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UNITED STATES DEPARTMENT OF COMMERCE

U NATIONAL bureau of standards

Alexander B. Trowbridge, Secretary

A.V. Astin, Director

Critical Analysis of the Heat-Capacity Data of

the Literature and Evaluation of Thermodynamic

Properties of Copper, Silver, and Gold

from 0 to 300 °K

George T. Furukawa, William G. Saba, and Martin L. Reilly

NSRDS—-NBS 18

' National Standard Reference Data SeriesNational Bureau of Standards 18

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

(Category 5—Thermodynamic and Transport Properties)

Issued April 1968

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 - Price 40 cents
Library of Congress Catalog Card Number: 67-62779
Foreword

The National Standard Reference Data System is a government-wide effort to give to the

technical community of the United States optimum access to the quantitative data of physical

science, critically evaluated and compiled for convenience. This program was established in 1963

by The President’s Office of Science and Technology, acting upon the recommendation of the Federal Council for Science and Technology. The National Bureau of Standards has been assigned

responsibility for administering the effort. The general objective of the System is to coordinate

and integrate existing data evaluation and compilation activities into a systematic, comprehensive

program, supplementing and expanding technical coverage when necessary, establishing and

maintaining standards for the output of the participating groups, and providing mechanisms for

the dissemination of the output as required.

The NSRDS is conducted as a decentralized operation of nation-wide scope with central

coordination by NBS. It comprises a complex of data centers and other activities, carried on in

government agencies, academic institutions, and nongovernmental laboratories. The independent

operational status of existing critical data projects is maintained and encouraged. Data centers

that are components of the NSRDS produce compilations of critically evaluated data, critical

reviews of the state of quantitative knowledge in specialized areas, and computations of useful

functions derived from standard reference data.

For operational purposes, NSRDS compilation activities are organized into seven categories

as listed below. The data publications of the NSRDS, which may consist of monographs, looseleaf sheets, computer tapes, or any other useful product, will be classified as belonging to one

or another of these categories. An additional “General” category of NSRDS publications will

include reports on detailed classification schemes, lists of compilations considered to be Standard

Reference Data, status reports, and similar material. Thus, NSRDS publications will appear in

the following eight categories:

Category

12

3

4

5

6

7

8

Title

General

Nuclear Properties

Atomic and Molecular Properties

Solid State Properties

Thermodynamic and Transport Properties

Chemical Kinetics

Colloid and Surface Properties

Mechanical Properties of Materials

The present compilation is in category 5 of the above list. It constitutes the 18th publication

in the new NBS series known as the National Standard Reference Data Series.

A. V. Astin,

Director.

ill
-
Contents

Page

Foreword Ill

1. Introduction 1

2. Units, symbols, abbreviations, and definitions 2

3. General appraisal of low-temperature heat-capacity measurements 3

4. Analysis of the heat-capacity data on copper, silver, and gold 5

4.1. Copper (Cu, 63.54), assessment of the data sources 6 Table 1. Sources of heat-capacity data on copper used in the analysis 12 Figure 1. Comparison of the reported values of electronic coefficients of heat capacity, -y, and Debye

characteristic temperatures, 6d(0), of copper 14 Figure 2a. Deviations of the heat-capacity data of the literature on copper from the selected values in the range 30 to 300 °K. The estimated limit of accuracy and the temperature derivative, dC/dT, in J °K~ 2 mol -1 of the selected values 15 Figure 2b. Deviations of the heat-capacity data of the literature on copper from the selected values in the range 0 to 30 °K and the estimated limit of accuracy of the selected values 16 Figure 2c. 1. Deviations of the heat-capacity data of the literature on copper from the selected values in the range 0 to 5 °K and the estimated limit of accuracy of the selected values. (Set 1) 17 Figure 2c. 2. Deviations of the heat-capacity data of the literature on copper from the selected values in the range 0 to 5 °K and the estimated limit of accuracy of the selected values. (Set 2) 18 Figure 2d. Comparison of some recently reported precise heat-capacity data on copper with the selected values in the range 0 to 30 °K 19 Table 2. Thermodynamic functions for copper (in joules) 20

4.2. Silver (Ag, 107.870), assessment of the data sources 21 Table 3. Sources of heat-capacity data on silver used in the analysis 25

Figure 3. Comparison of the reported values of electronic coefficients of heat capacity, y, and Debye

characteristic temperatures, 0i>( 0), of silver 26

Figure 4a. Deviations of the heat-capacity data of the literature on silver from the selected values in the range 30 to 300 °K. The estimated limit of accuracy and the temperature derivative, dC/ilT, in J °K -2 mol -1 of the selected values 27

Figure 4b. Deviations of the heat-capacity data of the literature on silver from the selected values in the range 0 to 30 °K and the estimated limit of accuracy of the selected values 28

Figure 4c. Deviations of the heat-capacity data of the literature on silver from the selected values in the range 0 to 5 °K and the estimated limit of accuracy of the selected values 29 Table 4. Thermodynamic functions for silver (in joules) 30

4.3. Gold (Au, 196.967), assessment of the data sources 31 Table 5. Sources of heat-capacity data on gold used in the analysis 33

Figure 5. Comparison of the reported values of electronic coefficients of heat capacity, y, and Debye

characteristic temperatures, 6i>( 0), of gold 34

Figure 6a. Deviations of the heat-capacity data of the literature on gold from the selected values in the range 30 to 300 °K. The estimated limit of accuracy and the temperature derivative, dC/dT, in J °K-2 mol -1 of the selected values 35

Figure 6b. Deviations of the heat-capacity data of the literature on gold from the selected values in the range 0 to 30 °K and the estimated limit of accuracy of the selected values 36

Figure 6c. Deviations of the heat-capacity data of the literature on gold from the selected values in the range 0 to 5 °K and the estimated limit of accuracy of the selected values 36

Table 6. Thermodynamic functions for gold (in joules) 38

Figure 7. The comparison of the Debye characteristic temperatures, 0i>{T), of the selected values of heat capacity of copper, silver, and gold in the range 0 to 300 °K. The values of di>(T) were calculated from

the relations Cv = C,,— yT — AC'f,T and D(6/T) = CJ3R 40

5. References 41

6. Appendix 1. Thermodynamic functions for copper (in calories) 44

7. Appendix 2. Thermodynamic functions for silver (in calories) 46

. 8 . Appendix 3. Thermodynamic functions for gold (in calories) 48

V

Critical Analysis of the Heat-Capacity Data of the Literature and Evaluation

of Thermodynamic Properties of Copper, Silver, and Gold from 0 to

300 °K

George T. Furukawa, William G. Saba, and Martin L. Reilly

The literature sources of heat-capacity data on copper, silver, and gold between 0 and 300 °K have

been compiled and the data critically analyzed. Tables of heat capacity (Cp ), enthalpy (H — Ho), entropy

(S°), Gibbs energy (G — HZ), enthalpy function H-mand Gibbs energy function G-HZ

have

been obtained from the analyses. The literature values of the heat capacity, the electronic coefficient of heat capacity (y), and the 0 °K limiting Debye characteristic temperature (0/dO)) are compared with

the selected values. The sources of the data are tabulated chronologically along with the temperature

range of measurements, purity of sample, and the pertinent experimental procedures used. A bibliography of the references is listed. A brief appraisal of low-temperature calorimetry is given.

Key Words: Calorimetry, copper, Debye theta (0), electronic coefficient of heat capacity, enthalpy,

entropy, Gibbs energy, gold, heat capacity, silver, temperature scales, thermodynamic

properties.

1. Introduction

This publication is the first of a series on the

intensive examination of low-temperature heatcapacity data of the literature to be issued in con- nection with the mission of the National Standard

Reference Data System. The objective of this

series of publications is to present critically evaluated tables of heat capacity and the derived thermodynamic properties between 0 and 300 °K to meet

the needs of physical chemists, physicists, and

engineers. In the investigation of chemical equilibria and thermodynamic properties the interest

is most often at the higher temperatures (room

temperature and above). The effect of small uncertainties in the evaluation of the heat capacities at the lowest temperatures (below about 50 °K) is usually less significant to these quantities. Aside

from precise cryogenic design applications, accurate

heat-capacity data at the lowest temperatures are, however, indispensable in studies of lattice dynamics, energy states of magnetic materials, electronic

distributions, order-disorder processes, and critical

phenomena. Heat capacity is that property through

which most experimental observations and theories

of physical properties can be correlated and

tested. Heat-capacity measurements can be ex- perimentally realized with high accuracy. The data

at the lowest temperatures have, therefore, been

evaluated as carefully as the accuracy of the

measurements would permit.

The scope of this series of publications is as

follows:

1. From selected “best” values of heat capacity

the derived thermodynamic properties (enthalpy,

entropy, Gibbs energy, enthalpy function, and

Gibbs energy function) will be calculated and

given in tabular form. Although the upper limit of

the tabular values will be 300 °K, selected data

whenever available up to 400 or 450 °K will be

included in the overall assessment. In the range

300 to 450 °K, the directly observed heat-capacity

data will be used wherever possible. If only relativeenthalpy data are available, comparisons will be

made in terms of the observed enthalpy increments

at the lowest temperatures. This procedure will

be followed because the 300 to 450 °K range is generally the lower extreme of the temperature

range of relative-enthalpy measurements and the

bulk of the existing equations representing the

measurements have been fitted to minimize the

absolute deviations over the complete range of

relative-enthalpy observations. The one or possibly

two relative-enthalpy observations between the

reference temperature and 450 °K would, therefore,

have comparatively little influence on the nature

of the overall equation. Depending upon the type

of material being investigated, states of thermodynamic equilibrium may also not prevail over the

complete range of measurements. In most cases

the values of heat capacity derived from relative

enthalpy equations do not, therefore, join smoothly

with the directly observed values of heat capacity

from the lower temperatures. The best values of

heat capacity above 300 °K that were selected but

not reported in this publication will be referred to as “expected” values.

2. As a part of the bibliographic information, a comprehensive listing of low-temperature heatcapacity data with sources of pertinent hightemperature data that were used in the analysis

will be given in tabular form in chronological order

1
of the journal publication date. Temperature

range of measurements and, when available, the

purity and physical state of the sample investigated will be given for each data source. The

values of the 0 °K limiting Debye characteristic

temperature, dD(0), the electronic coefficient of

the heat capacity, y, and the entropy at 298.15 °K

will also be tabulated along with the precision or estimated uncertainty figures whenever they were

published.

