ends of the fuse wires.

The terminal nut attached to the electrode outside of the bomb was replaced by one of the form

shown at (a), figure 6. The binding post shown

at (b), figure 6, has a split tube at its lower end

which can be slipped over the upper part of the

terminal liut, where it fits tightly so as to make

good electrical contact. The lead wire shown at

(b), figure 6, connects this binding post to one on

the calorimeter jacket which is connected in the

firing circuit. This wire is soldered to spade-type

terminals at each end, the larger of which normally

is permanently attached to the binding post shown

at (b). This wire should be so insulated as to avoid any electrical contact with the calorimeter

vessel. With alternating current the contact of the lead wire and bomb electrode with the water

in the calorimeter does not result in any appreciable electrical leakage, provided actual metallic

contact with the calorimeter vessel is avoided.

e. Calorimeter and Jacket

The calorimeter now used for fuel testing is of

the type described by Dickinson [8]. The calorimeter vessel is of the form shown at (a) and (b),

figure 1. The calorimeter cover is in the form of a flat circular disk with vertical wall about 1 cm

in height at the edge. The holes OT and OL (fig. 1(b)) are surrounded by metal collars about 1 cm

high. The cover fits tightly enough inside of the

calorimeter vessel so that it is held in place by

friction. Its lower surface is in contact with the

water of the calorimeter. The calorimeter vessel

is supported inside of the jacket by pins of stainless steel, in the manner described by Dickinson

[8].The Dickinson type calorimeter was constructed

in the NBS shops. There is a commercially available "submarine" calorimeter, 22 based on a design

developed at the National Bureau of Standards

[20], which has been found to be substantially

equivalent in performance to the Dickinson calorimeter. The submarine calorimeter is supplied

without a thermostat for the jacket bath, so that a thermostat for controlling the bath temperature

to a few thousandths of a degree must be purchased

or constructed.

The thermostat 23 used with the particular Dickinson type calorimeter used for fuel testing is similar to one previously described by Osborne,

Stimson, and Sligh [9]. It consists of a "bulb"

filled with toluene and connected to a glass capillary U-tube (1.5 mm i.d.) containing mercury.

Expansion of the toluene as a result of rising tem22 Catalog \"o. 63090, Precision Scientific Co.. Chicago, 111. This calorimeter embodies an improved method of supporting the calorimeter vessel inside

of the jacket |20).

23 Temperature-control units for which a control accuracy of 0.001° C. is claimed are available commercially. Numerous other temperature-control

devices are described in the literature. See for example the papers cited in reference [3]. For any temperature-control unit it is important that the rela- tive locations of heater, stirrer, and temperature-sensing element should be

as shown in figure 1, that is, the bath liquid should flow from the heater, through the stirring propeller, and over the temperature-sensitive element by

the shortest path possible.

perature causes the mercury to make contact with

a needle closing an electrical circuit through an

electronic relay 24 which shuts off the current in

the electric heater in the jacket bath. The "bulb"

TB (fig. 1) consists of about 3 m of %e in. copper

tubing with 0.01 in. wall thickness wound into a

helix and so located in the same tubular housing

as the jacket bath stirrer that the water flows over

the bulb immediately after leaving the stirrer. The glass U-tube and attached valve for admitting

or removing toluene are shown in figure 7. The

valve has tubular openings at the top and bottom

for attaching the reservoir B and the capillary

U-tube as described below.

Future 7. Valve and glass parts of thermostat.

V, valve; TB, tube to thermostat bulb; B, toluene reservoir; F, capillary U-tube; E, enlargement in capillary; H, platiuum wire; L, leads to relay; C, Pyrex tube; D, brass cap; S, screw; and N, steel needle. The Pyrex reservoir B contains a supply of

toluene which is separated from that in the "bulb"

TB (fig. 1) by the valve I7 when it is closed. This

valve is opened when the calorimeter is shut down

thus permitting toluene to flow from the reservoir

into the bulb as the bath cools. Failure to open

the valve when the bath cools usually results in

air being drawn into the system through the

capillary F (fig. 7). The Pyrex bulb C (fig. 7) also contains toluene which protects the mercury

surface in the capillary from oxidation. The en- largement E in the capillary is larger in volume

than the mercury in the capillary so that no mercury will be drawn into the metal parts of the

system if the valve V is inadvertently left closed

when the calorimeter is shut down.

2* American Instrument Company Catalog No. 4-5301. 257-19
Electrical connection between the Valve V and

the mercury in the capillary U-tube is provided by

a platinum wire H, long enough to reach from

the top of the capillary to near the bottom of the U. The upper end of the wire is flattened and bent at a right angle to the rest of the wire so as to insure

electrical contact with the valve.

The glass reservoir B and the capillary glass Utube are soldered into the tubular openings in the

brass valve Vwith pure tin following the procedure

described by Meyers [10]. To fill the thermostat with toluene the tube

C (with cap D removed) is connected to a large

bulb G above C (at least 250 cm3

, not shown in

fig. 7) by means of a short piece of Tygon tubing.

Somewhat more than enough toluene to fill the

thermostat is placed in the bulb G, and some is also placed in the reservoir B. Air can be removed

from the thermostat system by heating the

"bulb" (TB, fig. 1) to about 100° C and repeatedly

evacuating the bulb G above the toluene and

then admitting air. To test for air in the system,

air is admitted above the toluene in G, the valve

V is opened, the toluene meniscus is brought

into the capillary at F, and the valve is closed.

If the system is free of air, moderate air pressure

applied by mouth above the toluene will not

cause a movement of the meniscus in the capillary of more than 0.2 or 0.3 mm. The removal

of air from the system should be done before

introducing mercury into the capillary. If air

is inadvertently admitted to the system after mercury has been introduced into the capillary,

the mercury should be removed before attempting

to remove the air. In preparing for a calorimetric experiment the

jacket is first heated to the desired temperature,

the heating current is reduced to slightly more

than enough to maintain the temperature constant, and the valve V is closed. Final adjustment of the temperature can be made by moving

the needle N up or down by rotating the cap

D relative to the screw £ (fig. 7). The heating

current should be adjusted so that the on and

off periods are about equal in length.

The method of bringing the firing leads through

the jacket is illustrated in figure 1(c).25 Two

metal rods, one of which is shown at R, are ce- mented with wax into tubes T which pass through

the jacket, so that the rods are insulated from the

jacket. Each rod is drilled and tapped at each

end for a 4-40 brass screw, which is used to clamp

the terminal of the lead wire between the two

washers, W, thus forming a binding post at each

end of the rod. The terminal at the left end of the

lead wire shown in figure 1(d) is attached per- manently to one of the inner binding posts and the

clip at the other end of the wire (d) is slipped over the edge of the calorimeter vessel when it is

2! This method is not applicable to some types of calorimeters, for example, submarine calorimeters. The important feature of the method is that the

leads are in good thermal contact with the jacket, but are electrically insulated from it.

assembled preparatory to making an experiment.

The other lead wire, from the binding post on the

bomb (see fig. 6(b)), is attached to the other inner

binding post after the bomb has been put in the

calorimeter and the calorimeter cover has been

put in place. The two outer binding posts are connected through an ammeter and a switch to a small transformer having a secondary voltage

of 8 or 10. The switch should oe of the momentary

contact push-button type normally open except

when held closed by the operator.

f . Balance for Weighing Samples

The balance used for weighing samples of combustibles is an undamped semimicro balance

(capacity 100 g) having a sensitivity reciprocal

of 0.14 mg per division on the index scale. The

balance is provided with a keyboard arrangement

for adding and removing weights from 1 to 100 mg.

Temperature gradients parallel to the balance

beam are reduced by covering the walls of the

balance case inside and out with aluminum foil, and by locating the balance where temperature

gradients in the room are small. It has been

found, however, that best results are obtained

with the balance when there is a vertical temperature gradient such that the top of the balance

case is warmer by 0.03 to 0.1° C than the bottom.

The weights used with the balance are highgrade one-piece (class M) weights and were cali- brated in the Mass and Scale Section of the

National Bureau of Standards.

For most purposes a good analytical balance

woidd be satisfactory if provided with high grade

calibrated weights, and properly used.

g. Balance for Weighing Calorimeter

This is a magnetically damped heavy duty

balance having a capacity of 5 kg and a sensitivity

of about 0.5 mg. The tantalum-plated weights

used with this balance are of good quality but

are not calibrated. Calibration was considered

unnecessary since the purpose of weighing the

calorimeter is not to determine its absolute weight,

but to reproduce the same weight of calorimeter

plus water for each experiment. For this purpose

it is important that the weights remain constant

in value, and that the same weights be used at all times, but the actual masses of the weights used

need not be known accurately.

h. Oxygen Purifier Combustible impurities in the oxygen are re- moved by passing it through a cylinder containing

cupric oxide maintained at a temperature of 500° C (932° F). The purifier 26 consists essentially of a heavy-walled alloy-steel cylinder having

inside dimensions of approximately 1 in. diameter

by 10 in. length, and capable of withstanding

a pressure of at least 2500 psi at 500° C. The

cylinder is provided with an electric heater. It

2« American Instrument Company 1942 Catalog No. 406-31. 258-20
has inlet and outlet at opposite ends, and a well

for inserting a thermocouple for measurement of

temperature. The cyhnder is filled with wire-form

cupric oxide. The temperature and oxygen pres- sure in the purifier should not be allowed to rise above values consistent with safety. The manufacturers recommendations regarding safety pre- cautions should be adhered to rigidly. The

strength of materials decreases rapidly with in- creasing temperature.

The temperature of the purifier can be controlled by means of a "Fail safe" controller. Such

controllers are available commercially.27 The

pressure is easily controlled by a reducing valve

attached to the oxygen cylinder.

i. Laboratory Table for Bridge

This table should be large enough to accom- modate the bridge comfortably, and of a height

which will afford convenience in the manipulation

of the bridge dials. A table 22 in. square by

18 in. high is convenient for use with a G-2 bridge

as it allows space for batteries, etc

j. Pressure Gage

The Bourdon pressure gage used has a 6 in. dial

and is graduated from 0 to 800 psi in steps of 10

psi, so that it can be read to about 1 or 2 psi.

The gage was calibrated in the Mechanical Instru- ments Section of the NBS and was set so as to read correctly at 450 psi.

7.2. Glass Sample Bulbs

For measurements of heat of combustion of

kerosenes, gasolines, or other volatile liquids

it is necessary, in order to permit accurate weighing of the sample and to insure that it is all in the

liquid state until it is ignited in the bomb, to enclose the sample in a thin-walled glass bulb,

so constructed and filled that it will not break

under the pressure of the oxygen. The type of

bulb 28 used in testing of volatile fuels at the

National Bureau of Standards, and the method

of making such bulbs are illustrated in figure 8. Attempts to obtain bulbs of this type from manufacturers of glass laboratory apparatus have been

unsuccessful to date, and such bulbs are therefore

made in our own laboratory. A brief description

of the method of making the bulbs will be given

below. It should be recognized, however, that

it is virtually impossible to describe the method

in such detail as to enable an inexperienced

worker to make bulbs successfully on his first attempt. The best that can be done is to outline

the method, and to depend upon the individual

worker to develop the necessary techniques by

trial. It is to be expected that in the early

attempts failures will far outweigh successes, and

that a reasonable degree of skill can be acquired

only by long and patient practice.

27 For example American Instrument Company Catalog No. 49-9570. Arthur S. Laptoe and Company Catalog No. 357-70.

>8 Bulbs of this type were first described by Richards and Barry [11].

The starting material for making bulbs is soft glass tubing 4 to 6 mm in outside diameter.29 Approximately 2 cm of such a tube is heated in a moderately hot air-gas flame of an ordinary

laboratory blast burner. When the glass becomes

soft it is removed from the flame and drawn down

to a fine capillary having a minimum outside

diameter of about 1 mm. This procedure is then

repeated in such a manner as to leave a short

section of the same diameter as that of the original

tube, as shown at figure 8(a). The two capillaries are then broken at about their midpoints, leaving a piece such as that shown at figure 8(b). The

remaining glass-working operations are carried

out with an air-gas micro blast burner capable of

producing relatively small flames. Using such a micro burner the piece illustrated at (b), figure 8,

is rotated and heated by a small hot flame at the

point indicated by the arrows, and is then drawn

down to 1 mm outside diameter. This procedure

is repeated on the other side of the enlargement in

the tube, the final product being as illustrated at

(c) , figure 8 . This piece is then rotated and heated

by a small sharp flame at the center of the enlargement as indicated by the arrow at (c), and the

two halves of the piece are pulled apart as shown

at (d), figure 8, where the enlarged end of the

piece at the left has been reduced in size by removal

of surplus glass. This removal of surplus glass is accomplished by heating the end of the enlargement until it softens, and then pulling off small

filaments of glass until an enlargement of the

proper size remains. After such removal of

surplus glass from both of the pieces shown at

(d) a spherical bulb, not greater than 14 mm in diameter, is blown on each piece (fig. 8(e)). The

spherical bulb is then flattened on one side by

holding the bulb above a small soft flame (no

primary air) about % in. in diameter by ){ in. high,

and gradually lowering it until the glass on the

under side of the bulb softens and flattens. This

procedure is then repeated so as to flatten the

opposite side of the bulb. The final form of the

bulb is shown at figure 8(f). The operations of

bringing the bulb down on to the flame and

removing it after flattening is complete should be

done gradually, since too rapid heating or cooling

of the bulb may cause it to break.

The most difficult part of the procedure just

described is that of blowing a bulb of the proper

size. Success in this operation depends in part

upon having the proper amount of glass on the

end of the tube (fig. 8 (d)) and in part upon the

type of flame used, as well as upon the procedure

followed in blowing the bulb. A flame which

has been found to be satisfactory is one about

Yi in. in diameter by % in. in height with just

enough primary air so that there is a small yellow

tip in the flame. The end of the tube (fig. 8(d)) on which the bulb is to be blown is beated in the

39 Pyrex glass has been found unsatisfactory for this purpose, as unburned

carbon is usually found on such glass after a combustion. This may be

related to the fact that the Pyrex glass does not melt completely when the sample is burned, as does soft glass, and therefore partially retains its original form, thus inhibiting access of oxygen to the fuel. 259-21
Figure 8. Steps in making sample balbs.

flame until sufficiently hot, and is then removed

from the flame and the bulb blown immediately.

In order to prevent sagging of the end of the

tube when heated, the tube is held at an angle

of about 30° to the vertical and is rotated about

its axis continuously. Usually the first few at- tempts to blow a bulb will be unsuccessful because

the initial size of the bulb is so small that a rela- tively high pressure will be required to overcome

surface tension and the viscous resistance to flow of the glass. If the pressure is not high

enough the bulb will expand so slowly at first that the glass will harden before the desired size

is reached. If the pressure is high enough to expand the bulb at a sufficiently high initial rate, the bulb may suddenly expand to too large a

size before the glass hardens. The ideal procedure

would be to blow very hard at first and then less so as the bulb becomes larger. This is very difficult to do because the whole operation must be carried

out in a very short time before the glass hardens.

It is therefore usually more successful to repeat

several times the procedure of blowing the bulb

to a diameter of 4 or 5 mm and then shrinking

it by heating, before attempting to blow the

bulb to the required size. This procedure also serves to provide a somewhat more uniform dis- tribution of glass in the final bulb.

Too large an amount of glass in the bulb and

too hot a flame are both conducive to too large

size of the bulb. Too small an amount of glass

and too low a flame temperature have the opposite

effect. Success in blowing a suitable bulb of the

proper size depends upon the proper combination

of flame temperature, amount of glass and technique of blowing.

The spherical bulb should be not more than 14 mm in diameter, and the completed bulb should

not contain more than about 1.3 cm3 nor less than

0.7 cm3 of liquid. The flat sides of the bulb should

be thin enough to deflect visibly, but not so thin

as to break, under moderate air pressure applied

by mouth. The weight of the glass in the bulb

after sealing off the stem near the bulb should be

between 0.05 and 0.10 g. The outside diameter

of the capillary adjacent to the bulb should be

between 1.0 and 1.3 mm. The inside diameter

should be at least 0.5 mm and preferably a little larger in order to permit easy insertion of a No. 27

hypodermic needle (0.4 mm diam.) in filling the

bulb. The appearance of the flat sides of a completed bulb will give some indication as to whether

it will be satisfactory. Usually the flat sides

present a scalloped appearance, although if the

amount of glass in the bulb is greater than normal

they may be nearly plane. If the scallops are very

fine, say 1 mm or less apart, the bulb is probably

too thin and fragile to be satisfactory.

Samples of liquid fuel can be conveniently introduced into the previously weighed glass bulbs by means of a hypodermic syringe fitted with a No. 27

needle. The liquid should be introduced into the

bulb slowly in order to permit escape of the air initially present without undue increase in pressure. The bulb should be filled completely so that

the liquid extends up into the enlargement in the

stem as indicated at figure 8(f). Usually a small

bubble will be trapped in the bulb at the point

where it joins on to the. stem, but such a bubble can usually be removed without too much diffi- culty with the aid of the hypodermic needle or a

piece of wire. In filling the bulbs the usual safety

precautions for the handling of volatile organic

solvents should be taken, particularly if the fuel contains tetraethyl lead [13]. In filling bulbs with very volatile liquid fuels such as gasolines, great care should be taken to avoid loss of material by evaporation, as this causes fractionation of the material with a conse- quent change in heat of combustion. The container should be kept tightly closed at all times

except when withdrawing a sample with the hypodermic syringe. The sample can be withdrawn more quickly if the needle is detached from the

syringe. In replacing the needle after withdrawal

of the sample care should be taken to avoid contact of gasoline with the hands, particularly if it contains tetraethyl lead. After the bulb is filled, the capillary is sealed off so as to leave a stem about 3 or 4 mm long attached

to the bulb. In order to do this the bulb must be

cooled so as to draw the liquid out of the capillary,

and the bulb must be protected from the flame during the sealing operation. To protect the bulb

from the flame a small piece of asbestos paper with

a hole in the center and with a cut between the

hole and the edge (fig. 8(g)) is slipped over the

capillary via the cut so that the capillary goes

through the hole, and the piece of asbestos paper is in contact with the bulb. The bulb is then cooled

by placing it on a mass of shaved ice in a beaker,

or on a copper plate in contact with ice, and when

the meniscus in the capillary disappears below the

asbestos paper, the capillary is sealed off with a

small hot air-gas flame and removed from the

bulb. The bulb should then be removed promptly

from the ice to avoid possible breakage due to

260-22
excessive contraction of the liquid. The filled bulb is conveniently handled by the short projecting capillary by means of forceps of the type ordinarily used for handling balance weights. Particles of asbestos which may adhere to the bulb

should be removed by means of a camel's hair

brush. Any liquid remaining in the capillary

detached from the bulb in sealing it should be re- moved before weighing the filled bulb together

with this detached capillary. If the liquid is sufficiently volatile it can be removed by flaming

the capillary several times with the micro-burner

flame. The flame should be applied first to the

closed end of the capillary, and moved gradually

to the open end in such a manner as to avoid sof- tening the glass. If the liquid is of low volatility,

it should be washed out with a volatile solvent,

such as benzene or petroleum ether, introduced

into the capillary by means of a hypodermic syr- inge before flaming as described above.

When first sealed, the bulb may contain a small

bubble of air. This will dissolve in the liquid after a time leaving the bulb completely filled with

liquid. Bulbs prepared in the manner described

should withstand changes in room temperature of

10° C or more, and pressures of at least 30 atm

(450 psi) without breaking.

Glass sample bulbs of different types have been

described by a number of workers [16, 171.

Washington, April 14, 1959.

261-23
U. S. Department of Commerce

National Bureau of Standards

Research Paper RP1968

Volume 42, March 1949

Part of the Journal of Research of the National Bureau of Standards

Heat of Isomerization of the Two Butadienes

By Edward J. Prosen, Frances W. Maron, and Frederick D. Rossini

The heat of isomerization of 1,3-butadiene to 1,2-butadiene, in the gaseous state at 25° C

was determined by measurement of the ratio of their heats of combustion in oxygen to form carbon dioxide and water. The combustion of the gaseous hydrocarbon occurred in a flame at constant pressure in a glass calorimetric reaction vessel of improved design. A

complete description of the new calorimetric reaction vessel is given.

The following experimental value is reported for the reaction of isomerization:

l,3-butadiene(gas) = l,2-butadiene(gas), AH° at 25° C=12.78±0.16 kcal/mole.

Using the value for the heat of formation of 1,3-butadiene previously reported, the

following calculated values are given for the reactions of formation and combustion of 1,2-butadiene:

4C(solid, graphite) +3H2 (gas) =C4 H6 (l,2-butadiene, gas), AH° at 25° C = 39.53 ±0.28

kcal/mole.

C.H6 (l,2-butadiene, gas)+5^ 02 (gas) =4C02 (gas) +3H2 0 (liquid),

AH° at 25° C=-620.69±0.28 kcal/mole.

I. Introduction

This work, sponsored by the Office of Rubber

Reserve, is part of a thermochemical investigation

of monomeric compounds of importance in the

national synthetic rubber program, and is also a part of the work of the thermochemical laboratory

of this Bureau on the determination of the heats

of formation of compounds of importance to industry and science.

Calorimetric measurements have been made

that yield a value for the difference in the heats

of combustion at constant pressure of 1,3-butadiene and 1,2-butadiene in the gaseous state at 25° C. Combination of this value, which is the

heat of isomerization in the gaseous state at 25°

C, with the previously reported value for the

heat of formation of 1,3-butadiene [l],

1 yields

values for the heats of formation and combustion

of 1,2-butadiene.

II. Unit of Energy, Molecular Weights,

Uncertainties

The unit of energy upon which values reported

in this paper are based is the absolute joule,

1 Figures in brackets indicate the literature references at the end of this paper.

derived from mean solar seconds, and absolute

ohms and volts, in terms of which certification of

standard resistances and standard cells is made

by this Bureau. For conversion to the con- ventional thermochemical calorie, the following

relation [2,3] is used:

1 calorie —4. 1840 absolute joules.

The atomic weights were taken as 0 = 16.0000,

H= 1.0080, and C = 12.010 from the 1947 table

of international atomic weights [4]. The uncertainties assigned to the various quantities dealt with in this paper were dervied, where

possible, by the method previously described [5].

III. Method

The aim of this investigation was to determine

as precisely as possible the heat of isomerization

of 1,3-butadiene (gas) to 1,2-butadiene (gas) at constant pressure and 25° C. This was done by

determining the ratio of the heats of combustion

of these isomers [6]. The value of the difference

between this ratio and unity, multiplied by an

accepted value for the heat of combustion of

1,3-butadiene, gives the heat of isomerization of

1,3-butadiene to 1.2-butadiene. In principle, the

262-269
ratio of the heats of combustion of these isomers was determined as the inverse ratio of the masses

of carbon dioxide, whose formation in the combustion of the respective isomers produced identical increases in temperature in the standard

calorimeter system, measured as increases in resistance of the platinum resistance thermometer

as determined on the given resistance bridge.

With this procedure, the energy equivalent of the

calorimeter system or the heat of combustion of one of the isomers need be known only approximately, and other systematic errors tend to cancel out. The method of reducing the experimental

observations was as follows: Let

ARc =ihe corrected increase in temperature of

the calorimeter system, expressed as the

increase in resistance in ohms of the

given platinum thermometer at a mean

temperature of 25° C, as measured with

the given resistance bridge;

"^co2 =the mass of carbon dioxide formed in the

combustion of the hydrocarbon, in

grams;

.E,= the energy equivalent, over the ' standard" interval of temperature, of the

"standard" calorimeter system, obtained

as the ratio of a given quantity of

electric energy to the value of ARC produced by it, expressed as joules per

ohm;

2*= the energy introduced into the calorimeter

in the "ignition" process, consisting of sparking, igniting the flame, and ex- tinguishing the flame, but not including

any part of the heat of combustion,

expressed in joules; gf=the energy introduced into the calorimeter

by gases entering or leaving at a temperature different from 25° C.

gv=the energy (negative) introduced into the

calorimeter by the process of evaporating such water as leaves or remains in the calorimeter in the gaseous state. 2e=the energy introduced into the calorimeter

by the "standard calorimetric process"

of combustion.

The total energy, q, introduced into the calo- rimeter by the actual combustion process in an

experiment is

q=Es ARc =qc +qg +qv +qi . (1)

Letting

we obtain the following relation from which B is calculated for any given experiment:

For any two isomers, the ratio of the heats

evolved per gram of carbon dioxide is equal to the ratio of their heats of combustion per mole.

If the subscripts a and b refer to 1,3-butadiene

and 1,2-butadiene, respectively, and —AHc° is the heat evolved in the standard combustion of one mole of the hydrocarbon, then

Bb IBa =(-AHc°) b /(-AHc°) a , (4)

and

(~AHc°) a -(-AHc°) b =(-AHc°) a (l-Bb /Ba ).(5) For the reaction of isomerization,

1 , 3-butadiene (gas) = 1 , 2-butadiene (gas) , (6)

the standard heat of isomerization is AH° (isomerization) = - (-AHc°) a (l-Bb/Ba)

. (7)

It may be seen from eq 3 and 7 that the heat of

isomerization derived by this procedure is not

sensitive to the value of Es or of {—AHc°) a . The

total amount of energy in one experiment is about

60,000 j, and the largest variation in the value

of 3„+<Zg +<Zi is about 150 j. Therefore, an error

of 1 percent in the value of Es , used in eq 3, would

cause an error of not more than 0.002 percent in

the value of Bb/Ba . This corresponds to an error

of 0.01 kcal/mole in the value of AH° (isomerization). Similarly, an error of 0.1 percent in the

value of (—AHc°) a used in eq 5 would cause an

error of 0.01 kcal/mole in the value of AH° (isomerization) . IV. Apparatus

1. Calorimeter Assembly and Thermometric

System

The calorimeter assembly used in this investigation was similar to that used in other investiga263-270
tions in this laboratory [6, 7], with some improvements added. The jacket of the calorimeter was

maintained near 27.00° C, at a temperature

constant within ±0.002° C, by means of an automatic regulator. In all experiments, the

calorimeter uniformly contained 3627.56 ±0.02

g of water, together with the stirrer, platinum

resistance thermometer, calorimeter heater, and

the glass reaction vessel with its metal support.

The stirrer was operated at a substantially constant speed of 276 rpm with a belt drive from a synchronous motor.

The calorimeter heater consisted of about 65

ohms of enameled constantan resistance wire, No.

30 AWG, wound on a Pizein-coated, thin, copper

cylinder, the whole covered with Pizein [7]. The thermometer system consisted of a platinum

resistance thermometer No. 262,214 and Mueller

resistance bridge No. 404 [8].

2. Reaction Vessel

An improved glass reaction vessel was designed

and made for this and subsequent investigations

involving combustions in a flame at constant

pressure. The new reaction vessel is shown in figure 1. In the combustion of hydrocarbons other than

methane and ethane in a flame in a glass reaction

vessel, it is necessary to mix some "primary"

oxygen with the combustible gas before it reaches

the flame, in order to prevent deposition of un- burned carbon in the burner tube. For a given

rate of flow of the combustible gas, the flame

velocity is required to be such that the flame will neither flash back inside the burner tube, nor blow off from the burner tip. For a given combustible gas burning in an atmosphere of oxygen,

the position of the flame at the burner tip is determined largely by the amount of "primary"

oxygen mixed with the combustible gas. In the

previous design of reaction vessel [7], the admixture

of primary oxygen was determined largely by the

size of the Bunsen openings at the base of the

burner tip. The size of the Bunsen openings

could be changed only by cutting the reaction

vessel apart. As changes were always required

for different types of hydrocarbons, this was a cumbersome arrangement. In the new design,

the primary oxygen is introduced through a sep- Figure 1. Diagram of the reaction vessel.

264-271
arate line, and the fraction of primary oxygen in

the combustible mixture reaching the flame at the

burner tip is easily controlled by regulating sep- arately the rate of flow of the combustible gas

and of the oxygen.

In the present investigation, a rate of flow of butadiene equal to 29 ml/min (or 0.0012 mole/min) was found to be satisfactory. The primary oxygen was adjusted to produce a blue flame with a sharp

inner cone. The primary oxygen supplied about

30 percent of the oxygen requried for complete

combustion of the hydrocarbon. The total oxygen

(primary plus secondary) was about 150 percent

of that required for complete combustion. (In

order to avoid possible damage to the glass reaction

vessel, preliminary tests of the amount of primary

oxygen required for the satisfactory combustion

of a given hydrocarbon, at given rates of flow, were made with a similar burner tube made of brass

and provided with a glass chimney.)

The method of operation of the new reaction

vessel is as follows: The hydrocarbon enters through inlet tube A, the primary oxygen through

B, and the secondary oxygen through C. The

hydrocarbon and primary oxygen mix in the

chamber F and emerge through a hole (about

0.5 mm diameter) in the quartz tip 0. Sparking

across the platinum wires H, above the tip, ignites

the mixture, which burns in a steady flame in the a t- mosphere of secondary oxygen supplied through the

inlet C. One of the platinum wires enters through

the secondary oxygen inlet tube C; the other is grounded to the calorimeter can. The gap between

the platinum wires is about 3 mm. The gaseous

products of combustion leave the combustion

chamber at the top, are cooled to the temperature

of the calorimeter in their passage through the

glass spiral E, and leave the calorimeter through

the outlet D. Most of the water vapor condenses

to liquid, which collects at the bottom of the

vessel at J, or in the bulb K, at the bottom of the

spiral. The vessel is constructed to come apart

at the joint L, to facilitate adjusting the spark

gap and cleaning the vessel.

3. Sparking System

A new sparking system was assembled for this investigation. It consisted of a high-tension coil (Delco-Remy 538-z), a condenser having a capacity of 0.2 microfarad, and breaker points operated

by a hexagonal cam driven by a synchronous motor

having a speed of 1,800 rpm. Four dry cells were used as a source of energy. The spark gap

at the burner tip was about 3 mm, and the normal

time of sparking was 15 sec.

V. Chemical Procedure

1. Source and Purity of the Butadienes

The sample of 1,3-butadiene used was from a

lot of 1,3-butadiene labeled Research Grade,

Phillips Petroleum Co. The purity of this material, sampled from the vapor phase, was determined by measurements of freezing points by

A. R. Glasgow, Jr. to be 99.83 ±0.06 mole

percent [9]. The 1,2-butadiene used was a sample from the

API-NBS series of highly purified hydrocarbons,

which are being prepared through a cooperative

undertaking of the American Petroleum Institute

and the National Bureau of Standards. It was made available through the American Petroleum

Institute Research Project 44 at the National

Bureau of Standards on "Data on properties of

hydrocarbons" and was purified at the National

Bureau of Standards by the American Petroleum

Institute Research Project 6 on the "Analysis,

purification, and properties of hydrocarbons"

from material supplied by the Standard Oil

Development Co. through W. J. Sweeney. A

complete description of the purification and

purity of this compound is given by StreifT,

Murphy, Zimmerman, Soule, Sedlak, Willingham,

and Rossini [10], who reported the purity by

measurement of freezing points, to be 99.94 ±

0.05 mole percent.

It is calculated that in the extreme case, the heat

of combustion would be affected by less than the

following amounts because of the impurities: 0.012

percent for impurities in 1,3-butadiene; and 0.003

percent for impurities in 1,2-butadiene.

The butadiene was withdrawn in the vapor

phase from its container, passed through a tube of anhydrous calcium sulfate followed by a small

amount of anhydrous magnesium perchlorate to remove traces of water, and fed directly into the

reaction vessel in the calorimeter for the

combustion.

2. Purification of the Oxygen Used for Combustion

The oxygen used for combustion, including both

the primary and secondary streams, was" commer265-272
cial oxygen that was freed of combustible impurities by passage through copper oxide at about

550° C. The oxygen in both lines was freed of

carbon dioxide and water before entering the calor- imeter by passage through tubes containing,

successively, ascarite, magnesium perchlorate, and

phosphorus pentoxide.

3. Purity of the Reaction of Combustion

As a check on the purity of the reaction of combustion, both the water and carbon dioxide formed

in the combustion were collected and the masses

determined for each experiment. In eight combustion experiments with 1,3-butadiene, the mean

value of the ratio, r, of one-fourth of the number

of moles of carbon dioxide to one-third of the

number of moles of water, was found to be 1.00024,

with a standard deviation of ±0.00022. Similarly for six experiments with 1,2-butadiene, the

mean value of r was found to be 0.99994, with a standard deviation of ±0.00019.

Samples of the products of combustion were

analyzed for carbon monoxide by the Gas Chemistry Section of this Bureau [11]. In no case was

the total amount of carbon monoxide greater than

0.004 percent of the amount of carbon dioxide

formed in the combustion.

The effect of any possible incomplete combustion during the ignition or extinction of the flame was eliminated by the procedure, described below,

of determining the "ignition" energy in separate

experiments in which the flame was allowed to burn only long enough to produce a steady flame,

and then was extinguished. With this procedure,

the heat of combustion was in reality determined

from the portion of the combustion when the

flame was in a steady state, any constant errors associated with the ignition and extinction of the

flame cancelling out.

"4. Determination of the Amount of Reaction

For each calorimetric combustion experiment,

the amount of reaction was determined from the mass of carbon dioxide formed, taking 1 mole or 44.010 g of carbon dioxide as equivalent to onefourth mole of butadiene.

VI. Calorimetric Procedure

1. Calorimetric Combustion Experiments

The following procedure was followed in pre- paring the calorimeter for all experiments: The

calorimeter jacket was brought to temperature, near 27.00° C, where it was automatically maintained constant, within about ±0.002° C, throughout the whole experiment. The standard mass of

water, 3627.56 ±0.02 g, was weighed into the

calorimeter can on the pan of a 5-kg balance,

having a sensitivity at this load of 0.008 g per

scale division, using the same weights in all experiments. The calorimeter can was placed in the

calorimeter jacket, the dry reaction vessel with

the heater around it was lowered into the can, the cover was placed on the can, the jacket was

covered, the stirrer was connected, and the platinum resistance thermometer inserted into the

calorimeter can through the hole in the jacket

cover. The hydrocarbon and primary and secondary oxygen lines were connected to the reaction

vessel through flexible glass spirals. The weighed

absorption tubes for water and carbon dioxide, a guard tube containing magnesium perchlorate

and ascarite, a sampling bulb, and a flowmeter were connected to the outlet side of the reaction

vessel through a three-way stopcock near the

vessel. This stopcock permitted oxygen to bypass

the reaction vessel at the end of a combustion to flush any water and carbon dioxide in the lines into the absorption tubes. The calorimeter was

brought to near the starting temperature by

electrical heating, and a period of about 20 min

was allowed for equilibrium to be established.

The calorimetric observations were begun when

the calorimeter reached the selected starting

temperature. The standard temperature rise was about 4 degrees for the combustion experiments, and the final temperature was slightly

below the jacket temperature.

The calorimetric observations during an experiment consisted of: (a) a fore period of 20 min

during which the reaction vessel, containing oxygen at atmospheric pressure, remained closed, and

readings of the resistance of the platinum thermometer were taken every 2 min; (b) a "reaction"

period during which the reaction took place,

with a period allowed for equilibrium to be

reestablished in the calorimeter, and during which

readings of the resistance of the platinum thermometer were taken about every 15 sec or every

minute, depending on the shape of the timetemperature curve; and (c) an after period of 20

min during which the reaction vessel remained

closed, the calorimeter temperature was slightly

266-273
below the jacket temperature, and readings of

the resistance of the platinum thermometer were

taken every 2 min.

The manipulation of the apparatus controlling

the reaction during a combustion experiment was

as follows: Before the calorimetric experiment,

the two absorption tubes for water and carbon

dioxide were flushed with hydrogen and weighed

by a method previously described [12, 13, 14]. The hydrocarbon inlet tube Avas flushed with

helium to remove oxygen from this line and the

rest of the reaction vessel then flushed and left

filled with oxygen at atmospheric pressure. During the fore period, the rates of flow of the

primary and secondary oxygen and gaseous hydrocarbon were regulated through bypass flow- meters. At the end of the fore period, the threeway stopcock outlet on the reaction vessel was

opened to the absorption tubes, the primary and

secondary streams of oxygen were turned into

the vessel, the spark was turned on, and the

hydrocarbon was then turned into the vessel. The sparking was continued for 15 sec, or until

the flame was started, as indicated by the flowmeter at the end of the line. The flame was

allowed to burn until a final temperature slightly

below the jacket temperature was reached, when

the flame was extinguished by turning off the

hydrocarbon. The time of combustion was

usually about 22 min. The primary and secondary

streams of oxygen were left on for an additional

10 min and then cut off. The reaction vessel was closed by setting the three-way stopcock at the outlet such that the oxygen would bypass

the reaction vessel but would flow through the

absorption tubes. Thus, all the water vapor not

in the calorimetric reaction vessel was swept into

the absorption tube. An additional period of about 6 min was allowed for equilibrium to be

established before starting the after period. After

the experiment, the absorption tube for water was flushed with hydrogen and weighed to obtain

the amount of water carried out of the calorimeter

as vapor. The absorption tubes were replaced on the train and the reaction vessel flushed with

oxygen overnight to carry all the water and carbon

dixoide into the absorption tubes. Both tubes were then flushed with hydrogen and weighed.

The mass of carbon dioxide produced was used

to determine the amount of reaction, and the stoi- chiometric ratio of the masses of carbon dixoide

and water was used to check the purity of the

reaction of combustion.

The corrected increase in temperature of the

calorimeter system, ARc, expressed as the increase

in resistance in ohms of the given platinum thermometer at a mean temperature of 25° C, was

taken as the difference in the resistance of the

thermometer between the beginning of the after period and the end of the fore period, corrected

for heat of stirring and thermal leakage [15].

2. Determination of the "Ignition" Energy

Experiments to determine the energy associated

with the ignition and extinction of the flame

("ignition" energy experiments) were performed

in the same manner as the regular combustion

experiments, except that the flame was allowed

to burn only long enough to be sure a steady flame was attained. The flame was usually left burning

for about 40 seconds. The initial temperature in these experiments was a fraction of a degree below

the jacket temperature, and the rise of temperature was about 0.1 deg. Experiments were also performed in which only sparking energy was

added to the calorimeter.

The mean value for the "ignition" energy,

which is the energy associated with the process of

ignition and extinction of the flame, but not in- cluding any part of the heat of combustion,

obtained from seven experiments with 1,3-butadiene and two experiments with 1,2-butadiene,

with an average of 0.0005 mole of butadiene

burned in each experiment, was found to be 33.1 j, witb a standard deviation of ±2.8 j. In sep- arate experiments in which no hydrocarbon was

burned and sparking alone for the standard time

occurred, the sparking energy was found to be

31.1 j with a standard deviation of ±0.8 j. In making these calculations, the value of Es , the

standard energy equivalent, was taken as 154,446

abs j/ohm.

For the present experiments, the ignition energy

for the standard time (15 sec) of sparking was

taken as the weighted mean of the foregoing values,

31.3 j with a standard deviation of 0.8 j.

3. Reduction to the Standard Calorimetric Process

The process that actually takes place in the

calorimetric reaction vessel during a combustion

experiment is the following:

267-274
nC4 H6 (gas, 1 atm,? r )+ (m1 +m2 +m3 )02

(gas, 1 atm,^) = [rC02 +m2 02+6H2 0]

(gas, latm,^) + N302 + cH20](gas, 1 atm,f/) +

(a— b—c)H20(liq, 1 atm, t f). (8)

The energy evolved in this reaction and including the ignition energy is q = Es ABc

. In the fore- going equation, t r is the temperature of the. room;

t m and t f are the mean and final temperatures,

respectively, of the calorimeter; n is the number

of moles of hydrocarbon entering the calorimeter;

(?n 1 +7n 2 + m3 ) is the number of moles of oxygen

entering the calorimeter; mi=—n is the number

of moles entering during the actual combustion

period and being used in the combustion; m2 is the excess number of moles entering during the

actual combustion period and leaving the calorimeter as a mixture with r=4«< moles of carbon

dioxide and b moles of water vapor; m3 is the

number of moles of oxygen entering the calorimeter during the flushing immediately following the

actual combustion period and leaving the calorimeter as a mixture with c moles of water vapor;

(a-b-c) is the number of moles of water left in the

calorimeter in the liquid state; and a=3n is the

total number of moles of water formed in the combustion. The quantity c also includes a very

small amount of water left in the calorimeter in the gaseous state.

It is desirable to correct the results of each

calorimetric experiment to a common basis for comparison. This can be done by adjusting all results to the basis of a "standard calorimetric

process" defined by the equation

-».C4 H6 (gas, 1 atm, Z25) + (m1 + m2 )02 (gas, 1 atm, £25 ) = [rC02 +m2 G2 ](gas, 1 atm, £ 25 ) +

«,H20(liq, 1 atm, £25 ) (9) The energy evolved in this reaction is q c

. For the present experiments the various quantities have. the. values

mx =-^n, m2 =-^ n, r=4n, and a = 3n.

The difference between the energy, q c , evolved

in the standard calorimetric process expressed by

eq 9, and that evolved in the actual calorimetric

process expressed by eq 8, but including the

energy of ignition, is q —q=— (<fc+2,+gi)-

The energy associated with the adjustment of the composition of the carbon dioxide-oxygen

mixture issuing from the calorimeter in the individual experiments to the average composition as expressed in the "standard calorimetric process"

is negligible. The quantities qg and q v were

evaluated by the relations:

q g =Gl [>i(t-t25 )} +

C2 [m1 (tr —t25)+'m2 (t r ~tm)+m3 (tr —tf)] 4- C3 [b(t25 -tm)+c(t25 -tf)] +

C4[(o -b -c) (t25 -tf) ] +

C

6 [r (t25 -tm)],

qv =-(b+c)[AHv];

where d=80.1, C2 =29.4, C3 =33.6, C4 =75.3,

and C5 =37.1 are the approximate heat capacities

of butadiene (gas) , oxygen (gas) , H2 0(gas) , H2 0(liq)

,

and C02 (gas), respectively, in j/deg mole, and

A//^ =43,992 abs j/mole is the heat of vaporization

of water at 25° C and saturation pressure. To obtain the values of the standard heat of reaction, AH°, from the standard calorimetric

process indicated by eq 9, it is only necessary to take account of the change in heat content with

pressure at constant temperature for each gas

from its given pressure to zero pressure, so that

each substance will have the heat content of the

thermodynamic standard state. Since this cor- rection will not be significantly different for the

two isomers, the ratio of the values of AFI for the

standard calorimetric process will also be the ratio

of the values of AH0 for the standard thermodynamic process.

VII. Results of the Present Investigation

The results of the calorimetric combustion

experiments for 1,3-butadiene and 1,2-butadiene

are given in tables 1 and 2, respectively. For

these calculations, the. value of E„ the energy

equivalent, was taken as approximately 154,446

j/ohm. The value of B were calculated from eq 3

268-275
Table 1. Results of calorimetric combustion experiments on 1 ,3-butadiene

Experiment Mass of carbon di- oxide B

Deviation from mean

Ohms g } i i Ohmslg COi Ohmsjg CO2

1 0.38S04S 4. 17091 +16. 5 -342.3 31.3 0. 0934941 -0. 0000514

2 .381756 4. 10179 -2.4 -331.2 31.3 . 0935478 +. 0000023 3 ... . 381025 4.09487 +0.1 —360.

3

31. 3 . 0935695 +. 0000240

4 . 397671 4. 27289 -2.8 -355. 4 31.3 . 0935637 +. 0000182

5 . 384888 4. ldoay —16.

8

—352. 2 31.

3

. 0935665 +. 0000210

G .390584 4. 19985 -IS. 6 -362. 7 31.3 . 0935390 -.0000065

.391438 4. 20192 -23.9 -236. 5 31.3 . 0935099 -.0000356

8 ____ .378484 4. 07076 —17.2 -389.7 31.3 . 0935735 +. 00002SO

Mean.. ... . ... ... Standard deviation of the mean.. ..... . .. ..0. 0935455

-±. 0000104

Table 2. Results of calorimetric combustion experiments on 1 . 2-butadiene

Experiment Mass of carbon di- oxide

So Qi B

Deviation from mean

Ohms 9 j i i Ohmsjg CO2 Ohmslg CO2

1 0. 384743 4. 04783 -13.2 -304. 9 31.3 0. 0955079 -0. 0000048

0 . 3S0613 4. 00684 -5.5 -345. 8 31.3 . 0955080 -. 0000047 3 .388498 4. 09171 -10.1 -368.8 31.3 . 0954977 -.0000150

4 .395315 4. 16322 -7.7 -3S3.4 31.3 . 0955137 +. 0000010

5 . 397521 4.18337 -10.8 -352. 4 31.3 . 0955377 +. 0000250

6.... .38S279 4.08829 -16.6 -364.3 31.3 .0955112 -.0000015

0. 0955127 ±. 0000055

From these data, the ratio of the heat of combustion of 1, 2-butadiene to that of 1 ,3-butadiene is

(-AHc°)b/(-AHc0

) a =Bb IBa = 1.021029 ±0.000256.

(14)

The values previously reported [1] for the

heats of combustion and formation of 1,3-

butadiene (gas) are C4H6 (l,3-butadiene, gas)+~ 02 (gas) =

4C02 (gas)+3H2 0(hquid), (15)

-A£ft48 . I6 = 607.91 ±0.23 kcal/mole.

4C(c, graphite) 4- 3H2 (gas) =

C4 H6 (l,3-butadiene, gas),

AH/s98.16 =26.75±0.23 kcal/mole. (16)

The heat of isomerization at 25° C thus

becomes (from eq 7):

1,3-butadiene (gas) = 1, 2-butadiene (gas)

(17)

AH° (isomerization) =12.78 ±0.16 kcal/mole.

The heats of combustion and formation of

1, 2-butadiene become:

C4H6 (1, 2-butadiene, gas) + 7^- 02 (gas) =

4C02 (gas) +3H2 0(liquid), (18)

-Aff48 . 15 = 620.69 =0.28 kcal/mole.

4C (c, graphite) +3H2 (gas) =

C4H6 (1, 2-butadiene, gas),

A#/298.ie =39.53±0.28 kcal/mole. (19)

269-276
VIII. References

[1] E. J. Prosen and F. D. Rossini, J. Research NBS 34, 59 (1945) RP1628.

[2] E. F. Mueller and F. D. Rossini, Am. J. Phys. 12,

1 (1944).

[3] Selected Values of Chemical Thermodynamic Properties. National Bureau Standards. Values of Constants. (December 31, 1947.)

[4] G. P. Baxter, M. Guichard, and R. Whytlaw-Gray,

J. Am. Chem. Soc. 69, 734 (1947).

[5] F. D. Rossini and W. E. Deming, J. Wash. Acad. Sci.

• 29, 416 (1939).

[6] E. J. Prosen and F. D. Rossini, J. Research NBS 27,

289 (1941) RP1420.

[7] F. D. Rossini, BS J. Research 12, 735 (1934) RP686.

[8] F. D. Rossini and J. W. Knowlton, J. Research NBS

19, 249 (1937) RP1024.

[9] A. R. Glasgow, Jr., N. C. Krouskop, J. Beadle, G. D.

Axilrod, and F. D. Rossini, Anal. Chem. 20, 410

(1948).

[10] A. J. Streiff, E. T. Murphy, J. C. Zimmerman, L. F. Soule, V. A. Sedlak, C. B. Willingham, and F. D.

Rossini, J. Research NBS 39, 321 (1947) RP1833

[11] M. Shepherd, Anal. Chem. 19, 77 (1947).

[12] E. J. Prosen and F. D. Rossini, J. Research NBS 33,

255 (1944) RP1607.

[13] F. D. Rossini, BS J. Research 6, 1 (1931) RP259.

[14] F. D. Rossini, BS J. Research 6, 37 (1931) RP260.

[15] J. R. Eckman and F. D. Rossini, BS J. Research 3, 597 (1929) RP111.

Washington, October 29, 1948.

270-277
Journal of Research of the National Bureau of Standards Vol. 61, No. 4, October 1958 Research Paper 290

1

Heats of Formation of Diborane and Pentaborane

Edward J. Prosen, Walter H. Johnson, and Florence Y. Pergiel

The heats of formation of diborane and pentaborane have been determined by measure- ments of the heats of decomposition into amorphous boron and hydrogen in a calorimeter. The heats of formation at 25° C, from amorphous boron and hydrogen, are 6.73 ±0.52 kcal/ mole for diborane (gas) and 12.99 ±0.39 for pentaborane (gas).

1. Introduction

In order to ascertain the bond energy relations in the boron hydrides, precise values of the heats of formation of these substances from the elements are needed. Diborane, B2 H6 , and pentaborane, B5 H9 , were chosen for investigation as two of the simplest

members of this class of compounds.

The measurements reported in this paper were made in 1948 but have not been previously published.

No value for the heat of formation of pentaborane was available at that time. The value for the heat

of formation of diborane given by Roth and Borger, — 44 kcal/mole, [1, 2]

1 was based on measurements of

the heat of hydrolysis of diborane to boric acid, the

heat of combustion of boron to boric oxide, and the

heat of solution of boric oxide. This value was very

uncertain because it depended directly upon the

heat of combustion of elemental boron, a quantity

which could not be determined with any precision.

However, it was found that diborane and pentaborane could be decomposed quantitatively and

rapidly at 600° C into amorphous boron and gaseous

hydrogen. Hence this decomposition reaction could

be employed calorimetrically to give values of the

heats of formation of diborane and pentaborane

independent of the value for the heat of combustion

of boron.

2. Experimental Procedure

2.1. Materials

The diborane and pentaborane samples were obtained from the Naval Research Laboratory, Washington, D. C, through the courtesy of R. R. Miller.

A similar sample of diborane supplied to the Ohio

State University was found by the cryoscopic method

to have a purity of 99.95 mole percent [3]. The pentaborane was produced by the fractional

pyrolysis of diborane. A sample of the same lot supplied to the Ohio State University was found by

the cryoscopic method to have a purity of 99.97

mole percent [4]. Analysis by the mass spectrometer showed no impurities other than boron hydrides

with none heavier than B5 H9 [5].

2.2. Apparatus

The calorimeter was of the isothermal-jacket

type; the jacket temperature was maintained constant within ±0.001° C during each experiment.

Details of the calorimeter assembly have been

described in previous reports from this laboratory

[6,7].

1 Figures in brackets indicate the literature references at the end of this paper.

The calorimetric vessel used for the decomposition

of diborane and pentaborane is shown in figure 1. It consisted essentially of a quartz tube (A) upon

which was wound a nichrome wire heating coil (B)

surrounded by a silver radiation shield (C) and a vacuum jacket (D). The heating coil had a total resistance of 190 ohms and was tapped (E) so that

the upper portion had a resistance of 127 ohms.

Quartz wool plugs (F) were inserted in the tube

above and below the heating coil to retain the solid

products within the heated zone. The exit vapors

were carried out through the glass helix (G) to cool

them to the calorimeter temperature.

Calorimeter temperatures were determined by

means of a platinum resistance thermometer in conjunction with a Mueller bridge. The quantity

of electrical energy was determined from the current,

voltage, and time of current flow. The current and

voltage were determined by means of a White double

Figure 1.- Calorimetric reaction vessel. 271-247
potentiometer from measurements of the potential

drop across appropriate standard resistors included

in the power circuit [8]. Timing of the experiments was done by reference to standard seconds-signals

produced at the National Bureau of Standards. All

equipment was calibrated in terms of standards

maintained at the Bureau.

2.3. Procedure

a. Reaction Experiments

(1) Diborane. The gas train used for the diborane

decomposition experiments is shown in figure 2. The diborane was contained in a steel cylinder fitted with a needle valve and connected to the system

through a flowmeter and a mercury float valve.

Before each experiment the cylinder was immersed

in liquid nitrogen, and traces of hydrogen (produced

by slow decomposition of diborane into higher

boranes) were removed by evacuation. After re- moval of the hydrogen the valve was closed and dry

ice was substituted for the liquid nitrogen; at the

temperature of dry ice, the vapor pressure of diborane

is approximately 2 atm and the vapor pressures of the higher boranes are negligible. Helium was

passed through the system at a constant rate throughout the experiment. It was purified by

passing successively over copper oxide at 600° C

1

, ascarite, magnesium perchlorate, and phosphorus

pentoxide before it entered the system.

Temperatures were observed at 2-min intervals

during a 20-min "fore" rating period. At the end

of this period the current was switched from an ex- ternal "spill" resistor (having the same resistance

as the heater) into the upper portion of the calori- metrie vessel. After a warm-up period of 2 min

the needle valve was opened, which permitted the

diborane to pass into the vessel. The flow of diborane was cut off after 16 min and the float valve

closed. Four minutes later the current was swtehed

to pass through botli portions of the heater; this completed the decomposition of the polymerized

material usually formed near the lower end of the

upper portion of the heater. By means of appropriate resistors in the circuit, the current was nearly

constant in both cases. During this time readings

of current and voltage were made on alternate

minutes, and temperature readings were made at 1-min intervals. When the desired calorimeter

temperature was obtained the electric current was

discontinued. Temperature measurements were continued at 1-min intervals until thermal equilibrium was reestablished, after which observations were made at 2-min intervals during a 20-min "after"

rating period.

The gas mixture of helium and hydrogen passed

out of the calorimeter through a trap cooled in liquid nitrogen, a copper oxide furnace maintained

at 600° C, and a weighed absorption tube containing

magnesium perchlorate and phosphorus pentoxide.

HeDIBORANE

VAC

Figure 2. Gas train used in thermal decomposition of diborane. 272-248
Firu'RE 3. Gas train for use in decomposition of pentaborane (B5H9).

The trap was included as a safety measure, to pre- vent the diborane from reaching the furnace in the

event of incomplete decomposition. No material was collected in the trap in any of these experiments.

The quantity of reaction was determined from

the amount of hydrogen which was burned in the

furnace and collected in the absorption tube as water.

(2) Pentaborane. The gas train used in the

experiments with pentaborane is shown in figure

3. The pentaborane was inclosed in an internal

breakoff ampoule. For each experiment the system was evacuated and a portion of the pentaborane

transferred into the bubbling vessel. The experiments were carried out in the same manner as with

diborane except that purified helium was bubbled

through the pentaborane at 0° C in order to carry it into the calorimetric vessel. After each experiment,

the remainder of the pentaborane in the bubbler, as

well as that remaining in the original ampoule, was

transferred to a second ampoule and sealed in vacuum.

b. Calibration Experiments

The calibration experiments were performed in exactly the same manner and using the same system

as with the decomposition experiments except for omission of the boron hydride. Because the system

used for pentaborane differed slightly from that

used for diborane, a separate series of calibration

experiments was performed.

3. Results

The results of the calibration experiments for the

diborane system are given in table 1 in which E

corresponds to the electrical energy added to the

system, ARc the increase in resistance of the platinum

thermometer, and Es = EjARc, the energy equivalent

of the system.

The results of the diborane decomposition experiments are given in table 2, where q is the total energy

absorbed by the system and is given by the following

relationship

(ARc)(Es ) = q. This value of q when corrected for qe , the correction calculated from the heat capacities of the gases

involved, and subtracted from E, the electrical Table 1.

Results of the electrical calibration experiments on

the diborane system

Experi- ment E ARc E,

j Ohm j/ohm

1 49480.

9

0. 381239 129790

2 50329.

8

. 387803 129782 3 49804. 4 . 383708 129798

4 51630. 9 . 397799 129791

5 49551. 6 . 381761 129797

Mean

Standard deviation of the mean

129792 ±3

Table 2. Results of the diborane decomposition experiments

Exper- iment E 2 is 1> B2 Ht — AH

(25° C)

12

3

4

5

j 51311.2

48536. 9

48557. 9

49008. 7 48704.

1

Ohm

0. 397528

. 379034

. 377216

. 379105

. 376538

j

51596. 0

49195. 6

48959.

6

49204. 8

48871.

6

j

0. 6 -2.2

2.3

1. 1 0.3

j -284. 2 -660. 9 -399. 4 -195.0

-167.2

Mole

0. 010206

.021851

. 015966

. 007213

. 005444

kj/mole

27. 85

30. 25 25.02

27. 04

30.71

Meai

Stan

1 - --- 28. 17 lard deviation of the mean ±1.05

273-249
energy added to the system, yields qc, the energy

absorbed by m moles of reaction, or: I<J—(q—qg )=qc

. The heat of reaction at 25° C is then given by

the ratio of qc to rn, or:

qc /m = AH joules/ mole.

To convert to the conventional thermoehemieal

calorie, the following relationship was used:

1 calorie =4. 1840 joules.

The results of the calibration experiments on the

pentaborane system and the results of the pentaborane decomposition experiments are given in tables 3 and 4, respectively.

Table 3. Results of the electrical calibration experiments on

the pentaborane system

Kj pel i- E E, ment

i Ohm Hoh m

1 48651.0 0. 374654 129856

2 49904. 1 . 384457 129S01

3 48058. 8 . 370289 129787

4 49314.9 . 379834 129833

5 48547. 3 .374191 129739

6 48495.

9

. 373680 129779

48657.

3

. 374996 129754

8 48529. 6 . 373886 129798

Mean 129794 Standard deviation of the mean. .

.

±14

Table 4. Results of the pentaborane decomposition experiments

lixper- iment E it JhHt -MI

(25° C)

r i Ohm j j j Mole kjlmole

1 49998.

5

0. 386650 50185. 6 +0.4 -186. 7 0. 003409 54. 77

2 49709.

6

. 384273 49876. 3 -0. 1 - 166. 8 IIII28N9 57. 74

3 49802. 4 . 385107 49984. 6 +0.2 -182.0 . 003560 51. 12

4 Ittxor. s . 385605 50049.

2

+1.2 -241.2 . 004353 55.41

5 49709. 2 . 385471 50031. 4 +1.2 -321.0 . 006037 53. 17 6 51323. 0 . 397303 51567. .5 +0. 8 -243.

1

. 004508 53.93

Mean

Standard deviation of the mean

54. 36 ±0.91

The heats of decomposition obtained for the

reactions of decomposition are given by the following

equations:

B2H3 (gas) =2B (solid, amorphous) ±3H2 (gas),

AH(25° C)= -6.73 ±0.52 kcal/mole,

B5H9 (gas) =5B (solid, amorphous) + 9/2 H2 (gas),

AH(25° C)= -12.99 ±0.39 kcal/mole.

The uncertainties assigned have been taken as twice the standard deviation of the mean of the

experimental values, combined with reasonable

estimates of all known sources of error. Bv taking the amorphous form as the reference

state of boron and 7.30 ±0.10 kcal/mole [9] for the

274-

heat of vaporization of pentaborane, the following

heats of formation are obtained:

AHf (25 C)

kcal/mole

BS H6 (gas) 6.73 ±0.52

B6 H, (gas) 12.99 ±0.39

B5 H9 (liquid) 5.69 ±0.40

4. Discussion

It was not possible to recover the finely divided

boron quantitatively from the reaction vessel because

of its tendency to adhere to the walls of the vessel

as well as to the quartz wool plugs. It was therefore

not feasible to obtain an accurate check on the

completeness of the decomposition by determining

the stoichiometric ratio between the masses of boron

and hydrogen. In order to determine the presence

of hydrogen, either chemically bound or adsorbed,

samples of the boron produced were heated to 700° C in vacuum. Although traces of hydrogen

were detected in some cases it is not likely that any

significant error was introduced in the final result since the quantity of reaction in each case was based

upon the mass of hydrogen evolved. Obviously, if all the boron-hydrogen bonds were of the same

energy, the heat of decomposition as measured

would be independent of the proportion of hydrogen

removed in the process. The possibility that an extremely stable hydride was present was ruled out

because portions of the residue treated with chlorine

at 400° C were completely converted to boron

trichloride [10]. The Constitution and Microstructure Section of the Bureau examined portions of

the residue by X-ray diffraction methods. The

absence of a pattern indicated that the boron was in an amorphous form.

In view of this information we conclude that the

reaction of decomposition is quantitative and that

the only products are amorphous boron and hydrogen.

The thermal decomposition is probably the most

convenient method for preparation of small quantities of high-purity boron.

5. References

[1] W. A. Roth and E. Borger, Ber. [B] 70, 48 (1937).

[2] W. A. Roth, Z. Naturforsch. 1, 574 (1946).

[3] E. M. Carr, J. T. Clarke, and H. L. Johnston, J. Am.

Chem. Soc. 71, 740 (1949).

[4] J. T. Clarke and H. L. Johnston (private communication).

[5] V. H. Dibeler, F. L. Mohler, L. Williamson, and R. M.

Reese, J. Research NBS 44, 489 (1950) RP2095.

[6] J. R. Eckman and F. D. Rossini, J. Research NBS 3, 597 (1929) RP1 1

1

[7] E. J. Prosen and F. D. Rossini, J. Research NBS 27, 289 (1941) RP1420.

[8] E. J. Prosen and F. D. Rossini, J. Research NBS 33, 255 (1944) RP1607.

[9] W. H. Evans and D. D. Wagman, (manuscript in preparation).

[10] E. H. Winslow and H. A. Liebhafsky, J. Am. Chen.. Soc. 64, 2725 (1942). Washington, June 29, 1958.

250
JOURNAL OF RESEARCH of the National Bureau of Standards — A. Physics and Chemistry

Vol. 72A, No. 5, September-October 1968

Studies in Bomb Calorimetry. A New Determination of the

Energy of Combustion of Benzoic Acid in Terms of Electrical Units

K. L. Churney and G. T. Armstrong

Institute for Basic Standards, National Bureau of Standards, Washington, D.C. 20234

(July 20, 1968)

The heat of combustion of NBS Standard Sample 39i of benzoic acid under standard bomb conditions has been determined in terms of electrical units. A value of — 26,434.0 J g

_I was obtained. The total uncertainty in our determination is estimated to be ±3.3 J g

-1

. The uncertainty due to random

errors was 1.7 J

g~' and is based on the appropriate factors for the Student t distribution at the 95 percent confidence limits for eleven determinations of the energy equivalent of the calorimeter and six determinations of the heat of combustion of benzoic acid. The principal systematic error, neglect of surface temperature correction for our calorimeter, has been assigned a value of ±2.6 J g" 1 until more

reliable estimates of the correction can be made. Particular emphasis was placed on improving the precision of a calorimetric measurement over those previously obtained in this laboratory by the use

of more sensitive auxiliary measuring equipment and more accurate procedures to evaluate the cor- rected temperature rise.

Key Words: Benzoic acid, heat of combustion; bomb calorimetry, procedures and errors; heat of combustion; bomb-calorimeter, electrical calibration; Dickinson calorimeter.

1 . Introduction

Benzoic acid has served for many years as a ref- erence material of known energy of combustion for calibrating bomb calorimeters. At the National Bureau

of Standards (NBS), the Heat Division of the Institute

for Basic Standards, or its predecessors, has certified the energy of combustion of various batches of benzoic

acid in terms of electrical units for this purpose.

Maintenance of a capability of a high degree of accuracy

and precision in bomb calorimetry is a prerequisite

for this certification activity.

The calorimetric measurements on which the

certifications at NBS have been based have been made

in most instances with a calorimeter of the same

design, except for slight modifications, as that used

by Dickinson [l]. 1 In July of 1964, we started a study

whose goal was to design a new bomb calorimeter

capable of higher accuracy and precision than existing

calorimeters. The first step in this project was a study

of the performance of an existing Dickinson calorimeter

(NBS 57662). The study was made in the hope that it would lead to a better understanding of the limitations

inherent in the Dickinson calorimeter.

1 Figures in brackets indicate the literature references at the end of this paper.

A second reason for making the study is that the

last certification of benzoic acid in terms of electrical units at NBS was made in 1942 [2]. More recent certifi- cations have been based upon intercomparison of benzoic acid samples. It appeared likely that a certification in terms of electrical units could now be

made with greater accuracy than had been possible

heretofore, because of the substantial improvement in the precision and accuracy of the auxiliary measuring

instruments of the calorimetric station since 1942. Although there was no reason to suspect that the

intercomparisons of samples had introduced undetected systematic errors in the certification of batches

of benzoic acid, we wished to confirm the absence of

such errors. The general features of the calorimeter and its method of operation have been adequately described

elsewhere [3, 4, 5]. A summary of pertinent details

is given in sections 2 and 4. The basis for the correction of the observed temperature rise of the calorimeter for the effects of heat

transfer from its environment, Newton's cooling law,

and of stirring energy is found in the discussion of

Coops, Jessup, and Van Nes [4]. The particular

method of calculation used in this work is described

in section 5 in some detail because of the higher

accuracy obtained by the use of fewer approximations.

275-453
Previous analysis of extensive calorimetric data

from this laboratory had suggested that the uncertainty in our calorimetric measurements might be

due mainly to the uncertainties in temperature meas- urements during the drift periods. Increasing the

precision of the measurements of the resistance of

the platinum thermometer led to a substantial improvement in the precision of measurement of the

calorimeter temperatures but revealed the presence

of small systematic deviations from Newton's cooling

law. Modification of the calorimeter and our method

of operating it suggested some possible explanations

for these systematic deviations and reduced but did

not entirely eliminate them as is discussed in sections

3, 5.1a, and 6.2. A series of electrical calibrations to determine the

energy equivalent of the calorimeter and a series of

benzoic acid combustions to determine the energy

equivalent, in terms of electrical standards, of the

combustion of benzoic acid are described in sections

4 and 5. Presentation of the results is completed in section 6 by an analysis of random and systematic

errors.

2. Experimental Apparatus

The calorimetric apparatus consists of a stirred- water calorimeter surrounded by an isothermal jacket.

The calorimeter consists of a closed can which contains a stirrer, a platinum resistance thermometer

placed near the can wall, a combustion bomb with fuse

leads and handle, an electrical heater that fits snugly

around the lower half of the bomb, and a weighed,

fixed, quantity of water sufficient to be in contact with

the calorimeter lid after the calorimeter has been

assembled. The calorimeter temperature is always

kept below that of the jacket.

2.1. Calorimeter and Jacket

The calorimeter and jacket are essentially the same

as described previously by Jessup [6], except for the

following modifications.

The calorimeter jacket has been enclosed by an air bath, kept near 27.5 °C with a regulation of ±0.2 °C

by an on-off controller. The air bath was required to make sure the average jacket temperature did not change with time. Thermocouple measurements had

shown the lid (i.e., top) of the jacket was about 0.006 °C

colder than the rest of the jacket, presumably due to poor water circulation in the lid, when the room temperature was 3 °C below that of the jacket. The jacket

temperature regulator was replaced by a commercially

available proportional controller having reset action

and a nickel resistance thermometer for a sensor. To insure a constant stirring rate, the calorimeter

stirrer was turned by a synchronous motor. The oxygen combustion bomb and its internal fittings are those described previously [7], except for two

changes. The fuses were made of 2 cm of 0.002-in-diam

platinum wire rather than a combustible metal to eliminate any energy contribution due to fuse combustion as described by Prosen [5]. The stem of the bomb

needle valve was modified so that the inside of the bomb could be directly connected to the pressure

gage of the oxygen manifold during filling, for a more

accurate pressure measurement.

The calorimeter heater is an improved version of

a type described previously [8]. It consists of a

32-fl heater element of glass-insulated, 0.010-in-diam

Advance wire which was soft soldered at both ends to 18-gage, Formvar-covered, copper, current leads. The

element was inserted in a

3/i6-in-diam 0.030-in-wall,

soft copper tube. The tube was flattened against the

element after the space between the tube and element was filled with epoxy-resin cement. The tube (sheath)

length was selected so that, after the heater was coiled

to fit the bomb, at least 20 cm of each current lead of

the heater element was inside the calorimeter. The

length of each current lead between the calorimeter

and jacket was 5 cm. Of the two 26-gage copper potential leads, one was attached to a current lead at the

calorimeter boundary, the other to the remaining

current lead at the jacket boundary.

Four jacket terminals pass through the jacket to "temper" thermally the heater leads (or fuse leads in the case of a benzoic acid combustion). They are the same as those described previously [9], except the

electrical insulation was changed to a 0.008-in-thick

layer of Teflon tape and epoxy-resin cement. The insulation resistance both from the heater element to its tube sheath and from the jacket terminals to the jacket

wall is greater than 100 MO at 100 V.

2.2. Calorimeter Temperature Measurement

Equipment

The platinum resistance thermometer is of the

Meyers type of construction [10], having a 20-cm-long,

7-mm-diam Pyrex sheath, and an ice-point resistance

of about 25.5 fi. The resistance element is wound in a

single coil very close to the glass sheath to provide

fast response and to minimize self-heating. For these

experiments the thermometer head was protected from

thermal drafts by a cylindrical aluminum shield cov- ered with asbestos and aluminum. The thermometer

leads are connected to the bridge via a selector box.

The thermometer was reproduceably inserted to a depth of 21 cm in the calorimeter can (height, 23 cm).

The sensitivity of the measurement of the change in resistance of the platinum resistance thermometer was increased from 10"5 £1 (10~ 4 °C) to 10"6 H (10"5 °C).

This was accomplished by replacing the G-2 Mueller

bridge (smallest dial unit 10~4 £1) by a G~3 Mueller

bridge (smallest dial unit 10~5 fl) and using a more

sensitive detector of the bridge imbalance.

The main features of the G—3 Mueller bridge are discussed briefly elsewhere [10]. Special shielding of

the bridge and alteration of the heater supply for the

bridge thermostat have' been described previously [11]. 276-454
Two galvanometer systems were used with the

bridge. The new and more sensitive system consists

of a photoelectric amplifier, having a taunt suspension

galvanometer, and secondary galvanometer. A V2-mm

deflection of the secondary galvanometer corresponded

to a change in thermometer resistance of 1 fxfl (1 X 10"5 °C), with bridge current reversal and a thermometer

current of 2 mA. The less sensitive galvanometer

system, essentially the same as that described pre- viously [12], but with a somewhat more sensitive

galvanometer, was used to measure the thermometer

resistance only during the rapid temperature rise of the

main period of an electrical calibration experiment.

2.3. Ignition Energy Circuit The electrical energy required for ignition of the

benzoic acid pellet was determined by measuring the

voltage before (about 25 V) and after (about 24 V) the

discharge of a capacitor having a measured capaci- tance of (40.6 ± 0.5) X 103 /xF. The circuit is similar to that described by Boyd [13]. The fraction of the energy released by the capacitor

that is dissipated in the part of the circuit external to the calorimeter was 0.25±0.10. The first step in determining this number was to measure the corrected

temperature rise caused by 50 complete discharges

of the capacitor, when a short was connected across

the fuse electrodes in the bomb interior. The fraction

of energy dissipated external to the calorimeter for this particular experiment was calculated using the known

capacitance, voltages, etc. The fraction dissipated in actual combustion experiment was calculated by combining this data with the measured lead resistances

and the resistances between the bomb fuse terminals

in the actual combustion experiments. The main

source of the estimated uncertainty in the fraction is the assumption that the combustion fuse resistance

does not change before it melts.

2.4. Electrical Calibration Circuits The basic circuit for supplying electrical power to the

heater has been described elsewhere [4]. Two separate, commercially available, Zenerdiode-stabilized, d-c power supplies were used to supply electrical energy to the heater. One unit, with

a range of 0-2 A and 0-60 V and operated in the

constant-voltage mode, was used to supply power at levels of 60 and 110 W to the heater. The other unit,

having a range of 0-5 A and 0-105 V and operated

either in the constant-current or constant-voltage

mode, was used to supply power at 270 W. The stabilities of these power supplies in the constant voltage

mode was 2 to 10 ppm as inferred from measurements

of heater voltage.

2 The relative equality and stability (1 yrj of the resistors are ±0.0015 percent and ±0.0005 percent, respectively.

3 The other 1,000-Q resistor is used only when a volt-box ratio of 1:100 is required.

The time interval during which power is supplied to the heater was measured with a time counter accurate

to within ±0.0001 s. The heater current is determined by measuring the

voltage across a Reichsanstalt-type, 0.01-fl standard

resistor. The potential drop across the heater is determined

with a 1 : 1000 nominal voltage divider or volt-box con- nected to the heater potential leads. The resistive elements of the volt-box are: (a) a commercially available unit consisting of ten 2 equal

10,000-fl resistors and two 1,000-fl resistors hermetically sealed in an oil-filled box, and (b) a 100-fl standard

resistor. Permanent copper links connect the 10,000-fl

resistors in series with the parallel combination of one 3 1,000-fi resistor and the standard resistor. Movable

shorting bars are used to connect the 10,000-fl re- sistors in parallel with this combination. The bars are made from copper, have a 1-cm-square cross section,

and mercury-wetted surfaces to make electrical connections.

The volt-box is calibrated by measuring the resist- ance of the 100-1 ,000-fl parallel combination and then

the resistance of all the resistors connected in parallel. In calculating the volt-box ratio, use is made of the

fact that, because of the close matching of the 10,000-fl

resistors, the ratio of series to parallel resistance of

the 10,000-fl resistor set is equal to 100 : 1 within 1 ppm

[14].The imprecision of the volt-box ratio in 9 determinations made during the course of the electrical calibra- tions was 0.6 ppm (standard deviation of a single

determination). This is approximately the a priori

estimated precision of a measurement. The inaccuracy was estimated to be between 2 and 10 ppm.

Potential measurements were made to 0.03 tiV with

a six-dial double potentiometer using the more sensitive of the two galvanometer systems described in section 2.2. The range of the potentiometer extends

to 0.111111 V in steps of 0.1 /xV. The potentiometer

voltage reference consisted of three saturated, Weston

standard cells mounted in an improved version of a constant temperature box similar to one described

previously [15]. Since both short- and long- (3 months)

term temperature regulation of fhe box, as indicated

by a platinum resistance thermometer in the cell compartment, was within ±0.001 °C, the standard

cell voltage could be assumed to be constant to better

than 1 ppm during the course of the electrical calibra- tions (see sec. 5.3). The potentiometer interdial corrections were determined in the laboratory before and

after the set of electrical calibration experiments. The

potentiometer ratio was checked more frequently

using an auxiliary circuit similar to that described

elsewhere [16]. Its constancy, based on eleven determinations during the course of the electrical calibrations, was 1 ppm (standard deviation of a determination).

The resistors of the auxiliary circuit and the volt-box as well as the standard current resistor were kept in a

stirred-oil bath whose temperature was kept within

0.01° of 33.16 °C. At this temperature, the rate of

277-455
change of the resistances with temperature is ex- tremely small. Because of the constancy of the bath

temperature, the resistance of the resistors could be

assumed to be constant to better than 1 ppm during

the electrical calibration experiments.

The resistance ratios required in the calibration of

the volt-box and potentiometer were measured with the

Mueller bridge described in section 2.2.

2.5. Oxygen Handling Equipment

The oxygen manifold and associated purification

equipment are essentially as described by Jessup [3j. A high-purity grade of commercially available oxygen 4 was further purified for use in the benzoic acid combustions. The final oxygen pressure is measured to 0.01 atm on a calibrated Bourdon pressure gage. The

temperature of the oxygen in the bomb is measured

to the nearest 0.1 °C with a calibrated mercury ther- mometer inserted in a brass cup that fits snugly around

the bomb while the bomb is being filled.

3. Tests of the Apparatus

Numerous measurements of the variation of the

thermometer resistance with time during drift periods

not associated with the principal calorimetric measure- ments showed that the imprecision of the measurements, as indicated by the average deviation of the

observations from the best smooth curve drawn through

the data, could be reduced to a few microohms. This was done by making resistance measurements at

1 min intervals with the bridge commutator set in alternately the N and then (i.e., next minute) in the

R positions. Bridge current reversal and interpolation

to 10~8 fl were made in the usual manner [17]. The

effect of the time variation in the lead resistance was

eliminated by calculating the resistance R(t), at any

time t, from the observed readings, adjusted for interdial corrections, R'(t), R'(t-l), R'(t+1)

according to eq (1).

R(t]

R'(t-l) , R'(t) , R'(t+l)

Hi

Proper operation of the bridge commutator was

critical in making these more precise measurements.

This required replacing the mercury in the switch

every three to six experiments and periodic reamalgamation of switch contacts. Small systematic deviations of the best smooth

curves drawn through the values of R(t) from the

resistance-time curves predicted by Newton's cooling

law were observed. The shape of these deviation curves

differed. A study of possible causes of the deviations was inconclusive. The changes in the calorimeter

jacket, calorimeter stirrer motor, and the thermal

shielding of the thermometer head, mentioned in section 2, reduced but did not completely eliminate the

deviations.

The stirring of the calorimeter was varied in order

to test the possible effect of variation of the heat

generated by stirring as a source of deviations. Al- though the study of this factor was incomplete, we

found no clear evidence to indicate that random

fluctuations of the energy of stirring of the water might cause deviations either when the stirrer was operated

intermittently or when the stirrer was turning at a constant rate. The installation of a synchronous motor

to turn the calorimeter stirrer was made to insure a constant rate. We did obtain some results suggesting

that actual misalinement or flutter in the stirrer shaft might be a source of deviations.

To test the applicability of Newton's cooling law

over a wider range of temperature than usually occurs

in a drift period (0.01 °C or less), the average rate of

change of the resistance of the thermometer was

measured at six calorimeter temperatures below that of the jacket, 12 to 19 resistance measurements were made at each calorimeter temperature by the pro- cedure given above. Resistances were averaged according to eq (1). The drift rate, A/?(r)/Ai, corresponding

to a selected thermometer resistance, Rs(t), was

determined from the best straight line passing through

the first order differences plotted as a function of time.

The number of values of R(t) at each calorimeter

temperature, the value of R.s(t), AR(t)/At for the

selected values of R(t), and the estimated average

deviation of the first order differences from the straight

line are given in columns 1, 2, 3, and 4 of table 1.

Table 1. Calorimeter drift rate as a function of calorimeter temperature

No. of values

»{ Kin

Rdt)

AK(M/At, fl X 10* min 1

"Obs" Av. dev. "Obs"-"Calc." •

10 28.00717 568.7 0.5 -0.8

17 28.06315 460.7 0.7 + 0.7

13 28.11692 355.0 0.6 + 0.2 28.16559 260.0 0.7 + 0.4

15 28.21188 169.0 0.4 0.0

13 28.25985 74.7 0.5 -0.5

[IRtth

I Af / 1956.35 (28.29828 -/fint.

J Supplier's impurity analyses were 10.0. 84.0. 0.18. and 15.9 mular ppm fur argn

nitrogen, water, and methane, respectively.

It may be shown that, if Newton's cooling law holds,

AR(t)/At should be a linear function of R{t) with an

error of less than 3 X 10 8 fl min 1 in AR{t)/At for our

calorimeter and resistance thermometer. The differ- ences between the "observed" values and those cal- culated from a least squares fit of the data, assuming

that R(t) has negligible error in comparison to A/?(f)/Af, are given in column 5 of table 1. The root mean square

deviation, 0.5 X 10 -6

fi min -1

, is substantially smaller

than the value of 3.3xl0~ fi fl min -1 obtained pre- viously by Jessup [18]. Some of the differences is due

to the lower sensitivity of Jessup's resistance measure- 278-456
ment (10~ 5 fi) and some is due to the averaging effect of eq (l). 5 In any event, the random deviations from

Newton's cooling law appear to be substantially less than those obtained previously. This is consistent with an improvement in the calorimetric measurements

which is discussed further in section 6.1. A summary of the magnitudes and types of deviations from Newton's cooling law during drift periods

of the calorimetric measurements themselves is given

in section 5.1.

4. Experimental Procedures

4.1. Benzoic Acid Combustions

The general experimental procedure involved in a benzoic acid experiment closely follows that given by

Jessup [19]. Significant differences are given below.

The benzoic acid received no special treatment prior

to the experiment but was used as it came from the

bottle of NBS standard sample ' 39i. Pellets of

1.51 ±0.015 g were prepared and accurately weighed

after V2-hr temperature equilibration in a platinum

crucible in a balance having a readability of 1 /xg. After the bomb was filled to a pressure of 30 atm

of oxygen, 15 to 20 min were allowed to elapse, to ensure temperature equilibration of the bomb and

oxygen, before the final pressure and temperature were read. The temperature of the calorimeter jacket was

determined by measuring the resistance of the platinum resistance thermometer to ± 10 fxCl as originally

described in section 3 using bridge-current reversal. Fifteen to 20 min after the calorimeter had been

heated to a temperature about 3 °C below that of the

jacket, measurements of calorimeter temperature were

started. The preliminary calorimeter-temperature

measurements with lower sensitivity were essential to establish the values of the drift rate and the differences

between the readings with the commutator in the N and

R positions as a preliminary step to the much more

difficult measurements to follow. After 5 to 10 min of

these readings, the galvanometer sensitivity was in- creased to permit measurements to ± 1 /xCl, and these more precise measurements were carried out for an

initial period of at least 12 min.

One minute after the final resistance measurement

of the initial period, the fuse was ignited by discharging

the capacitor and initial and final capacitor voltages were noted. Time-temperature measurements during

the rapid temperature rise of the main period were made with the thermometer current reduced from 2 mA

to 0.6 mA.

After the change in thermometer resistance was

less than 0.002 ft min-1

, resistance measurements at one minute intervals were resumed with alternate

N and R commutator positions at a sensitivity of ±10 f/Sl. Measurements to ± 1 jxCl sensitivity were

s See section 5.1a.

started after the drift decreased to 0.000200 fl min-1 and continued through the remainder of the main per- iod (defined to end 20 min after ignition) and a final period of at least 12 min. The jacket temperature was

then remeasured as before.

Table 2 illustrates a typical set of resistance and

time measurements made during a combustion experi- ment. The letters N and R refer to the bridge commutator settings. Columns labeled average resistance

are values of R{t) calculated by eq (1) using uncor- rected rather than corrected dial readings. The

course of the experiment with time can be readily

followed by reference to table 2 while reading the

foregoing text.

Table 2. Observations of time and thermometer resistance during a combustion experiment

Resistance minus 28.0 Avt?r&g<? Time p (-"-.i si<inct Drift

/V R

minus 28.0

Min Ohms Ohms Oh ms ( )h ms mtn ~ 1 X 101" o

1 0.181690.18241

2 .18296

3 .18368 4 .18422

5 .18494

5 .185487

78 .186747 .186196

U. lOU 1 O.J 9 .187451 187412 627

10 . 188000 i Hftn 3 7 DZO

j i .188698 1 fWfiift 1

. looOO

1

624

12 .189246 189283 622

13 .189943 623

14 .190492 190527 AO 1 OZ 1 15 .191183 OZ 1 16 .191733 191769 M1

j

-j .192427 192389 620

18 .192967 616

19 .193660 193622 617

20 .194199 OlO

21 .194882 1 Q/tft/lQ 22 .195434 DID

23 .196110 . 1VOU 10 O J I 24 .196659 . IVOOoO 609

25 .197330 26 Ignition 26 2892 .20

.21 26.57 10 .24 26.651

1

.26 26 7207 .28 26.7993 .30 26.8762 .32 26.9740 .34 27.0828 .36 27.2201 .38 27.3731 .40 27.4658 .41 27.5742 .42 27.7227 .43 27.8993 .44 28.1146 .45 28.2697 .455 28.4495 .460 28.6790 .465 29.0040 .470 29.1801 .472 29.3914 .474 29.6697 .476 29.8461 .477 30.0682 .478 30.2112 .4785 30.3543 .4790 30.4885 .4795 30.7058 .4800 30.9726 .4805 31.1630 .4808 31.4654 .4812 32 .48175 33 0.48230 34 .48241 35 .482614 279-457
TABLE 2. Obsenations of time and thermometer resistance during

a combustion experiment — Continued

Time

Resistance minus 28.0 Average

resistance minus 28.0Drill

/V R

Mw Ohms Ohms Ohms Ohms min' 1 X 106 36 .482584

37

38 .482684 39 .482830 40 .482769

41 .482915 0.482863

42 .482854 .482906 43 43 .483000 .482948 42

44 .482938 .482989 41 45 .483080 .483031 42

46 .483024 .483074 43

47 .483166 .483116 42

48 .483107 .483158 42

49 .483250 .483200 42

50 .483192 .483241 41 51 .483331 .483282 41 52 .483274 .483323 41 53 .483413 .483364 41 54 .483355 .483405 41 55 .483496 .483446 41

.56 .483437 .483488 42

57 .483580 .483530 42

58 .483522 .483572 42

59 .483664 .48361.3 41 60 .483603 .483654 41

61 .483746 .483695 41 62 .483684 .483736 41 63 .483830 .483778 42

64 .483769 .483819 41 65 .483908 .483859 40 66 .483852 .483900 41 67 .483989 .483941 41 68 .483934 .483983 42

69 .484076 .484025 42

70 .484013

4.2. Electrical Energy Measurements

Much of the experimental procedure was similar to that outlined for the chemical heat measurements in the previous section. The procedure for making the

electrical calibration measurements is essentially that outlined previously [4, 2]. The combustion bomb was prepared without a pellet or platinum fuse but contained the usual platinum

crucible and the usual amounts of oxygen and water.

Just prior to a run, the temperature of the standard

cell enclosure was measured. The emfs at the output

leads of the volt-box and the 0.01-fi standard current

resistor were measured before and after a run when no power was supplied to the heater to obtain values of the residual (thermal) emf of the circuit. Thermometer-resistance measurements during the

rapid temperature rise (i.e., while the electrical power was on) of the main period were made in the same manner as in the benzoic acid experiments. Measurements of the potentials at the output of the volt-box

and across the current resistor which were 0.054 and

0.018 V, respectively, for the 110 W calibration experiments were made between temperature measurements.

(The time of each potential measurement was differ- entiated from those of the main period temperatures

by actuating the timer-printer with the standard second

signal to record two times, exactly 1 s apart, which

bracketed the time of the corresponding measurement.)

In this way it was possible to obtain up to eight meas- urements of both the heater current and voltage during

a 5 min heating period.

At frequent intervals during the course of the calibration experiments, the volt-box was calibrated, the

potentiometer ratio was determined, and the constancy

of the resistance of the 0.01-O standard resistor was

checked.

5. Calculation of Results of Calorimetric

Experiments

A series of 6 benzoic acid combustion experiments

and then a series of 16 electrical calibration experiments were carried out. The electrical calibration

experiments are separated into three groups depending

upon whether the amount of power supplied to the

calorimeter heater was approximately 110, 60, or 270 W.

5.1. Calculations of the Corrected Temperature Rise

Values of corrected temperature rises are listed for the appropriate experiments in tables 3 and 4. Observed temperature rises were of the order of 2.82 °C,

and the correction due to heat transfer between the

calorimeter and jacket was about 1.5 percent of this value.

a. Treatment of Initial and Final Period Data The observed readings of the bridge during the

initial and final periods, illustrated in table 2, were

converted to ohms by applying the various bridge

corrections and then averaging according to eq (1). Temperatures corresponding to each R(t) were calculated by the Callendar equation [10]. The parameters

in this equation that are characteristic of our thermometer were determined by the Temperature Section of

the Heat Division, NBS.

The calorimeter temperatures, 6(1, J), for the initial (7=0) and the final (1=1) drift periods were fitted to the integral form of Newton's cooling law, eqs (2). 6(I,J)=C(I)+D(I)-P(J) (2a)

P(J) = (\-e-K-l )K. (2b)

In eq (2), C(I) and D(I) are different constants for each drift period, J is the time of occurrence of the

temperature relative to the start of the appropriate

drift period, and K, the cooling constant of the calorimeter, is defined by eq (3). K=[D(0)-D(1)]I[C(1) -C(0)]. ( 3 ) A consistent fit of the temperature-time data by

eqs (2) and (3) was started by estimating values of

C(I), D(I), and K from the first and last datum points

of each drift period. Calculation of "improved" values

280-458
Table 3. Benzoic acid combustion calculations

Expt. No. Mass F x 106 A0 m,( 1 + r)/A0 E' (cont) A£„,„ — A£ (HINO3J A E (cal)

( — )

°C g °C~' j J 6 ^

1 l/23394 - 189.8 2.849658 0.5344869 + 1.43 + 1.49 + 0.49 -27.8 0.5344591

2 1.507283 -166.7 2.819376 0.5345267 + 1.79 + 1.60 + 0.52 -39.3 0.5344874

3 1.492242 -166.9 2.791449 0.5344869 + 1.80 + 0.93 +0.70 -46.0 0.5344409 4 1.493978 -160.8 2.794708 0.5344880 + 1.88 + 1.23 + 0.58 -46.6 0.5344414

5 1.525560 -157.2 2.853627 0.5345198 + 1.93 + 1.21 + 0.58 -46.3 0.5344705 6 1.501083 - 180.8 2.807857 0.5345043 + 1.57 + 1.38 + 0.52 -33.8 0.5344705

Average 0.5344616

Std. dev. of experiment 0.0000183(0.0034%)

Std. dev. of mean 0.0000075(0.0014%)

rAE„^-A£ (HNO,) A =

[ (Tlsj E

' ,con,)

1 (-A£„)

Table 4. Calculation of the energy equivalent of the calorimeter

Expt. j

E,E,dt [F-JF,)^ E*dt QrIF, <?. At) —E' (eont) E (cal) No.

(p

2 s) x 10*3 (p

2 s) X 10* 3 (p2 s) x 10* 3 J °C J°C- J °C"

Heater power 110 W

7 3550.0634 1.1258 0.0377 38,955.397 2.757342 0.30 14,128.18 8 3559.4812 1.1288 .0377 39,058.739 2.764372 0.32 14,129.66 9 3615.7432 1.1467 .0378 39,676.104 2.808623 0.39 14,126.92

10 3605.5325 1.1434 .0378 39,564.063 2,800523 0.02 14,127.40

11 3585.7557 1.1372 .0378 39,347.050 2,785424 0.20 14,126.25

12 3591.6315 1.1390 .0378 39,411.526 2.789739 0.16 14,127.48

13 3578.4748 1.1348 .0378 39,267.158 2.779515 0.16 14,127.50 14 3591.6153 1.1390 .0378 39,411.348 2.789528 0.14 14,128.46

15 3588.6870 1.1381 .0378 39,379.216 2.787293 0.14 14,128.26

Heater power 60 W

16 3575.0618 1.1342 0.0069 39,229.362 2.776922 0.07 14,126.99

17 3573.4132 1.1337 .0070 39,211.273 2.775357 0.07 14,128.44

Heater power 270 W

18* 3582.3213 1.1348 7.3177 39,389.320 2.788869 0.13 14,123.89

19* 3548.3917 1.1240 7.3241 39,017.047 2.762050 0.13 14,126.25 20* 3506.1535 1.1107 7.2380 38,552.619 2.729664 0.16 14,123.74 21* 3588.2289 1.1368 7.2382 39,453.237 2.792813 0.16 14,126.86 22 3612.1828 1.1440 0.0208 39,636.866 2.805518 0.19 14,128.36

*Constant current mode of power supply; all others constant voltage mode.

of these constants proceeded by computing the deviations, F{I, J), of the "observed" temperatures from

those calculated by eq (2) using the initial estimates of

C(/), D(I), and K. These deviations were fitted by

least squares with deviation equations linear in P{J) according to eq (4). F(I,J)=B(0,I)+B(1,I)P(J). (4) The values of 5(0, /) and B(l, I) were used to correct

the initial estimates of C(I) , D(I), and K. The cycle of

calculations, performed by a high speed digital computer, was repeated until either the sum of the squares

of the deviations of the initial and final drift periods

increased or the values of K calculated on two successive cycles differed less 6 than 1 X 10"7 min-1

6 The latter "stop" was inserted because there is no assurance of a distinct minimum in the sum of the squares of the deviations. It was, in fact, the terminating step of all the cal- culations after two or three iterations. The value of 1 X 10"' min -1

is based on the fact that the jacket temperature was constant to only about 1 X 10-4 °C, and K is approximately 2X 10" 3 min" 1

.

The observed temperature rise was computed from

the calculated values of initial and final temperatures

using eqs (2) and the final values of C(I) ,£>(/), and K. This method of curve fitting assumes the values of

6(1, J) of each drift period are independent which

cannot be so since the temperatures are calculated

from observed resistances which were averaged ac- cording to eq (1).

It can be shown that, because of the use of eq (1), runs or deviations of the same sign should occur when

the difference between "observed" and calculated

temperatures are plotted as a function of time even

though the errors are random. Usually, runs of three

to five deviations of the same sign were observed.

This indicates that in the case of random errors, those

in the resistance measurements predominate. The

systematic errors in the values of "observed" temperature and the calculated temperatures caused by

using eq (1) are negligible.

Although the deviation plots sometimes showed

systematic deviations from Newton's cooling law, they

281-459
were small. The average root mean square deviation

of "observed" from calculated values of 6{1, J) was

slightly less than 2 X 10"5 °C.

b. Treatment of Main Period Data The correction to be added to the observed temperature rise due to heat transfer from the jacket and

stirring energy is calculated according to a method

discussed by Dickinson (see [20, 4]). In this method,

the main period data is used to evaluate the parameter

tx , defined by eq (5), and the remaining parameters

are determined from the values of C{I), D(I), and K

determined from the drift period data in section 5.1a.

tx=tj1 (dr-Oi(d-9i)dt. (5)

In eq (5), 9; and 9j are the temperatures at the beginning, tj, and end, tf, of the main period, respectively.

To keep the error in the calculation of the correction to the observed temperature rise to 1 X 10~5 °C

in our experiments, t x must be calculated to 0.1 s and

the integral in eq (5) must be calculated with an ac- curacy of 1 part in 10,000. The following two procedures were adopted to minimize the calculation error.

First, the temperature-time data were graphed to eliminate gross errors and fill in gaps where data was

sparse by superimposing corresponding portions of

the main period of similar experiments.

Second, because eq (5) may be rewritten with an

integral whose integrand is independent of temperature, temperatures of the main period were calculated

in the same manner. Since virtually all the resistance

measurements during the rapid temperature rise were made with fixed commutator position, the formula

for the estimated correction for thermometer lead

resistance applied to these readings was used throughout the main period. Thus, although the method of

calculation of temperatures was in other respects the same as that for the initial and final periods, 0, and 6f in eq (5) are not quite the same as those used in cal- culating the observed temperature rise. We assumed

the thermometer lead resistance correction varied

linearly with the thermometer resistance in the main

period from the average initial to the average final

drift correction. Since the difference between these

corrections was about 15 fjcfl for all the experiments,

the net effect of an error in the assumption is negligible

in comparison to other errors in the treatment of the

data of the main period.

The integral in eq (5) was evaluated using the spline

numerical integration procedure whose characteristics are described in detail elsewhere [21]. Essentially, the method fits a piecewise cubic with continuous

first and second derivatives to the data. Calculations were carried out with a high speed computer using a program written in the Dartmouth BASIC language

[22 j. This program was based on a subroutine originally written in FORTRAN [23].

5.2 Benzoic Acid Combustion Calculations

Since benzoic acid is certified as a secondary heat

standard for use in determining the energy equivalent

of bomb calorimeters, it is convenient to express its energy of combustion per unit mass of benzoic acid

under so-called standard bomb-conditions [4]. Deter- mination of the energy of combustion of benzoic acid

under standard bomb conditions, A£b, is carried out

in two steps, the first of which is summarized in this section. In order to compare the benzoic acid combustion

data with the electrical calibration data, we defined the

standard calorimeter to be the calorimeter can containing sufficient water so that their combined weight

is 3750 g, the calorimeter lid, the electrical heater,

and the combustion bomb with its standard contents,

its external fuse leads and its handle. The standard

bomb contents were defined to be 1 g of water, the

platinum crucible, platinum fuse, and 0.441 moles

of oxygen (30 atm at 25 °C).

By selecting the temperature to which the iso- thermal bomb process is referred to be the final temperature the calorimeter would have if the heat transfer

from the calorimeter environment and stirring energy were zero, the ratio of the energy equivalent of the

standard calorimeter, Zs(cal), in joules per degree, to

Ais/j, in joules per gram, can be calculated from the

experimental results by eq (6) (see [20], [5]).

E(caT) (l + F)ms A0

A£"lGN AZShNOii (A0)

-E> (cont)

1 (-A£«) (6)

In eq (6), A0 is the corrected temperature rise, ms is the mass (i.'e., weight in vacuo) of benzoic acid in grams, &ElGN is the electrical energy supplied to the

calorimeter . to ignite the benzoic acid, ^Em0[l is the

energy of formation of nitric acid produced in the actual

combustion reaction, and E' (cont) is the correction

added to E(ca\) to give the energy equivalent of the

actual calorimeter prior to sample combustion. The

quantity F is related to the energy of combustion,

Ais#, per gram of benzoic acid under actual bomb

conditions by eq (7). AE^=(l+F)AEH (7)

Numerical values of F were calculated from the ap- proximate formula given by Coops, Jessup, and Van

Nes [4]. Since the second term on the right-hand side of eq

(6) constitutes only a small contribution to the total, an approximate value of AEh may be used in this term. For this we used —26,434 J g An error of 10 J g

_1 in this value of AEB would produce an error of only 1 ppm

in -£(cal)/A£«.

282-460
A summary of the calculations is given in table 3. In calculating F (col. 3), the pressure of oxygen at 6i, was calculated from observed pressures using the

equation of state for oxygen given by Coops, Jessup,

and Van Nes [4]. ^'(cont), listed in column 5, was

evaluated using 1.21 J g" 1 °C _1 [4] for the heat capacity of benzoic acid and a value of 21.17 J mol~'[20] for the constant volume heat capacity of oxygen at 30 atm. Measurement of A£7(;.v is summarized in section 2.3 and the determination of A£(HNO:j) was made in the

usual manner [4].

More accurate values of F were calculated by eval- uation of the Washburn correction by the procedure

described by Hubbard, Scott, and Waddington [20]

using the computer program developed by Shomate

[24]. A very slight difference was observed in the F

values, for which a correction is made in the calculation of (—A£H ) at the bottom of table 5. (The dis- persion of the values of £'(cal)/(— A£«) was not

altered significantly.)

5.3. Electrical Calibration Calculations

The energy equivalent of the calorimeter, £(cal),

is related to the total electrical energy, Qe , supplied

to the calorimeter during a calibration experiment, by

eq (8) Qe = [£(cal)+£'(cont)]A0. (8)

In eq (8), A0 is the corresponding corrected temperature rise and Zs'(cont) was defined in section 5. Qe was evaluated by eq (9)

Qe = Fx f EvEidt — F> j

T EUt + QT. (9)

In eq (9) the various terms on the right are, respectively, the energy calculated from the potentiometer

measurements, the correction for current passing

through the volt-box, and correction for transients

(i.e., any voltages not measured with the potentiometer). Ev and Ei are the observed dial readings of the

potentiometer at the output of the volt-box and across

the current resistor, respectively after applying inter- dial and "zero" corrections. T is the length of time

power is supplied to the heater. Fi and F> are constants which depend upon the volt-box ratio, resistance of

the current resistor, the standard cell voltage, and the

calibration of the potentiometer.

The numerical values of the terms on the right of eq (9) divided by F\ are given in the first three columns

of table 4. The unit p in these tables stands for a "potentiometer unit" and is nominally 1 V. The values

of Qe , A0, ^'(cont), and £'(cal) are listed in the remaining columns of table 4. Because of the constancy of the volt-box and potentiometer ratios and the inferred constancy of the

standard current resistor and standard cell voltage to

1 ppm or better, F\ and F> were assumed to be constants. This assumption causes negligible imprecision

in ^(cal) as compared to that from other sources. The

numerical values of F\ and F> are 1.09765196 F

2fl -1p

2 and 1.099975 X 10"\ respectively.

The standard cell voltage was determined by the

NBS Electrochemistry Section of the Electricity Divi- sion by comparison with the NBS voltage standard.

A correction of 1.4 microvolts [25] was added to this calibrated value since the average temperature of the

cells during our measurements was 0.024 °C less than

at the time the cells were calibrated.

The resistance of the standard current resistor was

based on its certified resistance at 25 °C and the temperature coefficient of its resistance as determined by

the supplier. The maximum error in this calculated

value of resistance at the oil bath temperature (33.16

°C), as determined by ten potentiometric comparisons

during the electrical calibration experiments of its resistance with that of a standard 0.1 fl resistor cali- brated by the NBS Resistance and Reactance Section, was found to be 0.002 percent or less. After our meas- urements were completed, a more accurate value for the resistance was determined by the NBS Resistance

and Reactance Section. The corresponding correction

to the data was made in the final calculation of (— AEh)

in table 5. The first potentiometer measurements were made

some 10 to 25 s after power was applied to the calo- rimeter heater. A total of 6, 13, and 2 measurements

of Ey otE/ were made for the 110, 60, and 270 W experiments, respectively. Smoothed values of Ey and E; were obtained from separate plots of the observed

values as a function of time; the time dependence, more or less unknown, of the 270 W measurements

had to be inferred from other considerations [26].

Values of the integrals in eq (9) were computed with

the spline integration subroutine of the computer

program used in the calculation of the integral in eq

(5).After the electrical calibrations were completed it was found that large voltage transients occur when the

power source supplying 270 W to the calorimeter

heater in the constant current mode is switched from

the dummy heater to the calibration circuit. These

transients had disappeared well before the first meas- urements of Ey and Ei were made with the potentiometer. Subsequent examination of the voltage-time

characteristics of this power source in the constant

voltage mode and of the power source used to supply

110 and 60 W to the calorimeter heater in the constant

voltage mode also indicated the presence of transients, but these were much smaller. Numerical values of the energy supplied to the calo- rimeter by these transients are based on separate

determinations of the transient voltage-time curves,

as observed on an oscilloscope, for the power supplies

operated in the appropriate mode of operation. Corrections to account for the slightly different average

values of power supplied to the heater in the actual

electrical calibrations were made assuming the length

of time required to switch the power supply from the

dummy to the calorimeter heater was constant. 283-461
Table 5. Summary of calculation of (— AEB )

Expl. Number of Heater power Average £(cal), J°C~ l Standard deviation of an Standard deviation of 95% confidence limits

N<i. expts. experiment, J °C -1 average, 7 °C~' J °c-'

7-15 9 110 W (constant voltage 14,127.79 0.99 (0.007%) 0.33 0.76 16-17 2 60 W (constant voltage)... 14,127.72 0.99 0.73 1.60 18-21 4 270 W (constant currentl. 14,125.19 1.6 0.80 2.55 22 1 300 W (constant voltage).. 14,128.36 Adopted value.. 14,127.79 0.99 (0.007%) 0.30 0.68

Summary of benzoic acid combustions

Expt. No. Number of Average E(cal)/(-A£„),g',C-' Standard deviation of an Standard deviation of 95% confidence limits expts. experiment, g °C -1 average, g °C ~ 1 g°C1-6 6 0.534461.6 (0.0034%) 0.0000075 0.0000193

Calculation o/ — AEB

26,433.69 J g

> +0.21 J g-' +.15Jg-'

26,434.05 J g-i with an uncertainty interval (random) ol 1.7 J g~'

Nominal (-A£«)

Correction for /\ n .oi... Correction for F

Corrected (—&£„)=

5.4. Summary of results The calculations of the energy equivalent of the

calorimeter are summarized at the top of table 5. Ninety-five percent confidence limits are calculated

by multiplying the standard deviation of the mean by

the appropriate factor of the Student £-distribution. Assuming equal precision, standard deviations computed for experiments 7—15 and for 16-17 are pooled

together. Comparison of the average values of £(cal)

listed in table 5 for the three heater powers used in experiments 7 through 21 show they lie within their combined uncertainty (random) intervals. However,

the results of experiments 18-22 were not used in computing a weighted average for £(cal) for the fol- lowing two reasons.

First, it will be noted from columns 2 and 4 of table 4 that the contribution of Qr to £(cal) is 0.2 percent in the case of experiments 18—21. For the other experiments, the power supplies were operated in the constant voltage mode and the contribution of Qr to£"(cal)

is less than 0.0012 percent. Since we feel that a sys- tematic error in the estimate of Qr of 20 percent is not unreasonable, the difference between the average

.fiscal) of experiments 18—21 and the remainder is probably caused by a systematic error due at least in part to the error in Qr.

Second, it will be noted that experiments 18-22 were carried out with the highest heater power and,

thus, the shortest time necessary to warm the cal- orimeter 3 °C. This resulted in the unfortunate situa- tion that we -were able to make only a few measure- ments of heater current or voltage when the change in voltage, or current, was the most rapid. We feel the

uncertainty introduced in E(cal) by the uncertainty

in our estimates of the time dependence of the voltage, or current may be appreciable. Thus, the agreement

of experiment 22 with 7-17 is regarded as being some- what fortuitous. Experiment 22 was given zero weight on the basis that we suspect its uncertainty is considerable larger than experiments 7-17.

The results of the benzoic acid combustions and the

value determined for A£B for benzoic acid are summarized at the bottom of the table 5. The precision

of &EH was calculated as suggested by Rossini [27]

;

the contribution of the imprecision due to the various

factors taken as constants in determining E (cal) was

neglected since it was estimated to be 10 ppm.

6. Appraisal of Experimental Results

6.1. Random Errors The standard deviation of a single combustion ex- periment with this particular calorimeter had never

before been lower than 0.012 percent, for an extended

series of measurements. It is clear from table 5 that the precision of the present measurements is sub

stantially better than the previous work.

We were particularly interested to see whether or not we could account for the standard deviation of a measurement of either —E{ cal)/ AEH or £(cal) in terms

of the various factors we might expect to vary from

experiment to experiment.

Common to both sets of measurements were the

uncertainty in the corrected temperature rise and the

absence of a buoyancy correction to the weight of the

water placed in the calorimeter can. The uncertainty in the corrected temperature rise was evaluated from the variances of the estimates of

the various parameters appearing in eqs (2) and (3), using the usual propagation of error formulas [27]

and assuming that the "average" root mean square

deviation of 6(t) for the initial and final drift periods

284-462
may be treated as a random error. These "averages" were arbitrarily multiplied by since they are probably too small due to the use of eq (1) (see sec. 5.1a).

The error in the integral in eq (5) was based on the

approximations that the main error is contributed by

the errors in the times recorded during the rapid temperature rise of the main period and that the integral

may be computed by the trapezoidal rule. The uncertainty due to the absence of the buoyancy correction in the calorimeter weight was esti- mated from the known variation in air density during

the benzoic and experiments (12 mg/1 7) and the ap- proximate volume of the calorimeter can plus water

(2.59 1). The resulting percentage error was arbitrarily multiplied by two because it is quite evident

from the method used to adjust the weight of water in the can (see [3]) that the aforementioned variation

in air density is a minimum estimate. Other factors,

such as convection currents, may also make a substantial contribution to the weighing error. The random error in £"(cal due to the uncertainty of the mass of the benzoic acid sample is based on a conservative estimate of ± 10 /xg for a sample

weight of 1.5 g. The estimates of the varous errors contributed by the

parameters which make up Fj are based on the deviations of their measurements. The standard current

resistor, Ro.oi, was assumed to have a stability of 2 ppm.

The estimate of the random error in E(ca\) due to the random error in the integrals in eq (9) was based

on the approximation that 13 smoothed pairs of values

of E\ and Ei separated by 30 s time intervals were

numerically integrated by the trapezoidal rule. The

errors in the smoothed values of E\ and Ei were taken

as ± 2 X 10-7 potentiometer units. The estimate of the random error due to the heater

leads is based on the analysis given by Ginnings and

West [28]. The dimensionless parameters Ls and Lc of that analysis were calculated to be 0.34 and 0.28,

respectively. The variation in the heater lead resist- ance was estimated to be ±0.002 O; the heater resist- ance is 32 fi. A summary of the errors and a comparison with the

observed standard deviation of an experiment is given

in table 6. The discrepancy between the observed and

estimated values for the electrical calibrations is probably greater than the uncertainty of our estimates.

6.2. Systematic Errors One of the main assumptions customarily made in using a stirred-water "isoperibol" calorimeter is that the correction to the temperature rise due to heat

transfer from the calorimeter jacket and heat delivered

by the stirrer can be computed from Newton's cooling

law and temperatures measured inside the calorimeter.

It is generally understood that this assumption would

be valid if the calorimeter temperature were strictly

uniform throughout the calorimeter.8 Real calorimeters have, of course, temperature gradients or, equivalently, temperature differences due to the effects of

lags. Thus, the surface temperature of the calorimeter,

which determines the rate of heat transfer between

the calorimeter and jacket, is in general different from

that measured by the thermometer, even though it is placed as close to the calorimeter wall as is practical.

The effect of a temperature gradient on calorimetric

measurements has been analyzed to some extent for "isoperibol" calorimeters [29, 30, 31], and in detail

for aneroid adiabatic calorimeters [32]. Harper [29]

has shown that if the lag of the temperature measure- ment system (i.e., including both thermometer and

electrical detecting system) is the same throughout

a calorimeter experiment then the lag causes no error

in the corrected temperature rise. White [30], in effect, considers the temperature gradient to be the

superposition of those due to (1) heat transfer from the

jacket and stirring, and (2) heat released in the calo- rimeter during the main period. By an argument

identical to that used by Harper, he showed that the

lag due to the first of these sources causes no error

in the corrected temperature rise, while the lag due

to the second source will cause an error. However, if the latter lag is a constant which is independent of

the source of heat (i.e., electrical heater or combustion

bomb), then it will cause no error in the heat of combustion of benzoic acid. White felt that the constancy

of the lag due to different heat sources could be veri- fied by appropriate experiments.

7 Square root of the sum of squares of the deviations divided by the number of measure- ments minus one.

8 Convective heat transfer between the calorimeter and jacket must also be negligible. For this discussion, we assume this is so.

Table 6. Estimated random errors in — E(cal)l( — AEB ) and E(cal)

Benzoic acid (-£ (cal)/A£„)Electrical calibrations t-E leal))

Corrected temperature rise Bouyancy correction Mass of benzoic acid j EvE,dl

klE'„ E„

fioo, Volt box ratio! Heater leads Estimated standard deviation of a measurement

Observed standard deviation of a measurement.

0.0022

0.0018

0.0007

0.0030

0.0034

0.U019

0.0018

0.0003

0.0001

0.0001 0.0002

0.0001 0.0005

0.0027

0.0070

285-463
Table 7. Summary of values of t— AEB ) for benzoic acid

Author Sample Value Uncertainty

Jessup and Creen [2. 18. 33] (1934) Prosen and Rossini [35] (1939-41).. Jessup [2. 33] (1942) Coops et al. [31] (1946—8) Coops et al. [31] (1954) Challoneretal. [34] (1954) This work (1966)

39d, 39e

39e 39c! 39f, B...

39b, 39f, VUS

39b, VUS

C

39i

Jg-<

26,432.0

26,434.7 26,433.8

26,438.0

26,435.0

26,436.0

26,434.0

J K- + 2.6 ±2.2

±2.6 ±4

±4±4

±3.3

Coops et al. [31], have suggested one method of making the lag due to different heat sources the same

and have incorporated this in the design of their calorimeter.

An experimental test that has frequently been ap- plied is that the lag is a constant if it can be shown that the energy equivalent of the calorimeter is invariant

with the power supplied to the electrical heater. This

criterion has been shown to be incorrect by West [32] for a calorimeter in which heat flow equations are

linear. It is interesting to note that part of this argu- ment depends upon showing that the contributions to the correction on the observed temperature rise of

the temperature transients due to turning the electrical heater on and off exactly cancel. Indirect evi- dence that this cancellation is the case for our calorimeter is given in section 7. This conformity of our

calorimeter with West's analysis of behavior of tran- sients suggests that the remainder of West's argu- ment may be applicable to the Dickinson calorimeter.

The invariance of the energy equivalent found in the

electrical experiments with varying electrical power

(see table 5), thus, does not provide information about

possible systematic errors. A series of tests was carried out to see whether or

not measurements based on the average surface temperature of the calorimeter in place of that registered

by the platinum thermometer would give a different value of kEH for benzoic acid. On the basis of these

tests, which must be considered to be preliminary in nature, it was found that there is a difference between

the temperatures of the calorimater surface and the

water in the vicinity of the resistance thermometer

and that this difference varies with time in the electrical calibrations in a different way than in the benzoic

acid experiments. Because of certain experimental

difficulties, we assigned an uncertainty to the differ- ence in values of A£« calculated from these observations that was about the same as the magnitude of the

difference. Until a more reliable estimate based on more accurate tests is obtained, we have somewhat

arbitrarily assigned an uncertainty of ±0.01 percent

of A£« to take into account the possible correction for the effect of surface temperature.

The net contribution of other sources of systematic

errors in the electrical calibrations is estimated to be

at most ±0.004 percent of AEH -

6.3. Discussion of Results

In table 7, we have listed the more recent determinations of (—i\Eb) for benzoic acid in joules per gram

of sample.9 Samples indicated by the number 39 fol- lowed by a letter refer to batches of the benzoic acid

standard sample issued by NBS. B refers to a sample

of 39e purified by fractional crystallization from

benzene. VUS and C refer to benzoic acid samples

from sources other than NBS and are described in the

corresponding references.

Uncertainty intervals listed in table 7 are those cited

by the authors except for the work of Jessup and

Green [2, 18, 33] which we assumed to be equal to the later work of Jessup [2]. The bounds for the un- certainty interval for our own work was computed by

the procedure recommended by Rossini [27] as V(1.7) 2 +(l.l) 2 +(2.6) 2

.

Aside from our own work, only that of Challoner,

Gundry, and Meetham [34] incorporates an uncertainty due to the effect of surface temperature. In the

latter, a correction of — 0.046 ± 0.0057 percent had to be applied to the energy equivalent of the calorimeter

to correct for the difference in surface temperature

effects during the main period of an electrical cali- bration and a benzoic acid combustion experiment.