A number of publications exist with corrections

or reinterpretation of data published earlier by

the same authors. In some cases earlier “letters” are amplified or revised in subsequent publications. Whenever this occurred, the new values

will be used in the analysis but the tabular chronological location of the first publication will be re- tained. Whenever reports, theses, and journal

publications are available on the same set of

measurements, the journal publication date will

determine the chronological location in the bibliography of data sources. When more than one litera- ture reference is given for a set of measurements,

one of the above cases is indicated.

In the analysis of the heat-capacity data, the cal- orimetric procedures used in obtaining the data were examined. The details of calorimeter design,

the method for cooling the sample, the thermometer for determining the temperature change, and

the temperature scale are given along with the sources of experimental data.

3.

In addition to providing the “best” values of

heat capacity, this series of publications will present deviation plots to demonstrate the relationship between the selected values (base line) and

those of the literature, and boundary lines to show the limit of accuracy (estimated) of the best

values. The plots should also permit rapid comparison of any new data that might become available.

When the same set of data appears more than once in the literature, reference will be made to the authors’ most appropriate publication. In certain cases a large number of unpublished experimental observations have been received from the

authors. These observations will be plotted whenever practical.

The plots include curves representing the dC/dT

of the selected values. The curves will show the

smoothness of the selected values and general

information on the manner in which the heat

capacity changes with temperature. The plots

will also show 6d(T) calculated for the selected

values using the relations:

Cv = C„-yT-kClT, (1) A= vf3-/kC*, (2)

D(d/T) = CVI3R , (3)

where

v= specific volume,

(3 = coefficient of thermal expansion,

k = coefficient of compressibility,

D(d/T) = Debye function of ( 6/T ). The value of A will be considered constant and

the most appropriate value will be used. In this

publication, A was obtained by an iterative method

to fit the data best above 200 °K according to eq. (1). In addition to theoretical applications,

the values of 6n(T) are highly sensitive to the

heat capacity, particularly at the higher temperatures, and are, therefore, useful in smoothing

heat-capacity data of high precision.

4. The reported values of the 0 °K limiting Debye

characteristic temperature, 0/>(O), and electronic

coefficient of the heat capacity, y, will be given on

line plots, with the frequency of values reported

shown by the number of literature references made

to the locations on the line. The selected values

of y and 0/>(O) will be given on the same plot along

with their estimated uncertainties.

5. Search of the literature will be as current and

complete as practical. Limited data or measure- ments incidental to measurements on other substances may, however, be overlooked because of

lack of reference to the data or the title not being

descriptive of the measurements.

6. The pertinent bibliography of the literature sources that have been examined, arranged alphabetically by author with the title of the publication

and journal reference, will be at the end of each

publication. A small number of references may be

found late in the study. These will be appended,

alphabetically arranged, to the first set.

2. Units, Symbols, Abbreviations, and Definitions

In this paper the following units, symbols, abbreviations, and definitions are used:

cm = centimeter

g = gram

sec = second

atm = atmosphere (pressure)

1 atm = 101 ,325 N/m2

J = joule = 10 7 ergs

mj = millijoule = 10-3 J = 104 ergs

cal = defined thermochemical calorie = 4. 1840J

mol = mass of a pure substance corresponding to the formula weight in grams based on C-12 [20]

t °C = temperature, t degrees Celsius

T °K = temperature, T degrees Kelvin, triplepoint of water = 273. 16 °K

6i>( 0)= 0 °K limiting Debye characteristic temperature in °K, calculated from heat-capacity

data.

2
6n(T)= Debye characteristic temperature at T °K,

calculated from experimental heat ca- pacity at T °K after subtracting nonlattice

heat capacities and ( Cp — Cv ). y = electronic coefficient of heat capacity, in

mj °K-2 mol-1

. C = heat capacity

Cp = heat capacity at constant pressure (1 atm)

Ct,= heat capacity at constant volume

H= enthalpy

S = entropy

G = Gibbs energy

Q = quantity of heat

W = watt = J sec

-1 R — gas constant = 8.3143 J °K -

1

mol -

1

R — resistance in ohms

W = resistance ratio = RrlKo °c, the resistance at T °K to that at 0 °C.

The prevailing energy unit of this publication

will be the MKSA unit of energy, the joule. The

tables of thermodynamic properties have been

calculated on the basis of joules. For the con- venience of a number of scientists who are more

comfortable with calories, tables of thermodynamic properties in calories have been placed in

the appendix.

The molal quantities have been converted to the basis of the 1961 atomic weights based on

carbon 12 [20] 1 whenever the experimental data

warranted the conversion.

In tables 1, 3, and 5, certain abbrevations have

been used to describe the experimental methods.

The abbreviations used are defined as follows:

Calorimeter Design

VI-I = isothermal vacuum calorimeter operated by incremental heating.

VA—I = adiabatic vacuum calorimeter operated by incremental heating.

VA-C= adiabatic vacuum calorimeter operated

by continuous heating.

GA—I = gas-filled adiabatic calorimeter operated by incremental heating.

GI—I = gas-filled isothermal calorimeter operated by incremental heating.

Thermometer

TC = thermocouple

PRT = platinum-resistance thermometer

Pb = Pb-resistance thermometer

Au-Ag = gold-silver alloy resistance thermometer

C = carbon-resistance thermometer

Ge = germanium-resistance thermometer

Cu = copper-resistance thermometer

MS = magnetic-susceptibility thermometer

Temperature Scale

ITS = International Temperature Scale

(since 1960 International Practical Temperature Scale) [106].

vp = vapor pressure

gas = gas thermometer

TC = thermocouple scale initially compared with a gas thermometer.

MS = temperatures based on the magnetic susceptibility of paramagnetic salts. year He = helium vapor pressure scale with

official recognition.

vp-He = helium vapor pressure scale with no official recognition.

SR—3 He = 3 He vapor pressure scale based on

the earlier measurements of

Sydoriak and Roberts [107].

1948 4He = 4 He vapor pressure scale [112, 98].

1948 ER 4 He = 4 He vapor pressure scale [38, 113].

1948 R 4 He = 4 He vapor pressure scale [94].

1948 W 4He=_4He vapor pressure scale [28].

1955 E

4 He = 4 He vapor pressure scale [22, 23].

1955 K 4 He = 4 He vapor pressure scale [66].

1955 L

4 He = 4He vapor pressure scale [111].

1958 4He = 4 He vapor pressure scale [14].

Cooling of Sample

gas = gas heat exchange with heat sink

liquid = direct liquid refrigerant cooling by

immersion.

cond = condensation of refrigerant in a small chamber of the calorimeter

vessel and subsequent removal,

circ = refrigerant circulation.

MHS = mechanical heat switch

SHS = superconducting heat switch

AD—MC = adiabatic demagnetization of a paramagnetic salt mechanically

attached to the sample through a metallic thermal conductor.

Other details regarding each source of data are given in the text dealing with each of the elements.

3. General Appraisal of Low-Temperature Heat-Capacity Measurements

For most of the temperature range below about

400 °K modern heat-capacity calorimeters and

associated instrumentation have advanced to the

state that, with reasonable care, a precision better

than 0.1 percent and accuracy of 0.1 to 0.2 percent can be achieved [19, 27, 80, 88, 114]. Below about

50 °K the precision and, consequently, the accuracy

begin to deteriorate with decreasing temperatures

because of the diminution in heat capacity while

1 Figures in brackets indicate the literature references on page 41.

relative errors in the determination of the energy

increments introduced and the corresponding temperatures of the system steadily increase.

In very careful work using calorimeters designed

for a limited temperature range and using rela- tively large samples, accuracies of about 1 percent

have been realized down to 1 °K [86, 87]. Ahlers [3]

has shown recently with measurements on several

copper samples that by using the same thermometer, temperature scale, and cryostat, the intralaboratory precision of 0.1 to 0.2 percent could be

283-739 0-68—2 3
achieved between 1 and 20 °K. Osborne, Flotow,

and Schreiner [86, 87] compared values of the

heat capacity of copper at 1.2 and 4.2 °K obtained

by 13 laboratories and showed the average deviation to be 0.8 percent at these temperatures.

In the measurements at the lowest temperatures

the errors become amplified if the heat capacity

of the substance under investigation decreases

relatively more rapidly than the “addenda,” which

include the thermometer, thermocouples, heater,

lead wires, thermal contact agent (e.g., cement,

grease, etc.) and the sample vessel. A sample vessel

by necessity is constructed of a metal of good

thermal conductivity and has, therefore, a relatively

high heat capacity. Other factors that contribute to the decline in relative accuracy at the lowest temperatures include the comparatively larger heat

leak, deterioration in thermometry, uncertainties

in the temperature scale, and loss in thermal contact between the sample and addenda.

With a single-piece sample, such as a short metal

rod, the use of a sample vessel is often avoided for

the measurements at the lowest temperatures by

attaching the addenda directly onto the sample.

Corrections to the measured heat capacity are made

using the known masses and heat capacities of the

addenda components. Significant uncertainties do

arise, in particular when the mass of sample is small, from errors in the masses of the addenda and

their heat capacities. For example, the heat ca- pacity of the cement used could be dependent on

the curing condition or the apportioning of the lead

wires to the addenda could be incorrect. These

sources of errors are obviously avoided by the

sample vessel technique in which two separate

series of measurements are made.

For measurements at the lowest temperatures,

cooling by means of a mechanical or superconducting heat switch is preferred to 4He exchange gas,

because of the 4 He heat of desorption effects. The

mechanical heat switch can, however, introduce

relatively large amounts of energy into the system

when the mechanical contact is broken and unduly

raise the sample temperature.

In the region above 90 °K many of the published

heat-capacity data are based on the International

Practical Temperature Scale [106]. There are, however, many data between about 15 to 300 °K

based on copper-constantan thermocouples cali- brated against gas thermometers and vapor pres- sures of hydrogen, oxygen, and nitrogen [49, 50,

99]. There are published considerable data between 10 and 300 °K, based on Pb-resistance thermometers and resistance tables originally obtained

by comparison with gas thermometers and vaporpressure measurements [26, 97]. No direct comparison of these temperature scales is available. In the United States, the NBS-1955 provisional

scale [60, 46] has largely been used for the region

11 to 90 °K. The scale is based on the resistances

of platinum thermometers calibrated against a helium-gas thermometer in 1939. In 1955 the whole

scale was translated downward by 0.01 °K. Temperature scales based similarly on platinum-resist- ance thermometers calibrated against gas thermometers have been established more recently

at the Pennsylvania State University (PSU) [82],

Physico-Technical and Radio-Technical Measurements Institute (PRMI) [13], and National Physical

Laboratory (NPL) [6]. Intercomparison of the

four scales showed that between 20 and 90 °K the

deviations from the mean of the four scales do not

exceed ±0.01 °K [85].

Heat-capacity determinations using resistance

thermometry are dependent on the dR/dT or essentially the “size of the degree” of the temperature

scale. Heat-capacity results, obtained using the

NBS-1955 and the IPTS, exhibit reproducible

anomalies as large as 0.2 percent that are attributable to deviations of these temperature scales from

the thermodynamic scale [47]. Barber and Horsford [8] recently compared a set of platinumresistance thermometers against a gas thermometer

between 90 and 273 °K and showed wide variations

in the IPTS from the thermodynamic scale. Differences of almost 0.04 °K were found.

The Working Group of the Advisory Committee

on Thermometry to the International Committee

of Weights and Measures has recently been considering a provisional reference table of resistance

ratios, Wr= Rr/Ro °r. of platinum thermometers as a function of the temperature for the range 12 to 273 °K which is as closely related to the thermodynamic scale as the present knowledge permits

[85, 7]. The table was derived in two parts. The

range 12 to 95 °K is based largely on the four temperature scales established at NBS, PSU, PRMI,

and NPL [60, 82, 13, 6]. The range 90 to 273 °K

is based on the work at NPL [8]. The two ranges

are made coincident at 90.249 °K within 0.001 °K

in T, 0.02 percent in dT/dW, and 0.067 percent in d

2 T/cTW2

. The new temperature scale, referred to as Provisional Reference Table CCT64, or its slight

modification is expected to be adopted internationally in the near future. The analysis in future publications will be made on the new scale when

enough heat-capacity data have been obtained

or converted to the new scale.

Carbon- and germanium-resistance thermometers

have been used in most of the recent heat-capacity

measurements below about 20 °K. For precise temperature measurements carbon thermometers

require calibration with every application at the

low temperatures. Germanium thermometers have

been found to be stable enough with respect to time and to cycling between room temperature and

liquid helium temperatures [73, 37, 10] that they

do not require calibration as often as carbon thermometers. The disadvantage of a germanium thermometer is its complex resistance-temperature

relation. Calibration at closely spaced temperatures over the complete range of application is, therefore, required to obtain a properly behaved

dRJdT versus T relation for the thermometer. The

4
values of dRJdT should change smoothly with the

thermodynamic temperature and any unknown

anomalies in dRJdT will be reflected as anomalies

in the heat capacity.

Many of the existing heat-capacity data below

about 5 °K are based on the helium vapor-pressure

temperature scales which are in turn based on the

helium gas and magnetic susceptibility temperature

scales or indirectly to these scales through resist- ance thermometers. The 1948 4 He scale [112, 98],

based on the vapor-pressure measurements of

Kamerlingh Onnes and Weber [64] and Schmidt

and Keesom [102, 103] and the calculations of

Bleaney and Simon [12] with experimental verification by Bleaney and Hull [11], has been shown

to deviate significantly from the thermodynamic

temperature scale [9, 38]. The 1955L [109] and

1955E [22, 23] 4He vapor-pressure scales are in- dependently obtained adjusted scales which differ

from each other at most by 4 mdeg [14]. The present 1958 4He scale [14] between 0.5 and 5.2 °K is the

result of cooperative efforts of the groups that

originated the 1955L and 1955E scales to decide

upon a single scale. The estimated uncertainty from

the absolute temperature scale given for the 1958

4He scale is ±0.002 °K between 1 and 4.5 °K and

larger uncertainties at temperatures above 4.5

°K [14].

The 1962 3He vapor-pressure scale [102] is useful between 0.2 and 3.3 °K. The scale, based on the

1958 4 He scale [14] and thermodynamic properties

of 3He between 0.2 and 2.0 °K, was developed by

4. Analysis of the Heat-Capacity

In the past few years the intensive interest in

the effect of alloying on the electronic heat capacity has resulted in a large number of publications on the heat capacity of copper, silver, and gold in

the range below 4 °K on samples of 99.999 percent

purity and higher. Unfortunately, in most of these

publications the numerical values of the observed

heat capacities have been omitted and, instead, the

derived electronic coefficients of heat capacity y

and 0 °K limiting Debye characteristic temperatures 6d( 0) have been reported. These values have

been obtained from a plot of C/T versus T2 or by

least-squares analysis of the experimental data to

fit the equation:

C = yT+ATs (4) or C/T^y + AT2

. (5)

In some of the cases the equation was of the form:

C = yT+ATi + BT> (6) or CIT=y + AT2 + BT4

. (7)

The coefficient A yields the 0 °K limiting Debye

characteristic temperature and corresponds to

Roberts, Sherman, and Sydoriak [109, 107, 95].

Prior to the establishment of the above scale some

of the measurements had been based on the earlier

vapor-pressure measurements on 3He reported by

Sydoriak and Roberts [107] in 1957.

The vapor pressure of hydrogen compiled by

Woolley, Scott, and Brickwedde [116] and the more

recent measurements of Hoge and Arnold [59] have

been used for thermometer calibration in the range

of about 14 to 20 °K. The vapor-pressure measure- ments of Hoge and Arnold [59] were based on the

NBS—1939 scale [60].

Gas thermometers have been used for calibration in the region 5 to 15 °K to fill the gap left by the

helium and hydrogen vapor-pressure scales [44, 87].

Germanium-resistance thermometers can now be

calibrated at the National Bureau of Standards

(U.S.) between 2 and 20 °K against germanium thermometer standards that have previously been cali- brated against an acoustical thermometer [90].

The acoustical thermometer scale has been shown

to be higher than the 1958 4He scale by 0.006 °K at 2.323 °K, 0.007 °K at 2.807 °K, 0.008 °K at 3.211 °K,

0.

010 °K at 4.212 °K, and 0.012 °K at 5.024 °K [90,

21]. Except at the lower temperature limit (11 °K)

of the NBS—1955 scale, the acoustical thermometer

and the NBS-1955 scales agree within ±0.005 °K

[90]. Not enough heat-capacity data have been

accumulated at this time to compare the results

from different laboratories using this new temperature scale referred to as NBS Provisional Temperature Scale 2-20(1965).

Data on Copper, Silver, and Gold

^tjARI^OdW) ]

3

- The B is the coefficient of the

higher-order lattice term in T5

. The values of y, A,

and B are expected to be slightly different depending

upon the method used to obtain them. The precision

figures that are reported with the values of y and

0d(O) in many of these publications are not clearly

defined. It is, therefore, difficult to decide whether

such precision figures represent the precision of y

and 0o(O) or the observed heat capacities. The fig- ures following the ± symbol found in the literature were given the interpretations defined in tables

1, 3, and 5 which list the sources of data analyzed.

Since the data analysis was to be performed in terms of heat capacities, each published set of

values of y and 6p(0) was first converted to heat

capacities at regular temperature intervals between

0 and 5 °K. The final analysis was based on those

calculated values of heat capacities corresponding

to the experimental temperature range for which

each set of y and 0d(O) was obtained by the in- vestigators.

A least-squares procedure was used with the

high-speed digital computer to obtain the smoothed

values of heat capacity between 0 and 300 °K from

the experimental data. In certain temperature re- gions some personal judgment was also applied.

5
Deviation plots reflect the relation between the observed data and the final selection. Deviations from

the selected values of the published experimental

data are plotted as points and heat capacities cal- culated from y and 0/;(O) are indicated as continuous

curves over the experimental temperature range.

The thermodynamic functions were calculated from

the smoothed values of heat capacity by numerical

integration using four-point Lagrangian integration

coefficients [110]. The thermodynamic relations

used were:

H°t -H°o =

j

T CpdT (8) rc°

S° = J

f>dT (9)

G°-H°0 = -

J

T S°dT=(H°-H°0 ) - TS°

. (10)

The thermodynamic functions {Hj — Hq)/T and

( G° — H°)IT were obtained from values of eq (8)

and (10) by dividing by the corresponding temperature T. The literature measurements are in general

reported for ill-defined experimental pressure conditions. The conversion from undefined but rela- tively low pressures to one atmosphere is considered negligible for solids. The values tabulated in

this study are thus defined to be at 1-atm pressure.

In the following sections the data sources for

each element are discussed and assessed. This is followed in succession by tabular chronological

arrangement of the data sources, line plots of y

and 0«(O), plots of the deviations of the literature

data from the selected best values of heat capacity,

and the tables of thermodynamic properties.

The line plots of y and fl«(0) include the selected

values of these quantities with their estimated uncertainties. The deviation plots give the limits of

the estimated uncertainty of the selected values of

heat capacity. The plots of dC/dT and 9d{T)

as a function of the temperature are given for the

selected values. The literature search is current to March 1967.

4.1. Copper (Cu, 63.54), Assessment of the

Data Sources

Harper [56] reviewed the heat capacity and re- lated data on copper published prior to 1914. For

the present analysis no data on copper prior to 1914 were considered. Below about 100 °K very

few of the data published before 1960 were given

weight in the selection of the best values since

they exhibited wide deviations from more recent

measurements that are considered more precise.

Most of the scatter can probably be attributed to inconsistencies in the temperature scales. Of

the more recent data, the results of DuChatenier

and DeNobel [34, 35] and Rorer, Onn, and Meyer

[96] were not given any weight because of their

excessive deviation (more than 3 percent) from all other data. Above 100 °K, more or less weight was

given to the results reported by Harper [56], Eucken

and Werth [41], Bronson, Chisholm, and Dockerty [15], Dockerty [32, 33] Maier and Anderson

[74], Giauque and Meads [51], Sandenaw [100], and

Martin [76].