Our preliminary experiments suggest that the magnitude of the surface temperature correction is not

insignificant for our results although it is smaller than

that of Challoner et al. A substantial contribution to the uncertainty of our results has been allowed be- cause of the unknown magnitude of our surface temperature correction. It would be preferable, in spite

of the difficulty of measuring it, to evaluate the cor- rection experimentally in absolute calorimetric meas- urements unless the calorimeter has been specifically

designed to eliminate the error.

54 We have been informed by private communication from Mosselman and Dekker [36], and from Head [37], of very recent electrical determinations of the energy of combustion

of benzoic acid in their respective laboratories. These determinations are both based on measurements made in calorimeters containing water flow channels of the type devised by Coops et al. [31], and both are reported to be in excellent agreement with the value we list for this work in table 7. The work of Mosselman and Dekker includes some measurements

on NBS Standard Sample 39i. 2861-464
7. Appendix. Analysis of Main Period of the

Electrical Calibration Experiments

If the temperature transients due to turning the electrical heater on and off make no net contribution to the corrected temperature rise, the two areas between

the main period curves of the electrical calibrations

and the straight lines given by eqs (10a), (10b), and

(10c) should be equal since the heater power does not vary with time.

0(t) = 0i+ (dd/dt) i(t-ti): ti^t^tj (10a)

0{t) = 03 +{d0ldth(t-t3 ); h^t^h+ tt (10b)

d(t) = df + (dd/dt) /(tf-t); tz + tb ^t^tf. (10c)

Equations (10a) and (10c) are linear extrapolations of

the initial and final drift period curves into the main

period, and the constants 6^, t3 and °f e(I (10b)

are determined from a linear least squares fit of the

main period data during the rapid temperature rise. The times t\ and t2 + tb are the times of intersections

of eq (10b) with eq (10a) and (10c). To test whether or not the areas are equal, we noted

that if they are, then the time t\ should be approximately equal to time 10 tb and both should be independent of the power supplied to the heater or (dd/dt) 3 . Comparison of columns 3 through 5 of table 8 shows

this is very nearly true. Further, the equality of the areas means that the integral in eq (5) for tx is the area enclosed by the lines of eqs (10a) through (10c) and 0*. Corrected temperature rises computed using values

tj—tx determined in this manner differed by less than one part in 10 5 from those listed in section 5. The

latter are based on values of tj—tx determined by

the more accurate spline integration procedure.

Table 8. Average main period characteristics, electrical calibration

Heater power

watts No. ofExpts. u

min

It, min

ide/dih

°C min _l h

min

'max min

60 2 0.238 0.224 0.252 11.2 12. .5-13 110 9 0.242 0.235 0.480 5.8 8.5 270 5 0.230 0.254 1.15 2.5 4-5.5

8. References

[1] Dickinson, H. C, Bull. BS 11, 189 (1914).

[2] Jessup, R. S., J. Res. NBS 29, 247 (1942) RP1490.

[3] Jessup, R. S., NBS Monograph 7, February 26, 1960.

[4] Coops, J., Jessup, R. S., and Van Nes, K., Calibrations of Calorimeters for Reactions in a Bomb at Constant Volume,

10 We assume the transient can be represented by a single exponential.

ch. 3, Experimental Thermochemistry, Vol. 1, F. D. Rossini, Editor (Interscience Publishers, Inc., New York, N.Y., 1956).

[5] Prosen, E. J. Compounds Containing Carbon, Hydrogen, Oxygen, and Nitrogen, ch. 6, Experimental Thermochemistry,

Vol. I, F. D. Rossini, Editor (Interscience Publishers, Inc., New York, N.Y., 1956).

[6] Jessup, R. S., ibid, figures la, lb, and Appendix 7.1e.

[7] Jessup, R. S., ibid., Appendix 7. Id.

[8] Domalski, E. S., and Armstrong, G. T., J. Res. NBS 69A (Phys. and Chem.), No. 2, 137 (1965).

[9] Jessup, R. S., ibid., p. 20, figure lc. [10] Stimson, H. F., Precision Resistance Thermometry and Fixed

Points, ch. 9, Temperature, Its Measurement and Control in Science and Industry, Vol. II, H. C. Wolfe, Editor, American

Institute of Physics (Reinhold Publishing Corp., New York,

1955).

[11] Armstrong, G. T., Wong, P. K., and Kreiger, L. A., Rev. Sci.

Instr. 30, 339-343 (1959).

[12] Jessup, R. S., ibid., Appendix 7.1c.

[13] Boyd, R. H., Rev. Sci. Instr. 35, 1086, 1964.

[14] Pailthrope, R. M., and Riley, J. C, An Improved Technique for Establishing Resistance Ratios, ESI Bulletin No. 35 (Electro

Scientific Industries, Portland, Oreg., November 1962).

[15] Mueller, E. F. and Stimson, H. F., J. Res. NBS 13, 699 (1934), RP739.

[16] Osborne, N. S., Stimson, H. F., Ginnings, D. C, J. Res. NBS 23,

197, 261 (1939), RP1228.

[17] Jessup, R. S., ibid, p. 7. [18] Jessup, R. S. and Green, C. B., J. Res. NBS 13, 469 (1934), RP721.

[19] Jessup, R. S., NBS Monograph 7, Sec. 3.2 and 4. [20] Hubbard, W. N., Scott, D. W., and Waddington, G., Standard

States and Corrections for Combustions in a Bomb at Constant Volume, ch. 5, Experimental Thermochemistry, Vol.

I, F. D. Rossini, Editor (Interscience Publishers, Inc., New

York, N.Y., 1956).

[21] Walsh, J. H., Ahlberg, J. H., and Nilson, E. H., J. Math, and Mech. 11, (No. 2), 225 (1962).

[22] Darmouth Basic Library, Code: Spline, Converted to Basic Language by Messina, C, NBS, September (1965).

[23] Katsanis, T., NASA Technical Note, D-2546, December (1964).

[24] Shomate, C. H., Fortran IV Computer Program for Reduction

of Heat of Combustion Calorimetric Data, Code 5052 (U.S. Naval Ordnance Test Station, China Lake, California, January 1967).

[25] Hamer, W. J., NBS Monograph 84, January 15, 1965.

[26] Ginnings, D. C, West, E. D., Principles of Calorimetric Design,

ch. 4, Experimental Thermodynamics, Vol. I, Calorimetry

of Non Reacting Systems, J. P. McCullough, Editor (Butter- worth and Co., Ltd., In press).

[27] Rossini, F. D., Assignment of Uncertainties to Thermochemical

Data, ch. 14, Experimental Thermochemistry, Vol. I, F. D.

Rossini, Editor (Interscience Publishers, Inc., New York.

N.Y., 1956).

[28] Ginnings, D. C, West, E. D., Rev. Sci. Instr. 35, 965 (1964).

[29] Harper, D. R., J. Res. NBS 8, 659 (1912).

[30] White, W. P., The Modern Calorimeter (Reinhold Publishing

Corp., New York, 1928), p. 89, p. 36. See also J. Am. Chem.

Soc. 40, 1861-1863, 1918 and Phys. Rev. 31, 568-570, 1910.

[31] Coops, J., Adriaanse, N., Van Nes, K., Rec. Trav. Chim. 75,

237(1956).

[32] West, E. D., J. Res. NBS 67A (Phys. and Chem.), No. 4, 331

(1963).

[33] Jessup, R. S., J. Res. NBS 36, 421 (1946), RP1711.

[34] Challoner, A. R., Gundry, H. A., Meetham, A. R., Phil. Trans. Roy. Soc. (London), A24 7 , 553 (1955).

[35] Prosen, E. J. and Rossini, F. D., J. Res. NBS 33, 439 (1944), RP1619.

[36] Mosselman, C, and Dekker, H., The Free University, Amster- dam, Private Communication.

[37] Head, A. J., Natl. Physical Laboratory, Teddington, private communication.

(Paper 72A5-511)

287-465
JOURNAL OF RESEARCH of the National Bureau of Standards — A. Physics and Chemistry

Vol. 72A, No. 2, March-April 1968 Constant Pressure Flame Calorimetry With Fluorine

II. The Heat of Formation of Oxygen Difluoride*

Reatha C. King and George T. Armstrong

Institute for Basie Standards, National Bureau of Standards, Washington, D.C. 20234

(December 27, 1967)

The heats of the following reactions were measured directly in an electrically calibrated flame

calorimeter operated at one atm pressure and 303 °K. OF2 (g) + 2H2 (g) + 99H2 0(l)-* 2[HF • 50H2 O](l) F2 (g)+H2 (g)+ 100H2 O(l) — 2[HF • 50H,O](l)

V2 02 (g) + H2 (g)-> H2 0(1)

The reactants and products were analyzed for each of the reactions. From these heats we calculated

the corresponding heats of formation, as follows: OF2 (g) A//;2 „H , 5 = + 24.52 ±1.59 kj mol" 1 (+5.86 ±0.38 kcal mol" 1

) HF • 50H,O(l) AH?2m ,, = -320.83 ±0.38 kj mob 1 (-76.68±0.09 kcal mol" 1 ) H2 0(1) A//;2!)H .. S = - 285.85 ±0.33 kj mol" 1 (-68.32±0.08 kcal mol" 1 ) The uncertainties indicated are the estimates of the overall experimental errors. The value of the average O — F bond energy in OF2 was calculated to be 191.29 kj mol-1 (45.72 kcal mol-1

)-

Key Words: Bond energy (O — F), flame calorimetry. flow calorimetry, fluorine, heat of formation,

heat of reaction, hydrogen fluoride (aqueous), oxygen, oxygen difluoride, reaction calorimetry, water.

1 . Introduction

Thermochemical data for the fluorine oxidizers are very important for their present-day applications. This

group of oxidizers includes elemental fluorine, and its compounds such as OF2, C1F3, OF.-,, and BrF:! . These

substances are typically very reactive and combine

with most other elements and compounds, yielding

large heats of reaction and in many cases the highest

valence state of the oxidized element. Two important

uses of these oxidizers are for the production of

fluorides, and as possible ingredients in rocket pro- pellants and explosive systems. Because of their

reactivity, they make possible chemical reactions

which have not been investigated, e.g., reactions at extremely low temperatures.

Until a few years ago, very few thermochemical

studies involving these materials had been conducted.

This lack of work was caused mainly by the nonexistence of corrosion-resistant construction materials

*This research was sponsored by the Air Force Office of Scientific Research under Order No. OAR ISSA 65-8. For the first paper (if this series see Reference

and the unavailability of sufficiently pure samples

the fluorides. In recent years several of the problen.s

hindering earlier research have been solved, and

precise calorimetry has been demonstrated to be

possible.

For measuring heats of reactions of the fluorine oxidizers, a new flame calorimetric apparatus has

been set up in this laboratory. An earlier version of

this apparatus has already been described [1, 2]. 1 An

investigation of the heat of formation of oxygen di- fluoride is the first study carried out with the new

apparatus and is described in this presentation.

For many years there has been interest in the heat

of formation of oxygen difluoride. In 1930, von Wartenberg and Klinkott [3|, and Ruff and Menzel [4], reported

two different thermochemical studies on this compound. In various reviews of thermochemical properties [5—8 j . the data from these studies have been

reevaluated repeatedly in attempts to derive a selected

"best" value for the heat of formation of this compound. For some time, the selected value for

1 Figures in brackets indicate the literature references at the end of this paper.

288-113
Afl£»H.i5[OFs] was + 7.6 kcal moh 1 [5J. In 1965 Bisbee,

et al. [9| reported on a more recent study from which

they derived A///

o

2!)8 .,.-,[0F, | =- 4.06 kcal moh 1

. In

spite of the large amount of earlier work, there thus

remained considerable uncertainty in the heat of formation of oxygen difluoride and, at the start of this work, it was not clear whether the compound was

exothermic or endothermic. The results of the earlier experimental work are compared with those from the

present study in another section of this paper. For

comparison with the present experiments, it is important to mention here the reactions which were

studied in the earlier investigations.

The measurements of von Wartenberg and Klinkott were carried out in a flow system in which they

reacted OF2 (g) with (1) KOH (excess KOH aq 40%),

(2) f6KI + 2HF| (in excess aq). and (3) HBr (excess

HBr, aq 45%). They measured the heats of reaction

and derived a value for the heat of formation of oxygen

difluoride based on each reaction. Ruff and Menzel

used a flame calorimeter to measure the heat of the

overall reaction of combustion of OF2 with hydrogen

and neutralization of the product HF in NaOH (aq). In

the same apparatus they also measured the heats of the

F2 — H2 — NaOH and the O2 — H2 reactions. The latter measurements provide the auxiliary heat data needed

for calculating LHf[OF2 |. Bisbee, et al. reacted oxygen

difluoride with hydrogen in a combustion bomb, which

contained water for solution of the product HF. For

calculating AH°[OF>] they obtained their auxiliary

data for the HF (aq) from the literature. It is interesting

to note that in the earlier work, three different calo- rimetric methods were used. With well-developed

procedures, suitably selected reactions for study,

and pure reaction materials, it seems possible that each of the above calorimetric methods could lead

to a reliable value for A//^[OF2 ]. However, it appears

that these methods were not used to their best ad- vantage in the earlier work.

There are few known reactions of oxygen difluoride

which are suitable for a thermochemical study for deriving A///[OF2 |. Because the magnitude of this heat-of-formation value is small, it is desirable to derive it from a reaction with a small heat effect. Such

reactions with oxygen difluoride unfortunately tend

to lead to multiple products, which are not readily

recovered and separated for quantitative analysis.

Under ordinary conditions fluorine and oxygen do not combine directly to form oxygen difluoride. With the above points in mind, the OF2 — H2 — H>0

reaction was selected for this study despite the large

heat effects to be expected. This reaction leads to only a few products, goes readily to completion, is amenable to analysis of reactants and products, and

requires auxiliary data that can be measured in the same apparatus. Oxygen difluoride was reacted with

hydrogen in a flame, and then the product hydrogen

fluoride was dissolved in water present in the reaction

vessel. Using the same apparatus and similar procedures, heat measurements were made also for the

F2 — H2 — H2 0 and 02 —

H

2 reactions.

The reliability of the heat-of-formation value derived

is increased by several factors inherent in this experimental plan. (1) The hydrogen fluoride is dissolved in water, yielding a well-defined thermodynamic state for the acid. (2) Dissolving the hydrogen fluoride inside

the calorimeter lessens the possibility of loss of the acid by corrosion and retains it for later quantitative

analyses. (3) Because the auxiliary data are measured

in the same way as the principal reaction, several of

the systematic errors cancel in the calculation of AHf[OFz ]. This plan is similar to that used by Ruff

and Menzel. Our work differs from theirs mainly in the solution of the hydrogen fluoride in water instead

of aqueous sodium hydroxide, and in the design of the reaction vessel.

2. Experimental Apparatus and Procedures

2.1 . The Samples

a. Hydrogen

A commercially available high purity grade of hydrogen was used. A mass spectrometric analysis was

performed directly on the contents of the cylinder and

the composition (mole percent) of the gas was: H2 , 99.9; H2 0, 0.04±0.02; and N2 , 0.05±0.01. The hydrogen was used directly from the cylinder.

b. The Oxidizer Gases Commercially available samples of oxygen, fluorine,

and oxygen difluoride were used. Each of the samples was transferred from the large cylinder to a spherical

weighable container for the analyses and calorimetric

experiments. The design of the sample containers has

already been described [1, 2]. They were constructed

of Monel and equipped with either Monel or 316-

stainless-steel valves with Teflon packing. The weight

of a typical bulb was approximately 150 g. Extensive

analyses were carried out for each of the gases and the procedures used are described in detail in the

Appendix.

Oxygen. The oxygen was of high purity and is the

grade used in this laboratory for bomb combustion

experiments. The purity was reported by the supplier

to be greater than 99.99 percent. It was analyzed for argon and nitrogen by mass spectrometry and gas chromatography, respectively. The composition of the sample is estimated to be oxygen, 99.987; nitrogen,

0.009; and argon, 0.004 weight percent.

Fluorine. The fluorine sample was of ordinary

commercial quality and therefore not of the high purity

desirable for a definitive thermochemical study of the hydrogen-fluorine reaction. While being sampled,

the gas was passed over activated sodium fluoride

for removal of hydrogen fluoride. The total analysis of the fluorine sample was ob- tained using a combination of analytical methods.

The total mole percent fluorine was determined by

the mercury absorption technique and the relative amounts of the constituents of the residual gas were measured with mass spectrometry and gas chromatography. The chromatographic method was developed

to provide a check on the results from the mass

spectrometric method, which we have usually used

289-11/+
for analysis of the residual gas. The results from the

two methods were in good agreement (see appendix).

Table 1 gives the complete analysis of the fluorine sample.

Table 1. Analysis of the fluorine sample

Constituent Mole percenttotal impurities fl Mole percent in fluorine sample

Weight

percent

1" 11 (based on 111

98.75

0.77

.39 .0025

.015

.055 .0004

.0037 .0035

.0010 nolo

.0009

.0007

98.92

0.54

.33 .003

.017 .128

.001 oio

.013

.004

.005

.005

N2 61.8

28.6

0.2 34

5.0

62.0

31.3

0.2

1.2 4.4 0.03

.3.28

.08

.08

.07 .06

02 Ar

<:o2 CF,

SiF, CF,

0.3

SF«

C:,F, C^Fh (unsat.) Remaining fluorocarbnns 0.6

" Mass spectrometry analysis of volatile impurities after removal of F, by reaction with mercury.

h Sample pressure of I was factor of ten less than that of II. Analysis of I server only for comparison of the analysis for major impurities.

Oxygen difluoride. The supplier's analysis of the oxygen difluoride sample showed it to contain: OF>,

99.25; 0>, 0.69; and CO,, 0.06 weight percent, and

0.01 volume percent CF^. The gas was reported to contain no free fluorine. Kesting, et al. [10] compared

the methods of gas chromatography, iodimetry and

infrared spectroscopy for analysis of OF, and their

tests show that gas chromatography yields the most

reproducible and accurate results. Because of the importance of the analysis to the

accuracy of the calorimetric data, the oxygen difluoride sample was reanalyzed in this laboratory by gas chromatography, following procedures similar to those

described by Kesting. The results from two of the

analyses are shown below.

Analysis I Analysis II Av

Mole % wt. %

pOF2 99.07 99.10 99.36 o2 0.76 0.73 0.45 CF4 .06 .07 .11 C02 .10 .10 .08

For qualitative identification, an infrared spectrum of the sample was obtained and is shown in figure 11 (appendix).

2.2. Reaction Vessel and Flow System Designs

a. The Reaction Vessel The general method is to react the oxidizer in a flowing atmosphere of excess hydrogen and then to form the aqueous acid solution of the products. The

overall design is illustrated in figure 1. In the upper

chamber (A) the oxidizer and hydrogen (excess) are mixed, ignited, and reacted in a flame. The effluent

FIGURE 1. Burner for fluorine flame calorimetry.

A, Combustion chamber; B. Primary solution vessel; C. Heat exchanger; D, Cooling

coil; E, To secondary solution vessel; F. From secondary solution vessel; G. Igniter; H.

Inlet and Outlet connectors.

hydrogen removes the reaction products to the lower

chamber (B), which is the primary solution vessel and

contains 100 cm3 of water. A gas dispersion system

forces the gas mixture as fine bubbles through the

aqueous solution, to cause complete removal of the

hydrogen fluoride from the flowing hydrogen, and

simultaneously to mix the solution making it homogeneous in concentration and temperature.

The gases are brought to the burner from the exterior of the calorimeter system by Monel tubes pass- ing through the heat exchanger (C). The exit gas

enters from the coiled tube (D) into the lower end of the outer tube of the heat exchanger, and while leav- ing the calorimeter, circulates among the small tubes

which contain the entering gases. The outlet (E) on the

primary solution vessel connects to a smaller vessel

which is seen in the foreground in the complete burner

assembly shown in figure 2. For an experiment this secondary vessel contains 20 cm3 of water. As can be seen by reference to figures 1 and 2, the effluent gases

leave the secondary solution vessel at F and pass through a helix of Monel tubing before entering the heat exchanger. Except for the primary solution vessel,

the reaction vessel is composed almost entirely of 290-115
Figure 2. Assembly of reaction vessel.

Monel and silver-soldered at all of the permanent

joints.

Details of the combustion chamber are shown in figure 3. The inlet tubes for the reacting gases, the

igniter, and the flame tip are attached to the lid of the

combustion chamber so that they are readily accessible

when the lid is removed. The oxidizer is introduced

through inlet C, and the major part of the hydrogen

atmosphere enters through inlet B. Additional hydrogen is introduced through a third gas inlet (not shown).

The joint between the cover and the combustion

chamber is made by a Teflon gasket placed in a groove on the flange of the cup. The reaction is initiated with an electric spark from

a high voltage electrode which is a nickel rod, insulated

by Teflon from a Monel sheath. A calcium fluoride disk is placed over the electrode (E) to further shield

it from the reaction heat and product hydrogen fluoride. The platinum tube (F) leading into the solution

chamber is fitted with a polyethylene cap having a porous lower surface. The cap is held in place with a small Teflon adapter (G). The primary solution vessel

is made of nickel-plated copper and has a Teflon liner.

5 cm

FIGURE 3. Combustion chamber and primary solution vessel.

A, Combustion chamber; B, Hydrogen inlet; C, Oxidizer inlet; D, Flame position; E, Spark electrode; F, Platinum tubing; G. Teflon adapter; H, Polyethylene gas disperser;

I, Primary solution chamber; J, Lid for solution vessel; K, To secondary solution vessel.

The flange on the liner makes the seal when the vessel

is closed. The water in the secondary solution vessel removes

any hydrogen fluoride from the effluent gas that may

be transferred from the primary solution. This provision assures also that upon leaving the burner the

effluent gas flows through a solution for which the

partial pressure of HF does not change during the

experiment. In the primary solution vessel, the liquid

contains no HF during the fore-period, but contains

about two weight percent hydrogen fluoride in the

final drift. The vapor pressure of hydrogen fluoride over the final solution is about 0.048 mm Hg at 25 °C

[11 J. Consequently, very little hydrogen fluoride is transferred to the secondary solution.

b. The Flow System

The layout of the gas flow system is similar to that used previously for flame calorimetric work in this laboratory [1, 2J. The components of the flow system

are schematically shown in figure 4. Preceding the

calorimeter are three flow lines which connect to inlet ports on the reaction vessel. These consist of the two

flow lines for hydrogen, and one for the oxidizer. 291-116
Figure 4. Flow system.

A, Flow inlet (helium); B, Oxidizer sample container; C, Flowmeter (oxidizer); D, Flowmeter (hydrogen, II); E, Flowmeter (hydrogen, I); F, Saturator (I); G, Saturator (II); H, Calorimeter; I, Absorber (magnesium perchlorate);

J, Absorber (sodium fluoride); K, Sampling bulb; L, Bubbler (Kel-Foil); M, Flowmeter (effluent gas); N, Fluorine absorption tower.

The oxidizer line begins with the spherical sample

bulb at B. Not shown in the diagram is an absorber

of magnesium perchlorate placed immediately after the helium cylinder. Predrying of the helium is desired for the helium that enters the fuel line, but

as is explained below, dried helium is not necessary

for the hydrogen lines. The flow rate of the oxidizer was regulated by manual adjustment of the valves. Each hydrogen line includes a flowmeter and

weighable "saturator." The saturator is Pyrex and

with the water, weighs about 69 grams. The hydrogen

entering the reaction vessel is saturated with water

to compensate for the water removed by the effluent hydrogen.

The items after the calorimeter used in these experiments are the absorption bulb (I), the sampling bulb

(K), the bubbler (L), and the flowmeter (M). The ab- sorption bulb contains magnesium perchlorate and

is used to measure the amount of water removed from

the reaction vessel by the effluent hydrogen. The final flowmeter is useful in monitoring the reaction. The

remaining items serve the same purpose as described

earlier [1].

2.3. The Calorimeter and Its Operation

The calorimeter is similar in design to the Dickinson

Calorimeter [12J, with modifications which were intro- duced by Prosen, et al. [13J. It is enclosed in a constant- temperature submarine-shield in the surrounding

water bath. The calorimeter can is separated from the

enclosure by a V2-in air space. It is supported by three

metal pegs and has a volume of 5.5 liters. The calo- rimeter lid has three holes for bringing out the platinum resistance thermometer, the leads to the electrical calibration heater, and the flow lines to the reaction

vessel. The reaction vessel and most of the heat ex- changer are immersed in the stirred water of the

calorimeter. The water is stirred at a rate of 300 rpm.

The reaction vessel is placed on a small brass platform, supported by three small cones. This positions

the bottom of the reaction vessel about V4 in above the

bottom of the calorimeter can.

In the manner customary in this laboratory, temperature measurements were made with a calibrated

platinum resistance thermometer, used in conjunction

with a G—2 Mueller bridge and a high-sensitivity

galvanometer. A displacement of 0.5 mm on the galvanometer scale represented 10 /xCl on the bridge or one-tenth millidegree. At 0 °C the thermometer has a resistance of 25.4668 CI. The temperature of the jacket water was kept constant at 32 °C by an automatic regulating system

consisting of a thermistor sensing element, linear dc

microvolt amplifier, strip-chart recorder (— 5 to + 5 /xV).

current-adjusting-type controller, and a 50-W magnetic

power amplifier [14|. The jacket bath has two heaters,

a 14-H heater for raising the jacket temperature to 32 °C, and a 131-H heater for temperature control. A 500-mA meter is connected between the magnetic

amplifier and the control heater. The thermistors form

two opposite arms of a Wheatstone bridge circuit of which the two remaining arms are formed by adjustable temperature-insensitive resistors. Each thermistor arm of the bridge consists of four bead thermistors

of about 1000 fi each. The thermistors are encased in flattened thin-wall copper tubing and are immersed

in the jacket water near the heaters and stirrer. A

1.5-V mercury cell supplies a current of 0.040 mA to the bridge. The current is kept very small so that self heating of the thermistor elements remains below

0.001 °C. The temperature was usually controlled to better than ±0.0015 °C.

a. Electrical Calibration System

The calibration heater was made from B&S gage

No. 30 Advance wire covered with a double layer of glass insulation. The current leads were 22-gage

copper wire and the heater sheath was thin copper

tubing flattened onto the resistance wire. The resist- ance of the heater was 23 fl. The heater was formed

in a 1-in o.d. coil which was suspended from the calo- rimeter lid. The ends of the sheath passed through a small copper plug which was fastened securely to a ring on the lid. 292-117
The potential leads are attached so that there is a

negligible disturbance in the current leads [15]. The

first potential lead is soldered to the current lead just

inside of the copper sheath at the physical boundary

of the calorimeter. The three leads are then brought

up to a copper plate and the second potential lead is attached at the point where the current lead contacts

the copper plate. Then all four wires are coiled on

the lower side of the plate and cemented firmly in place. By means of a bakelite rod, which passes

through a tube in the submarine lid. the copper plate

is secured firmly against the lower side of the submarine lid to achieve good thermal contact with the

calorimeter shield. The power for the electrical calibration was obtained

from a precision regulated power supply. The unit has a power output of about 500 W maximum, with a current range from 0-5 A and a voltage range from

0-103 V. The supply was operated in the constant

current mode.

With the parameters and switching arrangement

in these experiments, operation in the current mode

gave more constant current and voltage readings.

The double-pole, double-throw switch which connects

the calibration heater and a dummy heater of similar

resistance alternately into the circuit posed a problem

in the calibrations. While interchanging the heaters,

a transient voltage appeared. In a separate investigation [16] the magnitude and decay time of this transient

voltage were observed. Because the transients were

over in about ten seconds, while the heating periods were usually about sixteen minutes long, we believe

that this effect does not significantly affect the accu- racy of the calibrations performed. Current and voltage

readings were made on alternate minutes. The time

interval for the electrical heating was measured with an electronic counter, with an internal quartz oscillator generating at 100 kHz, which gave the time readings

to 10 -5 second. The timer was actuated by the switching arrangement which initiated the heating to the calorimeter.

Other equipment used in measuring the electrical energy input consisted of a 0.01 ft standard resistor, a volt box with a ratio of 20,000 to 20 fi. a thermostated

standard cell, and a Wolff Diesselhorst potentiometer.

During the calibration experiments the calibration of the potentiometer was checked daily. Details on a

similar calibration circuit are given by Churney and

Armstrong [16J. The resistors, potentiometer, and

standard cells were calibrated at the National Bureau

of Standards.

b. The Ignition System

A high voltage coil was used for the igniter and the

sparking was timed with an electric clock connected

in the ignition circuit. The sparking power was measured in blank experiments to be 1.4 J sec

-1

.

c. Conduct of an Experiment

Preliminary Actions. Before and after each experiment, the oxidizer-sample container, saturators, and

magnesium perchlorate absorber (see figure 4) are

weighed to 0.1 mg. In preparing the reaction vessel,

the sparking lead is positioned over the flame position

and demineralized water is added to the primary and

secondary solution vessels and then the reaction vessel

is assembled. The weight of the calorimeter can with water is adjusted to 5950 ± 0.0005 g on a 6-kg capacity

balance. This weight also includes the support for the

reaction vessel. Immediately the reaction vessel is positioned and the calorimeter is covered with its lid from which is suspended the calibration heater. Then the remaining assembly of the calorimeter and

its accessories is completed.

Reactions. The three inlet flow lines are purged with

helium to remove air and a flowing hydrogen at- mosphere is established in the hydrogen inlets. The

total flow rate of hydrogen varied, depending on the

reaction being studied, from about 350 to 450 cm3 min -1

. Though the oxidizer line is initially flushed with

helium, no gas is flowing through this line during the

initial drift period. After a fore drift period of about

20 min, during which time-temperature readings of the calorimeter are made, the reaction is initiated by

simultaneously initiating the sparking and releasing gas from the sample bulb. The sparking is discontinued

when there is certainty that the fuel has ignited. This

is usually after 10 to 15 seconds of sparking. The in- crease in the rate of the temperature rise of the

calorimeter and the decrease in the flow rate of ef- fluent gas are the main signals that the reaction is taking place smoothly.

In most experiments, a 2.5-2.7 deg temperature

rise was achieved in a 15- to 18-minute reaction period.

Near the end of the reaction period the oxidizer sample

container is closed and the material remaining in the

flow line is flushed into the burner with helium. The

helium flow is reduced and continued for the remainder

of the experiment while hydrogen flows through the

other lines. After the reaction experiments the solution in the primary solution vessel is transferred, with

washings, to a weighed 250-cm3 polyethylene bottle. The secondary solution (20 cm3

) is also recovered for

titration. Calibrations. The procedure for conducting the

calibration experiments is similar to that used for the

reactions. The solution vessels contain 100 and 20 cm3 water, respectively. A hydrogen flow through the

bubblers is maintained at a rate comparable to that used for the reactions. The regulation of the helium

flow in the oxidizer flow line constitutes the main

difference between the gas handling procedures for the calibration and reaction experiments. In the cali- brations a small flow of helium is maintained in the

oxidizer line throughout the experiment, whereas

for the reactions the helium flow is begun at the end

of the reaction period.

d. Calculations All of the values for the corrected temperature rise were calculated on an electronic computer with a computer program developed by Shomate [17]. For

the calculation, it was necessary to give the computer

the following data: (1) dial corrections for the Mueller

bridge; (2) time and resistance readings taken during

293-118
the reaction and drift periods of the experiment; and

(3) constants for the platinum resistance thermometer.

A comparison of some hand-calculated and computercalculated values showed that the program satisfactorily calculates the corrected resistance change,

Arv(corr); the initial and final drifts; the conversion

dR. factor, the initial and final temperatures for the

reaction; the correction to the temperature rise,

Ar(corr); the corrected temperature rise, Af c ; and the

cooling constant. The definition, 1 cal = 4.184 J, was used for expressing the results in calories. All atomic weights were

taken from the 1961 Table of Atomic Weights based

on Carbon 12, adopted by the International Union of Pure and Applied Chemistry [18J. The heat capacity

data used for the gases and liquid water are tabulated

below. The heat of vaporization of water was taken

as 2,439 and 2,428 J/g at 298.15 and 303.15 °C, respectively [19]. Values for the heat capacity of aqueous

hydrogen fluoride were obtained from the work of Thorvaldson and Bailey [20].

Substance

J mol~ 1 deg~ 1 Reference

F2 (g) 31.30 [81 CMg) 29.355 [8] OF2 (g) 43.30 [8] H2(g) 28.823 [81 H2 0(1) 75.2911 [8]

e. Water Removal from the Reaction Vessel One general problem encountered in all the experiments was to account for and minimize loss of water from the reaction vessel. This was done by using a weighable drying tube on the outlet of the calorimeter

and weighable saturators on the inlet tubes. The water

entering and leaving the calorimeter could thus be

monitored and the net change kept to a small value. The largest part of the residual heat effect due to condensation or evaporation could be presumed to form part of the causes of the initial and final dritt rates, along with heat of stirring and heat transfer by conduction between the calorimeter and jacket.

However, by keeping the net change in the amount of water small, it is believed that the uncertainty intro- duced by assuming the associated heat effects were

constant would also be small. With this assumption,

the results which are given in table 2, do not require

further discussion. However, it is interesting to note

the consistency in the signs of the differences for

a given set of experiments.

A net removal of water is observed for all of the

calibration experiments. This is consistent with the use of the helium in the oxidizer line throughout the

experiment. Because the helium is not passed through

a saturator, it causes a removal of water from the reaction vessel. The signs in the changes of water in the reaction vessel during the reaction experiments

nearly correlate with the amounts of excess hydrogen

used. The stoichiometric and actually used reactant

ratios are summarized below.

Table 2. Water changes in reaction vessel

Expt. Water removed Water carried Increase

No. in B

1

Electrical calibrations

4 0.8033 0.S246 -0.2787

5 .8084 .4813 -0.3271

6 .7025 .4644 -0.2381

7 .7478 .4637 -0.2841

( >xygenhydr< gen reaction

1 0.6680 0.6483 -0.0197

2 .6483 .7264 + 0.0781

3 .8313 1.0051 + 0.1738

I .8676 0.8887 + 0.0211

.9486 .9740 + 0.0245

6 .9345 .9161 + 0.01 16

Oxygen difluoride hydrogen reaction

7 0.5466 0.5656 + 0.0190

8 .7458 .7135 -0.0323

9 .7069 .7288 + 0.0219

10 .6102 .6805 + 0.0703

1

1

.5034 .6186 + 0.1152

Kluorine- hydrogen reaction

1 1 1 1.0715 -0.3285

2 1.2908 1.0127 -0.2781

3 1.1670 1.0396 -0.1274

5 0.9910 0.8310 -0.1591

6 1.0987 1.0397 - 0.0590

7 0.8431 0.7853 -0.0578

8 1 .0606 .9651 -0.0955

9 0.9137 .8323 -0.0814

10 .8322 .7700 -0.0622

reactii in stoichiometric actual

0->- H. 2 2.8-3.4 F,- H. /ln,/rt Fj 1 4 OF.- 2 4

A much larger excess of hydrogen was used in the

fluorine reactions. This shows in the net removal of water from the reaction vessel, compared to the deposition of water observed for the other reactions.

3. Electrical Calibration Results

A series of seven electrical calibration experiments was conducted and the data are given in table 3. Included in this table are the experiment

number; the average calorimeter temperature,

f(av); the correction to the temperature rise, Af(corr);

the corrected temperature rise, Ai f ; the average current; average voltage; heating time; electrical energy;

and the energy equivalent of the calorimeter. For

the seven experiments the average value for the

energy equivalent was 21887.9 J (°C)"' with a standard

deviation of the mean of 0.006 percent.

294-119
Table 3. Calibration of the calorimeter

Expt. No. i 2 3 4 5 6 7

1 (av) °C... 30.37 30.36 30.38 30.39 30.37 30.38 30.48

°c... 0.04724 0.04976 0.04658 0.04332 0.04878 0.04709 0.04368

A/r °c... 2.73616 2.75413 2.72360 2.71066 2.74159 2.77289 2.55693

A... 1.62580 1.62770 1.62706 1.62711 1.62770 1.62817 1 .62737

V... 37.3949 37.4378 37.4236 37.4280 37.4385 37.4483 37.4282

984.857 989.160 979.206 974.077 984.874 995.612 y 18.805

<t J... 59875.9 60276.9 59624.3 59320.7 60016.8 60704.6 55964.0 E jrcr'... 21883.2 21886.0 21891.7 21884.2 21891.2 21892.2 21887.2

4. Examination of the Reaction Products

The corrosivity of fluorine and hydrogen fluoride

is a general problem to be minimized and checked in these experiments. This was partly accomplished by

using Monel as the construction material for the

flow line and combustion chamber. Prior to the ex- periments these parts of the flow system were ex- posed to a flowing fluorine atmosphere to condition

the surfaces. Consequently, all of the fluorine re- leased from the weighed sample bulb should enter

into the reaction with hydrogen.

Most of the corrosion problem in these experiments was caused by the product hydrogen fluoride. The

appearance of the combustion chamber after the ex- periments suggested that more corrosion resulted

from the hydrogen fluoride in the Fo-rT reaction than

from the HF-rFO mixture in the OF2-H2 reaction.

The solutions and washings from the primary solution vessel were transferred to a weighed polyethylene

bottle from which weighed aliquots were taken for

titration with standard sodium hydroxide solution. After the analyses for H +

, samples of these solutions were analyzed by atomic spectrophotometry for Cu+ +

, Ca+ +

, Ni ++ and Ag+. These results for the F2 -H2 -rFO

and OF2-H2-H2O reactions are given in table 4.

Table 4. Quantities of metal ions in hydrofluoric acid solutions

Expt. No. Ag Ca Cu Ni n Hr equiv

M moles (total) F2 -H2 H2 0 Reaction

1 <0.05 <0.3 7.4 20.0 0.00005

2 <.05 < .3 9.0 16.1 .00005 3 <.05 < .3 2.2 9.1 .00003 4 <.05 < .3 1.5 3.9 .00001

5 < .05 < .3 1.5 4.5 .00001 6 < .05 < .3 3.2 8.4 .00002

7 < .05 < .3 0.6 3.9 .00001

8 < .05 < .3 < .1 4.7 .00001

9 < .05 < .3 1.2 7.7 .00002

10 <.05 < .3 3.5 10.0 .00003 OFrH2-H2O Reaction

1 0.3 1.4 16.1 32.9 0.00010 4 < .05 0.9 15.1 23.4 .00008 7 <.05 .9 16.8 29.2 .00009 Blank <.05 < .1 < 0.1 < 0.2

For the fluorine reaction, the solution from each

experiment was analyzed, and in the OF2 reaction

solutions from three selected experiments were tested. The blank is a sample of the demineralized water used

for the solutions. Because the blank showed no ions

(outside the uncertainty intervals), we concluded that the metal ions resulted from the corrosion of the

reaction vessel. The total amount of corrosion cannot be deter- mined from these tests. The total quantity of aqueous

fluoride salts amounts to less than 10 percent of the

deficiency of HF. (Compare n HF(equiv) in table 4 with

A/2 H F(°bs-calc) in tables 7 and 9.) However, the tests do reveal some interesting features about the reactions.

The solutions from, the fluorine reaction contain a smaller concentration of the metal ions, in spite of the more corroded appearance of the reaction vessel.

It is possible that only the metal fluorides that exist

in the vapor phase near the flame position are flushed

downward by the effluent gas in this reaction. On the

other hand, the product HF(aq) in the oxygen difluoride

reaction may dissolve some metal fluorides and serve

as a transport medium to the solution. Approximately

1 g of water was formed in each experiment, more than

enough to wet the surfaces of the combustion chamber.

Much more erosion of the CaF2 disk was observed for the OF2 reaction. This is consistent with the larger

amount of Ca++ present in the solution, and suggests

that the CaF2 is slightly dissolved by the HF(aq), and

then transferred to the solution.

5. Reaction Heat Measurements

5.1. Oxygen-Hydrogen Reaction

For six of the nine experiments on this reaction

(series I) the contents of the calorimeter were the same

as for the electrical calibrations. In the other three

experiments (series II), the water in the solution vessel was omitted, so that the product water could be

weighed and compared with the amount calculated

from the weighed quantity of oxygen reacted. In these

three experiments the water was flushed from the

reaction vessel with helium and absorbed in magnesium perchlorate outside the calorimeter [21].

The data for the experiments are given in table 5. ms is the mass of sample and mo, is the mass of oxy- gen, based on the analysis given in section 2.1.b. mHiQ

(obs) is the measured mass of water formed in the reaction and mH2 o(obs)/mH2o(calc) is the ratio of the observed

to calculated quantities of water. £(av) is the average

temperature of the calorimeter during the reaction

and is the reference temperature for the reaction.

Af(corr) and \tc are respectively, the correction to the

temperature rise and the corrected temperature rise. 295-120
Table 5. 02 — H2 reaction

a. Heat measurements

Series II

Expt. No.

3.3032

3.3028 3.38503.3846

3.4945

3.4941 3.22083.2204 3.22483.2244

3.2376

3.2372 m Hjll(obs) m„„,(obs)/m Hin(calc)..

r av A/(corr) A(r m Ha(J (in soln vessels).. Ae, Ae,

£(ealorim)

globs)

"H,/"n>

.°c.

.°c.

.°c.

.J(°C)- JCC)-

.J(°C)-

J

30.36 0.06586

2.70570

119.64

7.8 0 21895.7

59243.2

2.81

30.38 0.06620

2.77304

119,64

7.50 21895.4

60716.8

2.88

30.43 0.05722

2.86490

119.64

8.20 21896.1

62730.1

3.02

30.31 0.04966

2.64052

119.64

7.60 21895.5

57815.5

3.35

30.32 0.05286

2.64704

119.64

7.6

0 21895.5

57958.3

3.35

30.32 0.05159

2.64914

119.64

7.60 21895.5 58004.2

3.23

3.2342 3.2338

3.6417

1.0001 30.34 0.07163

2.67368

0

7.6 -499.9

21395.6

57205.0

2.96

3.2325

3.2321

30.34 0.06773

2.67882

0

7.6 -499.9

21395.6

57315.0

2.96

b. Corrections to the heat measurements

g(ign) J... </Uemp) J... if'(vap) J...

23.2 -37.5

271.5

36.3

16.0 -40.3

278.1

39.6

11.5 -25.1

371.1

29.1

19.6 -42.0

256.6

26.2

22.4 -28.0

279.5

26.1

18.2 -38.9

265.3

26.1

16.4 -18.4

10.5 -46.417.1 -38.5

(?"(vap) J... ?"'(vap) J... -366.9 -33.9

-402.8

57607.8 0.20212

285.02

-227.6 -33.8

-297.3

57612.3 0.20202

285.18

-181.6 -33.8

-236.8

56181.7

0.19702

285.16

tf'Nvap) J... Total J... 9m J-

?o,/"hio kj mol-1

...

293.5 58949.7 0.20644

285.55

293.4 60423.4

0.21154

285.64

386.6 62343.5

0.21838

285.48

260.4

57555.1 0.20!28

285.95

300.0 57658.3

0.20154

286.09

270.7 57733.5 0.20234

285.33

a Water formed was not measured.

b Attempt to measure water was unsuccessful.

f7i H2o(in soln vessels) is the total mass of water in the

solution vessels. Ae> is the correction to the energy

equivalent for the water formed in the reaction (the

heat capacity of half the water formed). A?2 is the

correction for the omission of water from the solution

vessel, ^(calorim) is the energy equivalent of the cal- orimeter corrected for the deviations from the standard

calorimeter, <?(obs) is the observed heat effect. g(ign) and ^(temp) correct for the ignition energy

and the energy required to temper the reacting gases

from room temperature to £(av), the average calori- metric temperature during the reaction. <?(ign) was

calculated from the sparking power, 1.4 J sec

-1 and

the measured sparking times. <7(temp) was calculated

from the heat capacities and the measured amounts

of the gases reacted.

g'(vap) is a correction for the addition of water to the reaction vessel during the reaction period by the

reacting hydrogen. The hydrogen that enters into reaction is saturated with water, which condenses

and is not carried out of the calorimeter. The amount

of water added to the calorimeter is calculated from

the volume of hydrogen reacted (based on stoichiometry of reaction) and the vapor pressure of water at the room temperature. <?'(vap) is then the heat of con- densation of this water at t(a\). In contrast, the helium used for purging the oxidizer

line causes a net removal of water from the solution

vessel. We reason that if the gas flow were begun at the time when one-half of the temperature increase

is achieved, no correction would be needed for the

vaporization of the water because the heat effect would

then be properly accounted for by the final drift rate measurements. q"(\ap) is a correction for the energy

of vaporization of the additional water that would

have been removed from the solution vessel had the

helium flow been started at t m at the rate that was

continued through the final drift period. <7'(vap) and

g"(vap) apply to all experiments with water in the solu- tion vessel, whereas the corrections <7"'(vap) and

g

lv (vap) pertain only to the experiments in which the

product water was measured, </"(vap) is the amount

of heat required to vaporize the water removed from

the reaction vessel by the hydrogen and helium during

the reaction. This quantity of water was measured by

weighing the absorber immediately after the experiment, and using another weighed absorber for col- lecting the water remaining in the reaction vessel.

<7 ,v (vap) is the heat of vaporization of the water in the

vapor phase in the reaction vessel. We have assumed that the nitrogen impurity present

in the hydrogen and the oxygen sample does not react and therefore no correction was applied. Under the

conditions the nitrogen impurity may react to give

NH3. No test was made for NH^ in these experiments.

In similar calorimetric work Rossini [21] reported the

presence of nitrogen in his oxygen sample. For some

of his experiments in which oxygen was burned in a hydrogen atmosphere, he tested the product gases for NH.i and found the amount present to be negligibly

small. The heat of the oxygen-hydrogen reaction is given in table 6. The values given represent averages for the

number of experiments shown in parentheses. The

data are given for 303.4 °K and 298.15 °K. The factor,

cr, is the standard deviation of the mean. As mentioned above, the series II measurements were con- ducted mainly for confirming the amount of reaction.

Because water was not contained in the solution vessels for these measurements, we believe that the heat

296-121
Table 6. Heat of the oxygen-hydrogen reaction

H2 lg)+'/202( s )=H20(1) — A//° — A/y° ift

Series I (6) kj mol-1

.. 285.67 285.84 0.12 Series II 13) 285.12 284.30

Series I (6) kcal mol-1

... 68.28 68.32 0.03 Series II 13) kral mob' . 68.14 68.18

cr is the standard deviation of the mean.

data are less reliable than the series I data. The fact

that they are less negative suggests that all of the heat

from the reaction was not dissipated by the effluent

gas. We do not propose the value found here, AH°H8 = — 68.32 kcal mol-1

, as a replacement for Rossini's

determination [21], but use the agreement with the

earlier work as an indication of the general validity of these and other experiments conducted in this study.

5.2. Fluorine-Hydrogen-Water Reaction

Ten experiments were conducted for the Fo-tL-HjO

reaction. For the first five experiments only the oxidizer

flow line was conditioned with fluorine, whereas in the remaining experiments the flow line and combustion chamber were conditioned. On this basis the

data for the experiments are presented in two series. The data for these experiments are given in table 7. The heat measurement data have been explained for the oxygen reaction. Ae is a correction to the energy

equivalent for the hydrogen fluoride formed in the

reaction (one half the heat capacity of the hydrogen

fluoride). nH20/nHF is the ratio of the moles water in the solution vessel to the moles of hydrogen fluoride formed in the reaction, as determined by the analyses

of the solutions. For the reaction quantities, /i H f(F2 ) and n HF(CF4 ) are the numbers of moles of HF produced from

F> and CF4 , respectively. They were calculated from

the analyses in table 1. The deficiency of HF in these

experiments varied greatly. For the ten experiments,

the values of /7 H F(°bs)//? HF (calc) ranged from 0.9772

to 0.9964, with a mean of 0.9844. We assume that the

deficiency of HF is caused by corrosion. However,

the erraticity of the recovery is difficult to explain.

The ignition, vaporization, and gas temperature

corrections are the same as described above. q0z , qCF4

, and <7 C02 are corrections for the reactions of the

impurities. These corrections were calculated on the

basis of eqs (1), (2), and (3).

Ar7fl,2!>8.15 °K [8 | H2 (g)+V202 (g)-> HtO(l) -68.32 kcaKmol H.O)- 1 (1)

2H2(g)+CF4 (g)+50H2 (l)^4[HF:50H2 OJ(l)+C(c) -84.2 kcal(mol CF4) _1

(2)

2H*(g)+COs(g)-»C(c) + 2H2 0(l) -42.59 kcaKmol CO,)" 1 (3)

Table 7. F2 -H2-H2 0 reaction

a. Heat measurements

Series 1 Series 2

Expt. No. 1 2 3 4 5 6 7 8 9 10

3.5504 2.7483 2.7084 1.3165 2.7981 2.9859 2.4623 2.6524 3.1136 2.4048

At(corr) °c... 0.05552 0.03351 0.03381 0.07354 0.02279 0.07565 0.02937 0.03237 0.04481 0.05046

A(r °c... 2.71469 • 2.10439 2.07278 1.01125 2.14415 2.29429 1.89230 2.04004 2.39349 2.61824

i(av) °c... 30.35 30.73 30.73 30.02 30.74 30.16 30.78 30.69 30.51 30.30 Ae Jt°C) 1.8 1.4 1.4 1.0 1.4 1.6 1.6 1.4 1.6 1.8 £(calorim) J(°C)->... 21889.7 21889.3 21889.3 21888.9 21889.3 21889.5 21889.5 21889.3 21889.5 21889.7

g(obs) •. J... 59423.7 46063.6 45371.7 22135.2 46933.9 50220.9 41421.5 44655.0 52392.3 57312.5

nHio/ n HF 30.4 38.9 39.8 82.9 38.2 35.8 44.3 40.9 34.8 31.8

b. Reaction quantities

0.09243 0.07155 0.07051 0.03427 0.07284 0.07773 0.06410 0.06905 0.08111 0.08864 nHF(CF4 ) .00020 .00016 .00016 .00008 .00016 .00016 .00012 .00016 .00016 .00020 nHP(ealc) mol... .18506 .14326 .14118 .06862 .14584 .15562 .12832 .13826 .16238 .17748

rtHrlobs) .18277 .14267 .13965 .06706 .14532 .15502 .12545 .13596 .15938 .17453 AnHF |obs-calc) mol... -.00229 -.00059 -.00153 -.00156 -.00052 -.00060 -.00287 -.00230 on ',1111 -.00295

1„ f '..l.»'.>! 1 .9876 .9959 .9891 .9772 .9964 .9961 .9776 .9833 .9815 .9833

c. Corrections to heat data

9(ign) J... 17.6 30.0 14.8 19.6 23.2 22.4 19.0 23.8 30.2 24.1

ij'(vap) J... 122.6 100.3 100.3 56.9 90.8 120.9 89.9 95.8 109.2 104.0

?"(vap) J... 31.4 24.3 25.5 14.2 22.4 26.3 21.4 21.3 25.1 30.7 g(temp) J... -15.5 -7.3 -13.8 - 1.5 -25.1 - 11.1 -15.5 - 14.6 -19.2 -34.9

9<02 > J... 205.8 159.8 159.8 74.0 165.7 177.0 142.0 154.4 182.8 200.0 qCV,) J... 17.6 14.1 14.1 6.7 14.1 14.1 10.5 14.4 14.1 17.6 ?(C02 ) J... 1.7 1.7 1.7 .8 1.7 1.7 1.7 1.7 1.7 1.7 7(dilnl J... -12.2 -6.5 -5.3 7.0 -6.1 -7.1 - 1.0 -3.4 -8.0 - 11.7 Total (1) 369.0 306.4 297.1 163.7 286.7 344.2 268.0 293.4 335.9 331.5

J... 764. 197. 510. 520. 173. 200. 958. 767. 1001. 984. Total (2) 1133.0 503.4 807.1 683.7 459.7 544.2 1226.0 1060.4 1336.9 1315.6 WD J... 59054.7 45757.2 45074.6 21957.5 46647.2 49876.7 41153.5 44361.6 52056.4 56981.0

9f,(2) J... 58290.7 45560.2 44564.6 21437.5 46474.2 49676. 40195.5 43594.6 51055.4 55997.0

«F,(l)/nHr(Fa) kj mol-1

... 319.45 319.76 319.63 320.36 320.20 320.83 321.01 321.23 320.90 321.42 Q>AVn'HF

' 323.46 321.08 323.14 327.82 321.35 322.08 328.36 326.67 326.95 326.86

'<frJ3)ln'm kj mol 1

.

.

319.28 319.70 319.48 320.06 320.16 320.78 320.72 321.02 320.66 321.21

' n'ur — «HF(obs) — n HF(CF.i).

297-122
<7(diln) corrects for diluting the acid solution from

a concentration, HF:nH2 0, to HF:50H,O. Total (1)

is the sum of the corrections to this point and total (2) includes </(corros), a correction for the corrosion of the combustion chamber. Equation (4) is the cor- rosion reaction assumed and shows the heat of re- action used for calculating </(corros) [22J. The number

of moles of reaction (4) is taken to be « HF(obs-calc)/2.

F2 (g)+ Ni(c)-> NiF2 (c) - 159.5 keaKmol F,," 1 (4) The corrections Total (1) and Total (2). table 7, were applied to the observed heat effect to give

</ F2 (l) and qri(2), respectively. We now have three

ways of calculating the results. Referring to experiment (1) for example, in the first way the heat of reaction corrected by Total (1) to give q

{^ is pre- sumed to be caused by the measured amount of

¥• introduced, giving gK2 (l)/n HF (F-.>) = 319.45 kj moH.

In the second way the same heat of reaction is at- tributed to reaction of enough fluorine to form the observed amount of HF, giving qr2 (l)/n'HF = 323.46

kj mol-1

. In the third way the deficiency of HF is attributed to corrosion forming NiF2 (c), introducing an additional energy correction, ^(corros), and al- lowing a new total energy, qp2 (2) to be attributed to the amount of F> needed to form the observed HF.

This gives qV2(2)jn'H? = 319.28 kj mol-1

, which we consider to be the best representation of the data. All experiments are treated each way at the bottom ol table 7.

The results of two series of five measurements

each are summarized in table 8 in which the results obtained by the three methods are listed in columns (1),

(2). and (3). respectively. The calculation in column (3)

is preferred for reasons described above and experiments of series 2 are considered to be preferable

because of a better conditioning procedure for the

reaction vessel. Hence, the value A//°o;j = — 76.69

kcal mol-1

is selected for use in later calculations.

This value, corrected to 298.15° gives

A///W,[HF-50H2 OJ = - 76.68 kcal moF1.

TABLE 8. Heat of fluorine-hydrogen-water reaction

'/2F2 lg)+ '/2H2 (g)+ 50H2 O(l) = [HF • 50H2 O](l)

Series 1 (5) kj mol-1.. Series 2 (5) kj mol" 1 ..

(1)

O"

(2) u

(3) - AH3„3 cr

319.88 321.08 IU7

0.11 323.37326.18

1.21 1.07 319.74

320.87

0.15

0.11

Series 1 (5) kcal mol-1

.. Series 2 (5) kral mol-'..

76.43 76.740.04

0.03

77.29 77.960.29

0.25 76.42

76.69

0.04

0.03

O" is the standard deviation of the mean.

5.3. The OFj -Hydrogen-Water Reaction

The data obtained for this reaction are shown in table 9. No new features are involved. The experiments

in series 1 were conducted before the electrical caliTabi.E 9. OF2-H2-H2O reaction

a. Heat measurements

Expt. No I hi 12

e

Aftcorr) °C

A(r "C

flavl °C Ae J(°C)-' E JCC)-'

olobs) J "hio/RhP

Iofi mol

hhfICFj) mol

nfip(calc) mid

n Ht lobs) mol

AriHFvobs— calc) mol

n HF (obs)/n„ F lcalcl

olignl J

(Jlvapl J ?"lvap] J (/Hemp) J

(Jldiln) J <7(02 > J <?(CF,I J i/il.Ojl J Total 11) J ^fcorros) J Total 121 J 7of.H1 J

Oot,l21 J 9oF,U)/n0F, kjlmolr'

'/..>,! !'/"„f,

' kjlmolr'

»or.<2)/»L, kjlmolr'

2.9080

0.052.53 2.34591 30.16

3.8 21891.7 51356.0

52.6

3.437(1 0.04624

2.77485

30.37

4.0 21891.9 60746.7

44.6

3.0869 0.05224

J l'i|00 30.25

3.9 21891.8 54533.8

49.4

3.5261 0.04464

2.84661

30.41 4.0 21891.9

62317.7

43.2

3.4556 0.05456

2.78877

30.38

3.9 21891.8

61051.2

44.3

3.4512 0.05402

2.78491 30.38

3.9 21891 .8 60966.7

44. t

3.4558 0.05216

2.78889

30.39

3.9 21891.8 61053.8

44.4

3.41115 11.05179 2.74369

30.37

3.9 21891.8

601164.3

45.1

3.3549 0.05348

2.70657

30.37

3.9 21891.8

59251.7

45.8

3.3785 0.05228

2.72699

30.36

3.9 21891.8 59698.7

45.5

3.4021 0.04842

2.74267

30.50

3.9 21891.8 60042.0

45.3

3.4929

11 11462

1

2.81633

30.45

4.0 21891.9 61654.8

43.8

b. Reaction quantities

0.05351

.00016

.10718

.10669 -.00049

.99.54

0.06224

.00016

.12664

.12602 -.00062

.9951

0.05680

.00016

.1 1376

.11380 +.00004

I nun -:

0.06488

.00016 129V2

.13009 +.00017

1.0013

0.06359

.00016

.12734

.12682 -.00052

.9959

0.06351

.110016 .12718

.12634 -.00084

.9934

0.06359

.001116 .12734

.12658 -.00076

.9940

0.06259

.00016 .12534

.12462 -.00072

.9942

0.06173

.00016

.12362

.12266 -.00096

.9922

0.06217

.00016 .12450

.12355 -00095

.9924

0.06260

.00016

.12536

.12399 -.00137

.9890

0.06427

.00016

.12870

.12811 -.00059

.9954

Corrections to heat measurements

17.1 18.9 19.3 14.11 21.6 21.6 16.8 19.6 18.5 14.8 14.8 19.0 19.9 140.6 155.0 130." 162.7 179.1 169.4 148.1 146.1 143.9 154.8 165.7 156.9 148.1 31.8 55.6 43.6 45.2 53.1 53.1 53.1 45.2 50.6 50.6 49.8 50.6 50.6 -22.8 -36.8 -30.