The recent interest in the application of copper

for a low-temperature heat-capacity reference [87]

has resulted in the publication of several sets of

smoothed values of heat capacity or heat-capacity

equations based on experimental observations in

the range 1 to 30 °K. These data are compared with

the selected values in figure 2d. The smoothed

values reported between 3 and 30 °K by Frank,

Manchester, and Martin [43] are shown to deviate on the average about ±0.3 percent from the se- lected values. More recent measurements were

reported between 3 and 30 °K by Martin [78J;

below 15 °K, these values are on the average

about 0.5 percent lower than his earlier measure- ments [43] and between 15 and 30 °K, the two sets of measurements differ from each other by about

0.2 percent. Ahlers [3] reported a six-term polynomial equation in odd powers of T from 1 to 11

obtained by a least squares fit to 153 observations

between 1.3 and 20 °K. The maximum deviation of

the equation from the selected values is —0.4

percent. More recently, Osborne, Flotow, and

Schreiner [87] reported a “reference equation"

containing similar terms as those of Ahlers [3] based on new measurements and previously published dat<L The reference equation is within

±0.1 percent of the selected values. When a polynomial equation containing the same powers of

T was fitted by the method of least squares to the

observations reported by Osborne, Flotow, and

Schreiner [87], the equation obtained was found

to deviate by ±0.2 percent from the selected

values. The observations of Osborne. Flotow,

and Schreiner [87] deviate on the average by

±0.1 percent from the equation obtained.

Harper [56] reported measurements from 0 to 50 °C (273 to 323 °K) on a 99.87 percent copper

wire sample. The average deviation of the observations from a linear equation is reported to be 0.1

percent. His values are, however, slightly low and

are on the average about 0.2 to 0.3 percent lower

than the selected values.

A series of three papers on copper was published

from the H. Kamerlingh Onnes laboratory. Keesom

and Kamerlingh Onnes reported measurements in

the range 15 to 22 °K [67] and 14 to 90 °K [68] on

an electrolytic sample. The gold-resistance thermometer used was calibrated against the vapor

pressure of hydrogen, a platinum-resistance

thermometer, and a gas thermometer. The published results between 15 to 22 °K [67] scatter from

±6 to —2 percent about the selected values, while

those between 14 to 90 °K [68] scatter from ±2 to —5 percent. The later observations of Kok and

6
Keesom [72] from 1.2 to 19.6 °K on a sample of

99.9 percent purity are on the average 5 percent

higher than the selected values. Kok and Keesom

[72] used phosphor-bronze and constantan-resistance thermometers calibrated against the vapor

pressures of 4 He and H2 and a gas thermometer.

Eucken and Werth [411 reported measurements

from 95 to 215 °K on electrolytic copper. A vacuum

isothermal-jacket calorimeter was used. The temperatures were based on a Pb-resistance thermometer. Their values are, except for a few points,

0.2 to 0.4 percent higher than tbe selected values.

Mendelssohn and Closs [129] reported measure- ments from 5 to 15 °K. The measurements are presented graphically only with the average Debye

characteristic temperature given as 315 °K. The

low value is expected since the electronic contribution was not taken into account.

Bronson, Chisholm, and Dockerty [15] determined the heat capacity of several copper samples

in the range —20 to 500 °C (253 to 773 °K) by the

“method of mixtures” or the “drop method” and

by the electrically heated adiabatic method. Only

the results obtained with the adiabatic method

in the range —5 to 110 °C (268 to 383 °K) have been

considered in this analysis. The results reported

by them are actually the copper equivalent of three

copper calorimeters of about 1, 3, and 5 kg that were intended to be the “receivers” for the method

of mixtures. Equations fitted to the three sets of

measurements agreed within ±0.1 percent of each

other. The 3- and 5-kg samples were considered to be “100 percent” pure and the 1-kg sample to be

“especially” pure. All three sets of measurements

are slightly lower than the selected values, being

at most 0.2 percent lower.

Using an improved adiabatic calorimeter,

Dockerty [32] determined the heat capacity in the

range -72 to 116 °C (201 to 389 °K) of the 1-kg

copper specimen used earlier by Bronson, Chisholm

and Dockerty [15]. In the range of about 200 to 385 °K where the two measurements overlap, the

values agree within 0.1 percent. The observations

reported by Dockerty [32] are lower than the

selected values, ranging from about 0.5 percent

at 200 °K to 0.1 percent at 300 °K.

Dockerty [33] made further improvements by

designing a vacuum adiabatic calorimeter and by

reducing the mass of the adiabatic shield. (The

earlier calorimeters used by Bronson, Chisholm,

and Dockerty [15] and by Dockerty [32] were of

the non-vacuum adiabatic type.) With the new

calorimeter Dockerty [33] made measurements in

the range 28 to 194 °K and test measurements

around room temperature on commercially pure

cold-rolled copper. The statement is made that his

earlier measurements [32] with the nonvacuum type

adiabatic calorimeter are too low by 0.2 percent

and after corrections were made the agreement was

within 0.05 percent of his new results obtained at 200 °K and room temperature. No information is given on how the corrections were made. Below

about 90 °K, Dockerty’s new observations [33]

scatter ± 1 percent about the selected values but

above 90 °K they are within ±0.1 percent.

Sykes [1351 reported measurements from 369 to 834 °K (96 to 561 °C) using a continuous-heating

method. Thermocouples were used for temperature

measurements. The value at 369 °K is about 5

percent higher than the expected value. No weight was given to the data in selecting the final values.

Maier and Anderson [74] reported measurements

from 53 to 294 °K on hard-drawn and annealed

copper wire samples. The two series of measure- ments reported show no difference in heat capacity

within 0.2 percent relative accuracy claimed. Their

results, however, scatter as much as ±2 percent

below about 100 °K but are within ± 0.5 percent

of the selected values above this temperature.

Honda and Tokunaga [125, 126] reported a single

measurement at 298.6 °K (25.4 °C) on an electrolytic

copper sample. A vacuum, isothermal-shield cal- orimeter was used. The temperature change was

determined by means of a copper-constantan

thermocouple. The reported value is about 1 percent lower than the selected value.

Thomas and Davies [136] reported measurements

on a sample of 99.95 percent purity using a calorimeter in which the specimen was heated by eddy

currents induced by an alternating magnetic field. Measurements were made at different frequencies

ranging from 1775 to 1980 Hz. A thermocouple was

used for the measurement of temperature change.

The average of six observations at 293 °K (20 °C)

is about 0.1 percent lower than the selected value.

Persoz [132] reported making measurements at five temperatures between 287 and 640 °K (14 and

367 °C) using a unique vacuum-adiabatic method.

The sample was suspended within the sample

vessel (copper shell) to achieve a relatively high

degree of thermal isolation. The adiabatic shield

was controlled relative to the sample vessel temperature. The sample when heated transferred heat

to its vessel mainly by radiation. The temperatures

of the sample and its vessel were observed as a function of time in the usual manner and the changes

in temperature of the two parts were related to the

respective heat capacities and to the electrical

energy increment introduced to the sample. The

two values at about 287 °K deviate ±0.2 and —0.4

percent from the final selected values. The values

reported at the higher temperatures deviate by

larger amounts from the expected values.

Aoyama and Kanda [5] reported measurements

from 82 to 273 °K on a sample of 99.92 percent

purity, major impurities being Fe, C, and S at 0.02,

0.01, and 0.003 percent, respectively. The vacuum

adiabatic method was used. Description of the

method used for thermometry is not clear, but

platinum-resistance thermometry was probably

used. Their results are 1 to 2 percent higher than

the selected values.

Giauque and Meads [51] reported measurements

from 15 to 300 °K on an annealed sample of 99.96

7
percent purity. An isothermal-shield calorimeter

was used. The temperatures were measured by

means of a gold-silver alloy wire calibrated against

a standard copper-constantan thermocouple [49,

50]. Below about 100 °K, the results reported by

Giauque and Meads [51] deviate as much as ±2

percent from the selected values, but above 100 °K

they are on the average about 0.4 percent higher.

Estermann, Friedberg, and Goldman [39] re- ported measurements from 1.8 to 4.2 °K on a polycrystalline sample of 99.6 percent purity. The

principal impurity was Pb; the trace impurities

found were Fe, Ni, and Ag. Helium exchange gas

was used in cooling. The germanium-resistance

thermometer used was calibrated on the vapor

pressure of helium reported by Schmidt and

Keesom [102, 103]. An error in the correction for

the addenda in the results of Estermann et al. [39],

was subsequently pointed out by Burk, Estermann,

and Friedberg [18]. The value for 6p(0) in the table

has been adjusted for this correction. No correction

was needed for y. The relatively high value of

y (0.75 mj °K -2 mol -1

) is consistent with the

presence of Fe and Ni impurities and the relatively

low value of 0d(O) (340 °K) is also consistent with

positive excess heat capacity observed by Franck,

Manchester, and Martin [43] for Cu-Fe alloys containing small amounts of Fe. The heat capacities

calculated from the corrected values of y and

9i){ 0) reported by Estermann, Friedberg, and Goldman [39, 18] are on the average 6 percent higher

than the selected values.

Rayne [133] reported measurements on a “commercial stock” copper sample of 99.9 + percent

purity from 0.2 to 1 °K. In the experimental method,

the copper sample was attached to a paramagnetic

salt (CuS04 •K2 S04

, 6H2 0) through a heavy-gage

copper wire. The salt was used for adiabaticdemagnetization cooling of the copper sample and

for the measurement of temperature. The 1948

4 He scale [112, 98] was compared with the magnetic

susceptibility temperature scale based on the salt. Helium exchange gas was used in cooling the paramagnetic salt during the magnetization period. No

numerical observations are given in the paper. The

lattice contribution was considered negligible and

the electronic coefficient of the heat capacity y

based on the observations between 0.2 and 0.65 °K

is given. The value of y reported (0.724 + 0.033 mj

°K -2 mol) is higher than most of the recently

published values. The values of heat capacity based

on the above value of y are significantly higher

than the selected values (see figure 2c. 1). Hirano, Maniwa, and Takagi [124] reported meas- urements from about 323 to 723 °K (50 to 450 °C) on a sample of 99.998 percent purity using a vacuum-adiabatic continuous-heating method. Thermocouples were used for temperature measurements. The observations are presented graphically

only on the sample slowly cooled from 873 °K (600

°C) and on the sample quenched from 873 °K to room

temperature and annealed at 403 °K (130 °C). Significantly higher values of heat capacity were

observed between 423 and 623 °K (150 and 350 °C)

when the sample was quench-annealed than when

slowly cooled.

Corak, Garfunkel, Satterthwaite, and Wexler

[28] reported measurements between 1 and 5 °K on

an annealed sample of 99.999+ percent purity.