1

- 35.6 -22.0 -28.4 - 38.2 - 42.0 -40.2 -34.2 -29.3 . -37.0 -41.5 + 1.8 - 1.0 -.4 -2.2 -1.0 -1.0 - 1.0 -.5 — .5 -.5 -.5 -1.0 -1.0

234.3 274.0 245.6 285.8 274.0 274.0 274.0 274.0 268.6 268.6 268.6 279.9 279.9

14.1 14.1 14.1 14.1 14.1 14.1 14.

1

H.I 14.1 14 1 14.1 14.1 14.1 8.8 10.5 10.5 10.5 10.5 10.5 10.5 10.5 10.5 10.5 10.5 10.5 425.7 490.3 433.5 494.5 529.4 513.3 477.4 467.0 465.5 478.7 493.7 493.0 480.6

240. 303. II 0 254. 411. 372. 352. 469. 465. 670. 288. 401. 665.7 793.3 433.5 494.5 783.4 924.3 849.4 819.0 934.5 943.7 1163.7 781.0 881.6 50930.2 60256.4 54100.2 61823.2 60521.7 60453.4 60576.4 59.597.3 58786.2 59220.0 59548.2 61161.8 60717.8

50690.2 59953.4 54100.2 61823.2 60267.7 60042.4 60204.4 5924.5.3 58317.2 58755.0 58878.2 60873.8 60316.8

951.79 952.82 952.47 952.88 951.75 951.87 952.61 952.18' 952.31 952.55 951.25 951.64 952.29 956.17 957.51 952.13 9.51.71 955.66 958.21 958.33 957.69 959.77 959.96 961.85 956.10 958.45 951.66 952.70 952.13 951.71 951.64 951.69 952.45 952.04 952.12 952.35 . 951.03 951.52 952.12

[nHP(obs)-nI1F (CFJ]/2. 298-123
brations were performed, and those in series 2 were

conducted later. Otherwise, the procedures used were

identical. The average recovery of hydrogen fluoride was better than 99.5 percent, g(corros) for this system was calculated from eq (5) using the heat of reaction

given there and a number of moles equal to AnHF(obsealc)/2.

OF2 (g)+ Ni(c)+ H2 (g)= H2 0(1)+ NiF2 (c)

-233.78 kcal (mol OF2 )-' (5) The treatment is the same as for the fluorine reaction.

The three alternative calculations of the reaction

energy are shown at the bottom of table 9 and in table

10, of which the preferred one is based upon the

amount of energy, adjusted for the energy of cor- rosion, and the amount of hydrogen fluoride actually

observed. This is given as A//303 (3) of table 10.

TABLE 10. Heat of OF2-H2-H2O reaction

0F2 + 2H2 + 99H2 0 = 2 [HF 50H,O] ( /

)

- Aff;03(2) o~ -A//3°

ra(3) a

Series 1 kj mol-1... 952.26 955.23 951.92

Series 2 kj mol-1... 952.12 958.88 951.95

Total (13 expts) 952.18 0.14 957.20 0.80 951.94 0.14

Series 1 . kcal mol-1

. Series 2 kcal mol-1

. Total 113 expts)

227.60

227.56

227.58 0.033

228.31

229.18

228.78 0.19

227.51

227.52

227.52 0.033

cr is the standard deviation of the mean.

6. Discussion of Errors The uncertainties are summarized in table 11 for the

three reactions and for the calculation of the heat of formation of OF2 (g). The observed standard deviation

of the OF2 -H2 -H2 0 measurements is 0.14 kj mol-1 or

0.015 percent and that for the electrical calibrations

is 0.015 percent. Hence the overall imprecision

in the experiments expressed in 2-sigma limits is ±2 V(0.015) 2 + (0.015) 2 = ±0.042 percent (0.40 kj mol"1 ).

Systematic errors in calibration are 0.02 percent

for "irrelevance" and 0.02 percent for the transient.

Systematic errors in the reaction heat measurements

are 0.02 percent for uncertainty in the oxygen content

of the sample, and 0.02 percent for uncertainty in the correction for corrosion. Each of these sources

of error is explained below. Assuming that these er- rors are independent we apply them as the square

root of the sum of the squares and obtain 0.040 per- cent (0.38 kj mol-1

) as the overall systematic error. The overall uncertainty in the heat of reaction is, therefore the sum of 0.042 and 0.040 or 0.082 percent

(0.78 kj moh 1 or 0.19 kcal mol" 1 ). The error treatments for the two other reactions are summarized in much the same way. The systematic

errors for the 02 -H2 experiments do not include any

uncertainties for analysis or corrosion, but do include

systematic errors listed for the calibration. To place

these on the same basis as the other calculations, we

combine these two systematic errors as the square

root of the sum of the squares.

In estimating the uncertainty in the heat of formation of OF2 we combine the contributions in joules for the three reactions in the following way. The random

errors and the chemical errors, which are presumed

to be independent for the various reactions, are added

without regard to sign; and the systematic calibration errors are added with due regard for the sign with

which the reaction equations are added, in order to obtain their contributions to the uncertainty in the

heat of formation of OF2 . These contributions, listed

Table 11. Summary of errors

A//k 303 °k W mol" 951.94 .'-420.88 285.67

Random errors: Calibration (crc ) Reaction measurement (o>).

Imprecision 2 vcrf+oj..

Systematic errors: Irrelevance of calib Transient

Total systematic calib. Analysis Corrosion

Total chemical

Overall systematic error.

Uncertainty

Uncertainty (kcal mol-1

).

OF2 -H2 -H>0 F2-H2-H2O 1/2 O2-H2 %

0.015

.015

0.042

0.02

.02 .028

.02

.02 .028

0.040

0.082

kj mol

0.14

.14

0.40

0.19

.19

.27

.19 .19

.27

0.38

0.78

0.19

0.015

.034

0.074

0.02

.02 .028

.02

.02 .028

0.040

0.114

kj mol"

0.05

.11

0.24

0.06

.06

.09

.06

.06

.09

0.13

0.37

0.09

%

0.015

.042

0.089

0.02

.02 .028

0.028

0.117

kj mol"

0.04

.12

0.25

0.06

.06

.08

0.08

0.33

0.08

OF2

kj~

1.13

11.111

.45

0.46

1.59

0.38

299-124
in the right-hand column of table 11, are added to obtain 1.59 kj mol-1 (0.38 kcal mol-1

) for the uncertainty in the heat of formation of OF2 (g). Recent experiments in this laboratory have indi- cated that to obtain accurate heat measurements in calorimetric studies such as these, using the Dickin- son calorimeter, the chemical energy and the energy

from the calibration heater should be liberated at nearly the same position in the calorimeter [16]. This

would tend to cancel the effect of temperature gradi- ents on the surface of the calorimeter. In the experiments described in this paper, the heater was near the

side of the calorimeter (closer to the thermometer),

whereas the reaction vessel was near the center. The

earlier investigation shows that the energy equivalent

determined from the electrical energy measurements

may be inappropriate for the calorimeter as used in the chemical energy measurements. This possible

uncertainty in the calibration is listed here as the

"irrelevance" error and is estimated to have an upper

limit of 0.02 percent for these experiments. It is noted

that this error probably affects all of the heat measure- ments by the same fractional amount. It would thus cause an effect too small to be observed in the heat of formation of OF2 which is calculated from differences

between the measurements reported here; however, it could have an observable effect on the values for A#;2HH . 15 [HF- 50H 2 O[(l) and Atf° MIU5 [H2 0(l)]. The

close agreement of the value found for the latter quantity with that reported by Rossini suggests that no important error is involved.

The "transient" effect has already been discussed

in the description of the calibration procedures. Exact

measurements of the effect were not made, but the

maximum systematic error that could arise from this source was calculated to be 0.02 percent.

On the basis of earlier work [1, 2], we believe that the error in the analysis of the fluorine sample is 0.02 percent. Assuming that this amount of uncertainty is distributed among the F2 , N2 , and 02 analyses, dif- ferent values for nHF(calc), q02 , and g(corros) are ob- tained (table 12). The variations amount to less than

.02 percent.

We can demonstrate the validity of the overall cor- rosion correction applied in the following way. In

figure 5 we have plotted the heats of reaction, cor- rected and uncorrected for corrosion, versus the per- centage correction for corrosion for the F2 -H2 -H2 0

Table 12. F2-H2-H2O reaction

Expt. #8

wt F: sample, 2.6524 g Column 1 2 3 4 Fa m 98.92 98.90 98.90 N2 (%) 0.54 0.56 0.54 02 1%) .33 .33 .35 CF< (%) .13 .13 .13

0.13826 0.13824 0.13824

.13596 .13596 .13596

AriHFlobs-calc) .00230 .00228 .00228

J.. 767.0 761.0 761.0

Qo. J... 154.3 154.3 165.7 sum of glcorros) and q0t J... 921.3 915.3 926.7

J.. 44655.0 44655.0 44655.0

-0.013 + 0.012

_ 970 o1 960

I

1 1 1 ! OFj-H

2 -H

20

1 1 1

y=A+B(X)

1

y °i B T-

I 952 06 C2? 9.37 0.43

» n

a..(2)/n'

'of, 952 07 0.27 -0 25 044

i i i 320 84 0 50 3 28 0 17

qF (ZVh'

HF 320 88 0 32 -00015 0.18

F

2 -H2 -H

20

i i l 1

II

0 02 04 06 08 10 1.2 14 16 18 20 22 24

X. % CORRECTION FOR CORROSION

Figure 5. Plot showing the variation of the heats of the F2 — H2—

H

2 0

and OF2 — H2 — H2 0 reactions versus the percentage correction for

corrosion.

(X = <?(corros) x 100/<7(1), tables 7 and 9)

and OF2 -H2 -H2 0 reactions. The data plotted are obtained from tables 7 and 9, respectively. The data were fitted to the lines shown by the method of least squares and the equations are shown on the illustra- tion. For both reactions there is a linear variation of the

uncorrected heat of reaction with the ^(corros) which was essentially eliminated, when ^(corros) was applied.

This illustration also shows why, in tables 8 and 10, the

standard deviation of the mean of A//(3) is much less than for AH(2). The application of g(corros) smooths

out an effect present in varying degrees in each of the

experiments.

7. The Heat of Formation of Oxygen

Oifluoride. The (O-F) Bond Energy

We summarize the heat measurements and the heat

of formation of OF2 in table 13. The calculated heat of formation at 303.4 °K becomes the same value at 298.15°Kto yield AHfc»8.i5[OF2 (g)] = +5.86±0.38 kcal

mol-1. The uncertainty shown represents the esti- mated accuracy based on the errors discussed. The

value for the average O—F bond energy in OF2 is calculated from this value for A///[OF2 (g)] , using

A#?[0(g)] = 59.553, and A//?[2F(g)] = 37.75 kcal moH

[8J, to be 45.72 kcal mol- 1

.

Table 13. The heat offormation of OF2

A//«. ana aK kcal

OF2 (g)+ 2H2 (g) + 99H2 0(l) > 2[HF-50H2 O](l) -227.52±0.19 (6)

F2 (g)+H2 (g)+ lOOHsO(l) • 2[HF-50H2 O](l) - 153.38 ±0.18 (7)

1/2 02 (g)+H2 (g) > H2 0(1) -68.28±0.08 (8)

F2 (g)+ 1/2 0,.(g) OF2 (g) AtfjW. ,«[OF2 (g)] = + 5.86 kcal±0.38 (9)

In table 14 we give the reactions investigated in the

earlier work and compare the value reported for AH/2H«., 5[OF2 (g)] with the value [ + 5.86 ±0.38 kcal

300-125
Table 14. Earlier thermochemicul studies involving OF^Ig)

Temp - A«° AHJ2.„[OF2 ] Kef °K kcal mol-1

1. 291 125.75 + 6.9 [3. 6. 23]

2. C\F („ix ff^k"! -1- 9HIT1 liw^^cc m ,.,,| n| — f AV"C _|_)WI -uHr\l / . It" 1 -1- HIT -..I., i 29 1 1 76.55 + 1 .4 [3. 6. 23]

3. OF2 (g)+4HBr (excess HBr aq 45%)= [2HF + 2Br-| (aq HBrt+H.O 291 134..% + 8.8 [3. 6. 23] Av+5.7±2 ;1

4. OF2{g)+2H-.C)+2NaOH (excess aq 20%)=2NaF (in aq NaOH) + 3H O(l) 254.9 [4. 23]

5. 14. «J

6! F2 (g) + H.(g) + 2NaOH (excess aq 20%) = 2NaF (in aq NaOH)+ 2H2 0(1) 181.7 [4. 23] + 4.7±2"

7. OF2(g) + H2 (g) (excess)+ nH2 Ol!) = [2HF+ (n + 1)H2 0] (l){n = *} 222.93 -4.(16±2.2 a [9. 23]

8. + 5.86 ±0.38

a Estimated overall uncertainty given in original report.

mol-1

] derived from the present study. Our value agrees

consistently with those reported by von Wartenberg

and Klinkott [ + 5.7 ±2 kcal mol -1

], and Ruff and

Menzel [ + 4.7 ± 2 kcal mol-1

], but differs from Bisbee's

results [-4.06 ±2. 2 kcal mol-1

]. In the various reviews which have been conducted

on these studies so far, the biggest improvement in the re-evaluation of the original data has been to substitute current auxiliary data for the reactions studied

by von Wartenberg and Klinkott. Ruff and Menzel

measured the heats of principal reaction (4) and the

auxiliary reactions ((5) and (6)) for calculating

their value for A/$>!W .i.-> [OF2 ] . Bisbee's value for

A/Z/oHH.i.itOF^] will change as improvements are made

in the A/ZjoHK.istHF, aq, x ], the principal auxiliary data on which their results are based. However, it seems

unlikely that the A//j 2!)H .i5 [ HF, aq. °°] will ever be re- vised by an amount that will change the sign of their value for A#jW15 [OF2 ]

.

No attempt will be made here to review completely

the earlier studies. However, in re-examining the

work of Bisbee et al., we note several points about

their experiments which may lead to a less negative

observed heat of reaction, and therefore explain the more negative heat-of-formation value which they

reported. They give little information on the (1) analysis

of the sample, (2) the technique used to insure mixing

of the solution, (3) the corrosion by the product HF,

and (4) the quantitative basis for the heat of reaction.

Each of these aspects of their experiments is very important in the accuracy of the work. For example,

oxygen is a usual impurity in the OF2 produced by the

present-day method {¥> + NaOH) and would react with H2 under the conditions of these experiments.

These authors mention no test for oxygen and therefore no correction for its heat of reaction.

The measurements were made in a stationary bomb,

using a fairly massive internal container for OF2 (g) which was ruptured to initiate reaction with H2 . The

reaction products consisted of H2 0 and HF in a condensed phase, formed in the presence of excess H2 0(1). The formation of a homogeneous HF(aq) phase was presumed. However, experience in reactions in which condensation occurs in a stationary bomb

indicates that much of the condensation would occur

on the walls and would form droplets of a solution

quite different from the bulk solution. Mixing these

two solutions would evolve heat in addition to that which was measured. The massive OF2 ampoule

could also retain significant quantities of heat for an appreciable time, and the complete equilibration

of the heat distribution was not described. Both of these processes would appear to act in the same

direction, causing the measured amount of heat to be less than could have been evolved if equilibrium

had been achieved. If any errors of these types exist

in the experiments, a less negative heat of formation

would be indicated for OF2 than was reported.

The authors wish to acknowledge assistance re- ceived from several staff members of the National

Bureau of Standards. Mr. James Baylor of the Shops

Division made several valuable suggestions for the

design of the reaction vessel. Mr. William Dorko and

Mr. E. E. Hughes performed the mass spectrometric

analyses, and Mr. T. C. Rains performed the analyses

for metal ions in the hydrofluoric acid solutions.

8. Appendix

8.1. The Analyses of the Oxidizer Gases

a. Oxygen

The oxygen sample was transferred from the large

cylinder to the weighing containers with a manifold

of a type also used for filling oxygen combustion bombs

[16|. Prior to being filled the container was evacuated

and then purged three times with 2-3 atm of oxygen.

Finally, the container was filled to about 14 atm. Although further purification probably was unnecessary, during the filling procedure the oxygen was

passed through a column of CuO, heated to 500 °C,

and through successive columns of Ascarite and

magnesium perchlorate.

The oxygen in the weighing bulb was analyzed for argon by mass spectrometry. The concentration of argon was found to be 29 ± 10 parts per million. Nitrogen was determined by gas chromatography

using the method reported by Kyryacos and Boord

[24J. The equipment consisted of a commercially

available chromatograph equipped with an electrically

301-126
heated column oven, a thermal conductivity cell, and a strip-chart recording potentiometer (—0.2 to + 1.0 mV). Molecular Sieve Type 5A was used as column material with helium as carrier gas. The

sample was introduced into the column with a commercial gas sampling valve, modified with a 10-cm3 sample loop. Nitrogen could not be detected in smaller samples. The reliability of the method was

checked with one-cm3 samples of air. The conditions are given on the chromatogram in figure 6. The small effect attributed to nitrogen was

quite reproducible, and verified by the injection of

air.

b. Fluorine The fluorine was transferred to the spherical sample

containers using the manifold and apparatus shown

in figure 7. The general procedure for filling the

containers consists of (1) evacuating the containers

and connecting lines, (2) conditioning and purging

the manifold and parts of the connected apparatus

with fluorine, (3) filling the bulbs to the desired pres- sure, and (4) disposing of the fluorine in the connecting

lines. To insure that the bulbs were conditioned thor- oughly, they were filled repeatedly with a low pressure

of fluorine (2 atm), and emptied. Finally they were

filled to a working pressure of 13 atm. Mercury absorption is a well-known technique and

has been used extensively for the analysis of fluorine

[1, 25, 26]. Although this method appears to be satis- factory, there is some question as to whether the

mercury selectively absorbs fluorine from other

reactive gases like NF:) and OFL

> which possibly are present as impurities. These substances may react with mercury under the conditions of the test and

produce some Pi> and O2 which are the major impurities ordinarily contained in fluorine. The chromatographic procedures developed for analysis of the residual gas are independent of the mass spectrometric method. However, the qualitative

Column Material

Column Mesh

Column length

Column Temp. Carrier Gas Flow Rate : 17 cnJ Detector Current: 155 mA

Mol. Sieve Type 5A

llS-60

6 ft., (0.250 in. o.d.) 100° (isothermal)

Helium

J I L

6 8 10 12 14 TIME ,min

FIGURE 6. Chromatogram of the oxygen sample on Molecular

Sieve Type 5A.

identification ot the impurities obtained in the latter method is useful for selection of chromatographic

column materials.

In addition to the usual chromatographic equipment,

the method developed requires (1) a fluorine source,

(2) a flask containing mercury for reaction of the

fluorine, (3) a loop for containing chromatographic

samples of the residual gas, (4) a soda-lime column

for disposal of fluorine, and (5) a vacuum source. All of these items were arranged around a manifold as shown in figure 8.

FIGURE 7. Gas sampling manifold and connected apparatus (F2 and OF2 ). A, Nitrogen; B. Fluorine or oxygen difluoride; C. Sodium fluoride column; D. Sample bulbs; E. Pressure gauge;

I. Fluorine absorption tower; G. Vacuum source; H. Vacuum gauge; I. Fluorine absorption tower; J. Outlet to hood; K. L, to calorimeter flow system. 302-127
1

1

•zzzzzzzzzzzzzzzz

FIGURE 8. Manifold and apparatus for chromatographic analysis of impurities in fluorine.

A, Helium: B. Chromatography C. Recorder; D. Detector block: E. Column heater; F. Valves; G, Flask with mercury (300-cm3 flaskl; H, Magnetic stirring motor; [, Vacuum gauge; J, Fluorine sample: K. Fluorine absorption tower; L, Vacuum source.

The equipment preceding valves (F) is ordinarily

used in chromatographic analyses and has been

described for the oxygen analyses. The steps in the preparation of the system to receive the sample are:

(1) close valves (F) and then evacuate remaining

parts of system; (2) close flask and admit small amount

of fluorine from container (J) for conditioning manifold;

and (3) remove fluorine from lines by evacuation

through soda-lime column (K). The conditioning

procedure is repeated several times. The sample

is then introduced by placing one atm of fluorine in the flask. A surface film forms on the mercury which

prevents further reaction until the mercury is agitated.

The flask contains a Teflon-covered magnet and is placed on a magnetic stirring motor so that the mercury can be agitated with the flask in place. However,

to insure complete reaction of the fluorine, it is preferable to disconnect the flask from the manifold

so that it can be shaken vigorously by hand. After

the fluorine has completely reacted, the flask is reconnected to the manifold and the sample loop is evacuated. Appropriate valves are adjusted so that when the flask is opened the residual gas expands

into the sample loop. To introduce the sample into the chromatograph, the valves are adjusted so that the helium from the chromatograph flushes the

residual gas into the column. The reaction flask is left in place so that the analyses can be repeated.

Mass spectrometric analyses on other samples of residual gas from commercial fluorine had shown

that the major impurities were nitrogen, oxygen,

carbon tetrafluoride, and carbon dioxide, with smaller

amounts of silicon tetrafluoride, sulfur hexafluoride

and fluorocarbons. On this basis Molecular Sieve

Type 5A and silica gel were selected for the chromatographic column materials. Molecular Sieve Type 5A,

used in the procedure of Kyryacos and Boord [24],

separates nitrogen from oxygen, but shows no separation efficiency toward the other impurities. Silica gel

[10J separates oxygen plus nitrogen from the carbon

tetrafluoride and carbon dioxide. Typical chromatograms are shown in figures 9 and 10, respectively.

The conditions for the analyses are given on the

chromatograms. The peak components were checked

with injections of air, pure carbon tetrafluoride and

carbon dioxide. Prior to the analyses both columns

were conditioned at 300 °C under a flowing helium

atmosphere.

After the chromatographic analyses, the sample

loop was disconnected from the chromatograph at the two valves, F. On one valve a Pyrex breakofftip type ampoule was attached, and the ampoule and

connecting lines were evacuated. The ampoule was

filled with residual gas from the flask and sealed. A

mass spectrometric analysis was performed on this sample. The results from the two methods are compared in table 15. Considering that these are two

completely different techniques, the results are in good agreement. This agreement suggests that the

chromatographic method may be developed further

and used routinely as a second way of analysing for the impurities in ordinary commerical fluorine, which

is usually reported to be of a purity of not better

than 98 percent.

303-128
n r "i—i—

r

Column Mat. Column Mean

Column Temp. Column Length

Carrier Gas Flow Rate Detector Current Li!

Mol. Sieve Type 5A —

kS-60

100 "0 (isothermal)

12 ft., (0.250 in. o.d.) Helium

25 cir.3 min"^- 155 mk

J L J I L J I L

Figure 9. Chromatogram of impurities in the fluorine sample on Molecular Sieve Type 5A.

i—

r

i i i i i i

i i i i r

Conditions

Column Material : Silica Gel Column Length i 6 ft., (0.250 in. o.d.)

: 30 - 60

50 - 85°C (programmed) Helium

Column Mesh Column Temp Carrier Gas

FIovj Rate UOa.i min

Detector Current i 155 mA

J I J I J I I I I L

FIGURE 10. Chromatogram of Impurities in the fluorine sample

on silica gel.

The data in tables 1 and 15 show a difference be- tween the relative amounts of oxygen and nitrogen

in the residual gas in the flask used for chromatography, compared to the residual gas used from the

Table 15. Comparison of chromatographic and mass spectrometric

analyses for impurities in fluorine

Impurity Mole percent of total impurities

Chromatography Mass spectrometry

N2 45.

47.3.6

4.6

42.6

47.7

2.8

5.1 0.22

.2 1.1 0.21

.04

Ozrrco2 S02 F, Ar

SiF, OF.

C3 F»

spherical bulbs. The larger amount of oxygen impurity

in the Erlenmeyer flask suggests that some oxygen

may have arisen from the mercury because there was lOOOg mercury in the Erlenmeyer flask, as compared to 150g of mercury in the flask used for the

analysis given in table 1. There is reason to believe

that the analysis can be improved by conditioning

the mercury and flask surfaces also with a small

amount of fluorine, prior to filling the flask with the one atmosphere of gas needed for the analysis.

c. Oxygen Difluoride The oxygen difluoride was transferred to the

sample containers using the same manifold and

equipment shown in figure 7. The procedures used were the same as those used in sampling the fluorine,

except that the oxygen difluoride was not passed over

the sodium fluoride. The sample containers were

filled to approximately 8 atm with OF2.

An infrared spectrum of the oxygen difluoride

sample was made and compared with spectra in the

literature [27, 28J. The cell was Pyrex with silver chloride windows. The windows were clamped in place and sealed to the cell with Kel-F O-rings. The

spectrum is shown in figure 11. An absorption band

presumed to be due to the impurity CF4 , is indicated.

The equipment used for the chromatographic

analyses already has been described for the oxygen

and fluorine analyses. The OF2 sample container is connected to a loop which can be purged with helium

from the chromatograph. Silica gel was used for the

column material. Prior to the analyses, the column was conditioned at 350° for one hour under a flowing

helium atmosphere. The other conditions for the

analyses are given on figures 12 and 13 which show

the chromatograms obtained.

In the complete chromatogram, four peaks were

obtained. These were verified to be due to O2 (or air), OF2 , CF4 , and CO2. Analyses were made with the

column temperature at 0° and 50 °C. At 0 °C nearly

complete separation was achieved between the O2

and OF2 (figure 12), but the C02 peak was either very

slurred or the fraction did not elute at this temperature. At 50 °C, the separation between the O2 and OF2 was poor but separation and elution of CO2 could be

obtained by temperature programming. After elution

of the 02 and OF2 , the column was temperatureprogrammed to a final temperature of 150 °C for 304-129
FIGURE 11. IR spectrum of the 0Y> sample.

Note CF4 band at 780 microtis.

: -

0.2

0

1 1 ! i i i

i

1 1 1 1 1 1 \ 1 1 1 1

1

1 Cor.ditior^

1 Column Mat. Silica Gel

1 Colunr. length 12 rti, (2.250 in. o.d.)

1 o | Colunn Mesh 30-c0

1 Colunn Teny. 0°C(isothemal) __

1 Carrier Gas Helium

I Flow Rate •iOcnr* mln"1

1 Detector Current 155 mA.

i ! 1 i ! :1 1 ! 1 1 1 0 5 10 15 20

TIME.min

FiGIRE 12. Chrnmatogram of the OF. sample on silica gel (0 °C).

1 1 i ! I 1 1 1 1 1 ! 1

Condi ti

i i i i

i i

ColuEn Length ^ Colusn Mesh o ColuEn Tessp. x Detector Current Carrier Gas o Flow Rate12 ft. (0.250 in. o.d.) 30-60

50-150"C (programmed

155 =A

Helium UOcek miri"

C0

2 X 1 r I— I I i

I i i I I I I I 1 I I

I I ] I I 1 I l_ 0 5 10 15 20

TIME.min

FIGURE 13. Chromaivgram of the OF2 sample on silica gel (50 °C).

(The mlunm was programmed to ISO °C beginning at 12 mins.)

elution of the CO2 (fig;. 13). In agreement with Kesting's

observations [10]. the CF4 eluted on the "tail" of the

OFL> fraction. The CF4 peak was evaluated from other

chromatograms obtained with the instrument set on

the most sensitive scale. Repeated analyses were made on several bulb fillings

and the results were quite reproducible. We accepted

the findings of Resting, et al. [10], that the peak area percent for the observed components (OF2. CO>.

O2, CF4 ) was very nearly equal to mole percent. The

peak areas were evaluated both analytically and by

counting squares. Several preliminary analyses were carried out before

a procedure was accepted for these experiments.

Because of the reactivity of the OF2. it is conceivable

that OF2 reacts with the silica gel. During preliminary

analyses at various column temperatures, it was noted

that extraneous peaks appeared at a temperature of 75 °C. and also that even at 50°. the mole percent of OF2 decreased while the mole percent of O2 increased.

These preliminary analyses suggest that silica gel is not a generally useful column material for chromatographic analyses of the reactive inorganic fluorides. However, under the proper conditions silica gel has

good separation efficiency toward OF2 and inert component impurities such as O2 and CF4.

9. References

[1] G. T. Armstrong and R. S. Jessup, J. Res. NBS 64A (Phys. and Chem.) No. 1. 49 (1960).

[2] G. T. Armstrong. Experimental Thermochemistry. \ ol. II.. Ch. 7, ed. H. A. Skinner (Interscience Publishers. Inc., New York. N.Y.. 1962).

[3] H. v. Wartenberg and G. Z. Klinkott. Z. anorg. u. allgem. Chem.

193 , 409 (1930).

[4] O. Ruff and W. Menzel. Z. anorg. u. allgem. Chem. 190, 257

(1930).

[5] W. H. Evans. T. R. Munson. and D. D. Wagman. J. Res. NBS

55, 147 (19551 RP2614.

[6] R. C. King and G. T. Armstrong. Interagency Chemical Rocket

Propellant Group. Thermochemistry f orking Group. Bulletin of the Fifth Meeting March 15-17. 1967. Vol. 1.. Chemical

Propulsion Information Agencv. Publication CPIA No. 146.

pp. 69-96. May 1967.

305-130
[7] JANAF Thermochemical Tables. PB 168370, Dow Chemical

Co., Midland. Michigan (Clearinghouse for Federal Scientific and Technical Information. Springfield, Va., August 1966).

[8| D. D. Wagman, W. H. Evans. I. Halow, V. B. Parker, S. M.

Bailey, and R. H. Schumm, Selected Values of Chemical

Thermodynamic Properties. Part 1. Tables for the First Twenty-Three Elements in the Standard Order of Arrange- ment, NBS Tech. Note 270-1 (U.S. Government Printing

Office, Washington, D.C. 20402, 1965).

[9] W. R. Bisbee, J. V. Hamilton. R. Rushworth, T. J. Houser, and

J. M. Gerhauser. Advan. Chem. Ser. 54, 215 (1965).

[ 1 0 J W. R. Kesting. General Chemical Division, Allied Chem.

Corp., Baton Rouge, La., private communication; W. R. Kesting, J. E. Crosslin, and B. W. Bridwell, Analysis of Oxygen Difluoride, Report of the Analytical Chemistry

Working Group, 22nd Meeting, ed., John W. Gunn, Jr. (Chemical Propulsion Information Agency, Nov. 3, 1965.)

[11 1 J. C. Brosheer. F. A. Lenfesty, and K. L. Ellmore, Ind. Eng. Chem. 39, 423 (1947).

[12| H. C. Dickinson, Bull. BS 1 1, 189 (1915).

[13| E. J. Prosen, W. H. Johnson, and F. Y. Pergiel. J. Res. NBS

62, 43 (1959) RP2927.

[14| E. D. West and D. C. Ginnings, Rev. Sci. Instr. 28, 1070 (1957).

[15| D. C. Ginnings and E. D. West. Rev. Sci. Instr. 35, 965 (1964).

[16| K. L. Churney and G. T. Armstrong, submitted for publication

J. Res. NBS.

[J7] C. H. Shomate, Computer Calculations of Combustion Bomb

Calorimetric Data, Technical Progress Report 327, NOTS

TP 3288. U.S. Naval Ordnance Test Station, China Lake,

Calif., August 1963.

[18] A. E. Cameron and E. Wichers, J. Am. Chem. Soc. 84, 4175

(1962).

[19| N. S. Osborne, H. F. Stimson, and D. C. Ginnings, J. Res. NBS 23, 197 (1939) RP1228.

[20] T. Thorvaldson and E. C. Bailey, Can. J. Res. 24, 51 (1946).

[21) F. D. Rossini. J. Res. NBS 6, 1 (1931) R.P.259: see also Chapter

4 Experimental Thermochemistry, ed. F. D. Rossini (Inter- science Publishers, Inc.. New York, N.Y., 1956).

[22] E. Rudzitis, E. H. Van Deventer, and W. N. Hubbard, J. Chem.

Eng. Data 12, 133 (1967). [23 1 W. H. Evans. National Bureau of Standards, private communication.

[24-1 G. Kyryacos and C. E. Boord, Anal. Chem. 29, 787 (1957).

[25] L. A. Bigelow. Chem. Revs. 40, 110 (1947).

[26] H. Schmitz and H. J. Schumacher, Z. anorg. u. allgem. Chem.

245, 221 (1940).

[27] H. J. Bernstein and J. Powling, J. Chem. Phys. 18, 685 (1950).

[28] E. A. Jones, J. S. Kirby-Smith. P. J. H. Woltz, and A. H. Nielsen.

J. Chem. Phys. 19, 337 (1951).

(Paper 72A2-487)

306-131
6. Heat Transfer

Paper Page

6.1. Heat conduction through insulating supports in very low temperature

equipment.

Mikesell, R. P., and Scott, R. B., J. Res. Nat. Bur. Stand. (U.S.)

57, No. 6, 371-378 (Dec. 1956).

Key words: Low temperature insulation 309

6.2. Thermal conductivity of gases, I. The coaxial cylinder cell. Guildner, L. A., J. Res. Nat. Bur. Stand. (U.S.) 66A, No. 4,

333-340 (Jul.-Aug. 1962).

Key words: Gas thermal conductivity 317

6.3. A radial-flow apparatus for determining the thermal conductivity

of loose-fill insulations to high temperatures.

Flynn, D. R., J. Res. Nat. Bur. Stand. (U.S.) 67C, (Eng. and

Instr.) No. 2, 129-137 (Apr.-June 1963).

Key words: High temperature thermal conductivities 325

6.4. Measurements of the thermal conductivity and electrical resistivity

of platinum from 100 to 900 °C.

Flynn, D. R., and O'Hagan, M. E., J. Res. Nat. Bur. Stand.

(U.S.) 71C, (Engr. and Instr.) No. 4, 255-278 (Oct.-Dec. 1968).

Key words: High temperature thermal conductivity and electrical resistivity 334

6.5. Emissivities of metallic surfaces at 76 °K.

Fulk, M. M., and Reynolds, M. M., J. Appl. Phys. 28, No. 12,

1464-1467 (Dec. 1957).

Key words: Radiation emissivity measurements 358

6.6. An apparatus for measurement of thermal conductivities for solids at low temperatures.

Powell, R. L., Rogers, W. M. and Coffin, D. O., J. Res. Nat. Bur.

Stand. (U.S.) 59, No. 5, 349-355 (Nov. 1957).

Key words: Low temperature thermal conductivities 362

307

Journal of Research of the National Bureau of Standards Vol. 57, No. 6, December 1956 Research Paper 2726

Heat Conduction Through Insulating Supports in VeryLow Temperature Equipment 1

R. P. Mikesell and R. B. Scott

An apparatus is described that is used to measure the heat conduction through insulating supports of storage vessels for cryogenic liquids and presents the data obtained from

the conduction measurements. Two types of supports were tested: (1) multiple-contact

supports in the form of stacks of thin metallic plates or spirally wound strips, and (2) nonmetallic spheres. The high thermal resistance of the multiple-contact supports arises from

the numerous relatively poor contacts between the individual plates. Some special treat- ments of the plates were tried, and two of these, perforating and dusting, were found to be

effective. Pyrex-glass spheres were also found to be excellent insulators, but, of course, are not as rugged as a stack of metal plates. Of the untreated plates tested, those of stainless steel (0.0008 inch thick) were found to be the best insulators per unit length of stack. The heat conduction through these plates, at a load pressure of 1,000 pounds per square

inch, was found to be 2 percent of the conduction by a solid sample of the same metal having

the same dimensions.

1. Introduction

The most efficient containers for storing and trans- porting low-temperature liquids, such as liquid

oxygen, nitrogen, and hydrogen, are the vacuumjacketed type known as Dewar vessels. In the past,

several types of heat insulators have been used to bridge the vacuum space and furnish support for

the inner container. For small laboratory-type

Dewars, the design of insulators is not a major

problem, but when designing a vacuum-insulated

container of several hundred liters or more, which

must have ruggedness to withstand the shocks and

vibration of transportation by any type of carrier,

the problem of insulating supports becomes a serious one.The recent development of a large aluminum

Dewar at the Bureau's Cyrogenic Engineering

laboratory included the design of some new type

insulating supports, which were of such a nature

that their insulating properties could not be computed from the thermal conductivity of the materials from which they were constructed. For this reason, an apparatus was constructed to measure

the heat conduction through these supports. Some

of the supports were found to have such good in- sulating and structural properties that it is believed

they will have an extended usefulness, and that information obtained from the tests will have general

value in the design of Dewar equipment.

2. Experimental Details

2.1. Description of Apparatus

In order to simulate conditions actually encountered in practice, the calorimeter for measuring the

heat conduction was itself a Dewar vessel. With

this apparatus it was possible to measure the total heat conduction of the specimen when it was subjected to loads ranging from approximately 30

pounds to approximately 1,050 pounds and under the

following temperature conditions: (1) room temper1 This work was sponsored by the U. S. Atomic Energy Commission.

ature to liquid-nitrogen temperature (296° to 76° K),

(2) liquid-nitrogen to liquid-hydrogen temperature

(76° to 20° K), and (3) room temperature to liquidhydrogen temperature (296° to 20° K). These

temperatures are the boundary conditions encountered in liquid-hydrogen Dewars, which are provided

with a liquid-nitrogen-cooled radiation shield between the liquid hvdrogen and the room-temperature

shell. The apparatus (fig. 1) was designed so that the

calorimeter is a metal Dewar with the test specimen

acting as a separating and insulating member. The

specimen is placed between the bottom plate of the

inner container, into which is poured liquid nitrogen

or hydrogen, and the bottom plate of the outer container, which is at room temperature or liquidnitrogen temperature. A 5-liter Dewar containing

liquid nitrogen surrounds the calorimeter when it is required to have the exterior wall of the calorimeter

at liquid-nitrogen temperature.

The outside container is secured in a vertical position by means of the O-ring flange, which rests upon

a wall bracket not shown in the diagram. The

O-ring seal is completed by a top flange, through the center of which passes a lube (8-18 stainless steel,

1%-in. outside diameter, Ym-in. wall), which is con- nected to the inner container. The vacuum system,

consisting of a cold trap, diffusion pump, and fore- pump, is connected to the outer container.

The central tube serves both as the neck of the

calorimeter-Dewar and as the compression member

for transmitting the load from the fulcrum point of

the lever arm to the specimen. This vertical load is the force resulting from a movable weight mounted

on a lever arm. A metal bellows permits the central

tube to move vertically through guides that also prevent horizontal motion. The brass plate is soldered to the bellows, is sealed to the outer container by means of an O-ring ar>d is secured in position by four screws. The unit consisting of the inner

container or calorimeter, the central tube, the bel- lows, and the top flange may be easily withdrawn

from the outer container to enable one to change the

test specimen.

309-371
In order to reduce heat radiation from the side,

the surfaces that face the insulating vacuum are covered with bright aluminum sheet. To intercept

radiation from above, horizontal metal disks are placed along the central tube both inside and outside.

-TO GAS METER

i FULCRUM /LEVER ARM

'0- RING

FILL AND

BOIL -OFF TUBE

LIQUID LEVELSPECIMEN

2.2. Test Specimens

The specimens measured in the tests are described n tables 1 and 2. The round plates (A, fig. 2) 1 in. in diameter, are mounted between brass end plates of the same

diameter. Nylon threads tied through small holes

in the plates keep them in place. The rectangular

plates are mounted in the same manner, with the

diagonal of each rectangle approximately the same

length as the diameter of the circular end plates.

The spheres (B, fig. 2) are held between two stainless-steel plates, each of which has three matching

spherical depressions of somewhat larger diameter

than that of the spheres (spheres %6-in. radius,

depression %-in. radius). This assembly is also tied

together with threads to prevent dislodgment of the

spheres during test.

Table 1. Nonmelallic spheres

Specimen Dimensions Comments

Three Pyrex-glassspheres. Each sphere. 0.375-

in. diameter. Made from semipolish Xo.774 clear chemical glass, manufactured by the 7. R. Kilburn Glass Co., Chartley, Mass. Three soda lime

spheres. Average diameter of spheres, 0.42 in. Manufactured by Hans L. Landay, Boulder, Colo. Three ceramic

spheres. Each sphere, 0.39- diameter. Made from Coois type AB-2

ceramic "high-strength

alumina", manufactured by the Coors Porcelain Co., Golden, Colo. Three Micarta

linen-impreg- nated spheres.

Each sphere, 0.375-

in. diameter. Manufactured by Westinghouse Elect. Mfg. Corp.

Figure 1. Cross section of the calorimetric apparatus.

Table 2. Multiple-contact specimens (metallic)

Specimen Number

of plates Dimensions Comments

Monel round plates: Clean plates __ Greased plates Type 304 stainless-steel round plates: Clean plates... Type 302 stainless-steel round plates: Clean plates Clean plates ._ _ Clean plates Clean plates Dusted plates

Tyix: 304 stainless-steel rectangular plates: Clean, plain plates Clean, perforated plates

Alternate layered stack of plain and perforated

plates. Dusted plain plates

Teflon layered stack of plain plates

49

315

313

209

1 48 345

92

107

01 of each

1 10

110

jl-in. diameter, 0.017-in. thickness...

1-in. diameter, 0.0195-in. thickness

jl-in. diameter, 0.0008-in. thickness

!M6 by ?i in., 0.004-in. thickness. _ He by 3

j in., 0.004-in. thickness. 18 ;6<-in.- diamcter holes comprise approximately 40%

of total area of a plate

5i6 by ?i in., 0.004-in. thickness. 18 Tu-i-in.- diamcter holes comprise approximately 40%

of total area of a plate

9 i 6 by ?4 in., 0.004-in. thickness..

?i6 by 9i in., 0.004-in. thickness..

Greased with Dow-Corning high-vacuum

grease.

Dusted with a thin layer of manganese

dioxide.

The holes of each plate were staggered with

respect to the holes of the adjacent plate.

Holes of adjacent perforated plates were

staggered. The metal plates were separated from each

other by Teflon film 0.00025-in. thick.

310-372
BRASS

BRASS

TYPE 304 h

STAINLESS STEEL

NYLON THREAD

SPHERES

DISKS TYPE 304 A B Figure 2. Method for mounting the specimens

STAINLESS STEEL '

'

2.3. Experimental Procedure

With the specimen in place, the calorimeter supplied with liquid hydrogen or nitrogen, the required

load applied, and an adequate vacuum (less than

10-5 mm Hg) in the insulating space, the volume of

gas evaporated from the calorimetric liquid is determined with a wet test gas meter. Readings are continued until a constant rate of evaporation gives assurance that equilibrium has been reached. Volume determinations are adjusted to standard conditions and corrected for the partial pressure of water

vapor in the meter. Several sets of readings are made with applied load on the specimen.

The rate of heat flow through the specimen cannot

be calculated directly from the evaporation rate be- cause (1) part of the evaporation of the liquid during

the measurements is caused by heat transfer other

than through the specimen, and (2) the relation between evaporation rate and heat conducted through

the specimen is not quite linear because some of the

heat flowing down the central tube is intercepted by

the cold gas flowing up the tube; thus less heat is conducted down the tube when the rate of evaporation of the liquid is increased. Instead of trying to determine the magnitude of these incidental heat

leaks, their effects were taken into account simply

by calibrating the apparatus with a known heat

input. This was done by lifting the inner container

until it no longer made contact with the specimen

and conducting another series of measurements of

the gas evolved when known values of electric power

were supplied to a heater immersed in the liquid in the inner container. The amount of heat con- ducted through the specimen during a test measure- ment is assumed to be the same as that supplied to the heater to produce a given rate of evaporation.

This assumption is justified if the conditions during

the measurements of heat conduction with applied

loads are maintained during the calibration measurements.

3. Data and Discussion

3.1. Accuracy of the Data

The values of heat conduction obtained with this

apparatus are accurate in most cases to approximately 10 percent. The main causes of error were

the following: (1) The fluctuations in the magnitude

of the incidental heat leaks, though small, did be- come important in the measurement of the conduction through the very good insulators, and (2) there were small changes in heat conduction resulting from

variations in the exact manner of mounting or loading

the specimen.

3.2. Untreated Stacked Plates

Six multiple contact specimens were tested between nitrogen (76° K) and room temperature; five of these were stacks of stainless-steel plates, and the

sixth was a stack of Monel plates. Two specimens were tested between liquid-hydrogen temperature

(20° K) and liquid-nitrogen temperature (76° K).

Since the support of a Dewar is, in most cases, loaded

warm, i. e., the load is applied when the support is at room temperature, the data for each specimen, witli the exception of the Monel stack, is presented for

warm loadings. The Monel stack was loaded cold,

i. e. the load was applied when one end of the specimen was at nitrogen temperature. It was found

that the conduction by a stack of plates (0.004 in.)

subjected to a high pressure was approximately 30

percent greater when the stack was loaded warm than

when it was loaded cold. The results on clean multiple-contact, metal

supports 2 are shown in figures 3a, 3b, and 3c,

wherein the heat current per unit area is plotted

as a function of the pressure on the specimen. The

heat conduction through the plates increased with

the pressure for two reasons: (1) the area of contact

surface was increased, and (2) the heat paths be- came shorter through a given stack of plates. The

conduction was found to be proportional to something less than the first power of the pressure, there

being a tendency for the curves to level off as in- creased pressure had less effect. Thus, the stack

of plates acted as a good insulator, even at the

higher pressures. The points below a pressure of 300 psi were not

especially reliable because the exact values of the

lower pressures, as well as the measured conduction

rates, are somewhat in doubt.

Figure 4, on which these same curves are plotted on log-log paper, shows the conduction to be proportional to approximately the 0.67 power of the

pressure for the nitrogen- to room-temperature

range, and proportional to approximately the 0.86

power for the hydrogen- to nitrogen-temperature

range. As the heat conduction by a stack of plates was found to be proportional to less than the first power of the load, it is concluded that such a support

should be designed for high loading per unit area,

2 Such an arrangement for use as an'insulat tag support is the subject of a patent

application for the AEC by B.jW.tBiimingham, E. II. Brown, R. B. Scott, and P. C. Vander Arend. 311-373
0 500 (000 1500 PRESSURE , psi Figure 3a. Heat conducted as a function of mechanical pres- sure of stacks of type 302 round stainless-steel plates, each

plate 0.0008 in. thick. A (A), 148 plates; C (O), 209 plates; F (), 313 plates; H (#), 315 plates Boundary temperatures for A, C, and F are 76" and 296° K; for H, 20° and 76° K

0 500 1000 1500

PRESSURE, psi Figure 3b. Heat conducted through stacks of thick plates where the boundary temperatures are 76° and 296° K. D O. a stack of 52 round Monel plates, 0.017 in. thick; E (A), a stack of 49 type 304 round, stainless-steel plates, 0.0195 in. thick. Curve I shows the con- duction that would occur through a stack of O.OOOSin. plates the same height as the stack of 0.0195-in. plates. The conduction is extrapolated from the conduction by a stack of 313 plates, 0.0008 in. thick.

i

0

1 -OH

G

i i 0 500 1000 1500 2000 2500 PRESSURE , psi Figure 3c. Heat conducted through a stack of 92 type 304

rectangular, stainless-steel plates, 0.004 in- thick. The boundary temperatures for B (O) are 76° and 296° K; for G (), 20° and

76° K.

i. e., the cross-sectional area should be made as small as is consistent with strength and other design

considerations.

The concept of thermal resistance is introduced

here as an aid in comparing and correlating data on different specimens. Thermal resistance is defined as the temperature difference divided by the

10

5

-

F SLOPE - A to F > 0.67

-

Q

" SLOP E- S,H 0.86

H '

200 900 1000 2000 SOOO PRESSURE , psi Figure 4. A log-log presentation of the data given in figures 3a, 3b, and 3c, demonstrating that the heat current is approximately proportional to the 0.67 power of the pressure in the upper temperature range (76° to 296° K), and to the 0.86 power of the pressure in the lower temperature range (20°

to 76° K). A (O), 148 plates, 0.0008 in. thick; B (), 92 plates, 0.004 in. thick; C (A),

209 plates, 0.0008 in. thick; D O, 52 plates, 0.017 in. thick; E (A), 49 plates, 0.0195 in. thick; F (), 313 plates, 0.0008 in. thick; G (O), 92 plates, 0.004 in. thick; H (O), 315 plates, 0.0008 in. thick.

heat current (in analogy to its electrical equivalent).

Thermal resistance is temperature dependent, but

it is permissible to use an average value for comparing two stacks under the same temperature

difference. As there were a large number of stacked

plates in these tests, it was reasonable to expect

that the resistance would be proportional to the

number of plates, i. e., that the end effects would

be negligible.

Three specimens of the 0.0008-in.-round stainlesssteel plates were tested, each with a different number

of plates. In figure 5 it is shown that the thermal

resistance of a stack of plates varies linearly with

the number of plates in the stack. Thermal re- sistance of unit area per plate as a function of the

thickness of each plate is shown in figure 6. For

many design applications a certain volume may be

available for the insulating member. Hence, consistent with strength and cost considerations, it is desirable to know what thickness the plates should

have to provide adequate heat insulation. Thermal

resistance of unit area per unit length of stack as a function of plate thickness is plotted in figure 7. The length of the stack was determined by multiplying the number of plates by the thickness of

each plate; this calculated length was in close

agreement witli the length measured when the

stack was subjected to a pressure of 1,000 psi.

Points for the curves of figures 6 and 7 are. taken

from the curves of figures 3a, 3b, and 3c for the

312-374
100

. 80

_ 60

—

—

—

—

1 00 200 NUMBER OF PLATES Figure 5. Observed linear increase of the thermal resistance with the number of plates contained in a stack. The plate thickness is 0.0008 in.; the boundary temperatures are 76° and 2%° K.

0.0008-in. stainless-steel round plates, the 0.0195-

in. stainless-steel rectangular plates, and the 0.004-

in. stainless-steel round plates. It is seen that the

0.0195-in. stainless-steel round plates had a higher

thermal resistance per plate than the others, the

explanation being that the thin plates were pressed

into better contact with each other with a given

applied pressure. However, for a given length of

stack, the thin plates produced a greater total thermal resistance. This is shown by the dotted

curve, I, figure 3b. No implication is intended that

the slopes of approximately y2 and — K of the lines of

figures 6 and 7 have any significance other than

that of representing the observations. It is probable

that for different loads or plate thicknesses these

would have other values.

The heat conduction through a stack of plates was

considerably less than the conduction by a solid

member of the same metal having the same dimensions, showing that the difference in conduction was

due mainly to the total contact resistance of the

specimen.

The conduction through a stack of 0.0008-in. -thick

stainless-steel plates under a pressure of 1,000 psi was found to be approximately 2 percent of the

conduction by a solid member; for the 0.0195-in.

stainless steel round plates at 1,000 psi, 8.5 percent;

for the 0.004-in.-thick stainless-steel rectangular

plates at 1,000 psi, 4.5 percent; and for the 0.017-in.-

thick Monel round plates at 600 psi, 6.5 percent.

The 0.0008-in. and the 0.004-in. plates were tested

between liquid-nitrogen and liquid-hydrogen temperatures. Table 3 shows the comparison between these

specimens. In the case of both the 0.0008-in. and

the 0.004-in. plates, the specimen was loaded warm

at the higher pressures; the load was reduced to the

lower pressures after the specimen was cold. The

2.0

£ 3 °- 5

0.05

SLOPE = 0.55

O.0OO5 0.001 0.002 0.005 0.01 0.02 0.05 PLATE THICKNESS, In. Figure 6. A log-log presentation demonstrating that the heat

resistance per plate increases approximately as the square root of the individual plate thickness. The boundary temperatures are 76° and 296° K.

200

SLOPE » -0.45

1 1 1 1

1 ] 1 1 1 1 1

1 J, i 0.0005 O.OOI 0.005 0.01 PLATE THICKNESS, in. 0.05

Figure 7. A log-log presentation demonstrating that the heat resistance per unit length of a stack varies approximately as

the inverse square root of the individual plate thickness. The boundary temperatures are 76° and 296° K.

ratio of the heat conducted between 296° and 76° K

to that conducted beween 76° and 20° K is of

interest. The conduction ratio of a solid member of

the same type of metal and the same dimension

between the two temperature intervals would be

9 to 1. The greater ratio in the case of the stacked

plates is an indication that the thermal resistance of

the contacts increases as the temperature is decreased.

Table 3. Comparison of 0.0008-in. and O.OO^-ii . plates

Pressure Specimenplates

Conduction ratio (Conduction at 76°

to 296° Reconduction at 20"

to 76° K)

psi in. 754 0. 0008 15. 5 to 1 1,34ft .0008 13.3 to 1 1,407 .004 14. 2 to 1 2, 509 .004 10. 6 to 1

313-375
3.3. Specially Treated Stacked Plates

a. Dusted Plates Because the objective of the work was to devise

sturdy supports with the best possible insulating

properties, methods of decreasing the heat conduction were studied. S. C. Collins of Massachusetts

Institute of Technology predicted that a very slight

coat of dust would greatly increase the thermal

resistance. He had observed that a few dust particles

detectable only under a microscope were sufficient to spoil the effectiveness of a thermal switch. Manganese dioxide was chosen to be the insulating dust

for several reasons. It is only a fair conductor of

heat and has moderate hardness. It can be ground

into a fine powder that will cling to the surface of

the plates, so that little of the dust is lost in the

assembling of the supports. The dust coat on each

plate was of such a small magnitude that the total length of the multiplate specimen was not significantly changed. The results for the dusted plates, as illustrated in figure 8, curves A and E, show that

the heat resistance of unit area per plate of the stack

of dusted plates is much higher than that of the

stack of clean rectangular plates.

b. Perforated Plates Another good insulating device was found to be

a stack of perforated rectangular plates. The results on these plates are shown in figure 8, curve B. Figure 9 shows the plan of a perforated plate. The

net area is (if) percent of the area of a plain rectangular

plate. The thermal resistance of these plates* was

found to be higher than that of the plain rectangular

plates because of the smaller area of the perforated

plates and because the plates were stacked in such a manner that the holes of the adjacent plates did not

aline, resulting in longer heat paths through the

stack. Because the production of the perforated

plates that might be used for an insulating support

in a specific case was found to be expensive, it was

also decided to try stacking the perforated and plain

rectangular plates in alternate layers. In comparing

the thermal resistance of the stacks of the three

types of rectangular plates, each tested at a total load of 422 lb, it was found that the stack of plain

plates had a resistance of 0.260° K-in.2-watt_1 per

plate; the stack of perforated plates, 0.420, and the

alternate layered stack, 0.370.

c. Teflon-Separated Plates A stack of rectangular plates with thin (approximately 0.00025 in.) films of Teflon placed between

them was found to be a comparatively poor insulator

at the low pressures. The high compressibility of the

plastic resulted in a greater area of contact between

it and the metal layers than would be realized

between metal layers alone. However, at the higher

pressures, the Teflon-layered stack was a good

insulator, the area of the thermal contact having

approached a constant value. At all pressures the

plastic acted as a. good insulator because of its low

thermal conductivity. The conduction curvefor the

Teflon-layered plates is shown in figure 10, curve D.

d. Greased Plates The application of grease to the Monel plates of a stack residted in a decrease of heat resistance of

nearly 10 percent at a. pressure of 000 psi, as shown

in figure 10, curve B (the stack of greased plates was

loaded cold). A very thin lav or of Dow-Corning

high-vacuum grease was applied to each plate. The

considerable increase in conduction by the greased

plates may be explained in this manner: The coaling

of grease tilled in the small spaces between the plates,

\

>

£

1

^*"o

1 ^ _F ^ ^

1 1

1

ooo

oooo

9/16"

3/4

Fmuitic !). A perforated plate.

Fiourh 8.

PRESSURE, psi Comparison of the licit! resistance of clean plates with that of speciallij treated plates. The boundary temperatures are 7ii° ;ui<l 2!iii° K. A (A), a stuck of l).()((4-in. maiiKunese-dioxide-dustod plains; It (( )), (UX)l-in. perforated plates; V (A), idlcrnalo' layered slack of 0.004-in. plain and perforated plates; K H u.niHix-in. dusted plates; 1) (()), (UMH-iii. clean plates; I

1 ' (U), (MHIOK-in. clean plates.

314-376
Figure 10. Comparison of the heat resistance of clean plates with

that of specially treated plates. The boundary temperatures are 76° and 290° K. A (•), a stack of 0.017-in. clean Monel plates; B O. 0.017-in. greased Moncl plates; C (), 0.004-in. clean plates; D

(A), 0.004-in. Teflon-separated plates.

Figure 11. Heat conducted as a function of

total load on a type 304 stainless-steel strip, 0.0021 in. thick, 1 in. wide, which •*« dusted with manganese dioxide and rolled into a tight coil. The boundary temperatures ar 76° and 296° lv

resulting in a more positive thermal contact. It is seen, therefore, that caution should be taken when

one assembles a stack of plates, keeping each plate

as clean as possible.

3.4. Application of Multiple-Contact Supports

A liquid- hydrogen Dewar, designed at the NBSAEC Cryogenic Engineering Laboratoiy, was constructed with multiple-contact supporting members.

Each of these separating members was made by

tightly rolling a strip of type 304 stainless steel into

a coil, the strip being 0.0021 in. thick, approximately

400 ft long and 1 in. wide. The inner diameter of

the coil was approximately 2 in. and the outer

diameter approximately 5 in. The coil was tested

for conduction in an apparatus similar in operation to the original multiple-support testing equipment.

The results of the conduction tests between nitrogen

and room temperature, using a strip dusted with

manganese dioxide, are shown in figure 11. It was

not feasible to compute the heat conduction by a

coil from the conduction by a stack of plates because

it was not known how much heat flowed along the

circumference of the coil nor how large was the effec- tive cross-sectional area through which the heat

flowed.

3.5. Nonmetallic Spheres

The results of tests on nonmetailic spheres are shown in figures 12a, 12b, 12c, and 12d, wherein the

heat current per sphere is plotted as a function of the

load per sphere. Each of the spheres in its socket

made little more than point contact at no load. The

conduction increased with increasing loads because

the area of contact was increased, but it tended to

level off at the higher loads as this area approached

a constant value. The dependence of conduction on pressure also varied with the type of. material of

the sphere, e. g., if the material was soft, the sphere

would flow slightly at the higher loads, resulting in a greater area of contact.

It is seen that of the four types of spheres tested,

ceramic was found to be the best conductor and

Pyrex glass was found to be the poorest conductor of

heat. A load has more effect on the flow of heat

through the ceramic spheres because the contact

resistance has proportionally more effect in the case

of the better conductor. Although the conductivity

of Micarta is less than that of Pyrex, the conduction

through the Micarta spheres was found to be greater

than through the Pyrex spheres, possibly because of

the slight flow of Micarta at the higher loads.

There was a small error due to a comparative!}'

small temperature drop across the. stainless-steel

plates that .were used for support of the spheres.

The conduction through the spheres was actually

greater than was measured.

In all eases, the conduction from 76° to 20° K is very much less than that from approximately 296°

to 76° K. This is a consequence not only of the

smaller temperature interval but also of the great

decrease of the thermal conductivity of noncrystalline

materials below 76° K.

Because the purpose of these measurements was

to provide information about members that would be

expected to have usefulness as insulating supports, some tests were conducted on the spheres to determine their crushing strength. The Pyrex-glass

spheres failed at approximately 2,000 lb per sphere

(two measurements) . The ceramic spheres supported

10,000 lb each without failure. The conduction data on the spheres should be

considered in relation to their compressive strength.

At first sight it appears that the higher strength of

the ceramic spheres offsets their larger thermal conduction. This, of course, assumes that they will be

used at high loads. If a support is designed for loads

that would take the full advantage of the strength

of the ceramic spheres, it would be necessary to provide hard bearings for the spheres to rest against,

possiblv of the same ceramic material. For average

loads, the Pyrex spheres would be the most suitable.

315-377
0.3

* 0.2

0.1

—

' 1 '

1 100 200

LOAD, lbs /sphere

300 400

Figure 12a. Heat conducted through Pyrex glass spheres, each

sphere 0.375 in. in diameter. A (), r, = 20°K, 72=296° K; B (Q), Ti = 76°K, T2 = 29t>° K; C (A), T, = 20°K, r2 = 70° K.

c

1 1 400

Figure l2b.

100 200 300

LOAD, lbs /sphere Heat conduction through ceramic spheres, each

sphere 0.89 in. in diameter. A (A). T, = 20° K, 7\, = 2%0 K; B (O), 7"i=7fi° K. 7j=296° K; C (), T, = 20° K, T2 = 7li° K.

4. Previous Experiments

The use of multiple contact members as insulating

supports was suggested by the experience of other

workers who had to go to great pains to obtain good

thermal contact in a vacuum.

R. B. Jacobs and C. Starr, in an effort to design a good thermal switch, carried out experiments at MIT in 1939 3 wherein the heat conducted between

two optically Hat metallic surfaces inclose contact with each other in a vacuum was measured as a function of contact pressure. Three different thermal

switches were tested, one made of copper, another of

silver, and the third of gold. In 1949. S. C. Collins directed experiments 4 at MIT similar in nature to the Jacobs and Starr

experiment. The thermal resistance between optically flat copper surfaces was measured.

In both these experiments if was found necessary

to apply considerable pressure to obtain low thermal

resistance.

3 It. B. Jacobs and C. Starr. Thermal conductance! of metallic contacts, Kev

Soi. Instr. 10. 14(1 (April 1U39),

4 As described in a private communication from I). H. Ohciton, who was

work inn with Collins in 1!H9.

0.5

i: 0.4

0.3

0.2

0.1

Q, A^^

1 _ I- ... - 1 100 200 300

LOAO, lbs /sphere

400

Figure 12c. Heat conducted through Micarta spheres, each

sphere 0.375 in. in diameter. A (O). 7'. = 7i;° K, 7^=296° K; B (A), 7', = 20° K, r2 =7<>° K.

.00

Z 0.7 5

i 0.50

0.25

A

X °

o X

B

1 1 1 lOO 200

LOAD, lbs/ sphere

300 400

Figure 12ck Heal conduction throvgh soda lime spheres, each

sphere 0./f 2 in. in diameter. A (O). TWO0 K, 7'

2 =29G° K; B (A), T, = 20° K, 7i=76° K.

5. Conclusions

The most important conclusions to be drawn from

these, results are (1) the principle of multiple thermal

contacts offers the designer of cryogenic equipment

a simple rugged support that occupies small space,

(2) the best assembly tested consisted of a stack of

stainless-steel plates, 0.0008 in. thick. Its thermal

conduction when supporting a load of 1,000 psi was

only 2 percent of that of a solid conductor of the same dimensions, (3) the insulating value of such a support is enhanced by introducing a tiny amount

of dust (Mn02 ) between the plates, and (4) for best

results the support should be designed for high loading per unit area.

The authors thank K. L. Powell

in designing the apparatus and

experimental procedure

Bouldek, Colo., August 30, 1956.

316-378

'or his assistance

developing the
JOURNAL OF RESEARCH of the National Bureau of Standards—A. Physics and Chemistry

Vol. 66A, No. 4, July-August 1962

Thermal Conductivity of Gases. I. The Coaxial

Cylinder Cell

1

Leslie A. Guildner

(April 13, 1962)

By combining appropriate geometric configuration and mathematical analysis with

improved measuring techniques, the cell constant of a coaxial cylinder thermal conductivity

cell was determined within 0.1 percent.

An analysis of the rate of heat transfer in such a cell showed a way to treat the data

so that the error contribution of experimental deviations from idealized conditions is kept

small. The principal considerations are:

1. That heat transport by convection is significantly large in a dense gas. This trans- port was analyzed mathematically from basic principles. The agreement of experimental

results with the analysis indicated that the expressions are valid and that the convective

heat transport could be accounted for with little more error than was involved in the precision of the heat transfer measurements.

2. That the heat transfer in a vacuum corresponds to the heat transfer by radiation and solid contacts in the presence of a gas. The uncertainty was that associated with the accuracy of determining the vacuum values.

3. That other effects were small enough to be computed and corrected for without

increasing the uncertainty of the values of the thermal conductivity.

1. Introduction

The coaxial cylinder thermal conductivity cell, with large diameter of inner cylinder relative to the

conductivity gap width, is one of the forms of apparatus often used to determine the thermal conductivity of gases. Over a period of several years, refinements were made in the design of a cell, in the

analysis of heat transfer, in measurement techniques

and in the treatment of the data. It is the purpose

of this paper to set forth a summary of considerations which are applicable to measurements with a

cell of this general type.

The heat guards at the ends of a coaxial cylinder

cell can be designed so that the geometric form of the conductivity gap is simple. It is then possible

to make a reliable mathematical analysis of the heat

transfer by conduction. Consistent with a nearly

exact mathematical analysis, special techniques were

used for measuring the cell dimensions with improved

accuracy.

At sufficiently high gas densities, convective heat

transport becomes significant in a coaxial cylinder

cell. When the axis of the cell is vertical, the heat

transport by convection can be analyzed from basic

principles. This analysis indicates the proper measurements to be made and the required treatment

of the data.

Other effects which should be accounted for—

asymmetry of the heat flow, radiation from the

emitter and conduction through the mounting pins,

and the temperature gradient in the body of the

metal—are considered. The significance of these

effects will be clearer after understanding some of the

details of a cell, which will be described in the next

section.

1 This work was performed at the Massachusetts Institute of Technology and

sponsored by Project SQUID, which is supported by the Office of Naval Research, Department of the Navy, under contract Nonr 1S58(25) NR-098-03S.

Reproduction in full or in part is permitted for use of the United States Government.

2. Apparatus

The cell shown in figure 1 was made of silver. It consisted of an emitter EM, surrounded by a receiver

RE. The emitter was located by seven Pyrex pins

Figure 1. Vertical cross section of coaxial cylinder cell. 317-333
EP, one on the axis at the bottom, three spaced

uniformly around the receiver near the bottom, and

three (not shown) similarly spaced near the top.

Electrical energy was supplied to the emitter by a heater in the heater well EW. The heater was made

from Nichrome ribbon uniformly wound on a machined Grade "A" "Lava" form. The temperature

or the temperature difference was measured by

thermocouples inserted in the thermocouple wells

7TTof the emitter and receiver. The junctions were

at two levels in the receiver and emitter, one level being midway along the emitter close to the bottom

of the wells, and the other level just below the top

of the emitter. The thermocouples were installed

between the wall of the well and an inserted rod of

silver. The thermocouple wires were insulated by

thin sheets of mica, and they were packed tightly in the thermocouple wells. A heat guard HG provided a continuation of the

conductivity gap CG. It was positioned by six Pyrex pins HP, three spaced uniformly around the

side and three around the top. The top pins were

adjusted so that the width of the heat guard gap

HGG was equal to the width of the conductivity gap.

The heat guard temperature was maintained as close as possible to the temperature of the emitter, by

introducing electrical energy from a heater in the

heat guard heater well HW. The temperature was

measured by a thermocouple whose junction was

placed near the bottom of the heat guard thermocouple well HTW.

The leads from the emitter heater and the emitter

and receiver thermocouples passed through the heat

guard or the corresponding portion of the receiver,

the receiver extension REE. (The receiver extension

surrounding the heat guard was separate to facilitate assembly.) The thermocouple leads were insulated

with mica and in order to improve heat transfer were

held against the walls of the thermocouple wells,

by means of a split rod of silver, which was wedge

shaped.

The mounting pins were made in three parts: a Pyrex rod, 3 mm in diameter with a 60° included

angle conical point, a pure aluminum holder, and a

silver screw. The lengths of Pyrex and aluminum

were chosen such that their composite expansion was

close to that of silver over the temperature range

0 to 400 °C.

The dimensions of this cell, although not essential to the discussion in this paper, are used for illustra- tion, and were approximately:

Conductivity gap 0. 068 cm

Heat guard length 3. 8 cm

Emitter diameter 2. 2 cm

Emitter length 11. 4 cm. The dimensions should be chosen so that Ar/?<0.1.

The length of the emitter should be sufficient for 90

or 95 percent of the heat transfer to take place

radially, and the length of the heat guard should be

enough to reduce unaccountable heat loss from the

emitter satisfactorily. The choice of the size of the

conductivity gap represents a compromise. On the one hand, a narrow gap makes the ratio of the heat

transfer by conduction large relative to the heat

transfer by radiation and also ver}- effectively makes

the relative heat transport by convection small.

On the other hand, when the gap is made too narrow,

the uncertainty in the value of the cell constant is increased. The choice of dimensions will depend

upon the objectives of the investigation.

3. The Cell Constant

3.1. Mathematical Treatment

We can obtain the cell constant from the assumption that the rate of heat transfer, q, is proportional

to the temperature gradient and the surface area. In the steady state, we can integrate the temperature gradient over the region of heat flow, so that

q=CKAt, where C is the cell constant, K is the

thermal conductivity, and At is the temperature

difference across the region in the steady state condition.

The principal terms of the cell constant can be

evaluated by considering the radial heat flow across a section of length I of an infinite coaxial cylinder

and the linear heat flow across a circular section of

radius rt of two infinite parallel plates at the bottom.

The determination of an accurate cell constant

requires that recognition be made of the additional

heat flow which takes place at the heat guard gap

and at the bottom corner of the emitter. If both the

conductivity gap, Ar, and the heat guard gap are small compared to the radius of the emitter, rx , the

conductivity gap and adjacent portion of the heat

guard gap can be treated as if planar. In figure 2, the relaxation solution for the gas isotherms near

the heat guard shows that the perturbing effect of

the gap has practically vanished within two gap

widths in any direction. Therefore, it is proper to employ the Schwarz-Christoffel transformation which

is valid for an infinite cell. The transformations for both the heat guard gap and the bottom corner are given in Carslaw and Jaeger, [l]

2 pp. 444 and 445. In an analogous manner to the solution for the

bottom corner given on pp. 453^54, the correction

terms for the heat guard gap may be found. On

the assumption that the heat flow over the length

of the cell takes place as if unperturbed, the deviations may be combined as a factor times half the

heat guard gap, which is to be added to the length

of the cell. If the heat guard gap is equal to the

conductivity gap, Ar, the added length is 3

c2 =0.923 Ar/2.

The bottom corner of the emitter adds a term to the cell constant of 2xrjX0.559 for equal conductivity gaps on the sides and bottom. . Thus, the

total rate of heat transfer by gas conduction is [-2^+^ +2 x 0 5591 M (1) L hi r.2/ri Ar J

where r2 is the inner radius of the receiver. The

2 Figures in brackets indicate the literature references at the end of this paper,

s See appendix 1. 318-334
OOO O O—K) m r- iOU)h- 00 <TKT><T> 0~i <T> eg CJ (X) CM OJCMCO <M " — K* in

- oj ^center of Symmetry

EMITTER AXIS

Figure 2. Relaxation solution of the heat guard gap.

cell constant is

L In r2/ri Ar

1.118/-

-I

From eq (2), we find 99.4 percent of the heat transfer

from the cell illustrated in figure 1 is accounted for by the two principal parts: 94.9 percent by radial

heat flow, 4.5 percent by linear heat flow. The

transfer from the heat guard gap amounts to 0.25

percent, and the transfer from the bottom corner amounts to 0.33 percent.

3.2. Measurement of Receiver and Emitter Radii

Both to increase the flow of heat by conduction

and to reduce the heat transferred by convection,

the conductivity gap should be kept as small as

will permit the accurate determination of the cell Ar

constant. For the case of — <C1, the rate of heat

transfer by conduction from a section of length I

of an infinite coaxial cylinder is ^ =r^l]^lM. wi_thin

a relative error of 1/ArV

3

Ar

f J

> or 0.03 percent for 2r =2.2 cm and Ar=0.068 cm. The equation serves to emphasize that for the same error in the cell constant

two orders of higher accuracy of length measurements

are required to determine the conductivity gap, than

the radii themselves.

The measurements of the two radii were made with

a super-micrometer as measurements of two outer

diameters, the one directly, the other by use of a

''falling probe." If a "probe" is allowed to fall by

its own weight, as shown in figure 3, the gap between

the probe and the outer cylinder can be calculated

from the air flow [2]. In an annulus formed by two

coaxial cylinders of radius r p and r2 , length L, and

gap m=r2 —r P , the volume of gas of viscosity -n flowing in time 6 with a difference of pressure

PROBE RECEIVER

GAS TIGHT CHAMBER

Figure 3. Falling probe device for inner diameter measurement.

Ap — Aw.g and average pressure p can be expressed

within a relative error of

60 r\ as AV=irpAwgrm3 d

<OT\p2L

r = (r

p +r2 )/2 and p2 is the atmospheric pressure.

With the volume expressed as the probe displacement

Qr)p2riAlL

m

gpAw rd

(3)

where g is the gravitational constant and AZ is the

distance of fall in time 6 and Aw is weight of probe.

The average inner radius of the receiver is determined by adding the gap, m, to the radius of the

probe, r„. The determination of the gap, m, was

precise within 2.5X10-5 cm. The measurement of 2r p was precise within

2.5X10-5 cm, as well as 2rlt the outer diameter of

the emitter. The sum of m+rp for varying m was

consistent within 2.5X10"5 cm. Thus with differ- ences of radius between receiver and emitter as small as 0.06 cm, the length of Ar was determined

to an accuracy within 0.1 percent.

319''-335
4. Convection

In general, the hydrodynamical equation for nonturbulent flow of a fluid of velocity 7, viscosity

7j, pressure p, and density p is (div -q grad) v~grad

p—pg, where g is the acceleration of gravity [3]. For two infinite vertical plates at uniform temperatures t0 —At/2 and t 0 -\-At/2, the equation reduces to

d

2vt (x)

tlx2 (p—p)gThe axes are taken with the origin at the midpoint

between the planes. The .r-axis is normal to the

planes, the ?/-axis is horizontal, and the ^-axis is vertical. The average density, p is the density at ,r=0. xAt

If the separation of the planes is Ar, t(x) =t0 -\—Ar and

p=p[l—a(t— tn)]= p

Since r—0 when x-

- paxAt Ar where a— —= I ^-

p \d tj

Ar . Ar -— and x=-^>

(6)

In a closed system, the circulation takes place as a single stream, reversing direction at the top and

bottom. Conservation of mass requires a term

second order in At which does not affect the heat

transport by more than 1 percent for actual measurement, hence it was neglected.

The heat transported per unit horizontal distance is

f

Ar/2

/ \ / \ \ 4( w Ar*g ap2cpAt 2 q=Cp

J a Hx)p(r)At(x)dx=-~ —^

where c p is the specific heat capacity and the average

density is indicated without the bar. The horizontal

distance in the cell is very nearly 2wr. Then the

rate of heat transport per degree is

q/At-- 2wrAr3 g ap2cpAt 720 (7)

If the total heat transfer is studied as a "conductivity," j_/CAt, a portion is due to convection, which

may be written as 2.QXlO- 6aP

2 c p At CAt (8)

The value 2.6 X 10 -6 combines the constants of eq (7) and the value of the cell constant Cfor the cell of

figure 1. The neglect of terms of higher order in At for p(x) affects i^conv detectibly near the critical point of C02

. When At <5 deg C, these terms need not be

considered for other measurements to be reported.

Engineering investigations of convection have

been analyzed by use of several correlating functions.

It may seem at times as if serious discrepancies

exist when the correlation is extended to inappropriate conditions. Let us consider three dimensionless quantities:

(1) The Grashof-Prandtl product

r\K (9)

(2) The Grashof number

Gr:

<](Ar) 3ap2At.

(3) The Reynolds number

1. a 1 - {Ar) 2apgAt , m where the average velocity v=— 0 — and x0 =Ar/2.

Then

p

g{Arfap2 At Re~ 384,» ' (10)

Thus the Grashof number and the Reynolds number

are functionally the same for a gas in a vertical gap. Within the range of pressure and temperature such

that the Eucken factor, Kjric v , is a constant and

that 7 = cp /cc is a constant, the Grashof-Prandtl

product and the Reynolds number will serve equally

well for the correlation of laminar convective effects. The ratio of KQonv to iv"gas can be found by dividing

eq (8) by Keas , and is functionally (Ar/l) (Gr-Pr).

It can be seen from eq (8)/i£ga8 that the criterion of Kraussold, that convection is insignificant 4 for Gr-Pr<1000, leads to different error limits depending upon Ar/l. For the cell of figure 1, Gr-Pr =1000

involves a relative heat transfer bv convection of 8XIO-3

. Representing a ratio of the heat transport of convection to conduction, Gr-Pr is a logical correlat- ing function for heat transport by laminar convection. Over the range of variables that eq (9)/eq

(10) is a constant, either will serve as a criterion for the initiation of turbulent convection. Near the

critical point, however, cp —>°oand 7-^00. Since the

Eucken factor does not vary greatly, Gr-Pr can become enormous while the Reynolds number

remains small. The Reynolds number depends

upon the velocity resistance per se, and it is the

fundamental quantity, not Gr-Pr, which should be

used as the criterion for initiation of turbulent flow. The purpose of this section is to demonstrate

how the data can be treated to give the heat transfer

by thermal conduction alone. Measurements must

be made under conditions of laminar flow. For

C02 , Onsager and Watson [4] have shown that with

* Worse yet is the statement that convection does not exist for Gr-Pr<l,()00. The author hopes this idea will take its place with the phlogiston theory! 320-336
apparatus of the planar, vertical type, turbulence commences at a value of the Reynolds number of

about 25. Often it is clear that Re<<25. If there is uncertainty, the At for transition from

laminar to turbulent flow should be determined

experimentally. At constant pressure and constant average gas temperature, eq (8) indicates that

q/At versus At is linear for laminar flow. By straight

line extrapolation of q/At versus At to zero At, the

heat transport by convection is eliminated.

The essential requirements of eq (8) are confirmed

by the results. The heat transport correlates well

ctp

2c At

versus — The q/At versus At extrapolations

v are linear within the precision of the data, except

for very large values of eq (8) where second order

effects may be detectible. The values of At calculated from eq (10) (indicated by an asterisk on some extrapolation isotherms in the next paper)

are in satisfactory accord with the experimental

measurements.

5. Asymmetry of the Heat Flow

5.1. Coaxial Centering

If the emitter is not centered perfectly the geo- metrical factor of In /yrt should be replaced by

cosh -1[(r| +rf

d

2)/2rif2], where d represents the

displacement of the two axes. For the cell of figure

1, an error of 7X10-4 cm in the centering would

make a difference of only one part in 100,000 in the

cell constant.

5.2. Heat Loss From the Bottom of the Emitter

The cell with a single heat guard loses heat on the

bottom as well as on the sides. With a uniform

heater winding this leads to an asymmetric temperature distribution, which becomes larger as the

gas thermal conductivity becomes larger. A reasonable approximation permitting mathematical treat- ment assumes uniform heat flow from the center

heater to the emitter, no heat flow on the heat

guard end, and the heat flow across the conductivity

gap proportional to the temperature difference.

The solution for this problem is _K A//9-— ft ±\<*tn+h2 <-'oa (<x n 2)4>0 (r;n) ^ M orn {Wn +^]l+h)^{a;n)

where h=AK, A is the total exterior surface area, K is the thermal conductivity of the substance in the gap, and KAg the thermal conductivity of silver. 5 a<r<b

0<z<l

<t>o(r;n)=I0 {ran) [anK\ (ban )—hK0 (bar,)] +K0 (ran) K/i (&«„)+hh{bar)]

> If the cell were made of another material, the corresponding thermal con- ductivity would be used in place of K.k s .

an<f>i (a;n) =!

=/i (aan)

[<xn Kx (ban ) —hK0 (ban)] —Ki (aan ) [ajx (ban ) +hl0 (ba„) \ and the an are the ordered positive roots of

h=a„ tan (an

l). The value of v'al + h> 2 is taken

positive or negative in accord with the sign of

sin aj.

The functions I0 , I1} K0 , and Ki are Bessel functions of complex argument. The result shows that

the average temperature of the emitter is not at the

center but at

2 =0.66/ for ^=5.95X10-=,

2=0.675/ for i£=5.95X10-4

, and 2 =0.697/ for K= 1 1.90 X 10""1

. Conductivities calculated from the average of the top

and center temperatures must be increased by the

factor indicated in figure 4. This factor is accurate enough that usually no significant error is involved,

and could be reduced by adding measurement of the

temperature difference at the bottom of the cell.

6. The "Blank" and Conduction of Pins

When the cell is evacuated, the heat transferred

by radiation and by conduction of the pins can be

treated as a measurement of a "conductivity,"

called a "blank." The present cell had a blank at 0 °C of 0.138X10"5 cal cm"1 sec" 1 cleg C

_1

, about

4 percent of the conductivity of C02 at the same

temperature and 1 atm pressure. It was estimated

that no more than half of the heat transfer of that

blank was due to conduction of the pins.

It was assumed that the conductivity of a gas

could be found by deducting the blank from the

value of the apparent conductivity for zero temperature difference. However, the blank may not

adequately represent the heat transfer in the presence

of a gas for the following reasons

(1) The conduction of heat across the pin-emitter

interface may increase in the presence of a gas.

(2) The temperature distribution in the pins may

perturb the heat transfer in the gas significantly.

In the first case, if the pressure of the pins against

the emitter is high enough, the effect of the gas on

the conduction across the contact interface is negligible. Ascoli and Germagnoli [5] showed that the

temperature difference across a steel-aluminum interface with 8 urn. finish became nearly constant in a vacuum once the pressure of contact reached 100

kg/cm2

. For N2 at 1 atm, the temperature difference across the interface with the same heat flux became

nearly constant at 50 kg/cm2 contact pressure, and at 100 kg/cm2 was equal within experimental error to the corresponding vacuum value. Boeschoten and

Van Der Held [6] found three times the heat con- duction in the presence of 1 atm of helium as in a vacuum at 35 kg/cm2 contact pressure. The inference

from the preceding investigation is that at 100 kg/cm2

, 321-•337
the ratio would be 1.5/1. Rough surfaces approach

the behavior of smooth surfaces as the contact pres- sure is increased. These measurements were per- formed upon a steel-aluminum interface rather than

a Pyrex-silver interface used in the present apparatus.

However, the ability of silver to conform to the

harder surface of Pyrex is at least as great as for aluminum to conform to steel. The pins were forced

into the silver sufficiently that indentations 0.003 to 0.005 in. deep were made in the emitter, which is to say with sufficient force to exceed 1500 kg/cm2

, the

tensile strength of silver. The Pyrex pins were held

in an aluminum sleeve such that the composite ex- pansion of the two materials approximately matches

the expansion of the cell material from 0 to 400 °C.

Consequently the centering of the emitter and the

contact pressure between the pin and the emitter

should be maintained over the temperature range.

Hence it can be expected that gases of low con- ductivity caused an insignificant change in the rate

of transfer of heat through the pins. In helium, the

uncertainty in pin conduction should not exceed

0.1 percent of the gas conduction.

The additional heat transfer through the gas, which arises because the temperature distribution in the pins does not follow the radial gradient, can be

evaluated by relaxation methods, and leads to the

result that an 18 percent increase of conduction for the area of the surface occupied by the base of the

pin will be observed when the conductivity of the

gas is 10 percent that of Pyrex. The area occupied

by the bases of seven pins was 0.4 percent of the total

surface area of the receiver so that at a gas conductivity of 3X 10~4 cal cm-1 sec

_1 deg C_1 an increase

of conduction of 0.07 percent will be observed. If the conductivity of the fluid reached the value of

Pyrex, the pins would have no effect on the temperature gradient, and at low values of gas conductivity,

the effect is about the same as at a conductivity of

3X 10"4 cal cm-1 sec

_1 deg C

_I

.

7. Radial Temperature Gradient in the

Emitter and Receiver

A correction , in general small, must be made for the

fact that the thermocouples are placed in the body of

the emitter and receiver. This is a power series of KC0 „=Kmeas [l->raKmeiiS +((iKme!iS}

2 + . . . ] of

which only the first corrective term is large enough

to be significant. For the dimensions of the silver conductivity cell in figure 1, a= 10.70 cm sec deg

C/cal.

8. Discussion of Other Cells

There are only a few forms of thermal conductivity

cells suitable for accurate absolute determinations of

the thermal conductivity of gases. The "hot wire"

cell is an extreme case of a coaxial cylinder cell, with

a small radius of the emitter, but the cell constant

cannot be determined with the accuracy possible for a larger radius of emitter. The heat transfer analysis

is complicated, and in a dense gas convection is difficult to control because of the large temperature

gradient near the wire.

i.o3o| 1 1 1 1 1 i

1 1 1 1 r

Figure 4. Correction to the conductivity for asymmetric heat

flow. A coaxial cylinder cell with heat guards at both

ends would not have the end heat flow which requires

the corrections given in figure 4. However, there is an uncertainty in the results due to a possible heat

flow between the emitter and heat guards. When

the emitter is suspended or held in place by sleeve

or rod connections with the heat guards (as is customary for this design), the increased conduction

possible by a slight difference in temperature between the emitter and guards will increase significantly the uncertainty of the thermal conductivity

determination. The uncertainty is reduced if the

thermal conductivity is relatively large, and if the

emitter-receiver temperature difference is large. In

order to avoid these restrictions, the suspension

method could probably be modified.

In principle the flat plate cell, with an emitter

and guard above the receiver, should not be affected

by convection. In dense gas, there is good possibility that many such cells have had significant

convection transfer from "chimneys," but that no

special measurements were made to check. However, by proper design, it can be expected that convection difficulties would be eliminated. The cell constant can be determined with about the same

accuracy as for the coaxial cylinder cell, but instability of the flat plate cell alinement affects the cell constant directly. By contrast, a change of the

coaxial cylinder cell alinement affects the cell constant comparatively little.

9. Conclusions

By use of a heat guard and receiver extension

which extends the conductivity gap of a coaxial

cylinder, the conduction across the gap can be

expressed accurately. In combination with special

measuring techniques involving a "falling probe,"

the value of the cell constant can be obtained to an accuracy within ±0.1 percent.

The coaxial cylinder cell must be used with the

axis vertical in order to permit analysis of convective

heat transport. It was deduced mathematically and

found experimentally that the apparent conductivity

is affected by laminar convection linearly with the

temperature difference. The temperature difference

which causes the Reynolds number, eq (10), to be

322-33S
25 defines the highest temperature difference for which laminar flow can be expected. The effects of

convection can be eliminated by extrapolating the

apparent conductivity versus the temperature dif- ference to zero temperature difference, provided the

measurements lie in the range of laminar flow. For high accuracy, corrections must be made to the data for asymmetry of heat flow, perturbation

of the temperature gradient by the mounting pins,

and the temperature gradient in the emitter and

receiver. Of course, the rate of heat transfer in a vacuum is deducted. There lias now been sufficient quantitative measurement to show that the radiation

and pin transfer should remain constant within 0.1 percent in the presence of a gas. Of the various types of cells used for measuring

the thermal conductivity of gases, the coaxial

cylinder cell and the flat plate cell offer the most

promise of accurate results.

10. References

[1] H. S. Carslaw and J. C. Jaeger, Conduction of heat in

solids, 2d Ed., Oxford Univ. Press, London, 1959.

[2] W. H. MacAdams, Heat transmission, 2d Ed., McGrawHill Book Co., Inc., New York, 1942.

[3] R. C. Jones and W. H. Furry, Rev. Mod. Phys. 18, 151

(1946).

[4] L. Onsager and W. W. Watson, Phys. Rev. 56, 474 (1939).

[5] A. Ascoli and E. Germagnoli, Energia Xucleare 3, 113

(1956).

[6] F. Boeschoten and E. F. M. Van Der Held, Physica 23, 37 (1957). 11. Appendix

Given the conductivity 2;ap h and heat s,uard gap

2k. 6 We identify the points, A B C D E F G H in the complex s-plane. These points are transformed

in the £-plane by the Schwarz-Christoffel transformation, which is D C

T

y

-plane

B A

0,0

G H

E F

z=-icl: l—or h

[t+a][\-at +^(l-a2 )(l-t2 )}

<7V1

C=2kfr;

[t-a]\\+at +^(l-a2 )(l-t2)}

+sin~ 1 ^-j-71"-

a

2 =k2/(h2 +k2 ).

2a

1 Note that the symbolism is that of Carslaw and Jaeger, and in general should

not be identified with the symbolism of the rest of the paper.

Points A, H, C, D, E, and F are assumed to lie at

infinity in the z-plane. Corresponding values of the

points are shown for the i-plane.

f-plane

A B r,D 0, 0 E,F G H

— oo -1 -a 0 0 a 1 oo

By use of the conformal mapping function

7rw=ln^+a)/(f—

a)J the points in the 2-plane are transformed to the

indicated points in the itf-plane.

w-plane

w=u-\-iv

a A, H F

CO 0 0 CO D 0 0 E

— CO —i 0, — i

Thus in the w-plane, heat flow between two infinite parallel plates can be studied.

If the heat flow to w =u—i is studied, this corre- sponds to the heat flow to DE=—iy in the 2-plane.

By substituting 7rw=ln ^^—^ and w=u—i, z=—iy,

iy= —ih(u—t) In— , T [l+af +V(l-a2 )U-r2 )] -—2ik

sm-^+A.

7T

For u (and y) large, t^>-\-a~

y—hu+- In (1— a

2 )+— sin 1 a.

7T 7T

The heat transport to DE per unit width per unit

temperature difference is, in the w-plane, Ku (where

K is the thermal conductivity of the medium).

Ku=K (\-- In [l-a2 ]-

2\ sin- 1 a). \n w Tib /

Thus, there are two corrective terms to be added to the normal term yjh for the steady heat flow between two planes distant h apart. For the case that the heat guard gap (2k) is equal to the conductivity gap (h) a

2 =l/5.

323-339
Where the conduction is regarded as unperturbed

along FG and BC, we can get a relative correction

to the normal term for infinite plates over the

distance of the heat guard gap by taking y =2k =h. Then

Ku=K( [1-a2]— sin- 1 a") \ 7T 7T /

or we may add a length to the emitter equal to one

half the heat guard gap times the factor in parenthesis, i.e.,

c2 =k (l —In [1 —a

2

] —- sin -1 a\

=jfc(l-0.0766)=0.9234fr.

(Paper 66A4-10R)

324-340
JOURNAL OF RESEARCH of the National Bureau of Standards—C. Engineering and Instrumentation

Vol. 67C, No. 2, April-June 1963

A Radial-Flow Apparatus for Determining the Thermal

Conductivity of Loose-Fill Insulations to

High Temperatures

D. R. Flynn

(November 28, 1962)

A description is given of an apparatus used for determining the thermal conductivities

of loose-fill granular materials in the temperature range 100 to 1,100 °C. The method used

in making these determinations was that of radial heat flow through a hollow cylinder of specimen material contained between a central ceramic core and an outer ceramic shell. The heat flow through the specimen was determined by measurement of the power input to a heater in the central ceramic core. The radial temperature drop through the specimen was inferred from temperatures measured in the core and in the shell, thus avoiding entirely the problems of measuring a temperature difference within the specimen material. Experimental results with an estimated uncertainty of 3 percent or less are presented for diato- maceous earth having a density of 0.15 g/cm3

, and for aluminum oxide powders having

densities of 0.40 and 0.44 g/cm3. A discussion of the test method is given, with attention

to possible sources of error.

1. Introduction

Various loose-fill thermal insulations are used, in conjunction with appropriate guarding, to reduce

extraneous heat flows in several thermal conductivity

measuring devices under development in the Heat

Transfer Section at the National Bureau of Standards. Since such heat flows cannot be entirely

eliminated, it is necessary to know the approximate

thermal conductivity of these insulations in order to

effect appropriate corrections. In designing an

apparatus for determining the thermal conductivity

of these insulations, it was decided to aim for an

accuracy of 5 percent or better, because of the

general interest in thermal conductivity of loose-fill materials, both from an engineering and from a

theoretical viewpoint.

The purpose of tliis paper is to describe an apparatus and method used for determining the thermal

conductivity of loose-fill materials. Experimental

results are presented for diatomaceous earth and

aluminum oxide powder in the temperature range

from 100 to 1,100 °C. Factors affecting botli the

precision and accuracy of the measurements are

discussed.

2. Method

Radial heat flow in a hollow cylinder of loose-fill insulating material was selected as the method for the

measurements. A cross section of the essential

elements of the apparatus is shown in figure 1 . The

specimen was contained within the annular space

between the outer radius, a, of the ceramic core and

the inner radius, b, of the concentric shell. A known

quantity of heat per unit time generated electrically

in the ceramic core flowed radially through the specimen to the concentric ceramic shell. The ceramic

core had a concentric ring of equally spaced holes at a radius, r' , parallel to the axis, each containing a heater wire. Temperatures were measured by an

axial thermocouple in the ceramic core and by

tangential thermocouples in the ceramic shell at radius c, only one of which is shown in figure 1.

Figure 1. Horizontal cross section of the essential elements of

the apparatus.

In figure 1, if the cylindrical surfaces r=a and r=b

are each isothermal, the heat flow between these

surfaces will be radial except near the ends. In general, the thermal conductivity of the specimen material will vary with temperature, and the heat flow

rate, q, through a cylindrical element of unit axial

length is

2= -2^/-^. (1)

325-129
Temperature is denoted by the symbol T, the temperature-dependent thermal conductivity by k, and

the radial coordinate by r. For reasonable temperature differences, the thermal conductivity of the

specimen material can be assumed to vary linearly

with temperature; then (1) becomes

2=-2Tk{l+a(T-T)}r^. (2)

k is the thermal conductivity at an arbitrary refer- ence temperature, T, and a is the corresponding

temperature coefficient of thermal conductivity.

Integration of (2) yields, after substitution of

boundary conditions,

2irk (Ta -Tb )

) In b/a

(3)

where Ta is the temperature at r=a, Tb is the temperature at r=b, and k corresponds to the temperature

T, which is given by

f=T«+TK (4 )

If the circle of heater wires at r=r' were a contin- uous cylindrical heat source, the entire region r<Cr'

inside the heater circle would be isothermal. For

the case of a finite number of line heat sources at r=r', the temperature measured at the axis is equal

to the average temperature at the radius of the

heater circle [1]

1 (see also sec. 5). The heat flow

to the surface of the core per unit length is given by

2irkr (T0 -Tn) In a/r'

' (5)

where Tn is the temperature measured in the axial

well, and k c is the thermal conductivity of the

ceramic core material, corresponding to a temperature (T0 +Ta)/2. Similarly, for the outer ceramic shell,

2irks {Tb -Tc ) In c/b (6)

where Tc is the temperature measured at ?'—c, and

ks is the thermal conductivity of the ceramic shell material at (Tb +Tc )/2. If there are m heater wires at r=r/

J each generating

heat at the rate q' per unit length, the total heat

generated per unit length of core is q=ma'. (7) Combination of eqs (3), (5), (6), and (7) yields

mq' In b/a k=-

, f rp rp mq'' An a/r' \nc/b\\ ' T {

T°-Tc -^\r^r+

-k—)f

(8)

1 Figures in brackets indicate the literature references at the end of this paper.

which is the equation used for purposes of calculation of all thermal conductivity data presented in

this paper.

3. Experimental Procedure

3.1. Apparatus

A vertical cross section of the thermal conductivity

apparatus is shown in figure 2. The specimen was

contained in the annular space between the central

ceramic core, which was supported at both ends, and

the concentric ceramic shell, which was supported by

Transite end pieces. The space between the ceramic

shell and the outer stainless steel case contained a

loose-fill thermal insulation.

The ceramic shell was a hollow mullite cylinder,

61 cm long, with an inner radius of 3.2 cm and an

outer radius of 3.8 cm. A helical groove (about 1.6 turns/cm) on the outer surface was wound with three

separate heaters of 0.10 cm Kanthal A-l heater

wire. The main shell heater was 41 cm in length;

the upper and lower shell heaters were 5 cm in

length. A length of 5 cm at each end was not

wound. The upper and lower shell heaters provided extra heat needed to offset end losses, so that

longitudinal temperature differences in the central

region could be minimized.

The central core was an extruded mullite rod, 46

cm long and 1 .27 cm in diameter. Sixteen equally

spaced holes, 0.08 cm in diameter, extended the

entire length of the rod. The centers of the holes

formed a circle of 0.43 cm radius. The core heater,

which provided the heat flowing radially through the

specimen, consisted of a continuous length of platinum-20 percent rhodium (0.05 cm diam) wire

threaded back and forth through the 16 holes. Current lead wires to this heater, and lead wires to

its two voltage taps located at the upper end of the

ceramic core, were brought in through the hollow

ceramic upper support for the core. The core was

supported below by a ceramic pin, as shown in

figure 2. Both the upper and lower supports were

provided with small platinum-20 percent rhodium

heaters to minimize longitudinal heat flow at the

ends of the ceramic core. Temperatures in the apparatus were determined by means of six platinum: platinum-10 percent rhodium

thermocouples. These thermocouples were fabricated from calibrated thermocouple wire, 0.04 cm

in diameter.

Three thermocouples were positioned in the

ceramic shell at the midplane of the apparatus.

These were inserted into tangential holes (fig. 1) located 120° apart at a radius of 3.5 cm. The

temperature, Tc , in (6) and (8) was obtained by

taking the average of the temperatures indicated

by these three thermocouples. Two additional

tangential thermocouples were located in the ceramic

shell, one 15 cm above and one 15 cm below the

midplane of the apparatus.

Temperatures in the core were measured by means

of a thermocouple which was located in a 0.25-cm

diam axial well and which could be moved vertically

326i-130
Figure 2. Vertical cross section of the apparatus for deter- mining the thermal conductivity of powders.

A. Terminal head for current and

voltage leads.

15. Ceramic support tube. C. Upper support heater.

1>. Upper shell heater. E. Main shell heater.

V. Ceramic core,

(i. Specimen.

II. Ceramic shell.

I. Shell insulation.

J. Stainless steel case. K. Lower support heater.

L. Lower shell heater. M. Ceramic support rod. N. Removable plug. T. Thermocouple.

by exterior manipulation. A scale fixed above the

apparatus indicated the position of the thermocouple junction. The temperature measured at midlength was designated as T0

.

3.2. Instrumentation

The three heaters on the ceramic shell were fed b3r variable voltage transformers, which in turn were

fed by a voltage regulating transformer. These

heaters were individually regulated by on-off controllers actuated by thermocouples located in the

ceramic shell adjacent to the heater windings. The

heaters on the ceramic core supports were manually

adjusted by means of variable voltage transformers.

The ceramic core heater, which provided the heat

flowing radially through the specimen, was powered

by a 28 v, 4-amp, regulated d-c power supply,

with a small bank of power resistors in series for adjusting to the desired heater current. Power

input to the ceramic core heater was determined by

measuring the d-c current through the heater and

the voltage drop across the entire length of heater

wire in the core. These measurements were made

using calibrated shunt and volt boxes and measuring their output voltages by means of a precision

d-c potentiometer.

The noble metal leads of the six measuring thermocouples were brought to an isothermal zone box at room temperature. A thermocouple with one junction in the zone box and one in an ice bath was

placed in series with a double-pole selector switch,

so that each measuring thermocouple was automatically referenced against the ice bath [2]. Thermocouple voltages were read to 0.1 juv on the precision potentiometer.

3.3. Test Procedure

The specimen material was placed in the annular

space between the ceramic core and the ceramic shell through the opening at the top of the apparatus.

The bulk density of the specimen in place was computed from the weight of specimen material and the

volume of the test chamber.

The shell temperature controllers were set at the

desired temperature, which for the first test in any

series was about 100 °C, and all heaters were turned

on. The controllers and power for the heaters at the top and bottom of the ceramic shell were adjusted, if necessary, until the temperatures indicated

by the upper and lower tangential thermocouples

agreed to within 1 or 2 deg C with the average

temperature of the three midplane tangential thermocouples. The power to the core heater was adjusted

to attain the desired radial temperature drop across the specimen, and the power to the heaters on the

ceramic core supports was adjusted until a traverse

of the thermocouple in the axial hole indicated the

desired longitudinal temperature distribution.

When a satisfactory steady-state condition was

obtained, the test data were recorded. With t he

axial thermocouple in the midplane position, three

sets of readings (at about 20 inin intervals) were 327-131
taken of all thermocouples and of the output of the

volt box and shunt box. At the end of these readings, the nxial thermocouple was moved to a position near the top of the ceramic core. After this thermocouple again reached thermal equilibrium, its output was read on the potentiometer. Readings were

taken at 5 cm intervals over a region 15 cm or more

on either side of the midplane. When a complete

set of data had been taken, the apparatus was

adjusted to a new temperature level, as desired for the next test.

3.4. Calculation of Results

Calculations of thermal conductivity values by means of eq (8) were performed by means of a

digital computer. The data input to the computer

consisted of the average emf readings for each

thermocouple and the average readings from the volt

and shunt boxes. Equations for the estimated

thermal conductivities of the ceramic core and shell as functions of temperature, and for temperatures

as a function of thermocouple emfs, were contained

in the computer program.

4. Results

4.1. Diatomaceous Earth

Test results for a specimen of commercial diatomaceous earth are presented in figure 3. The

in-place bulk density of the specimen was 0.15 g/cm3. The temperature difference across the specimen

during the various tests was from 30 to 60 deg C.

The open squares in figure 3 represent results obtained in five tests before heaters were placed at the ends of the ceramic core to minimize axial heat

flows. For these five tests, the temperature differ-

<_> 1.6 e

lu 0.6 IH

04

DENSITY =015 g/cm5

NBS GUARDED HOT PLATE

NO END GUARDING ENDS GUARDED

SPECIMEN WAS SINTERED

SPECIMEN WAS PULVERIZED AFTER HAVING BEEN SINTERED

1 I

TEMPERATURE Figure 3. Thermal conductivity of a diatomaceous earth as a function of temperature.

ence between the ceramic core and shell was 10 to 25 percent less at positions 15 cm from the midplane than it was at the midplane. (These data, as

well as those presented below, were calculated using

eq (S) ; the effect of a nonuniform axial temperature

distribution is discussed in sec. 5.2.) After these five tests, the specimen was removed

and heaters were installed on the ceramic core supports. The same sample was then reinstalled as the specimen, and the data represented by the

open circles were taken in order of increasing mean

temperature. After the test at a mean temperature

of 946 °C, tests were conducted - at several lower

temperatures and finally at a maximum temperature.

The results of these tests, indicated in figure 3 by

circles with vertical lines through them, were significantly higher than those of previous tests. Removal of the specimen indicated that a slight

sintering had occurred. 2 The powder appeared to be slightly fused together, but was easily broken

apart. The same sample was pulverized by hand,

replaced in the apparatus, and the test results indicated by the open triangles were obtained.

The curve drawn through the data points in figure 3 is the quadratic equation of least-meansquares fit to the open squares, circles, and triangles.

The equation for this line is

£=0.414+1.114

1000/

+0.072 (—

Y

Viooo/ (9)

where k is expressed in milliwatts/cm-deg C and T

in °C For all data points except the circles with

vertical lines through them, the standard deviation

of a point, estimated from the residuals about the

fitted line, is 0.013 mw/cm-C, corresponding to

1.3 percent at 500 °C.

The solid chcles shown in the lower left hand

corner of figure 3 represent results of tests made on

a sample of diatomaceous earth from the same

container, at the same density, in the NBS guarded

hot-plate apparatus (ASTM C177).

Figure 4 presents some literature data on diatomaceous earth of various densities [3, 4]; the curve from figure 3 is reproduced for comparison. There

is substantial agreement between the results of

this investigation and those from the literature,

taking density into consideration.

4.2. Powdered Alumina

Test, results for an aluminum oxide powder are presented in figure 5. This alumina was produced

at the National Bureau of Standards by ignition

of hydrated aluminum chloride in a muffle furnace

at 1,150 °C. The method of production and some

of the properties of this type of alumina powder

have been described [5].

2 An uncontaminated diatomaceous earth should melt at the temperature of

fusion of silica, which is well above any temperatures obtained in these tests. A commercial diatomaceous earth, however, may contain sufficient clay to produce sintering at temperatures as low as 800 °C. No tests were conducted

to determine the actual temperature at which sintering began for the diatomaceous

earth discussed in this paper. In general, diatomaceous earth should be used

with caution at temperatures above 800 °C if sintering would cause difficulties. 328-132
1.6 -

I 1 1 1 1 1 1 1 I l I i I i I

i 1,1,1 0 100 200 300 400 500 600 700 800 900 1000 TEMPERATURE , °C Figure 4. Comparison of diatornaceous earth thermal conductivity results with literature data.

t

1

i

1—

r

—,—,—,—i—,—i—,—i , 100 200 300 400 500 600 700 800 9 00 1000 1100 TEMPERATURE, °C Figure .3. Thermal conductivity of an aluminum oxide powder

as a function of temperature.

The data indicated by the open squares in figure 5 were taken in order of increasing mean temperature on a specimen having a bulk density 3 of 0.44 g/cm3

. The curve drawn through the squares is the quadratic

equation of least-mean -squares fit. The equation

for this line is

I-1.I30+MW (^o)+0.333 (^y, (10)

where k is expressed in mw/cm-C and T in °C, The

estimated standard deviation of a point is 0.010

mw/cm-C, corresponding to 0.7 percent at 500 °C.

3 Later checks of the packing procedure used for tliis specimen indicate a possible uncertainty of 0.02 g/em3 in the reported in-place bulk density. All other

densities reported are believed to he accurate to within 0.005 g/cm3

.

The data indicated by the open circles were taken

in order of increasing mean temperature on a specimen having a bulk density of 0.40 g/cm3

. The specimen was the same sample as that previously tested,

but was intentionally packed to a lower bulk density.

After the tests up to 919 °C, a test, indicated by an open triangle, was made at 526 °C. The curve drawn

through the open circles and the triangle is the

quadratic equation of least-mean-squares fit to these

points. This equation is

i=0.947 +0.84l(

I^)+0.296(14)

!

, (11)

in the same units as above. The estimated standard

deviation of a point is 0.011 mw/cm-C, corresponding

to 0.8 percent at 500 °C.

The solid circles shown in the lower left-hand corner

of figure 5 represent results of two tests made in the

NBS guarded hot-plate apparatus on a sample of alumina powder, taken from the same batch as the

sample installed in the ceramic core apparatus, having a bulk density of 0.41 g/cm3

. The solid diamond

shown represents a guarded hot-plate test on the

sample of alumina which had been tested in the

ceramic core apparatus at higher temperatures. The

in-place bulk density for this test was 0.46 g/cm3. The higher density specimen (0.44 g/cm3

) had a room temperature thermal conductivity about 20

percent higher than that of the lower density specimen (0.40 g/cm3 ). However, the curves corresponding to these different densities converged with in- creasing temperature and crossed at about 7.30 °C.

This crossing of the curves is believed to arise from

increased radiation within the larger pores of the

lower density material.

5. Discussion of Test Method

5.1. Determination of Temperature Difference Across

the Specimen

Measurement of the temperature difference across the specimen, using the core and shell thermocouples

shown in figure 1, represents a departure from the

procedure used in radial flow methods for loose-fill materials described in the recent literature [6, 7]. The possibility of chemical contamination of thermocouples by the specimen material is greatly reduced,

and the often-difficult problem of determining and

maintaining the distance between thermocouples lo- cated within the specimen material is avoided. However, with the method of measurement used here,

account must be taken of temperature drops in the

core and shell, and at their interfaces with the specimen if necessary, to obtain the temperature drop

across the specimen.

The thermocouple in the axial hole at micllength

of the central ceramic core is located in a region

where there are substantially no temperature gradients, and therefore the thermocouple accurately

attains the temperature of its environment without

disturbing the heat flow pattern. The theory of a harmonic logarithmic potential function shows that

329-133
the value of the temperature at the center of a circle

is equal to the average of its values over the circumference of the circle [8,9]. Hence, the temperature

measured at the axis of the core is equal to the

average temperature at the fictitious surface, r=r'.

The difference between the average temperature of

the fictitious surface at r—r' and the average temperature of the surface of the core at r =a may be

computed from (5). It is to be noted that eq (5) is valid regardless of the distribution of heat sources on the circle r=r', as has also been shown by Peavy

[1] in analyzing the two-body system of the specimen

and the core with line heat sources. Similarly, the temperature difference, Tb —Tc , from the inner surface of the shell to the radius of

the tangential thermocouples may be computed

from {<o).

The uncertainty in determining the temperature

difference between the axial thermocouple in the

core and the three thermocouples in the shell is estimated 4 to be less than 1 percent. The computed

temperature drops in the core (T0 —Ta ) and in the

shell (Tb —Tc ) were less than 2.4 percent and 0.6 percent, respectively, of the temperature drop

through the specimen for all of the results presented

in section 4, using the best available values for the

thermal conductivities of the mullite core and shell,

the uncertainties in which may have been as much as 30 percent.

The effective radius, r', of the virtual heating

surface in the core is uncertain by not more than the

radius of the heater holes, thus introducing an additional error of not more than 25 percent of T0 —Ta . Similarly, the effective radius, c, to the tangential

thermocouple wells is uncertain by not more than

the radius of the wells, thus introducing an additional

error of not more than 35 percent of Tb —Tc

. Combining the errors arising from the uncertainties in k c and ks and those from In a/r' and In c/b, the esti- mated uncertainties in T0 —Ta and Tb —Tc are 40

and 50 percent, respectively, thus introducing an

additional uncertainty in Ta — Tb of 1.3 percent. For

fine powders of low thermal conductivity, such as those tested, errors due to thermal contact resistance

between the specimen and the surfaces of the core and shell are believed to be negligible. Thus, combining uncertainties, the temperature drop across the

specimen (the expression in braces in the denominator

of eq (8)) is considered to be known with an uncertainty of 1.5 percent.

5.2. Longitudinal Heat Flow

Equation (8) was derived on the assumption of no

longitudinal heat flow. For an apparatus of finite length, having imperfect end guarding, the effects of

axial heat flow should be considered. Jakob [11] considered the effect of axial heat flow for the symmetrical case in which both ends of the core are at the same temperature but are at a temperature

different from that at the center. An analysis is presented here which allows different temperatures

4 All estimated uncertainties in this paper represent the author's estimate of the "two-sigma" limit. All uncertainties are combined using standard propagation of error formulas (see, for instance, Davies [10]).

at the two ends of the core, and also takes into

account the effect of core temperature distribution on the power measurement if the electrical resistiv- ity of the heater wire varies linearly with temperature.

A simplified cross-sectional view of the apparatus

is shown in figure 6. It is assumed that the surface

/ =6 is isothermal at temperature Tb and that temperatures are measured in the core at three positions

equally spaced along the axis. It is assumed that,

for the purpose of analyzing longitudinal heat flow, a transverse cross section of the core can be treated

as being isothermal.

SPEC 1 MEN

SPEC MEN

2 0 SHELL

Figure 6. General core temperature profile used in analyzing

effects of longitudinal core temperature imbalance.

Neglecting longitudinal heat flow in the specimen,

the differential equation for heat flow along the core can be written as

d

2 v 2-wkv mq

dz2 C In b/a C

(12)

where

and

v=T—Tb , T being the temperature at any

point along the core;

2 =longitudinal coordinate;

6'= the longitudinal thermal conductance per

unit length of the core, including heater

wires and holes.

In general, the rate of heat generation, q' , per unit

length of heater wire will not be constant if the electrical resistivity of the heater wire varies appreciably

330-134
with temperature. For reasonable temperature variations, the electrical resistance per unit length of

heater wire can be assumed to be a linear function

of temperature,

p=Po(l+7*D, (13)

where p and pn are the electrical resistances of a unit

length of heater wire at temperatures T and Th , re- spectively, and 7 is the fractional change in electrical resistivity per unit change in temperature. The rate

of heat generation per unit length of heater wire is

2

/ =/*P=/2Po(l+7»), (14)

where / is the electrical current flowing through the

heater. Equation (14) must be substituted into (12).

The conditions which are to be satisfied are c=\\ at z=-

v—Vo. at 2=0

r=r., at z=L

L.