Helium exchange gas was used for cooling. The

carbon-resistance thermometer used was calibrated on the 1948 4He scale [112, 98] and adjusted for

deviation from the thermodynamic scale [38, 9]. Values of y and 0d(O) reported are typical of those

published and the calculated values of heat capacity

are slightly lower than the selected values, the

deviations ranging from about — 1 percent at 1 °K

to —0.1 percent at 5 °K.

Rayne [93] reported measurements from 1.5 to 4.2 °K on samples of 99.999 and 99.99 percent

purity “as received” and a commercial alloy

material containing 0.7 percent Cd and 0.5 percent

Zn. Measurements were also made after annealing on the 99.99 percent sample. Cooling was achieved

by means of a mechanical heat switch. A carbonresistance thermometer used was calibrated on the

1948 4He scale [112, 98] as adjusted by Erickson

and Roberts [38]. The value of y is relatively low

and that of 6p(0) high for the 99.999 percent sample

and calculated values of heat capacity are about

1 percent lower than the selected values. The

values of y and $d(0) are relatively low for both

of the measurements on the 99.99 percent sample.

The 6d(0) obtained for the 99 percent commercial

alloy sample is in the range of most values published; the value 0.799 mj °K -2 mol -1 obtained

for y is exceptionally high.

In a subsequent paper Veal and Rayne [1 13] re- ported measurements from 1 to 4.2 °K on a sample

of 99.999+ percent purity. A mechanical heat

switch was used in cooling. No explicit statement on the temperature scale used is given. The 1955E

4 He scale may have been used. The value of y and

#d(0) are typical of ihose published and the cal- culated values of heat capacity range from —0.3 to + 0.5 percent relative to the selected values.

Ramanathan and Srinivasan [91] reported meas- urements on an annealed sample of purity greater

than 99.95 percent from 1.3 to 4.2 °K. A mechanical

heat switch was used for cooling. The 1948 4 He

scale [112, 98] was used. The value reported for y

is relatively high and that of Qp(0) relatively low.

The calculated values of heat capacity range from

4.5 to 6.5 percent higher than the selected values.

No weight was given to these data in the final series

of analysis.

Griffel, Vest, and Smith [55] reported measure- ments from 1.8 to 4.2 °K on a 740 g sample of 99.99 +

percent purity. A carbon-resistance thermometer

calibrated on the 1955E 4 He scale [22, 23] was used.

Helium exchange gas was used for cooling. The

values of y and 9p(0) reported are typical of those

published and values of heat capacity calculated

8
are in agreement with the selected values at 1.8 °K

but deviate positively to almost 1 percent at 4.2 °K.

Sandenaw [100], using two calorimeters, reported

measurements from 4 to 300 °K on “dead-soft”

annealed, oxygen-free high-conductivity copper

(OFHC). Analysis showed 99.96 percent purity. In one calorimeter, measurements were made from 4

to 300 °K and in the other from 36 to 300 °K. Except

below about 60 °K, the results with the two calorimeters agree within about 1 percent. Above about

150 °K, the values reported by Sandenaw [100] are within about ±0.5 percent of the selected values.

Below this temperature the deviation increases

to as large as ± 12 percent at around 10 °K.

Manchester [75] reported measurements from

1.2 to 4.2 °K on a sample of 99.999 percent purity.

A mechanical heat switch was used for cooling.

The carbon-resistance thermometer was calibrated on the 1955E 4He scale [22, 23]. The values of y

and do(O) are among the middle values of those

published. Assumption is made that these measure- ments were reported again in the publication by

Franck, Manchester, and Martin [43] to be discussed

later. Zimmerman and Hoare [118] reported measure- ments from 1.8 to 4.2 °K and from 3 to 16 °K on a single-crystal sample using two calorimeters, but no numerical data are given. The subsequent

publication on measurements from 1.5 to 4.5 °K by

Crane and Zimmerman [30] also do not give any

numerical values.

Berge and Blanc [119] reported making measure- ments from 80 to 673 °K using the vacuum-adiabatic

continuous-heating method. No information is given on the copper sample used in the measurements

and no numerical values are reported. The temperatures were determined by means of thermocouples.

Martin [76] reported measurements from 20 to 300 °K on a commercially pure cold-rolled sample

and on annealed and heavily cold-worked samples

of 99.999 percent purity. The heavily cold-worked

copper sample is shown to have on the average about

0.15 percent higher heat capacity than the annealed

material. The results on the commercially pure

cold-rolled material are between the above two

samples. The measurements were made by means

of an adiabatic calorimeter using a continuousheating method. A copper resistance thermometer

scale originally calibrated against a platinumresistance thermometer was used. The results re- ported on the annealed sample by Martin [76] are

within about ±0.2 percent of the selected values

with predominance of the deviations being minus.

Franck, Manchester, and Martin [43] reported

measurements from 0.4 to 30 °K on the same an- nealed sample of 99.999 percent purity used by

Martin [76]. Three different calorimeters were used

to cover the temperature range. A 3 He cryostat was

used in the range 0.4 to 1.5 °K. A superconducting

Pb-wire thermal switch was used and temperatures were based on the 3 He vapor-pressure measure- ments reported in 1957 by Sydoriak and Roberts

[107]. The calorimeter for the range 1.2 to 4.2 °K

was the same as that used by Manchester [75]. A

mechanical heat switch was used for cooling and

temperatures were based on the 1955E 4 He scale

[22, 23]. The results reported for the 1.2 to 4.2 °K

range in this later publication [43] are probably the

same as those reported earlier by Manchester [75]. In the range 3 to 30 °K an adiabatic continuousheating calorimeter was used. The cooling was

achieved by condensing a small amount of helium

in a small chamber attached to the sample holder

and subsequently removing it by pumping. Temperatures were based on the 1958 4 He scale [14],

vapor pressure of hydrogen [116], a gas thermometer

[44], and the NBS-1955 provisional scale [60, 46].

The measurements obtained with the calorimeter

for the range 0.4 to 1.5 °K yielded y — 0.682 ±0.011

mj °K~ 2 mol -1 and 0d(O)= 327 ± 22 °K and the

values of heat capacity calculated using these values

of y and 9d(0) range from —1.7 percent at 0.4 °K

to +0.5 at 1.5 °K from the selected values. The

“smoothed” values reported are, however, within — 0.8 percent of the selected values. Considering

all of their results and those in the literature

Franck, Manchester, and Martin [43] adopted the

value 0.690 mj °K“ 2 mol -1 for y and calculated

6d(T) from the experimental data. The value

dp{0) = 344 °K was estimated from the values of

9o(T). Their “smoothed” values between 0.4 and

1.5 °K are almost identical to the values calculated

from y = 0.690 mj °K~ 2 mol -1 and 0d(O) = 344 °K;

their “smoothed” values were, therefore, probably

derived from these “constants.” The smoothed

values reported between 1.2 and 4.2 °K are within

±1.2 percent of the selected values, while those

calculated from y = 0.696 mj °K -2 mol -1 and

#d(0) = 344 °K are within about +0.2 percent. The

smoothed values reported for the calorimeter

operated between 3 and 30 °K are on the whole

about ±0.5 percent of the selected values, with

somewhat better agreement over about one-half

of the range.

Martin [127] reported measurements on annealed

and cold-worked copper samples of 99.999 percent

purity used earlier [76] after making modifications

to the sample holder to permit the use of a con- ventional capsule-type platinum thermometer. The

numerical values, reported only for the annealed

sample between 16 and 90 °K, are on the average

about ±0.4 percent of the final selected values.

No numerical values are reported for the measure- ments made in the range 283 to 304 °K; the deviation plot for the annealed sample shows about

±0.1 percent deviation from the earlier measure- ments reported by Martin [76].

Martin [128] reported measurements in the range

0.5 to 1.5 °K on a vacuum-cast sample of 99.999

percent purity using a specially designed sample

holder. The calorimeter was the same as that used

in earlier measurements [43]. Thermal contact

between the holder, in which the heater and thermometer were incorporated, and the sample was

9
achieved by multiple mechanical contacts maintained by means of springs and vacuum grease. A

superconducting Pb-wire thermal switch was used

in cooling the sample and the carbon thermometer

was calibrated using the 3 He vapor-pressure meas- urements reported in 1957 by Sydoriak and Roberts

[107], No numerical data were reported. A deviation

plot given in the paper shows the measurements

to be significantly higher than those reported earlier

by Franck, Manchester, and Martin [43].

Du Chatenier and DeNobel [34, 35] reported meas- urements from 1 to 30 °K on a polycrystalline sample

of 99.9999 percent purity. No impurities were

detected by standard spectrographic methods. The

temperatures were determined by means of a carbon

resistor calibrated on the 1958 4 He scale [14] and

on the vapor pressure of hydrogen reported by

Hoge and Arnold [59]. Helium exchange gas was

used for cooling. The relatively high value for y is consistent with possible heat of desorption at the

lower temperatures but the relatively low value for

0d(O) is inconsistent with this effect. These values

are, however, consistent with the relatively high

heat capacities reported by Du Chatenier and

DeNobel. The heat capacities calculated between

1 and 5 °K using the values of y and 0d(O) that were

first reported [34] and the smoothed values of heat

capacity between 1 and 30 °K [35] that were subsequently published are on the average about 4 to 5 percent higher than the selected values. The

“sinusoidal” deviation of large amplitude from the

selected values shown in figure 2b has also been

found with silver and gold measurements reported

from the same laboratory [35, 36].

O’Neal [84] reported measurements from 0.11 to 1.07 °K on a 900 g sample of 99.999 percent purity.

Both a mechanical heat switch and a superconducting niobium-wire heat switch were used for cooling.

A magnetic susceptibility temperature scale based

on 2Ce(N03 )3‘ 3Mg(N03)2’ 24H2 0 was used to cali- brate a carbon film thermometer. The values of y

and 0d(O) reported are typical of those published

and the calculated heat capacities are about 1 percent higher than the selected values.

Kneip, Betterton, and Scarbrough [71] made meas- urements from 1.2 to 4.5 °K on two very similarly

vacuum-annealed samples of 99.999 percent purity

from the same source. A mechanical heat switch

was used in cooling and the carbon resistance

thermometer was calibrated on the 1958 4 He scale

[14]. The values of y are in close agreement with

each other, but those of 6d( 0) differ by twice the

estimated uncertainty given for each value. The

heat capacities calculated from y — 0.697 mj °K” 2 mol -1 and 0^(0) = 345.1 °K are within about ±0.2

of the selected values, while those calculated from

y — 0.696 mj °K -2 mol~ 1 and 0/^(0) = 342.3 °K deviate

positively from 0.3 to 1.2 percent.