(15)

Substitution of these conditions into the solution of

(12) yields

v0 +(

in which

F,+F2 -2IY\ cosh (iz-l ) osh pL—l

, (V3 —T

7 A sjnh \iz 2 /sinh M/7

M

" =

rLin(^)-7W/" pnJ-

(16)

(17)

The thermal conductivity of the specimen is given bv

T_mPp0 In (bid)

[-

Vl+V2 -2V0 V0 C >sll pL

^-2F0_ "I

(18)

The total power delivered by the core heater is determined by the current, /, through the heater

and the voltage drop, E, across the total length of heater wire in the core. The total resistance of the

heater is given by

(19)

where S is the total length of heater wire and I* is the average temperature of the core heater, obtained

by integration of (16) over the entire length, 2M,

of t lie core.

V v:lz=V0

(Vi+Vs -2V0\ sinh pM _

2 I itJ/(cosh JL- (20)

Equation (18) can be rewritten as

k^k' [l +- * '{woCoahpL-Wi+V

where

7 (si nh pM—p

2pM (cosh pLj,_mEl In (6/a)

2tt1VV

MI

-1) }] (21)

(22)

is the apparent value of thermal conductivity obtained if no corrections are made for the effects of

axial heat How. Since k is defined in terms of p and p

in terms of k, iterations are necessary in order to obtain k. A first approximation to k is given by k'; substitution of k' into (17) yields a value of p which

can be used in (21). The resultant k can be used to obtain a better value of p, etc. The convergence is quite rapid in all practical cases; the first approximation did not introduce an inaccuracy greater than

0.00:-> percent in k for the case to be discussed below.

Equation (22) corresponds to (8), the equation that was used for purposes of calculation; EIIS corre- sponds to (/, and V0 corresponds to the expression

in braces in the denominator of (8). The first expression in the braces in (21) represents the correction

for axial heat flow; the second expression represents

the correction in power measurement to take account

of the variation of electrical resistance with temperature. It is of interest to note that, for a positive

value of 7, these corrections are of opposite sign.

Data were presented in section 4.1 for which the

temperahire difference between the ceramic core and

the substantially isothermal ceramic shell was 10 to 25 percent less at positions 15 cm from the midplane

than at the center. As seen in figure 3, t lie results

for these tests were not appreciably different from

the conductivities obtained later when the core was

substantially uniform in temperature along its length.

In order to investigate more thoroughly the effects of axial heat flow in the apparatus, a series of five tests was conducted in which the ends of the ceramic

core were held at temperatures different from that in the core at the midplane. These tests were all con- ducted at a mean temperature of 525 °(\ with the

alumina powder specimen discussed in section 4.2. The ceramic shell was maintained approximately

isothermal over a central region of at least 'M) cm

length. The core temperature at positions 15 cm

above and below the midplane was varied by adjustment of the small heaters at each end of the ceramic

core. The results of these tests are shown in figure

7, where the percent departure of the thermal conductivities from their mean' value is plotted against

the quantity (\',+ V3 )l2Vo. The solid circles represent experimental data; the solid curve is the straight

line of least-mean-squares fit to the data. A straight

line w;is used because, for the various values of pa- rameters involved, the departure can be shown to be

a nearly linear function of (V,^.- V>) /2Vn for values

331-135
not too different from 1.0. The slope of the straight

line in figure 7 was used to compute the value for /j. of 0.29 cm-1 where 7 was taken as 8.0 X 10~4 deg

C"\ Vo as 44 deg C, L as 15 em, and M as 23 cm.

Substitution of this value of n into (17) yields for

the longitudinal conductance of the core, C, a value

of 0.06 w-cm/C. This value agrees with the esti- mated longitudinal conductance of the ceramic core and heater wires.

(V,+

V

2 )/2V0 Figure 7. Effect of longitudinal core temperature imbalance,

(Vi + V2 )/2Vo, on thermal conductivity values obtained for alumina poivder.

With the exception of those tests in which core end

heaters were not used, all data presented in section

4 gave values of (Vi+ V2 )/2Vi) between 0.85 and 1.15. From figure 7, it is seen that this corresponds to an

uncertainty of less than 0.4 percent in the thermal

conductivity values obtained using (8). Values of

(F1 +y2 )/2yn could be held between 0.95 and 1.05

without undue difficulty, if desired, thus further

reducing this uncertainty.

5.3. Eccentricity

It has been assumed that the outer surface of the

ceramic core and the inner surface of the ceramic shell were concentric cylinders. Since concentricity may

not always be possible, the effect of eccentricities

should be considered. The thermal resistance between two eccentric parallel circular cylinders is given by Carslaw and Jaeger [12] and is, in the

notation of this paper,

Tb 1 . d

2 —= +b —_ arccosh

2irk 2ab

(23)

where e is the eccentricity, or the distance between

the centers of the two cylinders.

From (23), the thermal conductivity is given by

k=

2ir(Ta -T„

, l+X2 -e2 (X -l)2 ,„.,. arccosh — (24)

where, following El-Saden [13], the dimensionless

eccentricity e —e/(b —a) varies between zero (concentricity) and one (cylinders in contact), and

X —b/a is the ratio of the radii.56 For the case of eccentric cylinders, if (3) is used

instead of (24) to compute the thermal conductivity

of the specimen, an error will be introduced. Since

it is of general interest, the percent error due to neglecting the effect of eccentricity is shown in

figure 8 plotted against dimensionless eccentricity, e, for several radius ratios, X =6/a.

S^. 5.0

CLO

CCCE

bJ 20

1 1

-

1 1 1

'

1 1 / /'

-

\ = b/a

1 1

€ = e/(b-a)

1 1 1 1 1 1 1 05

e Figure 8. Calculated error in thermal conductivity due to neglecting the effect of eccentricity for radial heat flow between

isothermal cylinders.

For the apparatus described in this paper, the

ratio X was approximately 5.0. The dimensionless

eccentricity as defined above was less than 0.05, so that the uncertainty due to eccentricity was less than 0.1 percent.

5.5. Precision and Accuracy of Results

The precision of measurement is indicated by the

standard deviations (estimated) of the data, which

are of the order of 1 percent.

The accuracy of the reported measurements is more difficult to estimate. The total power generated in the core heater was known to within 0.1 percent. The length of wire between the potential

taps at room temperature was known to within 0.2 percent. Thermal expansion could have increased

this length by 1 percent at 1,000 °C if friction

between the heater wire and the ceramic core at points of contact did not prevent free longitudinal

expansion of the wire in the holes. Because the

5 Equation (24) can also be derived from tlie last equation presented by El- Saden. To convert El-Saden's eq (38) to the form presented above, it is helpful

to make use of the identity arccosh x —arccosh j/=arecosh (xy— yJ(x2 —l)(y2 —D).

6 Making use of the identity arccosh r=ln (j+V^2 — 1), eq (24) reduces to the equivalent of (3) for the case of concentric cylinders (£=0). 332-136
effect of expansion was uncertain, no expansion

corrections were made. The heat flowing radially

through the specimen is further in question by not more than 0.4 percent in an extreme case, due to the

uncorrected effects of longitudinal temperature variations along the core (see sec. 5.2). In section 5.1, it was estimated that temperature

drops across the specimen were determined with an

uncertainty of 1.5 percent. Uncertainties in the

ratio of the shell radius to that of the core did not

introduce more than 0.2 percent uncertainty in the

results. The error due to possible eccentricity of

the ceramic core in the ceramic shell did not exceed

0.1 percent. Combining all of the uncertainties

discussed, uncertainties in the thermal conductivity

results presented in section 4 are estimated to be

less than 2 percent at 100 °C, and, because of heater

wire expansion, 3 percent at 1,000 °C

5.5. Comments

It is felt that the type of central heater used in

this apparatus has advantages which may recom- mend it to others interested in radial heat flow

measurements. The particular advantages of this arrangement are, (1) the measuring thermocouple in the core attains the temperature to be measured and

does not interfere with the pattern of heat flow, (2) the measuring thermocouple is well protected both

mechanically and chemically but still can be easily

removed for calibration or renewal, and (3) temperatures can be measured at any desired longit udinal

position using the same thermocouple.

By means of suitable modifications, the equipment described could be extended to cryogenic

temperatures, or to more elevated temperatures.

If required, the accuracy of measurement could be

improved over that attained in the apparatus described by taking careful account of all the factors

discussed in sections 5.1 and 5.2. Applications for which a heated core of this type might be advantageous include determination of forced or natural

convection from cylinders and determination of the

thermal conductivity of pipe insulations or fluids. In the latter case, convective effects would need

to be excluded by extrapolating results obtained with

small temperature differences to zero temperature

difference.

The experimental measurements were performed

by C. T. Siu and J. E. Griffith. The author thanks

T. W. Watson for conducting the various tests on

the NBS guarded hot plate apparatus. The very

helpful suggestions and comments by B. A. Peavy

and H. E. Robinson are gratefully acknowledged.

6. References

[1] B. A. Peavy, Steady state heat conduction in cylinders

with multiple continuous line heat sources, J. Research NBS 67C (Eng. and Instr.) No. 2. 1 19-127

(Apr.-Junel963).

[2] W. F. Roeser, Thermoelectric thermometry, J. Appl.

Phys. 11, pp. 404-405 (1940); also in Temperature,

Its Measurement and Control in Science and In- dustry, p. 202 (Reinhold Publishing Corp., New York, N. Y., 1941).

[3] International Critical Tables, Vol. II, p. 315 (McGrawHill, New York, N.Y., 1927).

[4] R. Calvert and L. Caldwell, Loss of heat from furnace

walls, Ind. Eng. Chem. 16, pp. 483-490 (1924).

[5] J. I. Hoffman, R. F. Leslie, H. J. Caul, L. J. Clark and J. D. Hoffman, Development of a hydrochloric

acid process for the production of alumina from clav,

J. Research NBS 37, p. 409 (1946) RP1756.

[6] R. G. Deissler and D. S. Eian, Investigation of effective thermal conductivities of powders, National Advisorv

Committee for Aeronautics RM E52C05 (1952).

[7] M. J. Laubitz, Thermal conductivity of powders, Can.

J. Phvs. 37, p. 798 (1959).

[8] O.D. Kellogg, Foundations of Potential Theory, p. 223

(Frederick Ungar Publishing Co., New York, X. Y., 1929; reprinted bv Dover Publications, Inc., New

York, N. Y., 1953)/

[9] W. J. Sternberg and F. I. Smith, The Theory of Potential and Spherical Harmonics, pp. 74-76 (The Univ. of Toronto Press, Toronto, Canada, 1946).

[10] O. L. Davies, Statistical Method in Research and Production, 3d ed., pp. 40-41 (Hafner Publ. Co., New- York, N.Y., 1957).

[Ill M. Jakob, Heat Transfer, Vol. 1, pp. 246-250 (John

Wiley and Sons, Inc., New York, N. Y., 1949).

[12] H. S. Carslaw and J. C. Jaeger, The Conduction of Heat

in Solids, 2d ed., p. 451, equation 19 (Oxford Univ.

Press, 1959).

[13] M. R. El-Saden, Heat conduction in an eccentrically

hollow, infinitely long cylinder with internal heat

generation, J. Heat Transfer, Trans. ASME, Series

C, 83,510 (1961).

(Paper 67C2-126)

333-137
JOURNAL OF RESEARCH of the National Bureau of Standards — C. Engineering and Instrumentation

Vol 71 C, No. 4, October-December 1967

Measurements of the Thermal Conductivity and Electrical

Resistivity of Platinum from 100 to 900 °C*

D. R. Flynn and M. E. O'Hagan

institute for Applied Technology, National Bureau of Standards, Washington, D.C. 20234

(August 17, 1967)

1 . Introduction

Standards and standard reference materials are the

basis of a consistent and accurate measuring system.

The need for standard reference materials in thermal

conductivity measurements is two-fold. In the first place, such materials are required for comparative

measurements in which the thermal conductivity of

the material under test is determined in terms of that of the standard reference material. Secondly, such materials are required in evaluating the accuracy of apparatus designed for thermal conductivity measurements. The degree to which the measured value of the

thermal conductivity of the standard reference material agrees with the accepted value is a check on the

accuracy of the apparatus in which the measurements

were made.

The basic requirements for any standard reference

material are that it be stable, reproducible and appropriate for the measurements at hand, and that the

property in question be uniform throughout the material. In the case of standard reference materials for thermal conductivity other desirable requirements are

that the standard be usable over a wide range of temperature, that it be chemically inert so as not to be

*This research was the subiect of a dissertation submitted by M. E. O'Hagan to the Faculty of The School of Engineering and Applied Science, The George Washington

University, in partial satisfaction of the requirements for the degree of Doctor of Science. This work was supported in part by Engelhard Industries, Inc.. Newark. New Jersey, who supplied the platinum and financial assistance in the form of a grant to the National Bureau of Standards. M. E. O'Hagan was supported in part by Grant AFOSRH02.T-66

from the Air Force Office of Scientific Research and in part by the Institute for Industrial Research and Standards, Dublin, Ireland.

**Present address: Institute for Industrial Research and Standards. Dublin. Ireland.

affected by or affect other materials in the system and

that the thermal conductivity of the reference material

be close in value to that of the materials which are to be measured in terms of it. The advantages of using platinum as a thermal conductivity reference material have been pointed out by

Powell and Tye fl]

1 and by Slack [2]. Platinum is available in high purity in pieces of substantial size.

It has a fairly high melting point (1769 °C on the 1948

International Practical Temperature Scale), has no known transition points, and is relatively stable chemically in air and other atmospheres, with the exception of hydrogen, even at high temperatures [3, 4]. Its thermal conductivity, although relatively high for use as a reference material with nonmetals, is about

the geometric mean for metals and alloys.

Since the thermal conductivity of a pure metal is strongly correlated with the electrical conductivity of the metal, it is highly desirable that the electrical conductivity of a metal which is intended for use as a thermal conductivity reference material be very

stable under varying heat treatments. The stability of

the electrical conductivity of platinum is evidenced by

the fact that the International Practical Temperature

Scale is defined by a platinum resistance thermometer

in the temperature range — 182.97 to +630.5 °C [5, 6]. Studies are currently underway at NBS [7] and other

laboratories to investigate the possibility of extending

to the gold-point (1063 °C) the range over which a platinum resistance thermometer is used to define the

temperature scale.

1 Figures in brackets indicate the literature references al the end of this paper.

334-255
Platinum appears to be, in every way save one, an

ideal material to use as a thermal conductivity refer- ence standard. The exception is that the spread among

the literature values for the thermal conductivity of

platinum is considerable, to say the least. Powell, Ho, and Liley [8] show a plot of essentially

all of the published thermal conductivity data for platinum through the year 1965. The spread in the

data increases from about 10 percent at room temperature to over 30 percent at 1000 °C. Even if many of

the older data are discounted, the picture is not particularly improved. O'Hagan [9] has summarized the

methods used for previous measurements of the

thermal conductivity of platinum and also has summarized the characterizations of the various samples.

Prior to the measurements of Powell and Tye [1], all thermal conductivity values reported for platinum at temperatures above 100 °C were obtained by methods

in which the temperature gradient in the specimen was

produced by Joule heating due to passage of an electric current directly through the specimen. While the re- sults of all but one [10] of these higher temperature

investigations employing electrical methods essentially agree with one another, they disagree with those

of later investigations [1, 11, 12], which employed

nonelectrical methods. This raised the question as to whether or not electrical methods yield results that are

intrinsically different from those of nonelectrical

methods. This could mean that the theory which has

been used in analyzing electrical methods is in error, or it could mean that heat conduction is significantly

dependent on electric current density, at least in the case of platinum.

The considerations discussed above pointed to the

need for a comprehensive investigation of the thermal

conductivity of platinum. It was felt that both an

absolute steady-state method without an electric cur- rent flowing in the specimen, and also an absolute

steady-state method with a current flowing in the

specimen should be employed.

As regards the nonelectrical method, experience at NBS with guarded longitudinal heat flow methods in- dicated that such a method could be made to yield accurate results on a material having as high a thermal

conductivity as platinum, provided a specimen of

sufficient cross-sectional area was used. With a fairly

conductive metal, there were no particular advantages

in going to a radial heat flow method; furthermore, to do so would have required a much larger sample.

As regards the electrical method, an arrangement

utilizing quite large current densities would be more

likely to reveal deviations due to a dependence of thermal conductivity on current density. It was also desirable to use the same method as that used by most

of the previous investigators. Fortunately, these two

desiderata both pointed to the necked-down sample

configuration utilized for measurements on platinum

by Holm and Stbrmer [13], by Hopkins [14], and by

Cutler, et al. [15]. To give a direct and accurate comparison between

the two methods it was considered desirable to combine both sets of measurements in one apparatus and

on the same specimen thereby eliminating a number of

uncertainties which would arise in comparing data

derived from measurements in different apparatus

and on different specimens. The above considerations

led to an apparatus, described in section 3, in which

thermal conductivity measurements can be made by

both the usual longitudinal heat flow method and by an

electrical method.

It was also felt that thermal conductivity measure- ments should be made on platinum samples of at least two purities. Samples were obtained of a high purity

platinum (resistance 'thermometer grade) and of a somewhat lower purity platinum (commercial grade).

As of this writing, only the measurements on the lower

purity platinum sample have been completed. The

results obtained on that sample are presented in this paper and are compared with the results of other

investigators.

2. Description of Sample

In order for a valid comparison to be made between

the results of different investigators who measure on a particular kind of material, it is necessary that their specimens be characterized as extensively as possible

so that differences in specimens may be accounted for. For this reason a number of pertinent measurements

were made in an attempt to characterize the speci- men used in the present investigation. These meas- urements and the results thereof are described below.

The platinum was provided by Englehard Industries,

Inc., in the form of a solid bar 2.04 cm in diameter by

31 cm long, and was classified as being of commercial

purity. The fabrication and cleaning procedures used

in preparing the platinum have been described by

O'Hagan [9]. The as-received bar was annealed in air for 5.5 hr at 770 °C in a horizontal tubular furnace and furnace

cooled at a rate of approximately 120 deg/hr. Shortly

thereafter the bar was accidentally dropped causing

it to deform slightly at one end. After correcting the

damage the bar was reannealed for 1.5 hr at 680 °C

and furnace cooled at a rate of approximately 90 deg/hr.

Its thermal conductivity was then measured in the

NBS Metals Apparatus [34, 35] over the temperature

range -160 to +810 °C [32]. Following these measurements the bar was machined and ground to 25.4 cm long by 2.000 cm

diam. The density of this bar was measured (see

below) and the electrical resistance was measured

at ice and liquid helium temperatures (see below).

The thermal conductivity specimen (18.4 cm long by

2.000 cm diam) was then fabricated from one end of

this bar. A length of 6.4 cm was cut from the other

end for separate low temperature thermal conductivity

measurements [33]. The remaining disk, approximately 1 cm long, was reserved for metallographic and

spectrographic analyses.

A thin neck, approximately 0.1 cm in diameter and

0.3 cm long, was machined in the thermal conductivity

specimen at approximately 4 cm from one end. To

cleanse this necked-down region of oil and any con335-256
tamination contracted from the cutting tools, the fol- lowing cleaning procedure was followed. Degreasing was effected by immersion for half an hour in tri- chlorethylene vapor. The neck was then pickled for 10 min in hot 50 percent nitric acid. Following this the neck was washed in distilled water, pickled for 10 min in 50 percent hot hydrochloric acid, and again

washed in distilled water. There was equal likelihood

of the rest of the specimen having slight surface con- tamination as a result of machining but its effect on

the bulk properties of the specimen would not be nearly

as grave as the corresponding effect in the neck region.

It was considered sufficient to clean the surface of the

specimen with toluene and carbon tetrachloride.

A general qualitative spectrographic analysis, per- formed by the NBS Spectrochemical Analysis Section on the 2-cm-diam by 1-cm-long platinum disk mentioned above, detected Ag (10-100 ppm), Pd (10-100

ppm). Fe (< 10 ppm), and Mg (< 10 ppm). O'Hagan [9] reported the results of a quantitative spectrographic

analysis made on a portion of a 0.05 cm wire drawn

from the same platinum ingot as the thermal conductivity specimen.

Photomicrographs were also made of the platinum

disk cut from the bar sample. They showed grain size

to be of the order of 0.02 cm. No evidence appeared

of inclusions of foreign matter or of any irregularities

in microstructure. Hardness measurements were made

on the original platinum bar, after the second anneal,

using a Vickers Pyramidal Diamond Tester with a 10 kg

load. Values ranged from 36.5 to 38.0 Vickers hardness

number.

The density of the bar, when it was 25.4 cm long, was determined by mass and dimensional measure- ments to be 21.384 g/cm:i at 21 °C, accurate to within

±0.002 g/cm:{

. This density is an average value for the

whole bar and there is no guarantee that the density was uniform to that degree throughout the bar. The ratio of the resistance at the ice-point temperature to that at the boiling point of helium at atmospheric

pressure is a measure of the extent and condition of

impurities in a material and of the crystallographic

state of the material. This ratio was determined on the

2-cm-diam bar. The ice-point resistances were measured both be- fore and after the helium point measurements. The

current was supplied from a regulated d-c power

supply and was measured using a calibrated resistor and a precision potentiometer. The voltage drops in the specimens were measured on a high precision

6-dial potentiometer. In each case the resistance was measured at three or four different current levels and

the value corresponding to zero current obtained by

extrapolation. The ratio of the resistance of the sample

at the ice-point to that at the helium-point was found to be 393. This value is believed to be accurate to within

1 percent. However, it corresponds to an average

value over a considerable length of the sample and the

sample may not have been uniform in purity throughout.

A set of knife edges of known separation was fas- tened to the 2-cm bar during the first set of ice-point

resistance measurements. The knife edges acted as potential taps. Using the known separation ol the knile

edges and the cross-sectional area of the bar, the ice- point resistivity, corrected to 0 °C dimensions, was

determined to be 9.847/u.fl cm, accurate to within

±0.010^11 cm. A length of 0.05 cm platinum wire, drawn from the same ingot as the thermal conductivity sample, was

electrically annealed in air for 1 hr at about 1450 °C. The electromotive force of this wire versus the platinum standard Pt 27 [16] was measured by the NBS

Temperature Section with the reference junctions at 0 °C. The values obtained (at 100 deg intervals) in- creased in an essentially linear manner from 0 /xV at 0 °C to +15 jixV at 1100 °C. This indicates that the

sample used in the present investigation was less pure

than Pt 27. The temperature coefficient of resistance, a — (Rioo — Ro)/100Ro, between the ice-point and the

steam-point is often used as an indication of the purity

of resistance thermometer grade platinum. The limiting

value of a for extremely pure platinum is given by

Berry [17] to be 0.003928;). The size and low resistance

of the thermal conductivity specimen precluded a highly accurate direct determination of a on the speci- men using existing equipment. On the basis of the

electrical resistivity measurements (described later) on the necked-down portion of the specimen, a had a value in the range 0.003876«a^0.003916. The rela- tively large uncertainty in a arises from the use of

platinum versus platinum—10 percent rhodium ther- mocouples to measure the temperature near 100 °C. Berry [17] gives a plot which correlates a with the ratio of the resistance of a sample at absolute zero to that

at the ice-point. He also correlates the resistance at absolute zero with that at the helium-point. On the

basis of Berry's correlations, the ice-point to heliumpoint resistance ratio for the thermal conductivity

specimen used in the present investigation corre- sponds to 0.003907 s= a s£ 0.0039 16. This is not inconsistent with the range of values obtained from the

electrical resistivity measurements.

Although a could have been measured directly with

high accuracy on the 0.05 cm platinum wire, this was

not done since the results would not necessarily be

valid for the 2 cm bar, owing to possible differences in purity and annealing. Corruccini [18] gives an empirical expression, due to Wm. F. Roeser, correlating a with the electromotive force versus Pt 27 with the

junction at 1200 °C and the reference junctions at 0 °C. Extrapolation of the emf measurements mentioned above, indicates an emf of + 16 ^.V at 1200

°C, corresponding on the basis of Roeser's expression, to a ~ 0.003914 for the 0.05 cm wire drawn from

the same material as was used to fabricate the thermal

conductivity specimen.

A cooperative project, involving NBS and several

producers of thermometric grade platinum, is currently underway to study the properties of pure platinum. If as a result of this project, it appears that further characterization is indicated for the platinum

used in the present investigation, such characterization will be performed on material which is being

reserved for that purpose.

336-257
3. Method and Apparatus

3.1. Method

As discussed in the introduction, it was decided to build a single apparatus in which thermal conductivity

could be measured by both an absolute guarded longitudinal heat flow method (nonelectrical method) and

by a method in which a necked-down portion of the

sample was heated directly by passage of an electric current (electrical method). The specimen configuration selected for these measurements is shown in fig- ure 1. The specimen (A) was raised to the desired

temperature level by means of the heaters Q\ and

Q:t . In the longitudinal heat flow method, the heater,

Q>, located slightly above the center of the bar pro- duced a temperature gradient along the portion of the

bar below Q>. Heat from this heater was prevented

from flowing up the bar by adjusting Q% so that there was negligible temperature difference across the

necked-down region of the specimen. Lateral heat

losses from the bar were minimized by matching the

temperature distribution along the guard to that along

the specimen. Thermal conductivity was calculated

from the measured temperature distribution along the

lower portion of the bar, the power input to the central

heater, and the geometry.

8x

7*

6 -

5 -

4-

l :

V

10

Figure 1.

SCALE, cm

X — THERMOCOUPLE

<— CONTROL COUPLE

• — HEATER WINDING Schematic diagram showing locations oj heaters and

thermocouples in the apparatus.

In the electrical method, where the sample was

directly heated by passage of an electric current,

the voltage drop across the necked-down region of the

specimen was measured as a function of current, while

the maximum temperature rise in the neck was computed from the change in electrical resistance (due to a given change in current) and the temperature coefficient of resistance of the material. The thermal

conductivity was determined from the voltage drop

across the neck, the computed maximum temperature

rise in it, and the electrical resistivity of the material.

The apparatus is described in detail in this section. The experimental test procedures and calculation pro- cedures for the nonelectrical method are described in sections 4.1 and 4.2; those for the electrical method

are described in sections 5.1 and 5.2.

3.2. Mechanical Configuration

The mechanical configuration of the apparatus is illustrated diagrammatically in figure 2 and described

in detail below.

a. Specimen

The specimen (A) was a bar 2 cm in diameter by

18.4 cm long with a 0.11 cm diam by 0.33 cm long neck

machined in it 4.1 cm from the upper end. A special

technique, described by O'Hagan [9], had to be de- veloped for machining the neck due to its structural

^ZZZZA

o 20

I 30

Figure

SCALE, cm

The apparatus [components are identified in the text)

337-258
weakness. Hollow molybdenum extensions (B) of the same diameter as the specimen were screwed to the

specimen (A) at both ends. The open ends were brazed

to copper blocks (C) that served as heat sinks. The

molybdenum extensions were filled with high purity

"coral" alumina. The lower end of the specimen as- sembly (B-A-B) was bolted to, but electrically in- sulated from, a brass flange which was welded to a water-cooled brass column (D). This column was

firmly bolted to plate (E) which served as a base for the apparatus.

One of the major problems with the necked-down

specimen was that of protecting the neck from mechanical strain due to tension, compression, torsion, or bending. Any clamp supporting the neck would have

had to be electrically insulated from the specimen and

differential thermal expansion between the clamp and

specimen could have introduced strain in the neck.

As an alternative to a clamp it was decided to counter- balance the load on the neck due to the weight above

it so that there would be only a small net force on the

neck. The weight of platinum above the center of the

neck was computed from dimensional measurements

and from the measured density of the specimen, and

the components extending from the upper end of the

specimen were weighed before assembly.

The counterweight (W) was suspended from a string

which passed over two pulleys and attached to an aluminum hanger (H). The pulley wheels were mounted

on low-friction bearings having a starting force of less than 1 g each. A molybdenum well (F), which was

brazed to the upper copper block (C), passed through

a linear bearing (L) which served to maintain the up- per part of the specimen in precise alinement with the

lower part, and presented negligible resistance to the

free vertical motion of the specimen resulting from

thermal expansion. This bearing was mounted on the

upper plate (E) but electrically insulated from it. The

two aluminum plates (E, E) were connected by three

tie bars (K) to form a rigid framework for maintaining

proper specimen alinement. An auxiliary device, de- scribed by O Hagan [9], prevented the upper part of the

specimen from rotating but still allowed free vertical motion. Current was introduced to the specimen via a copper rod (N) at the lower end and through a hollow

molybdenum electrode (O) at the upper end. The upper

electrode was brazed to a copper support (S) which was

fastened to, but electrically insulated from, the upper

plate (E). The molybdenum well (F) contained a liquid

metal alloy into which the electrode dipped thereby

affording a flexible current connection. The buoyant

force of the liquid metal on the electrode contributed

to the load on the neck and was compensated for in the

counterweight. The electrode was fixed but the molybdenum well moved upwards with the specimen due to thermal expansion during test runs. This changed the buoyant force and consequently put a load on the neck.

The maximum change in buoyant force was only 3 g, however, which would not strain the neck significantly. The liquid metal used was a gallium-indium

eutectic alloy chosen primarily for its low vapor pres- sure and its comparatively low freezing temperature of

15.7 °C. The requirement for low vapor pressure was

dictated by a need to evacuate the system. Preliminary

tests were run to evaluate the uncertainty in buoyant

force due to surface tension and sticking of the galliumindium to the molybdenum surfaces. A very definite hysteresis effect was observed as the electrode was moved relative to the well and then returned to its initial position. The largest uncertainty in buoyant force was determined to be about 4 g. The choice of molybdenum as the electrode and well material stemmed

from its compatability with gallium, which reacts with

most other metals, and from the fact that molybdenum

is wetted by gallium. The current feed-in system also served as a heat sink for the upper part of the speci- men assembly. The hollow molybdenum electrode was

internally cooled by circulating water at a temperature

higher than the freezing point of the gallium-indium

eutectic alloy.

b. Furnace and Guard

The inner core (G), or the guard as it is called, was

a molybdenum tube of 5.7 cm inside diameter. Since

the inner core acted as a thermal guard to prevent

heat losses from the specimen, it was considered more

desirable to make it from metal rather than from ce- ramic so that the temperature distribution along it could be more easily controlled and more accurately

measured. The bottom of the guard was attached to a water-cooled brass plate (P). A water-cooled brass ring

(Q) was attached to the upper end of the guard. The

outer furnace core (V) was an aluminum oxide tube

supported top and bottom by three 1-cm diam aluminum oxide rods (U). The exterior portion of the furnace consisted of a water-cooled shell (X) supported between two water- cooled plates (P). Attached to the upper plate of the furnace was a split nut. This nut engaged a lead screw mounted between the plates (E, E) and by turning the screw the furnace could be moved up or down. Ready

access to the specimen was thereby afforded. The

three rods (K) acted as guide rods for the furnace.

Six linear bearings (Y) attached to the furnace plates

ensured alinement and permitted the furnace to move

up and down freely. The correct vertical location of the

guard relative to the specimen was determined when

a probe attached to the upper end of the guard made

electrical contact with a plate attached to the molybdenum well at the ijpper end of the specimen assembly. When the furnace had been positioned, the indi- cating probe attached to the guard was removed.

The space between the specimen and the molybdenum guard and that between the guard and the

water-cooled shell were filled with fine high-purity

aluminum oxide powder of low thermal conductivity i and low bulk density (0.16 g/cm3

).

y c. Environmental System

The entire apparatus was mounted inside a 24-in diam metal bell jar to enable operation in an inert atmosphere. A 4-in oil diffusion pump and a 5 cfm

mechanical pump were used to evacuate the system

prior to refilling with argon or helium. Initial evacua338-259
FIGURE 3. Schematic diagram showing the construction of the specimen heater.

tion was controlled to avoid disturbance of the fine powder insulation.

3.3. Thermal Configuration

The heater and thermocouple locations on the

specimen and guard are shown in figure 1.

a. Specimen

The heaters, Qi and Q.i, used to raise the mean temperature of the sample were located in the molybdenum extensions. These heaters consisted of six series-connected helical coils of 0.02 cm diam platinum—thirty percent rhodium wire insulated from the

surrounding metal by thin-wall aluminum oxide tubing.

Platinel 2 thermocouples were attached adjacent to heaters Qi and Q3 for use in controlling the temperatures at these locations.

The central heater, Q2 , was contained in six holes

drilled through the platinum bar and was constructed

as shown in figure 3. The inner four holes were 0.1 cm

in diameter and accommodated helical elements contained in thin-wall aluminum oxide tubing. The ele- ments were made from 0.013 cm diam platinum—10

percent rhodium wire, the outside diameter of the helix being 0.05 cm and the pitch 0.025 cm. The outer two

holes were 0.16 cm in diameter and accommodated

"swaged elements" having platinum—10 percent

rhodium sheaths insulated from platinum — 10 percent

rhodium heater wires by compacted MgO powder in- sulation. The swaged elements were a snug fit in the

holes so that there was good thermal contact between

the sheath and the bar, and consequently good thermal

coupling between the heater and the bar. The six ele- ments were connected in series as in heaters Qi and

Q3 . Platinum heater leads, 0.05 cm in diameter, were welded to the ends of the swaged elements.

The good thermal contact in the swaged elements en- sured that the temperature at the ends of the heater

2 Platinel has a high thermal emf. approximately that of Chromel P versus Alumel. The negative leg of the thermocouple is 65 percent Au, 35 percent Pd alloy (Platinel 5355) and the positive leg is 55 percent Pd. 31 percent Pt, and 14 percent Au (Platinel 7674).

closely approximated that of the specimen. Moreover,

the current leads extended radially from the heater in an isothermal plane. The combined result was to minimize heat losses via the leads. Two 0.02 cm platinum

10 percent rhodium potential leads were welded to each

of the current leads, one at the junction of the heater

and the current lead, and the other about 1 cm back

along the current lead. The two platinum—10 percent

rhodium potential leads together with the intervening

section of platinum current lead served as a differential thermocouple to determine the temperature gradient

in the current lead. By taking potential readings with

the current flowing in the forward and reverse directions, the IR drop in the current leads could be ac- counted for and the temperature gradients therein

determined. These data were used in computing heat

flows along the leads. The potential drop across the

inner taps was used in computing the power generated

in the heater. The distances from the heaters to the nearest thermocouples and potential taps were such

that perturbations in heat flow and electric current

flow generated by the presence of the heaters decayed

to an insignificant level at the position of the thermocouples or potential taps (see appendix B of O'Hagan

[9]).Five thermocouples, spaced 2 cm apart, were lo- cated in the gradient zone of the specimen, with the

lowermost one (designated 4 in fig. 1) being 2 cm from

the end of the specimen. The thermocouples were

fabricated from 0.020 cm diam platinum and platinum —

10 percent rhodium wires which were annealed

in air at about 1450 °C for V2 hr and then butt-welded

together. They were pressed into 0.018 cm wide by

0.023 cm deep horizontal slits in the surface of the

specimen thereby replacing the metal removed in machining the slits. By virtue of the fact that the speci- men was fairly pure platinum with essentially the same

absolute thermoelectric power as the platinum leg of

the thermocouple the junction of each thermocouple was effectively at the point where the platinum—10

percent rhodium leg first made contact with the specimen, and the temperature measured was the temperature at that point. The platinum—10 percent rhodium

wire emerging from its groove extended a short way

around the specimen in the same isothermal plane

insulated from the specimen in broken ceramic tub- ing—so as to minimize the amount of heat conducted

away from the junction. Similar thermocouples were

located in the molybdenum extensions, three in each,

to measure the temperature distribution along them.

This information was essential to the mathematical

analysis of the system.

Additional thermocouples were located on either

side of the neck (locations 9, 10, 11, and 12 in fig. 1). These were fabricated from annealed 0.038 cm diam

platinum and platinum—10 percent rhodium wire and

pressed into slits. In addition to measuring temperature, these thermocouples were wired at the selector

switches so that the platinum legs could be used to measure voltage drops across the neck when an electric current was flowing through the neck. With no current

flowing, the platinum—10 percent rhodium legs, in

339-260
conjunction with the platinum neck, could be used as a

differential thermocouple to control the differential temperature across the neck in the longitudinal heat

flow method of measurement.

b. Guard

The guard had three heaters, Q4 , Q5, and Qe, at positions corresponding to those on the specimen

assembly. All three were swaged heaters with platinum—10 percent rhodium sheaths and heating ele- ments, and MgO insulation. They were pressed into grooves machined in the guard, thus giving good ther- mal contact. The end heaters (Q4 and Q«) were used to keep the guard at the desired temperature. The central heater (Q5 ) was used to produce a temperature

gradient in the guard matching that in the specimen.

The guard was electrically grounded but the heaters were isolated. Platinel control thermocouples were peened into the guard adjacent to each of the heaters. Twelve thermocouples were located on the guard,

three in the gradient zone, three in the isothermal zone, and three in each of the end zones. All the thermocouples were 0.038 cm platinum versus platinum — 10

percent rhodium with the junctions pressed into slits machined in the guard. The thermocouple wires were

taken one turn around the guard in broken ceramic tub- ing in an isothermal plane and cemented to the guard

with high purity alumina cement. This helped to temper

the thermocouple leads and reduce the amount of heat

conducted away from the junction by the leads. Within

the furnace all the thermocouples were insulated in single-bore ceramic tubes. For the remainder of their lengths the wires were insulated in flexible fiber-glass

sleeving. All the thermocouples, both from the guard

and the specimen assembly, went to a junction box

mounted on the inside of the feedthrough ring. There

they were torch welded to identical wires which were

taken through wax vacuum seals to an ice bath. All the Platinel control couples went to terminal strips on

the upper plate of the furnace. There they were spotwelded to Chromel P and Alumel wires coming from

the temperature controllers. The aluminum oxide outer core (V) was provided

with a heater winding (0.1 cm diam molybdenum) to bring the furnace as a whole to temperature and to reduce heat losses from the molybdenum guard and

the power load on its heaters. A Platinel control

thermocouple was mounted on the outer core (V).

3.4. Instrumentation

a. Temperature Control

In the longitudinal heat flow method of measuring

thermal conductivity, the platinum—10 percent rho- dium legs of the outer pair of thermocouples in the neck region were used in conjunction with the neckeddown portion of the specimen as a differential thermocouple to control the power to heater Q3, and thus

maintain essentially a zero temperature differential across the neck. The signal from this thermocouple was amplified by a chopper-stabilized d-c amplifier

and fed into a current-adjusting-type proportional controller incorporating automatic reset control and rate

control. The output of the proportional controller regulated the power to the heater by means of a transistor- ized current amplifier fed by a regulated d-c power

supply. In the electrical method of measuring thermal

conductivity, an electric current flowed through the

specimen and the above system of control could not be employed. In this case the Platinel control couple

adjacent to heater Q3 was put in series opposition with

a signal from an adjustable constant voltage source and the resultant signal fed to the proportional controller which regulated the power to Q3. The external

signal was manually adjusted to give zero temperature

differential across the neck.

The specimen heater (Q2) was fed constant voltage

(±0.01%) from a regulated d-c power supply. Power

to heater Qi and to the three guard heaters (Q4 , Qs , and Qh) was supplied by variable-voltage trans- formers, which in turn were fed by voltage-regulated

isolation transformers. Power to each heater was

regulated by individual thermocouple-actuated controllers. Power to the heater winding (Q7 ) on the

alumina core was supplied by a variable-voltage trans- former fed by a voltage-regulated isolation transformer.

The current was manually ratioed among the three

heater sections. The total power to this heater was

regulated by a single thermocouple-actuated controller. All heaters were supplied by separate isola- tion transformers or power supplies to minimize

current leakage effects.

b. Temperature Measurement The noble metal leads of the thermocouples were

brought to an ice bath, where they were individually

joined to copper leads. The copper leads went in shielded cables to a bank of double-pole selector

svvitches of the type used in precision potentiometers.

The selector switches were housed in a thermally

insulated aluminum box with 1 cm thick walls. The

copper leads were thermally grounded to (but electrically insulated from) the switch box to minimize

heat transfer directly to the switches. The emfs of the specimen thermocouples were read on a calibrated

six-dial high-precision potentiometer to 0.01 , using

a photocell galvanometer amplifier and a secondary

galvanometer as a null detector. (Due to thermal emfs

in the potentiometer and circuitry, these emfs were

probably not meaningful to better than ±0.05 /xV.) The emfs of all other thermocouples were read on a second precision potentiometer to 0.1 using an

electronic null detector.

c. Power Measurement Power input to the specimen heater was measured

using a potentiometer in conjunction with a highresistance volt box to measure the drop across the inner set of potential taps, and a standard resistor in series with the heater to measure the current.

340-261
d. Resistance Measurement

All electrical resistance measurements were made

by measuring the current (from a 0-100 A regulated

d-c power supply) flowing through the specimen,

utilizing a calibrated 0.001 Cl standard resistor, and

by measuring the appropriate voltage drop in the specimen, using a potentiometer.

4. Longitudinal Heat Flow Method

4.1. Experimental Procedure

a. Preliminaries The furnace was heated to 150 °C and the system

evacuated to 3 x 10~4 torr. Initial pump-down was

through a needle valve to give a sufficiently low rate so as not to disturb the very light powder insulation.

When the pressure had fallen below 10_1 torr, the dif- fusion pump was turned on, pumping initially through

the needle valve, and, when the pressure was below

10"- torr, through the 4-in port. After pumping for 24 hr, the pumps were turned off and the system backfilled with high purity (99.99%) argon. The argon was

bled in slowly through a needle valve to avoid dis- turbing the powder. The pressure was allowed to build

up to almost 1 atm before the valves were shut off and the cycle of evacuating and backfilling repeated.

The final argon pressure after the second backfilling was about three-quarters of an atmosphere.

The cooling-water flows to the system were adjusted

to the desired levels as indicated on flow-meters. The

water was pressure-regulated to maintain constant flow

rate. A control thermocouple on the specimen was

wired to shut all the heaters off if its temperature ex- ceeded a predetermined level. This was a safety pre- caution in the event of an interruption in the cooling- water flow. The test procedures are described in detail below.

To facilitate the discussion let us refer to figure 1. The region of the specimen below the specimen heater,

Q2, will be referred to as the lower part of the specimen, and the region above Q2 as the upper part of the

specimen.

b. Description of Tests In the longitudinal heat flow method of measuring

1 the thermal conductivity each datum point was computed by simultaneous solution of three tests: L an "isothermal" test with no power input to the

specimen heater (Q2 ) and with the temperature distri- bution on the guard adjusted to closely match that on

the specimen.

2. a "matched" gradient test with sufficient power

input to the specimen heater to maintain the desired

longitudinal temperature gradient in the specimen and

with a matched temperature distribution on the

guard.

3. an "unmatched" gradient test with the power

input to the specimen heater and the temperature at the center of the measuring span the same as in the

"matched" gradient test, and with the temperature

distribution on the guard parallel to that on the speci- men but 10 deg cooler.

Matched Gradient Test The furnace temperature was raised by means of

heater Q7 . The power to the specimen heater, Q2 , was adjusted to give a temperature gradient of 5 deg/cm in the lower part of the specimen. Power to Q:! was automatically controlled, using a proportional controller, to maintain a minimum temperature drop across the neck. The Pt-10 percent Rh

legs of thermocouples 9 and 12 were used in con- junction with the necked-down portion of the speci- men as a differential thermocouple activating the

proportional controller. The temperature drop across

the neck never exceeded 0.1 deg. The specimen was

maintained at the required mean temperature by

thermostatting the power to the lower heater Qi.

The temperature distribution along the 'guard was

forced to match that along the specimen by adjusting

the controllers for heaters Q4, Q.-,, and Q«. Temperatures at corresponding locations on the specimen and

the guard generally agreed to within 1 deg.

After allowing time for the system to come to equilibrium, readings were taken of the thermocouple

emfs and the voltage and current to the specimen

heater, Q2 . Normally these data were taken three

times over a period of about 2 hr. The temperatures

never drifted more than a few hundredths of a degree

from one set of readings to the next and the three

sets of data were averaged. When the drift between

the first and second sets of readings was less than

0.01 deg, the third set of readings was not taken.

On completion of the last set of readings, the voltage

drops between the inner and outer taps of each cur- rent lead were measured with the heater current

flowing normally and then reversed.

Unmatched Gradient Test Upon completion of the "matched" gradient test the controllers for the guard heaters Q4, Q5, and

Qb were adjusted to lower the temperatures on the guard by 10 deg while maintaining the temperature

distribution parallel to that on the specimen. With

the guard at the lower temperature heat losses from

the specimen to the surrounding insulation were significantly increased and the heat flow in the specimen

reduced. As a result, the temperature gradient in the

specimen and its mean temperature were decreased.

The power to heater Qi was adjusted to restore the

specimen to the initial mean temperature. The system was then allowed to equilibrate and the same data were taken as for the "matched" gradient test.

isothermal Test For the "isothermal" test heater Q> was shut off and heater Qi adjusted until the specimen was approximately isothermal. No adjustments had to be made to Q3 as the controller automatically adjusted to maintain

Tu — Tio = 0. The guard heaters were likewise adjusted

until the temperature distribution on the guard once

again matched that on the specimen. When the sys- tem was in equilibrium, the data mentioned above were

taken, with the exception of the power to the specimen

heater which was shut off.

262
At 1100 °C an additional "matched'" gradient test was

run alter the three regular tests were completed. The

extra data obtained in this test served as a check on

drifts in thermocouple calibrations during the testing

period.

c. Testing Sequence

All of the measurements described above were made at a number of temperatures. Tests were first run in air at 100 °C, then in argon at 100. 300. 500,

700, 600, 400, and 200 °C in that order. One of the guard heaters would short out at about 750 °C and

consequently the upper limit on the first run was

700 °C. After completing that run in argon the system was evacuated and backfilled with helium (99.99%

pure) to a pressure of about three-quarters of an atmosphere. The helium, having a much higher thermal

conductivity than argon, changed the effective thermal

conductivity of the insulation surrounding the speci- men. Tests were run in helium at 200 and 400 °C to experimentally evaluate heat losses from the specimen

to the insulation. The system was then opened up and

the trouble with the guard heater corrected. The fur- nace was filled with fresh powder insulation, the powder being packed lightly around the neck to ensure

that the necked-down region was uniformly filled with

insulation. The system was refilled with argon as de- scribed at the beginning of this section and tests were

run at 300, 700, 900, and 1100 °C. Heater Q:! burned

out while tests were being conducted at 1100 °C by

the electrical method and those tests were incomplete.

The thermocouples started drifting at 1100 °C and

losing their calibration due to contamination. Consequently, it was decided to terminate the tests at that

point.

4.2. Calculation Procedures and Uncertainties

For one-dimensional steady-state heat flow, the

total heat flow, Q, through the specimen is given by

dT

dz

'

where K is the thermal conductivity, A is the cross- sectional area of the specimen, T is the temperature

and 2 is the longitudinal coordinate. For moderate

temperature ranges, the thermal conductivity of the

specimen can be assumed to vary linearly with

temperature; then (1) becomes

Q = -KA{l+frlT-T»)} dT

dz'

(2)

where A. 0 is the thermal conductivity of the specimen

at a reference temperature, T0 , and /3o is its corresponding temperature coefficient. The difference between

the heat flows in two tests is given by

Q-Q' = -XoA

-koA/30

dT\_(dT\'

dz) \dz)

\t-tM T'-T0 ) dz

(3)

where quantities of one test are distinquished from

those of the other by use of primes. If we define the

reference temperature as

T0 T(dTldz)-T'(dT/dz)'

(dTldz)-(dTldz)' (4)

the second term on the right-hand side of (3) vanishes,

and the thermal conductivity at the reference temperature, To, is given by

«?-<?';

4\(dT/dz)- (dTldz)']' (5)

The purpose of computing the thermal conductivity

from data corresponding to two different powers was

to correct for errors that did not depend on the power

transmitted through the specimen. The most obvious

errors of this type are thermocouple errors. In a simultaneous solution each thermocouple in effect measures a temperature difference so that errors in calibration of the thermocouples cancel out to first order. Further possible sources of error will become

evident below. Determination of A0 involved measure- ment of the cross-sectional area of the specimen, the

total heat flow in the specimen and the longitudinal

temperature gradient in the specimen for each of

the two tests. These quantities were evaluated at the

position of the middle thermocouple in the measuring

span.

a. Cross-Sectional Area The effective cross-sectional area of the specimen,

after correction of the measured diameter for surface

roughness, was determined to be 3.1331 cm2 at 21 °C. The uncertainty :! in this area was estimated to be less than 0.02 percent. The diameter at temperature t (°C) was computed from that at 25 °C using the equation

(1) D, = D23 (0.99978 + 8.876 x 10" 6 r+ 1.311 x 10" ;V

2

). (6)

This equation was derived from smoothed thermal ex- pansion data for platinum [19]. The cross-sectional area was then computed from the diameter.

b. Heat Flow The total heat flow through the specimen at the

position of the center thermocouple was calculated

using the expression

Q = P — qa — qt qn — qi — qc, (7)

where P is the measured electrical power input to the

specimen heater;

q„ and qi, are the heat losses along the two leads

carrying current to the specimen heater;

q„ is the heat loss across the necked-down portion

of the specimen;

3 Uncertainties stated in this paper represent either (a) statistical uncertainties based on

results of calibrations or (b) limits to errors conservatively estimated by the authors. 342-263
STD.

RES.

Figure 4. Circuit diagram for the specimen heater.

qi is the heat loss into the insulation surrounding

the specimen; and

qc is the heat loss down the thermocouple wires and

ceramic tubes next to the specimen.

Each of the quantities in (7) is considered separately

below.

Power Input to Specimen Heater (P): The electrical

circuit for the specimen heater is illustrated diagrammatically in figure 4. The power input to the heater was computed using

P = nEA 1 + R ,IR r )(EsIR t - nEv IR r ). (8)

where Er is the voltage drop across the output of the

volt box as measured with a potentiometer, n is the

resistance ratio of the volt box, Es is the voltage drop

across the standard resistor, Rs , as measured with a potentiometer, Ri is the total resistance of the potential

leads and R v is the total resistance of the volt box.

The potentiometer, voltbox, and shunt box were

each calibrated to 0.01 percent or better. The emf of

the standard cell was known to 0.01 percent or better. The correction terms in (8) for the voltage drop in the potential leads and for the current through the

voltbox were small (a few tenths of a percent) and

uncertainties in these corrections could not have

introduced more than 0.01 percent additional error

in P. Thus the percentage uncertainty in the measured

electrical power input was less than 0.05 percent.

Heat Flow in Current Leads (qa , qb)'- The circuit diagram in figure 4 shows only one set of potential leads coming from the heater. In fact there were two

sets as shown in figure 5, but only the inner set, i.e., the potential taps closer to the heater, was used in measuring the power input to the heater. The two sets

of potential leads were required in measuring heat

conduction along the current leads. The current leads were platinum and the potential leads platinum-10

percent rhodium. Consequently, each current lead

could be used along with its two potential leads as a

differential thermocouple to measure the temperature

drop, AT, between the potential taps. With current

flowing to the heater the voltage drop measured be- tween 1-2 or 3-4 was the algebraic sum of the IR drop

between adjacent potential taps (where / is the current

HEATER i

12AT12 AT34 3 4 rICURE 5. Arrangement of potential leads for the specimen heater.

and R is the resistance of the current lead between

the potential taps) and the Seebeck emf due to the

temperature drop, AT", between the potential taps.

Assuming no heat losses from the current leads,

it can be shown [9, 20-26] that the heat conducted

along the leads is given by

_Xp.„ E-R

qa , b - TAT g-, (9)

where p is the electrical resistivity of the current

lead and A its thermal conductivity. By taking measure- ments with the current flowing forward and reversed,

R and AT were determined for each lead, and con- sequently qa and qo. The heat conducted along the leads, as determined

using (9), was less than 0.05 percent of the heat flowing

in the specimen. These corrections were sufficiently accurate that no errors larger than 0.02 percent are believed to have been introduced into the measured

thermal conductivity values by uncertainties in qa and qi,. We will discuss below the possible magnitude

of heat losses from the current leads into the surrounding powder insulation. Heat Flow across Neck (q„): Referring to figure 1,

it is seen that heat could be conducted across the

necked-down region of the specimen by the neck itself and by the powder insulation surrounding it. The con- ductance of the powder was Kir{b'- — a-)\2l where k is the thermal conductivity of the powder, b the radius

of the specimen, a the radius of the neck, and 21 the

length of the neck. The conductance of the specimen

between thermocouple positions 10 and 11 was kF

where A is the thermal conductivity of the specimen

and F is a geometric factor which was determined from

the corresponding equation for electrical conductance.

I=crFV, where / is the current, a the electrical conductivity and V is the voltage drop between the thermocouples. These data were available from measurements

by the electrical method. The heat flow across the

necked-down region was given by

On KF-r

7T(b--

21 AT. (10)

where it is assumed that the temperature differential across the insulation was the same as that measured

between the thermocouples.

The correction for heat flow across the neckeddown region of the specimen was always less than

0.05 percent of P. Errors in the temperature drop

across the neck due to possible inhomogeneities in the thermocouple leads or to stray thermal emfs w

r ould.

for the most part, cancel since they were common to

q„ and q'

n (i.e., corresponding to Q and Q'). At 300

°C a series of tests were run in which the temperature drop across the neck was held in turn at about — 5, 0, and +5 deg, a range 20 times larger than that which occurred during normal measurements. The

corresponding values for (qn ~qn) were about +1

percent. 0 percent, and —1 percent, respectively, o'

343-264
P. The three thermal conductivity values obtained,

using (10) to effect the correction for heat flow across

the neck, fell within a range of less than ±0.02 per- cent. For normal tests, in which the temperature across

the necked-down region was maintained quite small,

it is felt that any uncertainty in the measured thermal

conductivity values due to this source was less than

0.02 percent.

Heat Loss into the Insulation (</,-): In order to determine qi, the heat exchange between the speci- men and the surrounding insulation, it was necessary to perform an extensive mathematical analysis.

If the temperature distribution along the guard exactly

matched that along the specimen there would have

been no radial heat exchange between the specimen

and the guard. However, there would still have been

an exchange of heat between the specimen and the

surrounding insulation in order to provide the longitudinal heat flow in the insulation adjacent to the

specimen.

The heat flow from an elemental length of the surface

of the specimen was

dqi = 27raK (—) dz, (11) \drj r =a

where a is the radius of the specimen, k the thermal

conductivity of the insulation, 6 the temperature in the insulation relative to an arbitrary fixed temperature, /' the radial coordinate, and z the longitudinal

coordinate. The net heat flowing across the surface

r=a between z\ and z-i was

£/,(zi , z-i) = 2ira j

k dz, (12)

where k is, in general, temperature dependent. Let us define a new potential, that satisfies the relation

K0 V£=K(d) V0, (13) where k ( > = k(0). Integrating (13),

£ = — \ K{d)dd, (14) Ko Jo

where we have selected the integration constant so

that £ = 0 when 0 = 0. Writing (12) in terms of £ we

get

qi{z\ , z-z) — KoD(zi , z2 ), (15)

where

D(zu z2 ) = 2iraj ' (j^j dz. (16)

The factor D(z\, z->) was determined by analyzing

the heat flow in the hollow cylinder of powder insulation between the specimen and the guard, using the

measured temperature distributions along the specimen assembly and along the guard cylinder as boundary conditions. Polynomial expressions relating temperature to longitudinal position were used to describe

these temperature distributions in the regions between

the heaters. In the intervening regions near the heaters,

smoothing cubics [27] were used which provided conti- nuity of temperature and longitudinal temperature

gradients. The evaluation of D{z\ , z> ) is described more

fully in appendix A. Since the heat flow in the specimen was to be evalu- ated at the position of the center thermocouple in the gradient region, all the heat loss to the insulation

from the location of the heater down to the position of

the center thermocouple had to be considered. In

addition, heat losses in the region between the speci- men heater and the neck had to be considered since

these had to be provided by the specimen heater. The neck, in effect, could be considered as the upper

end of the specimen for purposes of this analysis,

since any heat exchanges between the powder and the

specimen above the neck did not affect that part of the specimen below the neck as long as zero temperature differential was maintained across the neck.

Therefore, in evaluating q,, the limits of integration

for D(z\.z-i) were the position of the center thermocouple Ui) and the position of the center of the neck

(22).The correction {qj — q,') for heat exchange with the

powder insulation was potentially a large source of error and considerable effort was expended to, first, keep this correction small and, second, evaluate it accurately. Evaluation of this correction, as seen from

(15), required a knowledge of the integral, D(zi, z-z), and of the thermal conductivity, Ko, of the insulation.

, Numerous factors could have adversely affected the

determination of D{z\. z2 ). The use of logarithmic

functions to define the radial temperature distribution across the ends of the hollow cylinder of insulation was an approximation. However, it is easily

shown that the potential distribution near the speci- men was not significantly affected by the boundary

conditions at the remote ends of the extensions.