Phillips [89] reported measurements from 0.13 to 4.2 °K on a sample of 99.999 percent purity. Cooling

was achieved by means of a combination of mechanical and superconducting niobium-wire switches.

Below 1 °K, the temperatures measured by means

of a carbon resistor were based on the magnetic

susceptibility of CuS(VK2 S04 *6H2 0 and above

1 °K, on the .1958 4He scale [14]. Values of y and

$d(0) are typical of those published and the heat

capacities calculated from them deviate positively

from 0 to 0.5 percent from the selected values.

Ahlers [1, 2] made measurements from 2.3 to 19.7 °K on a sample of 99.999 percent purity. A

germanium-resistance thermometer was used,

calibration being made against the 1958 4He scale

[14] and the vapor pressure of hydrogen [116]. The

values below 5 °K are about 1 percent higher than

the selected values, while those above 5 °K are on

the average 0.5 percent lower. Over 90 observations

given in reference [1] have been plotted in figure 2b.

Ahlers [1] attributes the relatively large deviations

between 5 and 10 °K to errors in the temperature

scale. In a more recent publication Ahlers [3] reported

measurements between 1.3 and 20 °K on four

samples: a single crystal having the resistance ratio,

W = R,)m, oyJRs 9 oK . between 3000 and 6000 from one end to the other of the sample; annealed polycrystalline sample of 99.999 percent purity; severely

cold-worked sample prepared from the annealed

99.999 percent material; and a chill-cast sample of

99.999 percent purity distributed by the Argonne

National Laboratory in cooperation with the Calorimetry Conference (U.S.) [87]. The results on the

annealed polycrystalline and chill-cast samples

are essentially the same, i.e., within the ±0.1

percent precision of the measurements. The results on the single crystal are systematically slightly

higher (0.2 percent) than those on the above two

samples, actually outside by twice the limits of

precision. The results on the cold-worked sample

are decidedly higher, the difference being greater

at the lower temperatures (about 0.7 percent below

6 °K). The higher values obtained for the coldworked sample are consistent with the earlier work

by Martin [76]. The heat capacities calculated from

the published six-term equation based on the chill- cast sample follow very closely the selected values

with small “oscillations” of maximum amplitude

of — 0.4 percent.

Isaacs and Massalski [63] and Isaacs [61] reported

measurements from 1.6 to 4.2 °K using a carbon

thermometer on a sample of 99.999 ± percent purity.

Sargent, Isaacs, and Massalski [101] reported later

measurements using a germanium thermometer

on annealed copper of 99.999+ percent purity from

a different source. The values of y and 0/;(O) obtained are the same as those reported earlier [63.

61]. A mechanical heat switch was used for cooling

and the temperatures were based on the 1958 4 He

scale [14]. The values of y and 0d(O) are typical of

those published. Isaacs [62] recently recalculated

the earlier published data [61, 63] after changing

the formulation of the temperature-resistance rela- tion of his thermometer and obtained y= 0.698

±0.003 mj °K-2 mol -1 and 0n( 0)= 342.2 ±0.8 °K

10
which are not significantly different from the earlier

values. The heat capacities calculated from them

deviate positively between 0.6 and 1.2 percent from

the selected values.

Dixon, Hoare, Holden, and Moody [31] reported

measurements from 1.2 to 4.2 °K on chill-cast and

annealed samples of 99.999 percent purity. The

carbon-resistance thermometer used was calibrated on the 1958 4 He scale [14]. Cooling was achieved

using a mechanical heat switch. The values of y

and #d(0) obtained in the two measurements are

essentially the same and are in agreement with

other published values and the calculated heat

capacities deviate positively on the average by

0.5 percent from the selected values.

Pawel and Stansbury [131] reported measure- ments from 363 to 883 °K (90 to 610 °C) on an

electrolytic copper sample of 99.99 percent purity

using a vacuum-adiabatic calorimeter. Platinum

versus platinum-rhodium thermocouples were used

in the temperature measurements. After correcting

for variations that are dependent upon the heating

rate, a precision of ±0.25 percent is claimed. Except for the observation at the lowest temperature

(363 °K), where their reported value of heat capacity

is about 0.2 percent lower than the expected values,

the data at the higher temperatures tend to deviate

positively. Very little weight was given to the data

in selecting the best values in the region of 300 °K.

Senozan [134] reported making measurements on

a sample of 99.999 percent purity from 0.25 to 25 °K.

No numerical observations are reported. The values

of y and 0d(O) based on the measurements from

0.25 to 2 °K yield values of heat capacity that are from 0.4 to 0.8 percent higher than the final selected

values. In cooling the sample, the thermal contact

down to 78 °K was made using hydrogen exchange

gas and below this temperature using mechanical

heat switches. Germanium thermometers were used.

Below 1.1 °K the temperatures were based on the

magnetic susceptibility of 2Ce(N03 )3

• 3Mg(NO,3)2 • 24H2 O (CMN), between 1 and 4 °K on the 1958 4 He

scale [14], between 10 and 25 °K on a platinumresistance thermometer (temperature scale not

given), and between 4 and 10 °K on a carbon thermometer and an interpolation equation.

Rorer, Onn, and Meyer [96] made measurements

from 0.4 to 4.0 °K on a sample of 99.99 percent

purity. Cooling of the sample was done by a mechanical heat switch. The carbon-resistance thermometers used were calibrated on the 1958 4 He

scale [14], 1962 3 He scale [104], and the magnetic susceptibility temperatures of C^lSO-iL - (CH3 NH3)2S04-24H2 0 and 2Ce(N03 )3

• 3Mg(N03 )2

• 24H2 0. The value of y obtained is relatively high

and that of 0/;(O) is the lowest among a cluster of

recently published values and the calculated heat

capacities are on the average 3 percent higher than

the selected values.

Martin [78] reported new measurements from

3 to 30 °K on the same annealed copper sample

of 99.999 percent purity used earlier by Franck,

Manchester, and Martin [43]. Improvements on his

earlier calorimeter are reported. A germaniumresistance thermometer was used and the temperatures were based on the 1958 4 He scale [14], vapor

pressure of hydorgen [116], a gas thermometer

[44], and the NBS-1955 provisional scale [60, 46].

The value of y = 0.696 ± 0.005 mj °K~ 2 mol -1

re- ported earlier by Manchester [75, 43] was used to calculate 0d(T) from the experimental data. The

reported value of #d(0) = 345.6 ± 1.0 °K estimated

from the values of 6d(T), is the highest of those

published. Below 10 °K the smoothed values re- ported deviate on the average by —0.4 percent

from the selected values and above 10 °K within

±0.2 percent.

Clune and Green [24] reported two series of meas- urements from 2 to 4 °K on a sample of 99.999 percent purity. The carbon-resistance thermometer

used was calibrated on the 1958 4 He scale [14]. A

unique “adiabatic” technique was used in the

measurements. The calorimetric method involved,

at each selected temperature (req), the adjustment

of an auxiliary heater to compensate for the heat

leak of the sample through a small thermal link

to a heat sink maintained at 1.5 °K. The energy to heat the sample from Te(i — AT to Te(l + AT was then

determined, the AT being symmetrically displaced

about Tgq . The method allowed a number of meas- urements to be quickly repeated for each Tea . Cooling was achieved by a mechanical heat switch.

The method requires for maximum accuracy the

unbalances in the heat leak below and above Teq to be compensated and the heating time to be

shorter than the heat leak time constant but longer

than the thermal equilibrium time constant of the

sample and thermometer. Results of the two series

of measurements show that their precision is better

than the agreement in the values of y and 0d(O)

obtained. They are, however, typical of the values

published. The heat capacities from one set of

values of y and 6u(0) deviate positively by not more

than 0.3 percent from the selected values and those

from the other set deviate positively from 0.7 to 0.3 percent in the range 2 to 4 °K.

Osborne, Flotow, and Schreiner [86, 87] reported

measurements from 1 to 25 °K on an annealed

sample of 99.999 percent purity prepared by the

Argonne National Laboratory for distribution in

cooperation with the Calorimetry Conference. The

germanium-resistance thermometer used was

calibrated on the 1958 4 He [14] and 1962 3 He [104]

scales, vapor pressure of hydrogen, and a gas thermometer. A mechanical heat switch was used in cooling. The values of* y and 0/j(O) reported are

typical of those published. Below 2 °K the observed

values reported are lower, as much as 0.5 percent,

than the selected values and above 2 °K they are within ±0.3 percent. Osborne, Flotow, and Schreiner

[87] obtained a six-term polynomial equation in odd powers of T from 1 to 11 based on published

data and their new measurements and applicable

from 1 to 25 °K. The values of heat capacity from

the equation are within ±0.1 percent of the selected

values.

283-739 0- 68—3 11
Table 1. Sources of heat-capacity data on copper used in the analysis

Temper- Entropy at 298.15 °K Experimental method

range Purity of Electronic Debye 9 Year of heat specimen coefficient, y at 0 °K Refer- measure- Calo- Thermom- Temper- Cooling ences

merits J °K -

' mol -1 cal

U K 1 mol 1 rimeter eter ature scale of mj “K-z mol - ' design sample

°K Weight % X 10:l °K

1914 273-323 99.87 VI-I e Cu e PRT e [56] 1914 15-22 electrolytic VI-I Au vp-H2 . gas

e [67] PRT. gas 1915 14-90 electrolytic VI-I Au vp-H2 . gas [68] PRT. gas 1930 95-215 electrolytic VI-I Pb Pb. PRT. gas [41]

9 gas 1932 5-15 315 VI-I gas gas gas [129] 1933 253-773 “100" (74-

1

PRT ITS gas [15] 1933 201-389 99.5 (cold- GA-I PRT ITS gas [32] rolled) 1934 54-294 hard drawn VI-I Cu TC. vp-H2 . gas [74] wire vp-O'.. gas 1934 53-293 annealed VI-I Cu TC. vp-H2 . gas [74] wire vp-02 . gas 1935 298.6 electrolytic (Measurement was made at one temperature, 25.4 °C) VI-I TC ? gas [125. 126]

1936 1.2-19.6 99.9 743 335 VI-I phosphor- vp-4 He, gas [72] bronze. vp-H2 , constantan gas

1937 28-194 commercially VA-I TC, PRT ITS gas [33] pure (cold- rolled) 1937 293 99.95 (Measurement was made at one temperature, 20 °C) GI-I TC 9 gas [136] 1940 287-640 9 (Measurements were made at five temperatures) VA-I PRT 9 gas [132] 1941 82-273 99.92 VA-I PRT gas gas [5] 1941 15-300 99.96 (an- 33.31 7.961 VI-I Au-Ag TC, vp-H,. gas [51] nealed) vp-02 . gas 1952 1.8-4.