In the mathematical analysis it was assumed that the temperatures on the inner surface of the guard were the same as the temperatures measured on the outer surface. The molybdenum guard had high

thermal conductivity so that any radial temperature

gradients in the guard would be small and the asso- ciated errors would tend to cancel on simultaneous

solution of the gradient and isothermal tests. Angular

variations in the temperature distribution on the guard

could have arisen if the specimen and guard were not concentric or if the insulation between the specimen

and the guard was not packed uniformly. Great care was taken to avoid both of these conditions. Any

angular variations would have been approximately \ the same for two tests at the same mean temperature ! and so the associated errors would in large part cancel u under simultaneous solution. Such would not be the case for errors arising from uncertainties in the longitudinal positions of the thermocouples since the

temperature distribution along the guard cylinder in

344-265
the gradient test differed from that in the isothermal

test. The necessary steps were taken to ensure that the longitudinal position of the guard was accurately

known relative to that of the specimen, and the location of the thermocouple slits both on the guard and on

the specimen assembly were measured accurately

prior to installation of the thermocouples.

The details of the actual temperature distributions

in the heater regions where smoothing cubics [27] were used could conceivably have influenced D(z\, z->). Except for the regions of Q- and Q.-,, such effects should have been about the same in the gradient and

in the isothermal tests, and hence would have canceled

on simultaneous solution of these tests. Since the

guard heaters were on the outside of a considerable

thickness of high-conductivity metal, we feel that the

temperature on the inside surface of the guard cylinder

varied smoothly with position in the regions of the

guard heaters. Thus, no significant errors were

believed to be introduced by the use of a smoothing

function in the region of Q,->. R. W. Powell [28] has pointed out that a possible

additional source of error, not specifically discussed

by O'Hagan [9], is heat loss into the powder insulation

from the external platinum jumpers which connected

the elements of heater Q> (see sec. 3.3a and fig. 3). There were five such jumpers, each about 0.3 cm long,

contained in aluminum oxide tubing to electrically

insulate them from the specimen. Although the heat

generated in the jumpers was only a small fraction of the total heat generation in the heater, these jumpers

were heated, by conduction from the helical heater

coils inside the specimen, to a temperature above that of the specimen. This would have resulted in a heat

flow into the powder insulation surrounding the jumpers. A portion of this heat would have flowed back

into the specimen but, at least in principle, a net portion of the power input to the specimen heater could

have been lost from the heater jumpers with a corre- sponding error in the measured thermal conductivity

values. Since the temperature rise of the jumpers was de- pendent upon the power input to the specimen heater,

the heat loss discussed in the previous paragraph was

not eliminated, or even reduced, by the simultaneous

solution of a matched gradient test and an isothermal

test. The use of an unmatched gradient test also did

not help in evaluating this source of heat loss. The

smoothing functions used were quite adequate for the

isothermal tests but did not truly represent the temperature distributions in the region of Q> for the gradient

tests. In view of the importance of this potential source

of error, heat loss from the jumpers is considered

further in appendix B. where a mathematical analysis

is used to approximately evaluate this source of error. This analysis indicates that errors in the measured

thermal conductivity values due to heat loss from the

jumpers on heater Q2 were less than 0.2 percent at 100 °C and less than 0.5 percent at 900 °C. A calculation (see appendix I of O'Hagan [9]), based

on the degree of tempering provided by the swaged

elements to which the heater current leads were

attached, indicated that the current leads were only

1 to 2 deg C hotter than the adjacent specimen material. By comparison to the discussion of heat loss from the jumpers (see appendix B), which may have

been over 100 deg C hotter than the specimen, we see

that any errors due to heat loss from the heater leads

into the powder insulation were negligible. In analyzing the data the "isothermal" test was combined with the "'matched gradient" test and with

the "unmatched gradient" test to give two equations

of the form (5). Inspection of eqs (5), (7), and (15) shows that the value obtained for A.o depends in a linear manner on the value assumed for k». The ef- fective thermal conductivity of the insulation sur- rounding the specimen depends on the density of the powder and the pressure and type of gas present, and

is best determined under experimental conditions.

This was done by simultaneous solution of two equations of the form (5) which yielded values both for the

thermal conductivity of the specimen, A.», and the

thermal conductivity of the insulation, Ko. The thermal

conductivity values obtained for the aluminum oxide

insulation, in argon and in helium, were given by

O'Hagan [9]. If there was a significant heat exchange between the

specimen and the insulation that was not being

adequately corrected for, one would expect a systematic difference between the values obtained for the

thermal conductivity of the specimen in helium and

those obtained in argon, due to the large difference

between the thermal conductivity of the powder in the different atmospheres. In fact, however, the values

measured in helium fell within the scatter band of

those measured in argon indicating that any uncor- rected heat exchanges were certainly less than 0.2 percent, the width of the scatter band (see sec. 4.3). For all of the tests taken the correction \qi — qi\ was less than 0.1 percent of P. It is felt that D(zu z-z) and K( i were each known to better than 10 percent and

hence the uncertainty in (q; — q\) less than 0.02 per- cent of (P — P). However, in view of all the factors which conceivably could have influenced this correction, an uncertainty of 0.1 percent is assigned to the

measured thermal conductivity values due to possible

errors in (qj — ql). To this must be added the un- certainty due to heat loss from the jumpers on heater

Q2.

Heat Loss along Thermocouple Wires and Insulators

{qc ): The heat loss, qc , along the thermocouples and

ceramic insulators next to the specimen was computed

from the expression

where C, is the longitudinal thermal conductance of the ith wire and its insulator, n is the total number of wires crossing the plane where the thermal conductivity was evaluated, and dTjdz is the temperature

gradient at that plane. Each C, was computed from

the thermal conductivities and dimensions of the wire

345-266
and insulator. This correction was rather large, falling

from about 0.8 percent at 100 °C to 0.3 percent at 1100 °C, the falloff being due to the rapidly decreasing

thermal conductivity of the ceramic tubing. Although

the thermal conductivity of the thermocouple wires was known fairly accurately (5%) the thermal conductivity of the ceramic tubing was known only approximately (15%). Furthermore, the cross-sectional areas

of the wires and tubing were not accurately known

(5%). Thus the total conductance of the wires and the ceramic tubing was only known to about 25 percent.

The corresponding uncertainty in the measured

thermal conductivity values was 0.2 percent at 100 °C

and 0.1 percent at 900 °C. Departure from Steady-State: The ratio of heat

absorbed (or released) to that conducted in the speci- men is given approximately by

wcAL(dTldt) =

L (dTjdt)

KA (dTldz) D (dT/dzY

(

'

where w is density, c is specific heat, A is area, L is total length of specimen below the necked-down

region, dTjdt is time rate of temperature change, k is thermal conductivity, dT/dz is temperature gradient,

and D—k/wc is thermal diffusivity. Temperatures in the system did not drift at a rate greater than 0.03 deg/hr (i.e.. 10 r> deg/sec): the length, L, was about

14 cm; the temperature gradient was 5 deg/cm; and

the thermal diffusivity of platinum in the temperature

range 0-1100 °C is always greater than 0.2 cm 2 /sec

[12]. Hence the ratio of heat absorbed (or released)

to that conducted was less than ±0.02 percent. No

correction was made for departure from steady-state

conditions.

Total Uncertainty in Heat Flow: Using standard

propagation of error formulas, the estimated uncertainty in (Q — Q') was 0.4 percent at 100 °C and 0.7 percent at 1100 °C.

c. Temperature Gradient The temperature gradient in the specimen was computed from the measured temperatures at the

five thermocouple positions in the gradient region.

The separations between thermocouple grooves at "room temperature were accurately measured before

the thermocouples were installed; the separation at elevated temperature was computed using (6). Since

temperature gradients in the specimen were rather

small (less than 5 deg/cm) it was essential that the

conversion of thermocouple emfs to temperature not introduce any additional uncertainties. The equation

f = l5 - 83952 (uk)^ 918:' 28

(u5s)

!

+ 7 - 30572 (i4i)- 1 - 92753 (l^)'

- 2 . 50480 ( 1 . 0 - exp [ - 4. 183 12 ( t/1000) ]) , (19)

where t is temperature (°C) and E is emf (mV), was

found to fit to within 1 the calibration data for the platinum versus platinum — 10 percent rhodium

thermocouple wire from which the specimen thermocouples were fabricated. This equation was used for converting the thermocouple voltages to temperatures.

The temperature gradient was computed by evaluat- ing the slope, at the center thermocouple location, of the quadratic equation of least-squares fit to the five temperatures and thermocouple positions. The uncertainty in the temperature gradient due to uncertainties

in effective thermocouple positions is estimated to have

been less than 0.2 percent. Errors in reading thermocouple emfs did not introduce an uncertainty of more

than 0.05 percent for the temperature gradients used. Errors due to heat conduction along thermocouple

leads should have been negligible and were certainly

less than 0.05 percent (see Appendix G of O'Hagan

[9]). Due to the use of a simultaneous solution of a gradient and an isothermal test, errors in the measured

temperature gradient due to variations between in- dividual thermocouples are estimated to have been less than 0.05 percent. It is estimated that the conversion

ol thermocouple emfs to temperatures introduced

errors of less than 0.2 percent in the temperature

gradients.

The estimated overall uncertainty in the temperature

gradient is estimated to have been 0.3 percent.

d. Mean Temperature

In addition to the uncertainties discussed above in the area, heat flow, and temperature gradient, there

is an uncertainty in the temperatures to which the

thermal conductivity values correspond. For a 0.5 deg

uncertainty in temperature, the associated uncertainty

in thermal conductivity is less than 0.001 percent at 100 °C and less than 0.02 percent at 900 °C.

4.3. Results

The experimental values obtained for the thermal

conductivity of our platinum specimen by the longitudinal heat flow method are given in table 1. The

Table 1. Experimental values for the thermal conductivity of platinum as measured using the longitudinal heat flow method

The values given are eurrected for thermal expansion.

Mean Thermal

Test Run Atmosphere temperature

°C

conductivity W/cm deg

1 1 Air 99.6 0.715 2 1 Argon 99.8 .715

3 1 Argon 301.0 .728 4 1 Argon 501.5 .753

5 T Argon 701.2 .784 6 1 Argon 601.3 .769

7 1 Argon 400.2 .740

8 1 Argon 201.7 .721 9 1 Helium 199.6 .721

10 1 Helium 400.6 .740

1

1

2 Argon 300.0 .729

12 Argon 701.3 .786

13 2 Argon 900.0 .822

14 2 Argon 1100.5 (.866)"

" See text.

346-267
Table 2. Typical set of data from measurements of the thermal

conductivity of platinum by the longitudinal heat flow method

The data correspond to Test No. 6 in table 1.

Matched

gradient Unmatchedgradient Isothermal

Temperature distribution along the specimen °c... T

A

580.4 579.0 600.7

Tz, 590.9 588.9 600.6

Tk 601.3 598.8 600.3

T, 611.7 608.9 600.1

7s 622.1 619.0 600.0 Temperature gradient at the locatic n of dT

thermocouple T* deg/cm...

dz

5 18 4 96 0 QQ Power generated in specimen

heater W.. P 12.818 12.853 .0 Heat flow across the necked-down

region W.. <?» 0.003 -0.008 -.002

Heat flow along the current leads W- la .004 .017 .002 .003 .006 .002 Heat flow to the insulation W.. q„ .006 .542 .027 Heat flow along the thermocouple

wires and insulators W.. q, .051 .049 -.001

thermal conductivity values given there have been

corrected for thermal expansion of the specimen. A

typical set of data, including the various correction

terms, is given in table 2. A cubic equation of least-squares fit was found to

fit the data (corrected for expansion) from the longitudinal heat flow method with the residuals having a standard deviation of 0.08 percent. This was significantly less than the standard deviation of the residuals

from a parabola. The equation, valid over the range

100 to 900 °C,is

\ = 0.713 + 0.683x 10- 5

r + 0.173x 10- Kt J

-0.513 x 10 ~ wt\ (20)

where t is temperature in °C and A. is in W/cm deg.

Departures of the data points from (20) are plotted in figure 6. With the exception of the point at 1100 °C

all the data points, including the two obtained in helium, fall within ±0.1 percent of the curve. There

were no significant differences between the values

+0.20

1 1 1

1 + 0.6 ^

+ 0.15

+ 0.10 •

+ 005 •

•

• •

•

•

0 •

•

-0.05

-O.IO • •

• •

-0.15

-0.20

1 1 1 1

1 O 200 400 600 800 1000 TEMPERATURE, °C

Figure 6. Percentage departures from eq (20) of the thermal conductivity data points obtained by the longitudinal heat flow method.

Table 3. Summary of individual uncertainties contributing to the overall uncertainty in the thermal conductivity results obtained

using the longitudinal heat flow method

Uncertainty. %

Soou e of uncer am'lit >

100 (

' 'II H 1 1

Cro sectional an-a 0.02 0.02 Heat flow Power input to specimen

heater .05 .05 Heat flow in current leads .02 .02 Heat flow across neck .02 .02 Heat loss into the insulation .6 Heat loss along thermocouple wires and insulators .1 Departure from steady-state .02 .02 Temperature gradient .3 .3 Mean temperature .0111 .02

Combined" 0.5 0.7

a Each combined uncertainty was obtained by taking the square root of the sum of the squares of the individual uncertainties.

obtained on heating and cooling in the first run and

those from the second run. At 1100 °C the thermocouples started drifting giving rise to significant

uncertainties in temperature measurement. After

completing the "matched" gradient, "unmatched"

gradient, and "isothermal''' tests at 1100 °C a second

"matched" gradient test- was run. Two values lor the

thermal conductivity were obtained by simultaneous

solution of each of the two "matched" gradient tests with the "isothermal" test. The first value (0.820) was below the value predicted by (20) and the second

value (0.905) was above it. Assuming that the temperature drifts were linear with time, interpolation to the

time of the "isothermal" test gave a value of 0.866

for the thermal conductivity of the specimen at 1100

°C. This value is 0.6 percent above the value given by

extrapolation of (20) to 1100 °C. The 1100 °C point,

due to the larger uncertainty associated with its value, was not used in deriving (20). The thermal conductivity values corresponding to

(20) are believed to be uncertain by not more than 1 percent over the temperature range 100 to 900 °C. The estimated uncertainties arising from the various

known sources of error are summarized in table 3; these uncertainies were discussed in section 4.2.

5. Electrical Method

5.1. Experimental Procedure

Measurements of thermal conductivity by the

method in which the sample was heated directly by

passage of an electric current were made following

each measurement by the longitudinal heat flow method. Thus the preliminary procedures and testing

sequence described in section 4.1 also apply to these

measurements. Power to heaters Qi and Q:! was controlled to maintain Tio and Tu constant with \TU — 7^io| less than 0.2 deg. Temperatures along the guard in the region opposite the neck were maintained at the same value as TV Data were taken with currents (both

normally and reversed) of approximately 10. 58, 82. and 100 A dc flowing through the specimen. These

347-268
current levels correspond approximately to even

increments of power generation. Readings were taken

of thermocouples 9, 10, 11, and 12 (see fig. 1) on the

specimen and of the guard thermocouples between

heaters Q-> and Qk. The voltage drops between the

platinum legs of thermocouples 10 and 11 and also between 9 and 12 were measured with the current being measured simultaneously on another potentiometer.

The temperatures never drifted more than a few

hundredths of a degree during a test (approximately

three-quarters of an hour), and although the current showed drifts of 0.05 percent the measured resistances

remained constant to 0.01 percent with current and

voltage being read simultaneously.

5.2. Calculation Procedures and Uncertainties

Consider a conductor of arbitrary geometry which is perfectly insulated, both thermally and electrically,

except for the ends where electric current enters and

leaves the conductor. Joule heat will be generated in the conductor by the electric current. Let Tm be

the maximum temperature in the conductor. Let V be

the voltage drop between two surfaces, one on either

side of the surface of maximum temperature, which

are both at some lower temperature, 7V It is shown

in appendix C, where earlier work is referenced,

that the following relation holds:

where

F = + {2 j" \pddV'~ (23)

and R is the electrical resistance between the two

surfaces, one on either side of the surface of maximum

temperature, which are both at the same temperature,

T. The quantities Rti and po are the values R and p

would have if the conductor were isothermal at some

reference temperature. To. The quantity yo is the

coefficient of linear thermal expansion at 7V

Assuming that A and p can both be represented by

linear functions of temperature — a valid assumption

over small temperature intervals — we can write:

p = po(l + ao 0). (24) A=Ao(l+j3o0), (25)

\p = \oPo(l + T7o0), (26)

where a» is the temperature coefficient of resistance

evaluated at 0 = 0, /30 is the temperature coefficient of thermal conductivity evaluated at 0=0 and rjo = a0 + The term in a( >/3o0- in (26) has been neglected.

Substituting the above expression for Ap into (23) and integrating we get

YL.

8 TO KpdT kpdtt. (21) F(6,dm ) =

where 6—T—Tq, 6vi = T„, — To, A is the thermal conductivity of the conductor, and p is the electrical

resistivity of the conductor.

Equation (21) shows that the maximum temperature

rise, 6m , in an electrically heated conductor with

negligible lateral heat losses and with both its . ds

held at the same temperature is a function only ot the

voltage drop V across it, and of the thermal and

electrical conductivities of the material, and is in- dependent of the geometry of the conductor provided

the geometry is such as to make lateral heat losses

negligible. If the maximum temperature rise can be

measured as a function of the applied potential, Ap

is readily determined.

The maximum temperature rise, 9m , can be measured indirectly using the specimen as its own resist- ance thermometer. This method was employed by

Holm and Stormer [13] and Cutler et al. [15J. and

requires that the temperature coefficient of resistance

of the material be known over the temperature range

of interest and that it be large enough to yield sufficient

sensitivity. Platinum satisfies both requirements very

well and the resistance method of measuring the

maximum temperature rise was adopted in the present

experiments.

It is shown in appendix C that the following relation holds for a perfectly insulated conductor:

Ro_]L

(">» Ap„(l +>0)rf0

R~FJ„ F

(22)

2\„Po 0m 1 +

1?„

1/2

(27)

If the integration is evaluated for T=T() , or 0 = 0, we

have, from (27) and (21),

F = 2Aopo0„

1/2

and

L

2 =8A„p„0,„(l+^0,„).

(28)

(29)

Substituting F from (27) into (22) and performing the

indicated integration we have for 0 = 0,

/?» /3i) + y„ a„ — -y,i 1 —= - —I — arctanG,r (30) A 170 T/n O

/here

1 + y dm (31)

The coefficients at) and /3<i are the "true" coefficients

in that they correspond to electrical resistivity and

thermal conductivity values which have been corrected

for thermal expansion. If one considers "apparent"

coefficients a'{) and which correspond to "apparent"

thermal conductivity values which have not been

348-269
corrected for thermal expansion, then it is apparent

that a0 = ao+7o, /3o =/3o — yo, 170 = 170, and (30) can

be written as —R{) — —j8o . «i 1 r H—7 — arctan G, a 170 170 «

(32)

where, reiterating, a,'), /3 0 , and 170= a0 + are ap- parent coefficients corresponding to electrical resistivity and thermal conductivity values which have

not been corrected for thermal expansion. Thus

the maximum temperature rise in the conductor can be computed without knowing the coefficient of expansion.

Equation (30) gives 6,„ implicitly in terms of known

measured parameters, and its value can be determined

by iteration. In practice it would generally be necessary to measure R at at least two different levels of heating current and then extrapolate to zero current

to obtain Rt) . Once dm is obtained using (30), its value can be used in conjunction with (29) to obtain the

thermal conductivity. In the present investigation,

R and V were measured at four or five different current

levels. The data obtained were analyzed as described

below.

An adjusted voltage, V*. was defined as:

y*2. V-'

1 +

2

(33)

In the analysis given in appendix C and also that given just above, we explicitly assumed that there was no loss or gain of either electric current or heat across the surface of the conductor. In the present

investigation a necked-down sample was employed,

the neck and the specimen as a whole being sur- rounded by an insulating powder. Since this insulating

powder had an electrical conductivity many orders

of magnitude lower than that of the specimen material,

the assumption of no flow of electric current across

the boundaries was completely valid. The powder

surrounding the neck prevented heat loss by convection, and radiation through the powder was negligible.

However, the powder conducted heat away from the

neck and it was necessary to analyze this heat loss and develop an appropriate correction for it. Since

most of the temperature rise between thermocouple

positions 10 and 11 was in the neck itself, only heat

losses from the neck were considered and other heat

exchanges were neglected. O'Hagan [9| has shown that

in the presence of small heat losses from the neck,

(37) is replaced by

k0

1 aoRodV*-

1 + C 12p0 dR* '

/here

(39)

(40)

In the limit of small aS,n , (30) reduces to

ttllAo 3

(34)

Kd being the thermal conductivity of the powder

insulation at the reference temperature, To, and Ao the

thermal conductivity of the specimen at To. The geo- metrical factor, n, is given by

An adjusted resistance, /?*, was defined for the case where a^6m is not sufficiently small for (34) to be valid:

1 (35)

In the limiting case of small otodm , (35) reduces to (34) and R* to R.

Substituting (33) and (35) into (29), we obtain

f*2 =12A0po R*-R0 a0R0

Differentiating (36) and rearranging, we obtain

Ao : gogo dV*

12p„ dR

(36)

(37)

The thermal conductivity values in the electrical method were obtained from the slope of the V*2 versus R* curve, using (37). From (33) and (35) we see

that

dV*'1 dR* = L1m

dV1 dR (38)

64 /2/\ 3 Ki(77a/2Z) pg

7rV- \tt(i) Ko(iTal2l) R'£

(41)

where 2a is the diameter of the neck and 21 is the

length of the neck, and K{) and K\ are the modified

Bessel functions of second kind and order zero and

one, respectively.

The calculation procedure used was as follows: At any given nominal temperature, measurements

were made at n current levels. An approximate

value for Ro was computed from the resistance

corresponding to the lowest current level, lor which

Joule heating was minimal and the neck was nearly

isothermal. For each experimentally determined re- sistance a corresponding approximate value of dm was computed using (34). Values of a'0 were computed

from the data obtained in the resistivity measure- ments (see sec. 5.3a). Using this value of Bm as the

first trial value, Newton-Raphson iteration was used

to compute the value of B m which satisfied (30). 4 Values for R* and V*2 were then computed from (35) and (33) respectively. Since it was impractical to hold To (i.e., the average temperature of thermo4 Values for computed from the thermal conductivity values obtained by Watson and

Flynn [ 32 1 on the same specimen were used.

349-270
couple locations 10 and 11) at exactly the same value

for different current settings, it was necessary to adjust slightly the V*- and R* values to correspond to a common reference temperature. A straight line of least-squares fit through these values of R* and V*2 gave R» as the ordinate intercept and dV*-/dR* as the slope. This value for /?,> was a more accurate value

than the initial value used, as it was based on an

extrapolation to 7 = 0. The calculation was then re- peated using this value of /?<>. This in turn led to improved values for /? () and dV*2/dR*. The iteration converged in a few passes and the final values for /?,, and dV*-/dR* were used in (37) to compute the ap- parent thermal conductivity. Using this apparent

value for A. ( >, and eqs (40) and (41), the correction

factor for heat losses from the neck was computed

and used in (39) to give the final value for the thermal

conductivity.

a. Electrical Resistivity The electrical resistivity values were computed

from

That this is so is seen by considering that Ro was measured as a function, say R() =f(E), of the thermocouple emf, E. Then

Po — pK

. eR( )l (R») iCi (42)

where pice is the independently measured ice-point

resistivity, /? () is the resistance of the necked-down

region at zero current, and (Rt) ), ce is the value of Rt) extrapolated to the ice point. These values were then

corrected for thermal expansion. The uncertainty

in p ice was not more than 0.1 percent. The uncertainties in the measured values of Rn did not exceed

0.05 percent. However, an additional uncertainty

must be assigned to the values of Ru due to the uncertainty in the temperature to which these values cor- respond. Quite conservatively, temperatures were known to within 0.5 deg, corresponding to 0.14 percent

of R{) at 100 °C and 0.04 percent at 900 °C. The uncertainty in (Ro)lce , which was based on an extrapolation, was estimated to be less than 0.25 percent. At lower temperatures the uncertainties in Ro were

correlated with the uncertainty in (/?o)ice so tnat the

uncertainties in R() l(R a ) ice were lower than the uncertainties in either R„ or (Ro)lce at lower temperatures but not necessarily at higher temperatures. The

overall uncertainty in electrical resistivity was esti- mated to be less than 0.1 percent at 0 °C and less than

0.4 percent at 900 °C. The thermal conductivity was computed, using (39), from the ratio /?«/po. Since p() was taken from a smoothed curve, this quantity was further uncertain

by the scatter in the individual Ru data points around

a smooth curve, or about an additional 0.05 percent

(see sec. 5.3a). The overall uncertainty in Ro/pu was

probably less than 0.4 percent.

b. Temperature Coefficient of Resistance The uncertainty in the sensitivity, of the speci- men as a resistance thermometer was essentially the

uncertainty in the sensitivity of the thermocouples

used plus a small uncertainty in the resistance meas- urements and the thermocouple emf measurements.

1 dR0= 1 df(E) dE

Rn dT f(E) dE dT g(E

dE

df (43)

The uncertainty in the sensitivity, dE/dT, of the

thermocouples is estimated to have been less than 0.2 percent while the uncertainty in the resistance and

voltage measurements was less than 0.05 percent.

Thus an is believed to have been known with an uncertainty of less than 0.25 percent.

c. Slope of V*'1 Versus R* Curve The voltage drop across the neck and the resistance

of the neck were each measured with an uncertainty

of about 0.02 percent. The change in the resistance of the neck for the different current levels was small

compared to the resistance itself, so that any error in measuring resistance would be greatly magnified in computing the rate of change of resistance as a function of the voltage drop. For all of the data taken, the

departures of the /?* values from the least-squares

straight line fitted to the R* and V*- values were less than 0.01 percent and for a majority of the tests they were less than 0.005 percent. However, since (R — Rn)

<R, the small scatter in R was highly magnified in cal- culating dV*-/dR*. What departures did exist tended

to be systematic rather than random and tended to indicate that the plot of R* versus V*'1 was very

slightly concave downward rather than linear, as assumed. Such an effect could possibly have been due

to neglecting higher order terms in the temperature

dependence of the thermal conductivity and the electrical resistivity. The uncertainty in dV*2ldR* is estimated to have been less than 1.5 percent.

d. Heat Loss Correction The uncertainty in the heat loss correction, C, may

have been as large as 50 percent of C. For the tests in argon this corresponds to an uncertainty in the measured values for the thermal conductivity of the speci- men of 0.1 percent at 100 °C and 0.6 percent at 900 °C. For the tests in helium the corresponding uncertainties were 0.5 percent at 200 °C and 0.7 percent at 400 °C.

e. i 'ppartures From Theory In the derivation oi ihe mathematical expressions

used to compute thermai mductivity in the electrical method, there were a nut: '»er of explicit or implicit

assumptions made which c» I lead to erroneous re- sults if these assumptions wen not valid.

It is shown in appendix C that the Thomson effect cancels out to first order provided the temperatures

at the two potential taps (used to measure V) are approximately the same. The requirement that the

potential taps be at the same temperature is also necessary for the Seebeck emf and Fermi energy

terms in (C-50) to drop out. In all of the measure350-271
ments, the temperatures at the inner potential taps

(thermocouple positions 10 and 11) agreed within 0.2 deg or better, as compared with values of d,„ (for 100

A current) ranging from 35 deg at 100 °C to 100 deg

at the highest temperatures. Neglecting the Seebeck

term in (C-50) for \T-> — Z"i | <0.2 deg corresponds to an

uncertainty in the measured thermal conductivity

values of less than 0.05 percent. Neglecting the

Fermi energy term in (C-50) also involves an uncertainty of less than 0.05 percent (see O'Hagan [9, P- 127]).

It is explicitly assumed in appendix C that the con- ductor is homogeneous and isotropic; this should be a

valid assumption for platinum of the purity used in the

present investigation.

As stated in appendix C, the electron current is con- sidered to be the only mass current. In principle it would be possible for platinum, or any impurities

which might be present, to migrate under the in- fluence of the electric potential gradient (electromigration) or under the influence of the temperature gradient

(Soret effect). If such mass motion existed there would

be an associated entropy flow and equation (C-4) and

all following equations in appendix C would have to be

modified to include a term involving the mass current

density and its associated entropy transport. A

rigorous analysis including mass migration would be

quite complex and was felt to be beyond the scope of

the present investigation. However, a qualitative dis- cussion of the probable effect of such mass motion if it were to occur is given below.

In electromigration, the energy flow is proportional

to the electric field. Similarly, the energy flow due to the Thomson effect is essentially proportional to the

electric field. Thus if one were to introduce an electro- migration term into (C-4) and rigorously go through

the analysis, the equivalent expression to (C-31)

would include an electromigration term of a form

analogous to (i.e., proportional to the electric field) the term in (C-31) involving the Thomson coefficient. Provided this term were small compared with the first two terms in (C~35) it would, to first order, cancel in a

similar manner to the way the Thomson term canceled, provided the temperature at the two potential

taps were the same and the medium was homogeneous

and isotropic. Physically what happens is that the

energy transport due to electromigration adds to the

energy transport by conduction on one side of the

surface of maximum temperature and subtracts on

the other side, with no net effect on the maximum

temperature rise in the conductor or on the voltage

drop between the potential taps, at least to first order. To reemphasize, the temperatures at the taps must be

the same for this cancellation to occur and also the

medium must be homogeneous and isotropic. In the Soret effect, the energy transport is proportional to the temperature gradient. Thus the ratio of

energy transport due to the Soret effect to that due to heat conduction by other mechanisms is independent

of the temperature gradient. The Soret effect is a dif- fusion process, similar to heat conduction. For a homogeneous medium, therefore, the Soret effect simply

behaves as an additional mechanism for "heat conduction" and thus is a legitimate augmentation (or depletion, depending on the sign of the heat of transport)

of the thermal conductivity and should be included in the total thermal conductivity value. For the conditions of the present experiments, there

would be no errors involved due to electromigration or Soret effect provided the medium remained homogeneous and isotropic. Both of these effects can change

the distribution of impurities and vacancies in a solid. During the experiments the current was in one direction through the specimen about one-half of the time

and in the other direction about one-half of the time.

Thus, it is doubtful if there was significant inhomogenity introduced due to electromigration effects, even if they were occurring. The Soret effect, if large

enough, could cause a redistribution of impurities in the specimen.

For platinum of the purity used, the thermal conductivity at high temperatures would not be expected

to be significantly affected by changes in the impurity

and vacancy distribution. All of the data at low temperatures, where impurity concentration could affect the thermal conductivity, were taken before the speci- men was heated to temperatures where significant mass migration was likely to occur. In view of the

above discussion it is felt that neither electromigration nor Soret effect had any adverse effect on the

results.

5.3. Results

a. Electrical Resistivity The ice-point resistivity was determined on the

platinum bar before the neck was machined in it (see

section 2). The value obtained was

(p0 ) ice = 9.847 ± 0.010/i.fl cm, (44)

corrected to 0 °C dimensions.

In conjunction with the electrical method of measuring thermal conductivity, the resistance of the

necked-down region of the specimen at each temperature was determined at a number of current levels. The resistance, /? ( », at temperature To, was evaluated

by extrapolation to zero current as described in section

5.2. In the first series of tests, or the first run as it will be referred to, measurements were made in the

following order: 100, 300, 500, 700, 600, 400, and

200 °C in argon; and 200 and 400 °C in helium. The

apparatus was then opened up for repair of the guard

heater as described in section 4.1c. In the second

series of tests, or the second run as it will be referred

to, measurements were made at 300, 700, 900, and

1100 °C in argon, in that order. The values for the resistance of the neck obtained

during the second run were about 1.5 percent higher

than the values obtained at corresponding temperatures in the first run. This increase in resistance was

observed both for measurements at the inner potential

taps (10, 11) and for measurements at the outer potential taps (9, 12), indicating that the increase in values

351-272
were due either to contamination or to a change in the

geometrical factor of the necked-down region rather

than to, for example, a short circuit which changed

the effective position of one of the potential taps.

Since data taken in the first run at lower temperatures

after the sample had been heated to 700 °C agreed

quite closely with results obtained before the sample was heated to 700 °C, it is felt that there was no

evidence indicating that any chemical contamination

of the necked-down region occurred during the first run. Furthermore, 700 °C is rather too low a temperature to expect any significant contamination of platinum in a relatively clean environment. Exactly what

happened is not known but it is believed that the

necked-down region suffered some slight geometrical

change between the first and second runs, perhaps

while the guard heater was being repaired. In deter- mining the electrical resistivity, data from the first run had to be treated separately in view of this change

in the geometric factor. A quadratic equation was fitted, by the method of

least squares, to the measured values of Ro from the

tests in air, argon, and helium from the first run. The equation, extrapolated to 0 °C and normalized

to the ice-point resistivity, (44), gave

p = 9.847(1 + 0.3963 x 10" ~t - 0.5389 x lO" 6

*

2

) (45)

as the electrical resistivity (corrected for thermal

expansion) of the neck from 0 to 700 °C, t being in °C and p in pfl cm. The" standard deviation of the

residuals from this equation was 0.03 percent. Departures of the data points from this equation are plotted

in figure 7 where the overall scatter is seen to be

±0.05 percent. All but three of the points fall within

0.025 percent of the curve and there is no significant

difference between the values obtained on heating

and cooling.

A second quadratic equation was fitted to the data

points (corrected for thermal expansion) at 300, 700,

+ 020

1

1 1 1 1 # FIRST RUN

+ 015 SECOND RUN

+ 0.10

+ 0.05 o

0 • t • A •

• *

-0.05 CO

-0.10 A * -

-0.15

-0.20

1

1 1 1 0 200 400 600 800 1000 TEMPERATURE, °C FIGURE 7. Percentage departures from eq {45) of the electrical

resistivity data points. The values obtained during the seemid run have been normalized at 700 °< '. as <ljveu--se(i

lit tin- text.

and 900 °C obtained in the second run. The equation,

normalized to the value given by (45) at 700 ? C, gave

p = 9.767(1 + 0.4033 x \0~ 2 t -0.5802 x 10-«r 2), (46)

t being in °C and p in fxfl cm. While the geometric

factor of the neck changed between the first and

second runs there is no reason to believe the resistivity

would have changed. Any strains introduced when the

geometric factor changed would have annealed out

at 700 °C. Thus normalizing the data from the second

run to that from the first run at 700 °C is felt to be

justified. The departures of the normalized data points

at 300, 700, 900, and 1100 °C from the values given by

eq (45) are indicated by triangles in figure 7. The 1100

°C data point was not used in deriving (46). The

thermocouples started to drift at 1100 °C due to contamination so that greater uncertainty had to be

assigned to data obtained at that temperature. The

1100 °C data point agrees with the extrapolated value

given by equation (46) to within 0.02 percent. The

deviations from the quadratic equation (45) at the

higher temperatures as shown in figure 7 are in line with what one would expect. Recent measurements

at NBS [29] in conjunction with work toward extending

platinum resistance thermometry to the gold point

showed that the measured resistance of a certain high

purity platinum resistance thermometer at the gold

point (1063 °C) was about 0.07 percent below the value

obtained by extrapolating the Callendar equation [,5j for that thermometer from 630.5 °C to the gold point

(1063 °C). Laubitz and van der Meer [30], in measuring

the electrical resistivity of high purity (99.999% pure)

platinum, found that between 800 and 1200 °C their experimental results fell consistently below the values

extrapolated from an equation similar to (45) by an

average amount of 0.10 percent.

As stated in section 5.2a, the uncertainty in the

electrical resistivity values is estimated to be less than 0.1 percent at 0 °C and less than 0.4 percent at 900 °C.

b. Thermal Conductivity

The experimental values obtained for the thermal

conductivity ol the platinum sample by the electrical method are given in table 4. The values for p( » and «o used in computing these thermal conductivity values were computed using (45) in the first run and (46) in the second run. The thermal conductivity values given

in table 4 have been corrected for thermal expansion.

A typical set of data is given in table 5. The following equation, obtained by the method of

least squares, was found to fit the thermal conductivity

data (corrected for thermal expansion) obtained in air and in argon, using the electrical method, with a standard deviation of 0.30 percent:

A = 0.716-0.247 x 10- 5f + 0.182 x I0~ et

2

-0.783 x 10" 1(V

:! , (47)

where t is temperature in °C and A. is in W/cm deg.

352-273
Table 4. Experimental values for the thermal conductivity of platinum as measured using the electrical method

The values given are corrected for thermal expansion.

Mean Thermal

Test Run Atmosphere temperature conductivity °C W/cm deg

1 1 Air 99.8 0.719

2 1 Argon 99.7 .716

3 1 Argon 299.9 .732 4 1 Argon 500.0 .749 5 1 Argon 700.1 .779 6 1 Argon 599.6 .763

7 1 Argon HH).3 .738 8 1 Argon 202.0 .720

y 1 Helium 199.9 .722

10 1 Helium 400.2 .745 n 2 Argon 300.1 .731 12 2 Argon 699.9 .774

13 2 Argon 900.0 .804

Table 5. Typical set of data from measurements of the thermal

conductivity of platinum by the electrical method

The data con espond to Test N i. 6 in table 4.

Heating current through necked- down region A... 10.0 57.6 81.7 100.1 Average temperature at thermocouple locations 10 and 11.... .°C... T„ 599.5 599.6 599.6 599.6 Voltage drop between platinum

legs of thermocouples 10 and

11 mV... 1 12.03 70.80 102.14 127.52

Kleclrioal resistance between plat- inum legs of thermocouples 10 and 11 mil... ft 1.2086 1.2290 1.2509 1.2734 Calculated temperature rise in necked-down region deg... 8m 0.8 25.5 52.2 80.2 Square of adjusted voltage y*i 145. 4930. 10090. 15456. Adjusted resistance mil.. «* 1.2086 1.2292 1.2513 1.2746

Reference temperature °C

Electrical resistivity at reference temperature cm..

Electrical resistance corresponding

to reference temperature. ..mfl.. Temperature coefficient of

resistivity at reference temperature deg" '.. Temperature coefficient of thermal

conductivity at reference temperature deg" 1

.

.

Correction for heat loss Correction for thermal expansion percent.. Computed value for thermal

conductivity of speci- men W/cm deg..

599.6

31.16

1.2079

0.000267

0.0077

0.56

This equation is valid from 100 to 900 °C. Deviations

of the data points from eq (47) are plotted in figure 8. The scatter is random and there are no significant

differences between values obtained on heating and

cooling or between the first run and the second run. The value obtained in helium at 200 °C agrees within

0.05 percent of the value given by (47) but the measure- ment in helium at 400 °C shows a deviation of +0.9

percent. The measurements in helium were made

during the first run and there is a possibility that the

powder insulation did not uniformly and completely

fill the necked-down regiun. If the powder did not completely fill the space, the boundary conditions

assumed in deriving the heat loss corrections would

not have been met. Any errors in the heat loss correction would be amplified in helium, particularly at the

higher temperature, due to the high thermal conductivity of this gas. In the second run the powder was

carefully packed around the neck so that the neckeddown region was completely and uniformly filled with

insulation. The two data points obtained in helium were

not used in deriving (47). The thermal conductivity values corresponding to

(47) are believed to be uncertain by not more than 2 percent over the temperature range 100 to 900 °C. The estimated uncertainties arising from the various

known sources of error are summarized in table 6; these uncertainties were discussed in section 5.2. Table 6. Summary of individual uncertainties contributing to the overall uncertainty in the thermal conductivity results obtained

using the electrical method

Source ol uncertain!

100 °c 900 °C

Ceometrical factor lKJplt ) 0.4- 0.4 Temperature coefficient of resistance .25 .25 Slope of V *- versus R * curve 1.5 1.5 Heat loss correction (tests in argon) .1 .6 Seebeck effect .05 .05 Temperature coefficient of Fermi energy .05 .05

Inmbined" 1.6 1.7

Uncertainty. %

J Each combined uncertainty was obtained by taking the square root of the sum of the squares of the individual uncertainties.

400 600 800 TEMPERATURE. °C

Figure 8. Percentage departures from eq (47) of the thermal conductivity data points obtained by the electrical method.

6. Comparison of Results With Other

Investigations

The smoothed experimental results given in sections

4.3 and 5.3 are tabulated in table 7. The electrical

resistivity values correspond to equation (45) from

0 to 700 °C and to (46) at 800 and 900 °C. The thermal

conductivity values for the longitudinal heat flow

method and the electrical method correspond to eqs

(20) and (47), respectively. The values for the Lorenz

function, Ap/T, were computed from the smoothed

values for the electrical resistivity, p, the two sets of values for thermal conductivity, A., and the absolute

temperature, T. In this section the results of other investigations on

platinum are compared with the results of the present

353-274
investigation. Since many investigators do not correct

their thermal conductivity and electrical resistivity results for thermal expansion, it was necessary to convert all data to a common basis in order to make

valid comparisons.

Table 7. Smoothed experimental values for thermal conductivity,

electrical resistivity, and Lorenz function of platinum

All values are corrected for thermal expansion.

Tempera- ture °c

Electrical

resistivity pil cm

Thermal conductivity

W/cm deg

Lorenz function K2/deg2

Longitudinal methodElectrical methodLongitudinal method

Electrical method

0 9.847

100 13.70 0.715 0.717 2.62 x 10"K 2.63 x 10-" 200 17.44 .721 .722 2.66 2.66 300 21.08 .729 .729 2.68 2.68 400 24.61 .740 .739 2.70 2.70 500 28.03 .753 .750 2.73 2.72 600 31.35 .768 .763 2.76 2.74 700 34.56 .785 .776 2.79 2.76 800 37.65 .803 .790 2.82 2.77 900 40.63 .822 .804 2.85 2.78

+ 1.0

-1.0

1 1 1 1 1 1 1 1

4>

1

Jm ¥ # } '

j

» 1

I z" 1 1 I

1

i

*

i' i

1 I i i I

i I I 0 200 400 600 800

TEMPERATURE, °C

FIGURE 9. Electrical resistivity of platinum: comparison of pre- vious data with the results of the present investigation.

O Powell and Tye Reported purity was 99.999 percent for both samples tested. The

ratio of the ice point to helium point resistivity of their No. 1 specimen, which was

purer than their No. 2 specimen, was previously reported by Powell. Tye. and Woodman

[111 to be about 760. The uncertainties shown represent possible round-off error due to results only being reported to nearest 0.J pil cm. A l.aubitz and van der Meer |3()|. The reported purity was 99. "99 percent. The ratio of

ice point to helium point resistivity was about 1890. T Koeser [31 1. His sample was probably thermometric grade platinum having a purity of about 99.999 percent. Martin. Sidles, and Danielson [37|. The values shown correspond to their sample which

had a reported purity of 99.999 percent and a ratio of ice point to helium point resistivity of 5000.

6.1. Electrical Resistivity

The electrical resistivity values reported for platinum by Powell and Tye [1], Laubitz and van der Meer

[30]. Roeser [31], and Martin, Sidles, and Danielson

[37] are compared with the results of the present in- vestigation in figure 9. The reported purities and

resistivity ratios for the different samples are given

in the figure caption.

6.2. Thermal Conductivity

The thermal conductivity values reported for platinum by Powell and Tye [1], Laubitz and van der

Meer [30], and Martin, Sidles, and Danielson [37, 60] are compared with the results of the present investi- gation in figure 10. The base line in this figure is a weighted average of the two sets of data obtained

in the present investigation, the data from the lon- gitudinal heat flow method being given twice the

weight that was given to the data from the electrical method, which had a larger uncertainty. The derived curve of Slack [2J is also shown in figure 10; this represents essentially all of the thermal conductivity values reported for platinum prior to 1962 with

the exception of the data of Krishnan and Jain [10]. The previously unreported data of Watson and

Flynn [32J shown in figure 10 were made at NBS on

the bar from which the specimen for the present int

1 1

1 i i i i r

1111 I I I I L

t

1 1 1 r

I I I I I I I I I L 0 200 400 600 800 TEMPERATURE, °C

Fk.URE 10. Thermal conductivity of platinum: comparison of pre- vious data with the results of the present investigation. The curve in the upper drawing and the baseline in the lower drawing correspond to a weighted average of the two sets of data from the present investigation with the data from

the longitudinal heat flow method being given twice the weight of the data from the electrical method.

-- Present investigation —longitudinal heat flow method. — Present investigation — electrical method. T Watson and Flynn [32| — --ame sample as that used in the present investigation. The curve of Slack |2|. • Powell and Tye |1|. A Laubitz and van der Meer |30|. Martin. Sidles, and Danielson [37|. the values shown correspond to their sample D. 354-275
2O0

TEMPERATURE, °C

Thermal conductivity of platinum: comparison between existing lou temperature data and those of the present investigation.

Present investigation: the curve shown is that obtained by the longitudinal heat How method. Halpern and Klynn |33|: measurements madi Watson and Flynn |32|; measurements mad(

Powell and Tye 1 1 1. Bode [ZS\. Powell. Tye. and Woodman |39|: measurements made on one of the samples of Powell and Tye [I Moore and McElroy [4()|: measurements made on one of the samples of Powell and Tye [1|.

Figure 11.

>n a portion of the sample used for the present investigation, u a portion ol the sample used for the present investigation.

vestigation was later machined. Watson and Flynn

made their measurements in air in a longitudinal heat

flow apparatus which has been described by Watson

and Robinson [34 J and by Ginnings [35]. Several recent sets of thermal conductivity values

for platinum at lower temperatures are displayed in figure 11. The data of Powell and Tye [1], curve D, were also shown in figure 10. The data of Bode [38], curve E, were obtained using a longitudinal heat flow method; Bode stated that he considered his values

to be accurate to within 0.5 percent. Since the present

investigation was begun, Powell, Tye, and Woodman

[39], curve F, have used a longitudinal heat flow method

to make low temperature thermal conductivity meas- urements on one of the samples of Powell and Tye.

Also during this time, Moore and McElroy [40], curve

G, have made thermal conductivity measurements

on the same sample which Powell, Tye, and Wood- man [39J used for their investigation. In the temperature range shown in figure 11, the thermal conduc3.2 x IO- 8

r

TEMPERATURE, °C

FIGURE 12. Lorenz function for platinum: comparison between existing data and

those of the present investigation.

A. Slack |2|. H. Powell and Tye | 1 1. C. Wheeler |36|. D. Martin. Sidles, and Danielson |37|: the values shown correspond to their sample D.

E. Present investigation: the curve shown was computed from the thermal conductivity values obtained by the longitudinal heal How method.

355-276
tivity of platinum could be affected by small differences

in purity and this may account for some of the dif- ferences shown. However, the measurements of Powell, Tye, and Woodman [39] and those of Moore

and McElroy [40] were carried out on the same sample; hence the differences between the results of

these investigators must be presumed to be due to. experimental errors. Additional references to previous measurements

of the thermal conductivity of platinum are given by

Powell, Ho, and Liley [8J. Ciszek [61] has recently

reported some high temperature thermal diffusivity

measurements for platinum.

Values obtained for the Lorenz function of platinum are compared with those of other investigators

in figure 12. The present measurements indicate a Lorenz function increasing above the theoretical value

as the temperature increases. Laubitz and van der

Meer [30] point out that such behavior of the Lorenz

function can be understood qualitatively if one as- sumes a low Fermi energy for platinum.

7. Conclusions

The good agreement among the thermal conductivity values obtained for platinum by two different methods in the present investigation and by an in- dependent measurement by Watson and Flynn [32] lend considerable weight to these results. The values

indicate that the thermal conductivity of platinum

increases with temperature as found by Laubitz and

van der Meer [30J rather than being essentially in- dependent of temperature as found by Powell and

Tye [1|. However, there remains the possibility that there is a real difference between the samples of Powell

and Tye [1] and those of other investigators. In order

to explore this possibility, measurements should be

made at high temperatures in another laboratory on one of the actual samples of Powell and Tye. Steps

are being taken to see if this can be done.

The results of the present investigation indicate

that electrical methods of measuring thermal conductivity can yield equivalent results to those obtained

by the more conventional nonelectrical methods, at least for the conditions of this investigation. This can

be interpreted as indicating that the thermal conductivity of platinum does not depend significantly on

electric current densities in the range less than

104 A/cmA

Before platinum can be established as a thermal

conductivity reference standard, additional measure- ments by the same method on samples of differing

purity are indicated. It is intended to repeat the

measurements described in this paper on a sample

of platinum of higher purity than that used in the

present investigation.

We appreciate the advice and assistance provided

by Henry G. Albert and A. V. Lincoln, both of Engelhard Industries, Inc. We thank Henry E. Robinson,

Chief, Environmental Engineering Section, NBS, and

Adjunct Professor of Engineering, The George Washington University, for his advice and support. The

intricate and difficult machining required for this project was done by Raymond Chidester. Much good

advice in matters of fabrication came from John

Hettenhouser.

NOTE: Appendices 8, 9, and

10, have been omitted from

this copy.

1 1 . References

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temperature thermal conductivity reference material, Brit.

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[3| Hill. J. S. and Albert, H. J., Loss of weight of platinum, rhodium, and palladium at high temperatures, Engelhard Industries,

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[17| Berry, R. J., Relationship between the real and ideal resistivity of platinum. Canad. J. Phys. 41, 946 (1963).

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[19] Kirby. R. K., NBS, private communication (Dec. 1965).

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with heat generation and conductivity an arbitrary function

of temperature. J. Appl. Mech. 26, 685 (1959).

[26] Ginnings, D. C. and West, E. D., Heater lead problem in calo- rimetry, Rev. Sci. Instr. 35, 965 (1964).

[27 1 Peavy, B. A., Determination and smoothing of Fourier coeffi- cients representing sectionally discontinuous functions on a

finite surface, J. Res. NBS 71C (Engr. and Instr.) No. 2, 93 (1967).

[28] Powell. R. W.. Thermophysical Properties Research Center,

private communication to D. R. Flynn (Oct. 1966).

[29] Evans, J. P., NBS, private communication (Aug. 1966).

[30] Laubitz, M. J. and van der Meer, M. P., The thermal conductivity of platinum between 300 and 1000 °K, Canad. J. Phys.

44, 3173 (1966).

[31] Roeser, Wm. F., in American Institute of Physics Handbook, Second Edition, p. 4-13 (McGraw-Hill Book Co., 1963). The values given in this reference have been adjusted to correspond to temperatures expressed on the International

Practical Temperature Scale of 1948. The original reference

is to the work of W. F. Roeser as given in Temperature, Its Measurement and Control in Science and Industry, p. 1312

(Reinhold, 1941).

[32] Watson, T. W. and Flynn, D. R., NBS, private communication

(Jan. 1966).

[33 [ Halpern, Carl and Flynn, D. R., NBS, private communication

(Aug. 1966).

[34] Watson. T. W. and Robinson, H. E., Thermal conductivity of some commercial iron-nickel alloys, Trans. ASME J. Heat

Transfer 83C, 403 (1961).

[35] Ginnings, D. C, Standards of heat capacity and thermal conductivity, in Thermoelectricity, edited by Paul H. Egli. p. 320

(Wiley, 1960).

[36] Wheeler, M. J., Thermal diffusivity at incandescent temperatures by a modulated electron beam technique, Brit. J. Appl.

Phys. 16, 365 (1965).

[37] Martin. J. J., Sidles, P. H.. and Danielson, G. C, Thermal dif- fusivity of platinum. Report No. IS— 1261 , contribution No. 1810 of she Ames Laboratory of the U.S. Atomic Energy

Commission.

[38| Bode, K-H, Messung der Warmeleitfahigkeit von reinem Platin zwischen 0 °C und 100 °C, PTB Mitteilungen Nr. 5, 416 (1964).

[39] Powell, R. W., Tye, R. P., and Woodman, Margaret J.. The

thermal conductivity and electrical resistivity of polycrystalline metals of the platinum group and of single crystals of ruthenium, J. Less-Common Metals 12, 1 (1967).

[40[ Moore, J. P., and McElroy, D. L., Oak Ridge National Laboratory, private communication (Mar. 1967).

[41 1 Huntington, H. B., and Ho, S. C, Electromigration in metals,

J. Phys. Soc. Japan 18, Supplement II, 202 (1963).

[42] Ho, S. C, Hekenkamp, T. and Huntington, H. B., AEC Docu- ment Code No. RPI-1044-1, Contract HT(30-1 )-1044

(Apr. 1, 1964).

[43] O'Boyle, D., Observations of electromigration and the Soret ef- fect in tungsten, J. Appl. Phys. 36, 2849 (1965).

[44J Callen, H. B., The application of Onsager's reciprocal relations

to thermoelectric, thermomagnetic, and galvanomagnetic

effects, Phys. Rev. 73, 1349 (1948).

[45J De Groot, S. R., Thermodynamics of Irreversible Processes

(Interscience, 1951). [46 1 Domenieali, C. A., Irreversible thermodynamics of thermoelectric effects of inhomogeneous, anisotropic media, Phys. Rev. 92, 877 (1953).

[47] Domenieali, C. A., Irreversible thermodynamics of thermoelectricity, Rev. Mod. Phys. 26, 237 (1954).

[48] Domenieali, C. A. Stationary temperature distribution in an

electrically heated conductor, J. Appl. Phys. 25, 1310 (1954).

[49] Leech. J. W., Irreversible thermodynamics and kinetic theory

in the derivation of thermoelectric relations, Canad. J. Phys.

37, 1044 (1959).

[50] Ziman, J. M., Electrons and Phonons (Clarendon Press, Oxford. 1960).

[51] Beaumont, C. F. A., Connection between macroscopic and

microscopic transport phenomena in solid conductors, Am.

J. Phys. 33, 547 (1965).

[52] El-Saden, M. R., Theory of nonequilibrium thermodynamics

with application to the transport processes in a solid. Trans. ASME, J. Heat Transfer, Paper No. 65-HT-l (1965).

[53J Onsager, L.. Reciprocal relations in irreversible processes, Part I, Phys. Rev. 37, 405 (1931).

[54] Onsager, L., Reciprocal relations in irreversible processes.

Part II, Phys. Rev. 38, 2265 (1931).

[55) Callen, H. B., Thermoelectric and thermomagnetic effects in electrochemical constants, NBS Circular 524, 141 (1953).

[56J MacDonald, D. K. C, Thermoelectricity — An Introduction to the Principles (Wiley, 1962).

[57J Davidson, P. M., The theory of the Thomson effect in electri- cal contacts, Proc. Inst. Elec. Engrs. 96, Part 1, 293 (1949).

[58J Holm, R., Electric Contacts: Theory and Application, 4th ed. (Springer-Verlag, 1967).

[59) Llewellyn Jones, F., The Physics of Electrical Contacts (Uni- versity Press, Oxford, 1957).

[60[ Martin, J. J., Sidles, P. H., and Danielson, G. C, Thermal dif- fusivity of platinum from 300 to 1200 °K, J. Appl. Phys. 38,

3075 (1967).

[61 1 Ciszek, T. F., The Thermal Diffusivity and Electrical Resistivity of Platinum at Temperatures Above 1000 °K, Master's

Thesis, Iowa State University (1966). (Paper 71C4-258)

357-278
Emissivities of Metallic Surfaces at 76°K

M. M. Fuxk and M. M. Reynolds*

National Bureau of Standards, Boulder, Colorado (Received October 15, 1956; revised manuscript received July 29, 1957)

Heat transport by radiation between surfaces at 300°K and 76°K was measured to evaluate the effective emissivities of a number of technical grade or commercially available metals with unknown metallurgical

history. The surface with the lowest total hemispherical emissivity was an unbuffed silver-plated surface.

It was found that the emissivity of surfaces was lowest when used without any mechanical working and that

the ability to absorb radiant energy varied with the length of time the surface was kept cold, even at a

pressure less than 10-6 mm Hg, indicating surface contamination by residual gases.

I. INTRODUCTION

THERE have been a number of researches on vacuum jacketed vessels since the work of Dewar,

but the subject does not seem to have been studied as

carefully as the practical importance would seem to

justify. Owing to the importance of low-temperature

research and to the constantly expanding technological uses of low-temperature equipment and liquefied gases, more information is needed for the optimum design of cryogenic and cryostatic equipment.

Many experimental data on reflectivity, emissivity,

and absorptivity of various materials over a wide range

of temperatures and wavelengths of radiation are

available. There is, however, considerable difficulty in translating this information into numbers that can be used in the design of low-temperature equipment,

except in a few special cases. This hindrance has left obscure many points that are of considerable interest

in evaluating surfaces and their performances in low- temperature equipment.

The present work was undertaken to obtain more

information about heat transport by radiation and how

it depends on materials and their surfaces. The measure- ments of emissivities were made under conditions that

exist in practical vacuum vessels rather than being a study of the most pure metallic surfaces to check

theoretical arguments.

The metals used in this study were either technical grade or commercially "pure" with unknown metallurgical history. Their surfaces were cleaned of grease,

dirt, etc., but retained their normal oxide coat that is acquired at room temperature. In most low-temperature equipment there is seldom

a surface at a temperature greater than 300° or 400°K

facing the low-temperature parts. This means that the

wavelengths (X) of thermal radiation encountered are

practically all greater than 2 microns (/*) and 98% of the total radiation has wavelengths greater than 4

microns. The present interest is therefore confined to X>4/z where the frequency is comparable to or smaller

* Now at Titan Chemical Industries, Inc., Colorado Springs, Colorado.

than the collision frequency of electrons in most common metals.1 Biondi2 and others have shown that the absorptivity

of copper becomes nearly independent of X for X>2ju.