2

99.6 (poly- 750 340 VI-I Ge vp- 4 He gas [39. 18] crystalline) 1954 0.2-1 commercial 724 ±33 a VI-I MS MS. gas. [133] 99.9+ 1948 4 He ADMC

1955 1-5 99.999+ (an- 688 ±2 a 343.8 ±0.5 a VI-I C 194814 4 He gas [28] nealed) 1956 1.5-4.

2

99.999 (as re- 686 ±5 b 345.1 ±3 b VI-I C 1948ER 4 He MHS [93.113]

ceived) 1956 1. 5-4.2 99.9 (as re- 670 ±5 b 338.9 ±3 b VI-I C 1948ER 4 He MHS [93.113]

ceived) 1956 1. 5-4.2 99.9 (an- 670 ±5 b 338.9 ±3 b VI-I C 1948ER 4 He MHS [93.113] nealed) 1956 1. 5-4.2 99 (Cd 0.7%. 799 ±5 b - c 344.7 ±3 b VI-I C 1948ER J He MHS [93.113] Zn 0.5%)

1957 1.3-4.

2

99.95+ (an- 723 ±28 a 334.0 ±1.6 a VI-I C 1948 4 He MHS [91] nealed) 1957 1.8-4.

2

99.99+ 691 ±6 a 342 ±2 a VI-I C 1955E 4 He gas [55] 1959 4-300 99.96 (OFHC) 33.25 7.946 VA-C TC TC. liquid [100] vp- 4 He

vp-H2 . vp-N'» 1959 39-300 99.96 (OFHC) 33.45 7.995 VA-C TC TC. gas [100| vp- 4 He

vp-H2 . vp-N2 1959 1.2-4.

2

99.999 696 ±5 a 344 ±2 a VI-I C 1955E 4 He MHS [75. 43[ 1960 1. 8-4.2 single (No numerical data are given in the paper) VI-I C vp-4 He gas [118| crystal 1960 3-16 single (No numerical data are given in the paper) VI-I C gas gas [118] crystal 1960 80-673 9 (No numerical data are given in the paper) VA-C TC 9 gas [119] 1960 21-300 commercially VA-C Cu ITS gas [76] pure (cold- rolled) 1960 20-300 99.999 (an- 33.15 7.92 ±0.04 b VA-C Cu ITS gas [76] nealed) 1960 21-300 99.999 (cold- VA-C Cu ITS gas [76] worked)

1961 1.5-4.

5

“pure” (No numerical data are given in the paper) VI-I C vp4 He MHS [30] 1961 0.4- 1.5 99.999 682 ±1 1 a 327 ±22 a VI-I C SR-'He SHS [43| 1961 1. 2-4.2 99.999 VI-I C 1955E 4 He MHS [43] 1961 3-30 99.999 VA-C C 1958 4 He. cond [43] vp-H2 . gas, NBS-1955

12
Table 1. Sources of heat-capacity data on copper used in the analysis — Continued

Temper- Entropy at 298.15 °K Experimental method

range Purity of Electronic Debye 6 Year of heat specimen coefficient, y at 0 “K. Refer- measure- Calo- Thermom- Temper- Cooling ences ments J “K. 1 mol ' cal °K“‘ mol 1 rimeter eter ature scale of mj °K-2 mol -1 design sample

°K Weight % X 10‘ °K

1961 0.4-30 99.999 690 344 [43] 1962 16-90 99.999 (an- VA-C 11 PUT' NBS-1955 1

’ gas

c

‘ [127] 283-304 nealed) IPTS

1962 16-90 99.999 (cold- (No numerical data are given in the paper) VA-C PRT NBS-1955 gas [127] 283-304 worked) IPTS

1962 1-30 99.9999 721 338.9 VI-I C 1958 'He, gas [34, 35] vp-H2 1962 1-4.2 99.999 692 ±7 b 342.7 ±3 b VI-I C vp- 4 He MHS [113] 1963 0.11-1.07 99.999 (an- 702 342.9 VI-I C MS MHS, [84] nealed) SHS

1963 1. 2-4.5 99.999 (I) 697 ±7 b 345.1 ±1.4 b VI-I C 1958 4 He MHS [71] (annealed) 1963 1.2-4.

5

99.999 (II) 696 ±7 b 342.3 ±1.4 b VI-I C 1958 4 He MHS [71] (annealed) 1964 0.5- 1.5 99.999 (No numerical data are given in the paper) VI-I C SR-3 He SHS [128] 1964 0.13-4.2 99.999 695 343.4 VI-I C MS, MHS, [89] 1958 'He SHS

1964 2.3-19.7 99.999 704 344 VI-I Ge 1958 4 He, MHS [1,2] vp-H-2 1965 1.6-4.

2

99.999+ 698 ±2 a 342.3 ±3 b d VI-I C 1958 4 He MHS [63, 61, 62

1

1965 1.2-4.

2

99.999 (chill 695 ±l a 343.2 ±0.2 a VI-I C 1958 4 He MHS [31] cast) 1965 1.2-4.

2

999.999 (an- 698 ±2 a 343.2 ±0.4 a VI-I C 1958 4 He MHS [31] nealed) 1965 0.25-25 99.999 698 342 VI-I Ge MS, gas, [134]

1958 4 He, PRT (?) MHS

1965 0.4-4.

0

99.99 720 ±8 a 342 ±2 a VI-I C 1958 'He, MHS [96] 1962 'He. MS

1966 3-30 99.999 (an- 696 ±5 a 345.6 ±1.0 a VA-C Ge 1958 'He, circ [78] nealed) vp-H2 , gas, NBS-1955

1966 2-4 99.999 (an- 702 ±2 a 344.9 ±0.4 a VA-I C 1958 4 He MHS [24] nealed) 1966 2-4 99.999 (an- 696 ±2 a 344.1 ±0.4 a VA-I C 1958 4 He MHS [24] nealed) 1966 1.3-20 99.999 (chill 695 343.9 VI-I Ge 1958 'He, MHS [3] cast) vp-H2 , gas, NBS-1955

1966 1-25 99.999 (an- 694 344.5 VI-I Ge 1962 "He. MHS [86, 87] nealed) 1958 'He,

vp-H-2 ,

342.3 ±3 bd

gas

1966 1.6-4.2 99.999+ (an- 698 ±2 a VI-I Ge 1958 'He MHS [101] nealed

a These figures prefixed with the ± symbols have been interpreted from the authors’ description to indicate the precision of the values given.

b These figures prefixed with the ± symbols have been interpreted from the authors’ description to indicate the estimated uncertainties in the values

given.

c Not included in the analysis or plotted in figure 1.

d Isaacs [62] recalculated the experimental observations and found y = 0.698 ± 0.003 mj °K~2 mol-1 and 0o(O) = 342.2 ±0.8 °K.

e See section 2 for definitions of symbols and abbreviations used.

13
MILLI

JOULES

°K

2

mol

0.75

0.74

0.73

0.72

7

0.71

0.70

0.69

0.68

0.67

0.66

0.65

Figure 1

ELECTRONIC

COEFFICIENT OF

HEAT CAPACITY

r

39

72

DEBYE

CHARACTERISTIC

TEMPERATURE

345

133

34

96

39 340

93 , 93 , 34

284,24

61 , 31 , 62,134

7175 , 71 , 78,24

89 , 31 ,3

87

113 55

43

28

93

SELECTED VALUES

Y = 0.695 ± 0.005 mJ °K" 2 mol

-1 ®D (0) = 344.5 ± 1.5 °K

72

91

93,93

°K

335

43

325

Comparison of the reported values of electronic coefficients of heat capacity, y, and Debye characteristic temperatures, 0D(O). of copper.

14
15

Figure

2a.

Deviations

of

the

heat-capacity

data

of

the

literature

on

copper

from

the

selected

values

in

the

range

30

to

300

°K.

The

estimated

limit

of

accuracy

and

the

temperature

derivative,

dC/dT,

inJ

°K~ 2

mol~'

of

the

selected

values.
UJ

tr3

I-<

trUJ

Q.

N0I1VIA3Q ±N3Dd3d

~e

©•u

©

V.3u

-©e

£

©

-C

~ae

a

oc>«5

V

§Pa

©

-e

Q.

Q.©u

e

©

a

“T3

o

a

g,a

-QW

OSo

16
5

4

3

2

I

0

-I

2

3

4

5

TEMPER AT URE,°K

: 2c. 1. Deviations of the heat-capacity data of the literature on copper from the selected values in the range

0 to 5 °K and the estimated limit of accuracy of the selected values. (Set I)

17
5

4

3

2

I

0

-I

2

3

4

5

TEMPERATURE, °K

2c. 2. Deviations of the heat-capacity data of the literature on copper from the selected values in the range

0 to 5 °K and the estimated limit of accuracy of the selected values. (Set 2)

18
0.8

0LU

013

<

CCLU

CL

LU

(-

^ o

o

^ro

000

1 N0I1VIA3Q ±N30d3d

o

283-739 0-68—4 19

PlGURE

2d.