After reaching the region where X>4 or 5 y. most metals

are practically "flat" in their reflectivity (r) with in- creasing X. Thus it is seen that the assumption of "grayness" for the surface of metals for X>4 ju is fairly

safe. Emissivity (e) may be used in substitution for absorptivity (a) or (1—r) even though the temperature

of the radiator and absorber are not the same but

both less than about 400°K. Therefore in the following

it is assumed that e = a= (1 —r) for the conditions under

consideration. The terms "emissivity" and "absorptivity" have been used interchangeably, although

strictly speaking these measurements were determinations of the "absorptivity."

There are a number of works treating various aspects

of the interaction of light with metals and concerning

the anomalous skin effect in metals.1,3 The bibliography by J. R. Partington4 on metallic

reflection is fairly complete.

There are also a number of works2 ' 5 giving measured

values of r, a, and e at low temperatures.

The effects of surface films on metallic reflection have

1 N. F. Mott and H. Jones, Properties of Metals and Alloys

(Oxford University Press, New York, 1936). R. E. Peierls, Quantum Theory of Solids (Oxford University Press, New York,

1955).

* M. A. Biondi, Phys. Rev. 96, 534 (1954).

3 R. B. Dingle, Physica 19, 311, 348, 729 (1953). J. R. Beattie and G. K. T. Conn, Phil. Mag. 46, 989 (1955). T. Holstein, Phys. Rev. 88, 1427 (1952) ; 96, 535 (1954). R. G. Chambers, Proc. Roy.

Soc. (London) A215, 481 (1952). R. G. Chambers, Physica 19, 365 (1953). G. E. H. Reuter and E. H. Sondheimer, Proc. Roy.

Soc. (London) A195, 336 (1948). R. W. Ditchburn, Light (Inter- science Publishers, Inc., New York, 1955). Konig, Handbuch der Physik (Springer-Verlag, Berlin, 1928), Vol. XX, pp. 197-253. H. Rubens and E. Hagen, Ann. Physik 11, 873 (1903). J. A.

Stratton, Electro-Magnetic Theory (McGraw-Hill Book Company,

Inc., New York, 1941).

4 J. R. Partington, "Physico-Chemical Optics," Vol. IV of An

Advanced Treatise on Physical Chemistry (Longmans Green and Company, London, 1955).

6 K. G. Ramanathan, Proc. Phys. Soc. (London) A65, 532

(1952). M. Blackman et al., Proc. Roy. Soc. (London) A194, 147

(1948). F. J. Zimmerman, J. Appl. Phys. 26, 1483 (1955). K. Weiss, Ann. Physik 6, 1 (1948). H. Cheung, unpublished thesis, Georgia

Institute of Technology (1955). 35S-H64
been considered by a number of workers and win not be taken up here. 6 The bibliographies in the reterences given will serve

as guides to most work on metallic reflection, and for those engaged in radiation exchange problems the

Table of Radiant-Interchange Configuration Factors1 may be very helpful.

II. APPARATUS

A. Description

The method of measurement consisted of metering

the gas "boil-off" from liquid nitrogen contained in a Dewar-like calorimeter. The inside surface was the sample material that absorbed the heat transport by

radiation from the warm outside wall facing the sample

across the vacuum space. The heat absorbed by the

inside surface evaporated the liquid nitrogen and the gaseous nitrogen was measured with a gas flowmeter.

The arrangement is shown in Fig. 1(B).

Various forms of Dewar-like calorimeters were used

to measure the heat transport by radiation between

surfaces in vacuum. One calorimeter was made of Lucite, another glass, and others of metals. Figure 1 shows schematically the various geometries and designs

used so that various surfaces could be easily substituted

and yet provide as closely comparable results as possible.

Figure 1 (A) shows the form of the internal neck shields used to stop radiation down the neck into the liquid

nitrogen can or ball. The forms of external shields can

be seen in Figs. 1 (B) and 1 (C). The radiation shields in the tops of the calorimeters in Fig. 1 were "black" on

top and "polished" underneath.

Aluminum rods were added to the inside cans to prevent superheating and bumping caused by the hydrostatic head of liquid nitrogen. The gas pressure

in the vacuum space was always reduced to less than

10-6 mm Hg except in the case of the Lucite unit. In the

Lucite unit two to four measurements at different pressures were made and extrapolated back to 10-6 mm Hg.

The calorimeters were usually calibrated electrically

with the outside and inside of the calorimeter at 76°K.

This calibration gave the solid support and neck

radiation correction as a function of boil-off rate. Those

calorimeters not calibrated electrically were "calibrated"

by running a well-known surface. After calibration it was found that the radiant heat

transfer to the surfaces at low temperature was large

compared to the "corrections." The "corrections" could

have been ignored and the determinations would still have been well within the estimated accuracy of 5%.

6 C. S. Taylor and J. D. Edwards, Heating, Piping and Air Conditioning (January, 1939). P. Drude, Ann. Physik 36, 532, 865

(1889). C. Hilsum, J. Opt. Soc. Am. 44, 188 (1954). F. A. Lucy,

J. Chem. Phys. 16, 167 (1948). O. S. Heavens, Optical Properties

of the Solid Films (Academic Press, Inc., New York, 1955).

7 D. C. Hamilton and W. R. Morgan, Technical Note 2836, Radiant-Interchange Configuration Factors (National Advisory

Committee for Aeronautics, Washington, D. C, 1952).

STAINLESS STEEL OR

LUCITE ROD

COPPER

OR ALUMINUM

TO FLOWMETER

SHIELDS

LIQUID N 2 GUARD RING WATER BATH (THERMOSTAT

CONTROLLED) OUTER CAN INNER CAN,

LIQUID N 2

Fig. 1. Schematic diagrams of the various forms of Dewar-like

calorimeters and their respective radiation shields, used to study

the total hemispherical absorptivity of surfaces at 76°K for 300°K thermal radiation. (A) Internal neck shield to stop radiation down boil-off tube—used in all units. (B, C) Metal units. Note: All "shields" were "black" on top and "shiny" underneath.

The temperature drop through the wall of the calori- meter can for the Lucite unit was estimated at a maximum of 0.1 °K, and the temperature drop through the

walls of the metal calorimeters was of the order of 0.01 °K.

For a given metal sample the values were easily

reproducible within 2% and in the better calorimeters

1% or less. 3,59-1465
Table I. Total hemispherical absorptivity of metals at 76°K for 300°K thermal radiation

Metal Surface treatment Aluminum 0.001 in Kaiser foil unannealed 0.018 0.0015 in Cockron home foil 0.018

0.001 5 in. Hurwich home foil—mat side 0.02

1

0.0015 in. Hurwich home foil—bright

side 0.022 0.020 in. cold acid cleaned 0.028 0.020 in. hot acid cleaned, Alcoa

process 0.029 0.020 in. Alcoa No. 2 reflector plate 0.026 0.020 in. Alcoa No. 2 reflector plate sanded with fine emery 0.032 0.020 in. Alcoa No. 2 reflector plate cleaned with alkali 0.035 0.020 in. wire brush, emery paper, steel wool, cold acid 0.045 0.020 in. wire brush 0.06 0.020 in. Liquid honedb 0.014 Aluminum vaporized onto both sides

of 0.0005 in. plastic Mylar 0.04 Aluminum sprayed onto stainless steel 0.07 Aluminum sprayed onto stainless steel and wire brushed 0.06

Brass, yellow 0.001 in. Shim stock (65% Cu, 35% Zn) 0.029 Cadmium A very mossy and smeared-looking

plated surface 0.03 Copper 0.005 in. Millrun sheet (annealed) 0.015

0.005 in. dilute chromic acid dip 0.017

0.005 in. wet polished with pumice 0.018

0.005 in. dry polished with plastic polishing wax abrasive 0.019

0.005 in. electrolytically cleaned 0.017 0.020 in. liquid honedb 0.088

0.005 in. fine emery 0.023 Commercial copper sphere—polished 0.03 Commercial copper sphere—Oakite No.

33 cleaned 0.03

Metal Surface treatment Copper

Chromium

Gold

Gold plate

Lead

Nickel Rhodium

Silver

Stainless steel

Tin

Zinc 50-50 Solder

Commercial copper sphere—Alleghany

silver spray coated 0.01 Commercial copper sphere—tinned 0.02 Chromium plate on copper 0.08 0.0015 in. Foil 0.010 0.0005 in. Foil 0.016 0.000040 in. Foil 0.023 0.00001 in. Leaf 0.062 0.0002 in. on stainless steel 1% silver in gold 0.025 0.0001 in. on stainless steel 1% silver in gold 0.027 0.00005 in. on stainless steel 1% silver in gold 0.028 0.0002 in. on copper, 1% silver in gold 0.025 24K gold plate on stainless steel 0.017 Gold vaporized onto both sides of 0.0005 in. Mylar plastic 0.02 0.004 in. foil (commercial sheet) 0.036

0.004 in. foil 0.022 Rhodium plated on stainless steel 0.078 Sheet 0.008

Silver plate (careful preparation) nickel

strike on stainless steel 0.009

Silver plate (careful preparation) nickel and copper strike on stainless steel 0.007 Allegheny Silver Spray Process on

stainless steel 0.009

0.005 in. type 302 sheet 0.048 Commercial ball type 302 0.07 0.001 in. foil 0.013 Tinned copper ball 0.02 0.0065 in. foil 0.02 0.002 in. solder surface on 0.005 in. copper sheet 0.03

» All values were calculated on the basis of the equation aenA io Q= r (TV -TV).

eo+«i(l —eo)Ai/At> Since eo>0.& and Ai/Ao~-0.5 this equation reduces in our case to q =e%Ai X<r(TV — 7V) within experimental error, e =emissivity, A =area, a=Stefan- Boltzmann constant, T = temperature, 9=heat transport by thermal radiation, and the subscript 0 =outside and i =inside.

b Abrasive carried in a liquid jet.

B. Cryogen Level Effect

Test runs were performed with different quantities

of liquid nitrogen in the calorimeters to determine if boil-off varied with level. In the glass and plastic

units, which would have shown the most effect, there was no level effect down to 60-70% full with surfaces

of less than 0.10 emissivity. All readings were taken

with the calorimeter essentially full, in the metal units

as well as in the glass and Lucite units, since all calori- meters were level-sensitive for large heat leak.

C. End Effects

The end effect was estimated5 ' 7 to be less than 5%

and was ignored in the following determinations of emissivity. The neck radiation error was determined

in the electrical calibration of the original unit. End effects, spurious radiation leak problems, and

calibration, etc., can be eliminated in the cylinder-incylinder case by building two identical units, except

for length. Thus the differences in readings are simply

360-

related to the area differences. This refinement was not

justified by the accuracy needed at the time of these measurements.

D. Materials

The metals used are readily available and likely to be used in experimental low-temperature work and

cryogenic engineering.

Some samples in the form of thin sheet or foil were wrapped on the inner can and held in place with fine copper wire. Thermal contact was established with a

thin layer of Apiezon-L vacuum grease. Other surfaces were the can itself or metals electroplated, sprayed, or melted onto the surface of the can. The outside wall

facing the sample surface was made "black" (e>0.8)

with metal black and paints.

III. RESULTS

Table I contains a representative selection of materials checked at 76°K for their total hemispherical

+66
absorptivities for 300°K thermal radiation. The over-all accuracy was estimated to be 5%.

Table II shows the effect of lowering the temperature on the absorptivity of a surface for 300°K thermal

radiation.

IV. DISCUSSION

The equation

eo+ei(l — e0)Ai/Ao

-(TV- TV)

was used to calculate all values in the tables, where

e = emissivity, A = area, a = Stefan-Boltzmann constant,

T= temperature °K, q= heat transport by thermal

radiation, and the subscripts 0 = outside and i = inside. The warm wall of calorimeter had an emissivity of 0.8 or greater and the ratio of Ai to Ao was about 0.5. The problem was assumed to be more nearly a diffuse rather than a specular reflecting problem so the above

equation reduced in this case to q=eiAi<r(Toi— Ti4

), within experimentaferror.

The factors affecting the absorptivity of a surface

include material, purity, temperature, thickness, roughTable II. Total hemispherical absorptivity of metals at 76°K and 20°K for 300°K thermal radiation (showing effect of lowering temperature).

Metal Surface treatment Temperature

of surface a\

Silver plated on copper 76 0.017 20 0.013 Nickel plated on copper 76 0.033 20 0.027

ness, surface coat, wavelength of radiation with its angle of approach, and the number of scattering

impurities in the surface to the depth of penetration of the radiation wavelength under consideration.

Metal surfaces at low temperatures change with

time in their total heat transfer ability. Figure 2 shows

the change in ability of surfaces at 76°K to absorb heat

from a 300°K surface as a function of time. This increase was attributed to the adsorption or condensation of residual gases on the surfaces of the metals—since the

surfaces recovered their original e after being warmed

to 300°K and pumped.

4 6 8 TIME , DAYS

Fig. 2. The change in ability of a 76°K surface to absorb heat from 300°K surface as a function of time. This change was

attributed to the absorption of gases. The surfaces were various metals electroplated on to a copper calorimeter can and the

calorimeter was pumped to a pressure less than 10~e mm Hg,

except where noted.

Electroplating would appear an easy solution to many thermal radiation problems but there are attending difficulties. There is a wide spread in the properties

of electroplated surfaces. They have to be as pure as

possible, dense and fairly thick if plated on to an

insulator or metal of low electrical conductivity. Purity

and density of plate are more important than the highly polished look the electroplater likes to give to a

surface. The visual appearance of a surface is not a very

good criterion for the performance of this surface beyond 4 (i. It was found that the absorptivity of some

surfaces increased if mechanically polished. This observation was noted at least as early as 1947 by M.

Blackman el al.

V. ACKNOWLEDGMENTS

This work was sponsored by the U. S. Atomic Energy

Commission. The authors wish to thank J. Brown,

O. Park, J. Schrodt, and D. Weitzel for their assistance

in the work.

Reprinted from Journal of Applied Physics, Vol. 28, No. 12, 1464-1467, December, 1957

361-1467
Journal of Research of the National Bureau of Standards Vol. 59, No. 5, November 1957 Research Paper 2805

An Apparatus for Measurement of Thermal Conductivity

of Solids at Low Temperatures

Robert L. Powell, William M. Rogers, and Don O. Coffin

A description is given of an apparatus used for determining the thermal conductivities

of solids in the temperature range 4° K to 300° K. The apparatus is especially suited to the determination of thermal conductivity over a large temperature interval, enabling coverage

of the temperatures between the normal boiling points of liquefied gases. Illustrative

results are given for an insulator, polytetrafluoroethylene, and for a high-conductivity

commercial coalesced copper. The thermal conductivity of the insulator increases monotonically from 0.56 milliwatt per centimeter per degree K at 5° K, to 2.32 at 80° K. The

thermal conductivity of the copper has a maximum of 24.9 watts per centimeter per degree K

at 21° K, and a value of 8.15 at 5° K. The methods of data analysis and estimation of

errors are given.

1. Introduction

Data on thermal conductivity are necessary for the selection of suitable construction materials, and

the prediction of operating characteristics of lowtemperature apparatus used in research and industry. In addition, accurate thermal conductivity

values for pure metals and controlled alloys are important in the development and verification of

theories of electronic transport phenomena in metals.

The apparatus described in this paper is well suited

to the measurement of thermal conductivity of

metals and commercial alloys; it is also usable for

poor conductors such as plastics and other dielectric

solids.

2. Experimental Apparatus

2.1. General Description

The method of determining thermal conductivity

by axial heat flow through a long cylindrical sample

is used. A pictorial diagram of the apparatus is shown in figure 1. The apparatus is similar, in many respects, to some of those described in the

review by Olsen and Rosenberg [5]. The cryostat consists of concentrically mounted

sample, thermal shield, vacuum container, glass

Dewar, Dewar support, and outside metal Dewar.

The sample rod is clamped to the heat sink at the

top; the sample heater is attached to the bottom of

this rod. The temperature distribution along the

sample is measured by means of eight thermocouples

attached to thermocouple holders positioned along

the rod. Heat losses by gas convection and conduction are made negligible by evacuating the region

surrounding the sample. Losses by radiation and

conduction along the lead wires are reduced by enclosing the sample rod within a symmetric cylindrical

thermal shield maintained at approximately the same temperature and axial gradient as the sample.

Measurements of the temperature, thermal gradient,

Now at the Los Alamos Scientific Laboratory, Los Alamos, New Mexico.

SHIELD

RING

PLATINUM

RESISTANCE THERMOMETER

OEWAR SUPPORTr- y TO VACUUM _^

I SYSTEM-- |

HEAT

SINK

REFERENCE

JUNCTION POST

VACUUM

CONTAINER

THERMOCOUPLE HOLDERS

SAMPLE HEATER

AND" SHIELD

Figure 1. Thermal conductivity apparatus.

and power input to the sample, combined with data on the cross-sectional area, permit a calculation of

the thermal conductivity of the sample based upon

Fourier's equation for steady state, linear heat flow.

The heat sink is maintained at a constant low

temperature by a refrigerant, usually a liquefied gas. This refrigerant, poured into the glass Dewar from a

central fill tube, surrounds the heat sink and vacuum

can. The glass Dewar is supported by a metal

container that is, in turn, sealed to a top plate. For

temperatures below 80° K in the internal apparatus,

the Dewar support container is further surrounded

by a metal Dewar containing liquid nitrogen, reducing heat conduction down into the colder refrigerant.

The associated vacuum, electrical control, and

measuring equipment are located on nearby racks

and benches.

362-349
Fioure 2. Cryostat and associated equipment.

METAL HEATER

AND SINK MOUNT

PLASTIC HEATER

AND SINK MOUNT

Figure 2 is a photograph of this assembly. Two

similar cryostats are used concurrently to increase

the data output.

2.2. Sample Assembly

Metal and alloy sample rods are 0.367 cm in diameter and 23.2 cm long; plastic samples are 2.54

cm in diameter and 20.5 cm long. The metal and

alloy rods are turned, then ground to the final diameter with a tolerance of 0.0005 cm. Because of

their larger size, the plastics are turned with a toler- ance of only 0.001 cm. When required, the sample

is annealed after the last grinding operation. Then

the thermocouple holders shown in figure 3 are attached, and the holders are placed on the sample

with their centers 2.54 cm apart by means of gage

blocks. The thermocouple holders have a thin

interior edge that gives, essentially, line contact

between the holder and the sample. The actual

distances between flat surfaces on the holders are measured by a vernier height gage with an attached

precision dial test-indicator. The accuracy is about

0.0005 cm. The average diameters of the sample

are measured between the thermocouple holders to about the same accuracy.

The samples are attached to the heat sink by a clamping action for metals, or an internal tapered screw thread for plastics as is shown in figures 1 and

3. The details of the sample heaters are also in- cluded in figure 3. The heater for a metal sample is slipped onto the rod and clamped with a small screw. In order to improve the thermal contact, mercury is placed in the hole that surrounds the lower end of the

metal sample. The heater for plastic samples is screwed on so that it presses against a large copper

washer used to increase the heater-to-sample contact area. Both heater blocks made of copper are wrapped with No. 36 or 40 AWG constantan heater

wire in a single layer held in place with G. E. 7031

Figure 3. Heaters and thermocouple holders.

air-drying varnish. The sample heaters have a

resistance ranging from 175 to 500 ohms for metals,

and from 500 to 1,000 ohms for plastics. The power

measuring circuits limit the current to a maximum of

about 100 ma, and the voltage to a maximum of

about 16 v. A small sample heater shield is attached

to the sample by a split collet-and-screw clamp, so reducing radiation losses. These shields are covered on all exposed surfaces with aluminum foil to further

reduce radiation.

2.3. Thermal Shielding, Tempering, and Controls

Several factors, such as gas conduction, radiation,

and wire conduction, can lead to consistent errors in the experimental determinations of thermal conductivity. Heat losses by gas conduction or convection are reduced to an insignificant amount by

baking out and evacuating the system to at least 10-5 mm of Hg while the system is at room temperature. Cooling of the system during experimental

runs further reduces the residual gas pressure. Heat losses by radiation and lead wire conduction

are greatly reduced by surrounding the sample with

a cylindrical thermal shield as shown in figure 1. The bottom, middle, and top of the shield are held at approximately the same temperature as the sample

at the corresponding elevation. To provide a good

thermal contact to the heat sink when the shield is bolted in place, the upper shield fastening ring is made of copper. The bottom of the shield is also made of copper to provide a nearly isothermal region

surrounding the sample heater. The longer intermediate section of the shield is made of thin stainless

steel to reduce the power input necessary to maintain

any given temperature gradient. The shield is split in two, vertically, to allow rotation of the front half

during the mounting and assembling of the sample.

363-350
The two halves are bolted together near the bottom,

and a copper bar is soldered across the bottom to improve thermal contact. A mounted sample and the

split shield are shown in figure 4. Three heaters are wrapped on the shield to supply

power necessary to maintain the proper thermal gradient. The main shield heater, wrapped back and

forth across the bottom copper section, is made of

32 AWG constantan wire and has about 100 ohms re- sistance. The other two heaters at the midpoint

and near the top, made of 45 AWG constantan, have

about 300 ohms resistance. All three are kept in place with air-drying varnish. All wires connected

to the sample pass through the shield and are ce- mented to it at areas close to the same temperature

as that of their point of contact on the sample. These

wires are 10 to 20 cm in length between the sample

and shield. The temperature difference between the sample

heater and a horizontally opposed point on the lower

copper section of the shield is measured with a goldcobalt versus copper thermocouple. Potential differ- ences of about 0.1 /xv can be detected, corresponding

to from 0.02° K at liquid helium temperatures, to 0.002° K at room temperature. Similar differential

thermocouples are at midpoint and near the top.

The thermal electromotive forces developed across

the middle and top differential thermocouples are measured with a d-c amplifier-galvanometer. To

bring about thermal balance between the shield and

sample, as indicated by null readings on the two upper differential thermocouples, the a-c voltages supplied to the heaters at the middle and top of the

shield are adjusted manually. If the shield is hotter

than the sample at either one of the two upper

points, there is no way to obtain thermal balance.

The lower, or main, differential thermocouple is the

sensing device for a heater servomechanism. The

approximately correct voltage for the bottom shield

heater is adjusted manually by varying two auto- transformers in series. Heater and thermocouple wires are wrapped back

and forth upwards on the shield for thermal tempering and then are wound on the posts attached to the

heat sink. Two of the six cylindrical copper posts

are shown in figure 1 . The winding on the posts al- lows most of the heat conducted down the wires from

above to be shorted to the liquid bath. One of the

posts serves as a reference junction block for the

eight measuring thermocouples; another is used to hold a platinum resistance thermometer that indi- cates the reference temperature. The others are used for thermal tempering only.

The heat sink and posts are machined from free- cutting leaded copper, assuring both good conductivity and machinability [6]. The vacuum chamber

cylinder is soldered onto a lip of the heat sink with

Rose's Alloy. Two thin stainless steel tubes serve

as mechanical support for the internal apparatus, as

exit tubes for the wires, and as pumping lines for evacuation of the inside chamber.

For measurements at liquid nitrogen, hydrogen,

or helium temperatures, the entire apparatus is surFigure 4. Mounted sample.

rounded by liquid nitrogen in a large metal Dewar.

To further reduce heat transfer to the internal apparatus, all the wires are again tied down thermally

to a copper post inserted into the pumping line just

above the top plate. The wires are brought out

from the vacuum space through a hard wax seal. Near the top of the apparatus is a thermally insulated junction box where the various small wires

from the cryostat are soldered to larger copper wires,

usually 22 AWG, which lead to the control panel and

measuring instruments.

2.4. Measuring Apparatus

The reference junction temperature for the ther- mocouples is assumed to be the same as that of the

thermometer post. The measuring thermometer is a strain-free capsule platinum resistor with an ice point resistance of about 25 ohms, which is embedded

in one of the posts attached to the heat sink. The

resistance of this thermometer, calibrated down to | 12° K by the Temperature Measurements Section

of the Bureau, is measured on a five-dial Mueller

bridge. When actual readings are not being taken,

this thermometer is switched to a resistance recorder.

This switching allows a drift of the heat sink tern- 364-351
0

- TUPPMHFI 1 nc.nfViuc.LC.L' PCTDir I niu POWER OF

Au-2.1% Co vs Cu

I 2 3 4 6 8 IO 20 30 40 60IOO 200 TEMPER ATUREfK

Figure 5. Thermocouple calibration. perature to be observed without continual manual

measurements. With liquid helium, the temperature

of the heat sink is obtained from a reading of the

barometric pressure by using the 1955 d compromise

temperature scale [2]. Wire of 5-mil diameter, composed of gold with 2.1 atomic percent of cobalt, is used for the common

element of the eight thermocouples [1]. The com- mon reference junction is on one post of the heat

sink. The external common lead and the separate

wires going to each thermocouple junction on the

sample are standard thermocouple copper. The

thermocouple combination was calibrated in a sep- arate apparatus. Different spools of gold-cobalt

wire with the same nominal composition have been

found to vary in sensitivity by about 5 to 10 percent. A graph of the sensitivity of the spool that was used is shown in figure 5. Each thermocouple

junction has one separate external lead and is measured with reference to the common junction at the

heat sink. The junctions are electrically insulated

by epoxy resin from the thermocouple bolt and,

therefore, from the holder, sample, and ground.

The thermocouple leads are soldered to larger wires

at the junction box. The voltages are read on a

5-dial Wenner potentiometer, usually to 0.01 ^uv. A determination of the power to the sample heater

is obtained by measuring the d-c voltage and current. Figure 6 shows the circuit diagram. The

total current passes through a calibrated 1-ohm

NBS—type resistor, Rc ; the voltage developed

across it is measured on a Rubicon type-B potenti- ometer. The effective current passes through the

sample heater Rs and the lead resistances rh . The

currents range from several milliamperes to about

100. The voltage across the heater is divided across

three calibrated resistors, arranged to give either 2

to 1 or 11 to 1 voltage division. Resistor R3 is 10

K ohms; Rp is either 10 K ohms for 2 to 1 voltage

divider ratio, or 1 K ohm for 11 to 1 ratio. The

voltage, measured on the same potentiometer as the

current, ranges from 1 to about 16 v. The four cal- ibrated resistors are in an oil bath maintained at 25° C by a commercial mercury thermostat and

infrared heating unit.

CRYOSTAT TERMINAL REGION BOX

Fir.uRE 6. Heater circuit.

Galvanometer unbalance voltages from the bridge

and two potentiometers are directed to a commercial

d-c breaker amplifier rather than the more commonly

used moving-coil galvanometers. The input selector

switch to the amplifier can be set to any of the

galvanometer terminals of the bridge or potentiometers, or to some of the " differential thermocouples

between the sample and shield. The high sensitivity

and several-million-fold amplification of the breaker

amplifier allow interpolation one figure beyond the

last dial setting on either the Mueller bridge or the

Wenner potentiometer. The signal from the amplifier is switched to a 1-v, center zero, d-c voltmeter

for precise readings, or to a slow-speed recorder for following temperature drifts or approach to equilibrium.

Standard low-level electric techniques have been

used: that is, all wires are shielded; a special common

ground wire is used; the bridges are on insulated

ground plates; and all terminals, switches, batteries,

and standard cells are thermally insulated.

2.5. Auxiliary Equipment

A photograph of the equipment is shown in figure

2. The vacuum control unit is behind the cryostat;

the power panels and control arc on the left. The

sample space is evacuated through nominal 1 -in. tubes by an oil diffusion pump. Between the system

and the diffusion pump is a metal cold trap that can

hold liquid nitrogen over a weekend without refilling.

Between the diffusion pump and the rotary mechanical pump is a 2-liter reservoir that, with its valve to the mechanical pump closed, can normally hold the

diffusion-pump output for 4 hr before the pressure

builds up to 100 p. In parallel with the cold trap,

diffusion pump, and reservoir, is a bypass line for pumping the system down initially without breaking

the vacuum in the cold trap or diffusion pump.

The pressure in the sample system is measured with

a commercial ion gage when it is below 1 y., and with

a thermocouple gage when above that. The pressure

in the reservoir, that is, the back pressure of the

diffusion pump, is measured on another thermo365-352
couple gage system that has shutoff relays controlling

the diffusion pumps and ion gage. Whenever the

back pressure goes above 100 n, an alarm light turns

on, and the power to the diffusion pump and ion

gage turns off. The liquid refrigerant can be either maintained at a reduced pressure by a high-capacity mechanical

pump, or vented directly to an explosion-proof

exhaust system. These vent lines are necessary to reduce the explosion danger during liquid hydrogen

tests. The vapor space over the liquid is connected

to a mercury manometer, permitting measurement

of the vapor pressure of the bath.

The power panel supplies both a-c and d-c voltage

to the heaters and electronic equipment. The d-c

voltage is obtained from a large bank of nickelcadmium batteries in a nearby room. The current through the main sample heater, which is adjusted

by four variable decade resistors, is read preliminarily on a precision multirange milliammeter. The a-c power is obtained from a 110-v regulated power

supply. Power to each of the shield heaters is controlled by two autotransformers in series. The a-c power supply also furnishes voltage to a millivolt

recorder, breaker amplifier, and the main shield

heater servomechanism.

2.6. Measurement Techniques

For each metal sample, the thermocouple holders

are mounted in a temperature-controlled shop room,

where the dimensions are also measured. After these

preliminary measurements, the sample is mounted

in the heat sink and the heaters and thermocouples

are attached. The sample is not heated or soldered

after assembly of the thermocouple holders, and it is subjected to as little mechanical strain as possible

during insertion into the cryostat. After this as- sembly, the shield is closed and bolted; then the vacuum can is soldered into place with Rose's Alloy.

The sample space and tubes are evacuated and baked

out for several days, usually over a weekend. The

liquid refrigerants are not placed into the glass

Dewar until the pressure in the cryostat is down to at least 10-5 mm of Hg.

Experimental runs are usually begun at liquid

helium temperatures, after precooling first with

nitrogen, then with hydrogen; and then the runs are continued at the hydrogen triple point, hydrogen

boiling point, nitrogen triple point, nitrogen boiling

point, carbon dioxide sublimation point, and then

ice point. Normally, about six series of measure- ments at various temperature gradients are made in each temperature range. Two sets of measurements

are made for each gradient to insure against reading

errors or lack of steady state. The over-all temperature differences across the sample vary from 1° K

to a sufficiently large temperature necessary to overlap readings in the next higher temperature range. The approach to steady-state conditions is observed

by amplifying the unbalance emf from the Wenner

potentiometer with the input switch set for the lowest thermocouple. The amplified signal is switched

to the millivolt recorder, and, when this thermocouple emf no longer drifts with time, precise measurements of the voltage, current, and temperatures

are begun. Measurements are also made at each

sink temperature with no power input and with the

normal vacuum space filled with helium exchange

gas at a pressure of several hundred microns. Because the apparatus should be isothermal under these

conditions, these readings give the "zero" corrections

for the thermocouples. These corrections are attributed primarily to inhomogeneous emf's and are assumed to be constant for a particular sink

temperature.

Subsidiary measurements are made afterwards on

a short section of the sample. They include mounting and polishing of the metal for photomicrographs

of grain structure, measurement of hardness, meas- urement of density, and spectrographic or chemical

analyses.

3. Analyses of Data

3.1. Basic Calculations

The fundamental equation of heat flow is utilized

in its differential form:

where Q is the heat flux, X is the thermal conduc7 tivit}r

, and A the cross-sectional area. Because Q

and A are essentially constants of the sample for

each run, d(-Qx/A)

Because we do not measure the temperature directly,

but rather the thermocouple voltage E, we rearrange

the equation to d(-Qx/A)dE

dE dT

where dE/dT is the thermoelectric power of the

thermocouple at the given voltage E and for the

given reference temperature.

Several corrections to a straightforward calculation

of the heat power of the sample heater are necessary.

The various components of the power circuit are shown in figure 6. Basically, the power is the product of the voltage and current through the sample

heater. The effective current through the heater

is given by

Ieff =Ir lot where IT is the total current and ID is the current

through the divider circuit. The total current is given by the measured voltage Vc across the standard

resistor divided by its resistance Rc. Similarly, the

divider current is given by the measured divider

voltage VP divided by the resistance of the particular resistor RP. The effective current is then

le,f-Rc RP

'

366-353
The effective voltage is Veff=pVP—rh Ie/f , where rhIe!f is the temperature-dependent voltage

developed across the heater leads between the shield

and the sample, and p is the voltage divider ratio. The ratio is given by

RX +R2 +R,+RP

P = 7=. >

where if?! and R2 are lead resistances (7?i is temperature dependent), i?3 is a standard 10 K ohm resistor,

and RP is either 1 K ohm or 10 K ohm.

The cross section and distances along the sample

are measured at room temperature. These dimensions are corrected for thermal contraction at each

sink temperature range whenever thermal expansion

data are available. A preliminary plot is made ol Qx/A against E to check for points that are considered

to have too large a deviation.

For the acceptable runs, the Qx/A and E are tabulated, and the values are processed by an IBM

650 digital computer. The program fits the Qx/A

data by a least squares method to polynomials to the

first, second, third, and fourth degree in E. Generally speaking, the first-degree polynomials give

the best results for small temperature gradients,

and the fourth-degree polynomials give the best

for the large gradients. The computer is then

programed to take the derivative of each of the

polynomials, and then to multiply by the thermoelectric power oi the thermocouples at each temperature. The final result is the thermal conductivity at 1-deg intervals based upon each of the

above polynomials.

Thermal conductivities as a function of temperature for each run are then plotted on a large scale graph. Average or best curves are drawn through

the many points for each range, and the various

ranges are connected smoothly to give the complete

graph.

3.2. Estimation of Errors

Three main sources of error appear in the apparatus

described here: (1) Calibration of the thermocouples,

(2) placement of the thermocouple holders, and (3)

thermal contact resistance between the thermocouple

and the sample. The first can be improved by a more complete and accurate thermocouple calibration. A new series of thermocouple calibrations to improve the range and accuracy of the data has been

started in thermometry calibration apparatus. The

second source of error has been practically eliminated

because of better control of the dimensions and placement of the holders. The third source of error can

be reduced by increasing the length of the thermocouple lead wire between the shield and the sample,

and by obtaining better contact between the thermocouple bolt and its holder.

Even after improvement, the first and third will probably remain the main sources of error. The

thermocouple measurements can be improved, but

appreciable errors will still come from chemical

inhomogeneities, mechanical strains, uncertainty in

calibration, reduced sensitivity at the lowest temperatures, and thermal emf in the external circuitry.

The thermocouple error is estimated to be less than

1 percent over most of the temperature range. This

error will be systematic and cannot be estimated or eliminated by statistical methods. The error caused

by thermal contact resistance can be estimated by

deliberately holding the thermal shield hotter or colder than the sample.

Except for gas conduction and radiation at high

temperatures, the other sources of error have been

reduced to an insignificant amount, considering the

larger errors mentioned above. Errors in the cross- sectional measurements are probably about 0.2 per- cent; inaccuracy in locating the actual contact point

between the thermocouple holder and sample is about the same. Errors due to radiation below

100° K and conduction along lead wires were calc- ulated to be below 0.1 percent. To check these

radiation losses at higher temperatures, several trial runs with different gradients were made at the ice point. Apparently, for metals, an error of about

1 to 2 percent exists in the readings at that temperature as disclosed by a systematic dependence of the

apparent conductivity on the gradient. Several runs were made with a residual helium gas pressure

of approximately 1 X 10 -5 mm Hg within the system.

These runs differed by about 3 percent for most

temperature ranges. Experimental runs in each temperature range have

been analyzed for internal consistency. The deviations from an average curve are usually less than 1 percent in the liquid helium and hydrogen ranges, and less than % percent at liquid nitrogen temperatures and above. These inconsistencies are apparently due to the combined result of the various

errors mentioned above, the one exception being

thermocouple calibration error, which is systematic.

The inaccuracies increase if the sample has either a very high or a very low conductivity. The range of

usable sample diameters is not as great as the

variation in conductivity; therefore, at both ex- tremes of conductivity, optimum measuring conditions cannot be obtained. Recent measurements

on a very pure copper sample that had a conductivity

maximum over 100 w/cm °K gave inconsistencies of

about 5 percent between 4° K and 60° K. Measurements on very low conductivity alloys or plastics

have about this same inaccuracy, and, in addition, are usually not reliable above 100° K because of the

increasing significance of radiation exchange between the sample and shield. Many control experiments have been carried out

to test the self-consistency of the apparatus. Many

of the runs overlap in temperature range. For

example, some of the runs were carried out with the

heat sink at 4° K and the bottom of the sample

367-354
around 25° K, thus overlapping runs made with the

sink at 19.7° K. The conductivity curves from the

lower ranges fit smoothly with the curves at the

higher temperatures. Apparent conductivities from

runs with different thermal gradients on the sample

usually agree within the scatter normally characteristic of a single run. Various runs with different size samples and holders gave consistent results.

4. Results

4.1. Polytetrafluoroethylene

The graph of thermal conductivity of this plastic is given in figure 7. The estimated inaccuracy of the

results is about 10 percent. The sample was ex- truded and had a density of 2.218 g/cm3

. Thermal

contraction was calculated by using the data of Quinn, et al. [7] for the higher temperatures, and the

data of Head and Laquer [3] for the low temperatures [4].

4 6 8 10 20 40 60 80 100 TEMPERATURE, °K Figure 7. Thermal conductivity of polytetrafluoroethylene.

(The dashed lines indicate interpolated regions.)

4.2. Coalesced Copper

The graph of the thermal conductivity of this high-purity commercial copper is given in figure 8. The estimated inaccuracy of these results ranges

from 2 to 5 percent. The sample had a mill specification giving the impurities by weight as 13 ppm

02 ; 8 ppm Pb; 7 ppm Ni; less than 5 ppm each of Fe,

TEMPERATURE, 'K Figure 8. Thermal conductivity cf coalesced copper.

(The dashed lines indicate interpolated regions )

As, and Sb; 2 ppm Sn; less than 1 ppm Te and Ag;

and less than 0.5 ppm Bi. The sample was annealed

4 hr at 400° C, cooled slowly to 200° C, and then

kept at 200° C for 8 hr. During the entire heating

cycle, the sample was kept in a flowing helium atmosphere. The density of the sample was 8.90 g/cm3

, and its hardness on the Vickers diamond point

system with a 10 kg weight was 54.1 in the longitudinal section, and 48.8 in the transverse.

The authors thank R,. J. Corruccini, W. B. Hanson, and R. B. Scott for advice and assistance during

the progress of this project, and G. A. Yates of the

Phelps Dodge Copper Products Corp. for the generous supply of samples and fabrication information.

5. References

[1] G. Borelius, W. H. Keesom, C. H. Johansson, and J. O.

Linde, Commun. Phys. Lab. Univ. Leiden, No. 206b.

[2] J. R. Clement, liquid helium vapor pressure—temperature

scale. Distributed by the Naval Research Laboratory

as an informal report (1955).

[3] E. L. Head and H. L. Laquer, Low temperature thermal

expansion of various materials, Available from Office of Technical Services, AEC D-3706.

[4] Richard K. Kirby, J. Research NBS 57, 91 (1956). Received after completion of the data analysis.

[5] J. L. Olsen and H. M. Rosenberg, Adv. Physics 2, 28 (1953).

[6] R. L. Powell and D. O. Coffin, Rev. Sci. Inst. 26, 516 (1955).

[7] F. A Quinn, D. E. Roberts, and R. N. Work, J. Appl.

Phys. 22, 1085 (1951).

Boulder, Colo., December 8, 1956.

368-355
Author Index

[Reference is to volume number, boldface, followed by page number of this volume.]

A

Volume and Page Ambler, E., and Dove, R. B. Continuously operating He3 refrigerator for pro- ducing temperatures down to %°K J 6-159

Armstrong, G. T., and Churney, K. L. Studies in bomb calorimetry. A new determination of the energy of combustion of benzoic acid

in terms of electrical units 6-275

Armstrong, G. T., and King, R. C. Constant pressure flame calorimetry with fluorine. II. The heat of formation of oxygen difluo- ride_._

i. 6-288

B

Ball, A. F., Vier, D. T., and Ginnings, D. C. Calorimetric determination of the half-life of polonium 6-112

Beckett, C. W., and Cezairliyan, A. Dynamic measurements of heat capacity and

other thermal properties of electrical conductors

at high temperatures 6-226

c

Cezairliyan, A., and Beckett, C. W.

Dynamic measurements of heat capacity and

other thermal properties of electrical conductors

at high temperatures 6-226

Churney, K. L., and Armstrong, G. T. Studies in bomb calorimetry. A new determination of the energy of combustion of benzoic acid

in terms of electrical units 6-275

Churney, K L., and West, E. D. A two-body model for calorimeters with constant temperature environment 6-100

Coffin, D. O., Powell, R. L., and Rogers, W. M.

An apparatus for measurement of thermal conductivities for solids at low temperatures 6-362

D

Ditmars, D. A., and Furukawa, G. T. Detection and damping of thermal-acoustic oscil- lations in low temperature measurements 6-175

Dixon, H. D., Saylor, C. P., Furukawa, G. T., Reilly, M. L., Henning, J. M., Glasgow, A. R., Ross, G. S., Horton, A. T., and Enagonio, D. Comparison of cryoscopic determinations of purity of benzene by thermometric and calori- metric procedures 6-127

Volume and Page Douglas, T. B. A cryoscopic study of the solubility of uranium

in liquid sodium at 97.8°C 6-153

Douglas, T. B., and King, E. G. High temperature drop calorimetry 6-181

Douglas, T. B., and Krause, R F., Jr. The vapor pressure, vapor dimerization, and heat

sublimation of aluminum fluoiide, using the entrainment method 6-227

Dove, R. B., and Ambler, E. Continuously operating He3 refrigerator for pro- ducing temperatures down to M°K 6-159

E

Enagonio, D., Dixon, H. D., Saylor, C. P., Furu- kawa, G. T., Reilly, M. L., Henning, J. M.,

Glasgow, A. R., Ross, G. S., and Horton, A. T. Comparison of cryoscopic determinations of purity of benzene by thermometric and calori- metric procedures 6-127

F

Flynn, D. R. A radial-flow apparatus for determining the ther- mal conductivity of loose-fill insulations to high

temperatures 6-325

Flynn, D. R., and O'Hagan, M. E. Measurements of the thermal conductivity and

electrical resistivity of platinum from 100 to 900°C 6-334

Fulk, M. M., and Reynolds, M. M.

Emissivities of metallic surfaces at 760°K 6-358

Furukawa, G. T., and Ditmars, D. A. Detection and damping of thermal-acoustic os- cillations in low-temperature measurements 6-175

Furukawa, G. T., Reilly, M. L., Henning, J. M , Glasgow, A R., Ross, G. S., Horton, A. T., Enagonio, D., Dixon, H. D., and Saylor, C. P. Comparison of cryoscopic determinations of purity of benzene by thermometric and calori- metric procedures -- 6-127

Furukawa, G. T., Reilly, M. L., and Saba, W. G.

Electrical resistances of wires of low temperature

coefficient of resistance useful in calorimetry

(10°-380°K) 6-110

G

Ginnings, D. C. Calorimetry of non-reacting systems 6-1

369
Author Index—Continued

Volume and Page

Ginnings, D. C., Ball, A. F., and Vier, D. T.

Calorimetric determination of the half-life of polonium 6-112

Ginnings, D. C, and Stimson, H. F. Calorimetry of saturated fluids including deter- mination of enthalpies of vaporization 6-62

Ginnings, D. C., and West, E. D.

Principles of calorimetric design 6-15

Glasgow, A. R., Ross, G. S., Horton, A. T. Enagonio, D., Dixon, H. D., Saylor, C. P., Furukawa, G. T., Reilly, M. L., and Henning,

J. M.

Comparison of cryoscopic determinations of purity of benzene by thermometric and calorimetric procedures 6-127

Goodwin, R. D. Apparatus for determination of pressure-densitytemperature relations and specific heats of hydro- gen to 350 atmospheres at temperatures above

14°K 6-162

Guildner, L. A. Thermal conductivity of gases, I. The coaxial cylinder cell 6-317

m

Henning, J. M., Glasgow, A. R., Ross, G. S., Horton, A. T., Enagonio, D., Dixon, H. D

,

Saylor, C P., Furukawa, G. T., and Reilly,

M. L. Comparison of cryoscopic determinations of purity

of benzene by thermometric and calorimetric procedures ' 6-127

Hoge, H. J. Heat capacity of a two-phase system, with applications to vapor corrections in calorimetry 6-88

Horton, A. T., Enagonio, D., Dixon, H. D., Saylor, C. P., Furukawa, G. T. Reilly, M. L., Henning,

J. M., Glasgow, A. R., and Ross, G. S. Comparison of cryoscopic determinations of purity of benzene by thermometric and calo- rimetric procedures 6-127

I

Ishihara, S., and West, E. D. A calorimetric determination of the enthalpy of graphite from 1200 to 2600° K 6-220

J

Jessup, R. S. Precise measurement of heat combustion with

a bomb calorimeter 6-237

Johnson, W. H., Pergiel, F. Y., and Prosen, E. J. Heats of formation of diaborane and pentaborane 6-271

K

King, E. G. High temperature drop calorimetry 6-181

Volume and Page King, R. C, and Armstrong, G. T. Constant pressure flame calorimetry with fluorine.

II. The heat of formation of oxygen difluoride.. 6-288

Krause, R. F., Jr., and Douglas, T. B. The vapor pressure, vapor dimerization, and

heat of sublimation of aluminum fluoride, using

the entrainment method 6-227

L

Levin, E. M., and McDonald, C. L. Heats of transformation in bismuth oxide by

differential thermal analysis 6-117

M

Maron, F. W., Rossini, F. D., and Prosen, E. J. Heat of isomerization of the two butadienes 6-262

McDonald, C. L., and Levin, E. M.

Heats of transformation in bismuth oxide by

differential thermal analysis 6-117

Mikesell, R. P., and Scott, R. B. Heat conduction through insulating supports in very low temperature equipment 6-309

o

O'Hagan, M. E., and Flynn, D. R. Measurements of the thermal conductivity and

electrical resistivity of platinum from 100 to 900° C 6-334

P

Pergiel, F. Y., Prosen, E. J., and Johnson, W. H. Heats of formation of diborane and pentaborane. 6-271

Powell, R. L., Rogers, W. M., and Coffin, D. O. An apparatus for measurement of thermal conductivities for solids at low temperatures 6-362

Prosen, E. J., Johnson, W. H., and Pergiel, F. Y. Heats of formation of diborane and pentaborane, 6-271

Prosen, E. J., Maron, F. W., and Rossini, F. D. Heat of isomerization of the two butadienes 6-262

R

Reilly, M. L., Henning, J. M., Glasgow, A. R., Ross, G. S., Horton, A. T., Enagonio, D., Dixon, H. D., Saylor, C. P., and Furukawa,

G. T. Comparison of cryoscopic determinations of purity of benzene by thermometric and calorimetric procedures 6-127

Reilly, M. L., Saba, W. G., and Furukawa, G. T.

Electrical resistances of wires of low temperature

coefficient of resistance useful in calorimetry

(10°-380°K) 6-HO

Reynolds, M. M., and Fulk, M. M.

Emissivities of metallic surfaces at 76°K 6-358

370
Author Index—Continued

Volume and Page

Rogers, W. M., Coffin, D. O., and Powell, R. L. An apparatus for measurement of thermal conductivities for solids at low temperatures 6-362

Ross, G. S., Horton, A. T., Enagonio, D., Dixon, H. D., Saylor, C. P., Furukawa, G. T., Reilly,

M. L., Henning, J. M., and Glasgow, A. R. Comparison of cryoscopic determinations of purity of benzene by thermometric and calorimetric procedures 6-127

Rossini, F. D., Prosen, E. J., and Maron, F. W.

Heat of isomerization of the two butadienes 6-262 s

Saba, W. G., Furukawa, G. T., and Reilly, M. L.

Electrical resistances of wires of low temperature

coefficient of resistance useful in calorimetry

(10°-380°K) 6-110

Saylor, C. P., Furukawa, G. T., Reilly, M. L., Henning, J. M., Glasgow, A. R., Ross, G. S., Horton, A. T., Enagonio, D., and Dixon, H. D. Comparison of cryoscopic determinations of purity of benzene by thermometric and calori- metric procedures 6-127

Scott, R. B., and Mikesell, R. P. Heat conduction through insulating supports in very low temperature equipment 6-309

Volume and Page Stimson, H. F., and Ginnings, D. C. Calorimetry of saturated fluids including deter- mination of enthalpies of vaporization 6-62

V

Vier, D. T., Ginnings, D. C, and Ball, A. F. Calorimetric determination of the half-life of polonium 6-122

w

West, E. D. Heating rate as a test of adiabatic and the heat

capacity of a-alumina 6-96

West, E. D.

Techniques in calorimetry, I. A noble metal

thermocouple for differential use 6-111

West, E. D., and Churney, K. L. A two-body model for calorimeters with constant temperature environment 6-100

West, E. D., and Ginnings, D. C.

Principles of calorimetric design 6-15

West, E. D., and Ishihara, S. A calorimetric determination of the enthalpy of graphite from 1200 to 2600° K 1 6-220

371
Subject Index

A Volume

and page

Adiabatic calorimeters 6-62, 6-96

Aluminum oxide heat capacity 6-96

B

Benzoic acid combustion standard 6-237, 6-275

Block-type calorimeter 6-181 Bomb calorimetry 6-237, 6-262, 6-275 Bunsen ice calorimeter 6-181

Combustion calorimetry 6-237, 6-262, 6-275

Corrections in calorimetry 6-88

Cryoscopic measurements by calorimetry 6-153

Cryoscopic measurements of purity 6-127

D

Data correlation 6-181

Definitions 6-1 Density of hydrogen gas at low temperatures 6-162

Design of calorimeters 6-15

Differential thermal analysis 6-117

Differential thermocouple 6-111 Drop calorimetry at high temperatures 6-181, 6-220

Dynamic calorimetry 6-117,6-226

E

Electrical resistivity with pulse calorimetry 6-226

Emissivities of metal surfaces 6-358

Enthalpy measurements at high temperatures 6-181,

6-220

Errors in calorimetry 6-96, 6-275

F

Flame calorimetry 6-288

Flow calorimetry 6-288

Fluorine calorimetry 6-288

Furnaces for high temperatures 6-181, 6-220

G

Gas heat capacities at low temperatures 6-162

Gas oscillations at low temperatures 6-175

Gas thermal conductivity 6-317

H

He3 refrigerator for very low temperatures 6-159

Heat capacity corrections 6-88

Heat capacity measurement 6-62, 6-226, 6-162

Heat conduction at high temperatures 6-334

Heat conduction at low temperatures 6-309

Heat of fusion correction 6-88

Heat leak errors 6-15, 6-100 Heat radiation emissivities 6-358

Heat of sublimation at high temperatures 6-227

Heat transfer _. 6-15

Volume

and page Heat transfer by gas oscillations 6-175 Heat units and constants 6-1 Heater lead problem 6-15

Heating rate test of adiabatic calorimeter 6-96 Heats of decomposition 6-272 Heats of formation 6-272, 6-288 Heats of isomerization 6-262 Heats of transformation 6-117

High temperature calorimetry. 6-111, 6-181, 6-220, 6-226

High temperature thermal conductivity 6-334

High temperature thermal insulations 6-325

I Ice calorimeter 6-112, 6-181

Insulation thermal conductivity 6-325

Isothermal calorimeters 6-181

Isoperibol calorimeters 6-100, 6-181 L

Low temperature calorimetry 6-159

Low temperature gas oscillations 6-175

Low temperature insulation 6-309

Low temperature resistance wires 6-110

Low temperature thermal conductivities 6-362

M

Methods of calorimetry 6-1 N

Noble-metal differential thermocouple 6-111

P

PVT measurements at low temperatures 6-162

Platinum thermal conductivity 6-334

Principles of calorimetric design 6-15 Probable error 6-1

Pulse calorimetry 6-226

Purity by heat measurements 6-127

R

Radiation emittance measurements 6-226, 6-358

Radioactive power measurements 6-112

Radioactivity half-life by calorimetry 6-112

Reaction calorimetry 6-237, 6-288

Refrigeration for temperatures to %°K 6-159

Resistance wires for low temperatures 6-110

s

Saturated fluid calorimetry 6-62

Solubility measurements by calorimetry 6-153

Standard deviation 6-1 Standard reference substances 6-1 Symbols 6-1

372
Subject Index—Continued

T" Volume

and page Techniques in combustion calorimetry 6-237, 6-275

Temperature gradients in calorimeters. 6-15, 6-96, 6-100

Tempering of leads 6-15

Terminology 6-1 Theory of calorimetry 6-100

Thermal-acoustic oscillations 6-175

Thermal conductivity of gases 6-317

Thermal conductivity of insulation 6-325

Thermal conductivity of platinum . 6-334

Thermal conductivities of solids at low temperatures 6-362

Volume

and page Thermocouple for differential use 6-111

Thermometric measurement of purity 6-127

Two-phase calorimetry 6-88

V

Vapor corrections in calorimetry 6-88

Vapor equilibria at high temperatures 6-227

Vapor pressure by entrainment method 6-227

Vaporization heats 6-62

(377)

it U. S. GOVERNMENT PRINTING OFFICE : 1970 O - 379-831

Announcement of New Volumes in the

NBS Special Publication 300 Series

Precision Measurement and Calibration

Superintendent of Documents,

Government Printing Office,

Washington, D.C. 20402

Dear Sir: Please add my name to the announcement list of new volumes to be issued

in the series: National Bureau of Standards Special Publication 300, Precision

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Official SI Unit Names and Symbols

[For a complete statement of NBS practice, see NBS Tech. News Bull. Vol. 52, No. 6, June 1968.]

Name Symbol

meter m

kilogram kg

second s ampere A

kelvin 1 K

candela cd

radian rad

steradian sr hertz Hz

lumen lm

lux Ix

Name Symbol

newton N

joule J watt W

coulomb C

volt V

ohm . farad F

weber Wb

henry H

tesla T

Additional Names and Symbols approved for NBS use

curie 2 Ci

degree Celsius 3 °C

gram : g

mho mho

mole mol

Siemens 4 S

' The same name and symbol are-used for thermodynamic temperature and temperature interval. (Adopted by the

13th General Conference on Weights & Measures, 1967.)

- Accepted by the General Conference on Weights & Measures for use with the SI.

3 For expressing "Celsius temperature"; may also be used for a temperature interval.

* Adopted by IEC and ISO.

Table for Converting U.S. Customary Units to Those of the International System (SI) 5

To relate various units customarily used in the United States to those of the International System, the National Bureau of Standards uses the conversion factors listed in the "ASTM

Metric Practice Guide", NBS Handbook 102. These are based on international agreements

effective July 1, 1959, between the national standards laboratories of Australia, Canada,

New Zealand, South Africa, the United Kingdom, and the United States.

To convert from:

(1) inches to meters, multiply by 0.0254 exactly.

(2) feet to meters, multiply by 0.3048 exactly.

(3) feet (U.S. survey) to meters, multiply by 1200/3937 exactly.

(4) yards to meters, multiply by 0.9144 exactly.

(5) miles (U.S. statute) to meters, multiply by 1609.344 exactly.

(6) miles (international nautical) to meters, multiply by 1852 exactly.

(7) grains (1/7000 lbm avoirdupois) to grams, multiply by 0.064 798 91 exactly.

(8) troy or apothecary ounces mass to grams, multiply by 31.103 48 . . . (9) pounds-force (lbf avoirdupois) to newtons, multiply by 4.448 222 ...

(10) pounds-mass (lbm avoirdupois) to kilograms, multiply by 0.453 592 . . . (11) fluid ounces (U.S.) to cubic centimeters, multiply by 29.57 . . . (12) gallons (U.S. liquid) to cubic meters, multiply by 0.003 785 .. . (13) torr (mm Hg at O °C) to newtons per square meter, multiply by 133.322 exactly.

(14) millibars to newtons per square meter, multiply by 100 exactly.

(15) psi to newtons per square meter, multiply by 6894.757 . . . (16) poise to newton-seconds per square meter, multiply by 0.1 exactly.

(17) stokes to square meters per second, multiply by 0.0001 exactly.

(18) degrees Fahrenheit to kelvins, use the relation T68 = (<f + 459.67)/1.8.

(19) degrees Fahrenheit to degrees Celsius, use the relation f68 = (i F-32)/1.8.

(20) curies to disintegrations per second, multiply by 3.7X1010 exactly.

(21) roentgens to coulombs per kilogram, multiply by 2.579 760X10-4 exactly.

3 Systeme International d' Unites (designated SI in all languages).