Comparison

of

some

recently

reported

precise

heat-capacity

data

on

copper

with

the

selected

values

in

the

range

0

to

30
Table 2. Thermodynamic Functions for Copper

Gram atomic wt.=63.5400, T °K=273. 15+r °C, 1 ca!=4.1840y

T c?> If o 11 o lit no (.m-HDIT 5? -(G?-H°0 )IT

°K Jldeg-mol J/mol Jldeg-mol Jldeg-mol Jlmol Jldeg-mol

1.00 0.000743 0.000359 0.000359 0.000711 0.000351 0.000351

2.00 0.00177 0.00158 0.000790 0.00152 0.00145 0.000727

3.00 0.00337 0.00409 0.00136 0.00251 0.00345 0.001 15

4.00 0.00582 0.00860 0.00215 0.00379 0.00657 0.00164

5.00 0.00943 0.0161 0.00322 0.00546 0.01 12 0.00223

6.00 0.0145 0.0279 0.00466 0.00760 0.0176 0.00294

7.00 0.0213 0.0456 0.00652 0.0103 0.0265 0.00379

8.00 0.0301 0.0712 0.00889 0.0137 0.0385 0.00481

9.00 0.0414 0.107 0.01 19 0.0179 0.0542 0.00602

10.00 0.0555 0.155 0.0155 0.0229 0.0746 0.00746

11.00 0.0727 0.219 0.0199 0.0290 0.100 0.00913

12.00 0.0936 0.302 0.0251 0.0362 0.133 0.0111

13.00 0.1 19 0.407 0.0313 0.0447 0.173 0.0133

14.00 0.149 0.541 0.0386 0.0545 0.223 0.0159

15.00 0.184 0.706 0.0471 0.0660 0.283 0.0189

16.00 0.225 0.910 0.0569 0.0791 0.355 0.0222

17.00 0.273 1.158 0.0681 0.0941 0.442 0.0260

18.00 0.328 1.458 0.0810 0.111 0.544 0.0302

19.00 0.390 1.816 0.0956 0.131 0.665 0.0350

20.00 0.462 2.242 0.1 12 0.152 0.806 0.0403

25.00 0.963 5.703 0.228 0.305 1.917 0.0767

30.00 1.693 12.25 0.408 0.541 3.995 0.133

35.00 2.638 22.99 0.657 0.871 7.487 0.214

40.00 3.740 38.89 0.972 1.294 12.86 0.322

45.00 4.928 60.54 1.345 1.802 20.57 0.457

50.00 6.154 88.23 1.765 2.385 31.01 0.620

55.00 7.385 122.1 2.220 3.029 44.52 0.809

60.00 8.595 162.0 2.701 3.724 61.38 1.023

65.00 9.759 208.0 3.199 4.458 81.82 1.259

70.00 10.86 259.5 3.708 5.222 106.0 1.514

75.00 1 1.89 316.4 4.219 6.007 134.1 1.788

80.00 12.85 378.4 4.729 6.806 166.1 2.076

85.00 13.74 444.9 5.234 7.612 202.1 2.378

90.00 14.56 515.7 5.730 8.421 242.2 2.691

95.00 15.31 590.4 6.215 9.229 286.4 3.014

100.00 16.01 668.7 6.687 10.03 334.5 3.345

105.00 16.64 750.3 7.146 10.83 386.7 3.683

110.00 17.22 835.0 7.591 1 1.62 442.8 4.025

1 15.00 17.76 922.5 8.021 12.39 502.8 4.372

120.00 18.25 1013. 8.438 13.16 566.7 4.723

125.00 18.70 1 105. 8.839 13.91 634.4 5.075

130.00 19.12 1 199. 9.227 14.66 705.8 5.429

135.00 19.51 1296. 9.601 15.39 780.9 5.785

140.00 19.87 1395. 9.961 16.10 859.7 6.140

145.00 20.20 1495. 10.31 16.80 941.9 6.496

150.00 20.51 1597. 10.64 17.49 1028. 6.851

155.00 20.79 1700. 10.97 18.17 1 1 17. 7.206

160.00 21.05 1804. 11.28 18.84 1209. 7.559

165.00 21.30 1910. 1 1.58 19.49 1305. 7.910

170.00 21.53 2017. 11.87 20.13 1404. 8.260

20
Table 2. Thermodynamic Functions for Copper — Continued

Gram atomic wt.=63.5400, T °K=273. 1 5-H °C, 1 cal=4. 1 8407

T r° 11 o I/O ri TFi o ( H°-H°)/T s° -(G°t-h°) -(G°t -H°0 )/T

°K J/deg-mol J\mol J\deg-mol J/deg-mol Jlmol J/deg-mol

175.00 21.74 2125. 12.15 20.75 1506. 8.608

180.00 21.94 2235. 12.42 21.37 1612. 8.954

185.00 22.13 2345. 12.68 21.97 1720. 9.298

190.00 22.31 2456. 12.93 22.57 1831. 9.639

195.00 22.47 2568. 13.17 23.15 1946. 9.978

200.00 22.63 2681. 13.40 23.72 2063. 10.31

205.00 22.77 2794. 13.63 24.28 2183. 10.65

210.00 22.91 2908. 13.85 24.83 2306. 10.98

215.00 23.04 3023. 14.06 25.37 2431. 11.31

220.00 23.17 3139. 14.27 25.90 2559. 11.63

225.00 23.28 3255. 14.47 26.42 2690. 1 1.96

230.00 23.39 3372. 14.66 26.94 2824. 12.28

235.00 23.50 3489. 14.85 27.44 2960. 12.59

240.00 23.60 3607. 15.03 27.94 3098. 12.91

245.00 23.69 3725. 15.20 28.42 3239. 13.22

250.00 23.78 3844. 15.37 28.90 3382. 13.53

255.00 23.86 3963. 15.54 29.37 3528. 13.83

260.00 23.94 4082. 15.70 29.84 3676. 14.14

265.00 24.02 4202. 15.86 30.30 3826. 14.44

270.00 24.09 4322. 16.01 30.75 3979. 14.74

273.15 24.13 4398. 16.10 31.02 4076. 14.92

275.00 24.15 4443. 16.16 31.19 4134. 15.03

280.00 24.22 4564. 16.30 31.62 4291. 15.32

285.00 24.28 4685. 16.44 32.05 4450. 15.61

290.00 24.34 4807. 16.57 32.48 4611. 15.90

295.00 24.40 4929. 16.71 32.89 4775. 16.19

298.15 24.44 5005. 16.79 33.15 4879. 16.36

300.00 24.46 5051. 16.84 33.30 4940. 16.47

Ho is the enthalpy of the solid at 0 °K and 1 atm pressure.

4.2. Silver (Ag, 107.870), Assessment of the

Data Sources

There seems to have been relatively little interest

in the heat capacity of silver prior to 1952. The

final selected values of heat capacity above 30 °K

are based on those reported by Griffiths and Griffiths

[120, 121, 122, 123]; Eucken, Clusius, and Woitinek

[40]; Bronson and Wilson [16]; and Meads, Forsythe,

and Giauque [81]. Between 5 and 30 °K, the data

reported by Martin [78] and by Ahlers [4] were

given the most weight. Below 5 °K most of the

published data were used in obtaining the selected

values. The data of Keesom and Kok [69, 70] and

Ramanathan and Srinivasan [91] were not given

any weight.

Griffiths and Griffiths [120, 121, 122, 123] re- ported six measurements in the interval from 158 to 371 °K on a sample of 99.99 percent purity. A gasfilled isothermal-shield type calorimeter was used

in conjunction with a platinum-resistance thermometer calibrated in close accordance with the present

definition of the IPTS [106]. The values reported

at 158 and 187 °K are more than 1 percent higher

than the selected values. The other values at the

higher temperatures are within ±0.2 percent of

the selected and expected values.

Eucken, Clusius, and Woitinek [40] measured a sample of 99.99 percent purity in the range 11 to 205 °K by means of an isothermal-shield calorimeter. The temperatures were determined by means

of a Pb-resistance thermometer. Above 20 °K their

values are generally within ± 1 percent of the

selected values, but below 20 °K they deviate

positively as much as 8 percent.

Mendelssohn and Closs [129] reported measure- ments from 2 to 20 °K. The observations are presented graphically only. The average Debye

characteristic temperature given as 210 °K is expected to be low since the electronic contribution was not taken into account.

Keesom and Kok reported two sets of measure- ments on samples of equal purity (99.95 -P percent)

in the ranges 1.4 to 20.3 °K (1932) [69] and 1./ to

21
4.9 (1934) [70]. In the first set helium exchange

gas was used for cooling and in the second a mechanical heat switch was used. The two results

below about 5 °K scatter more than 25 percent.

The precision of the data above 5 °K is better, but

the values are as much as 9 percent higher than the

selected values. No weight was given to their data.

Bronson and Wilson [16] used a non-vacuum type

adiabatic calorimeter to determine the heat capacity

of a sample of 99.98+ percent purity from —80 to + 120 °C (193 to 393 °K). The impurities were

Cu: 0.0095 and Fe: 0.0018 percent. The temperature of the specimen was determined indirectly by

measuring the temperature of the relatively massive

adiabatic shield by means of a platinum-resistance

thermometer when thermocouples indicated the

specimen and the shield to be at the same temperature. Smoothed values were reported. The

values obtained from a smooth curve through the

observed values and those calculated from an

equation fitted to the observed values are shown to agree within 0.005 percent. Their values are consistently lower than the selected values, the maximum deviation being— 0.4 percent.

Moser [83] made measurements on a sample of

99.99 percent purity from 52 to 652 °C (325 to 925 °K)

by means of a vacuum-adiabatic calorimeter operated by a continuous heating method. The

temperatures were measured by means of silverconstantan thermocouples calibrated against a platinum-resistance thermometer. These higher

temperature values of heat capacity were used

primarily to decide on the values in the region of

300 °K and are, therefore, not shown in figure 4a.

Moser’s values tended to be relatively low in the

range up to 450 °K.

Meads, Forsythe, and Giauque [81] made meas- urements on a single crystal of 99.99 percent

purity. The sample was melted and crystallized

in an atmosphere of nitrogen. Measurements made

in the years 1931 to 1939 are reported. The initial series of measurements made in 1931 soon after

the sample preparation was found to disagree in

the range 15 to 25 °K with measurements made in

1935 and 1939. The sample was considered to have

changed with time, consequently the material was

remelted and recrystallized in vacuum. Measurements made soon after on this material agreed with

the 1935 and 1939 measurements. No further

explanation is given for the discrepancy in the 1931

measurements. Their values above 50 °K are generally higher than the selected values, with the

maximum deviation of about +1.2 percent at 290

°K. Between 30 and 50 °K their values are mostly

lower (maximum deviation being —1 percent) and

below 30 °K mostly higher (maximum deviation

being +7 percent) than the selected values.

Mustajoki [130] reported measurements on a sample of 99.96 percent purity from 339 to 758 °K

(66 to 485 °C) using a vacuum-adiabatic continuousheating method. Silver-constantan thermocouples were used for the temperature measurements. Up

to the temperature of interest (450 °K), the observations are about 0.5 percent lower than the ex- pected values. The data were used mainly to select

the best values of heat capacity in the region of

300 °K.

Keesom and Pearlman [65, 66] made measure- ments between 1.2 and 4.2 °K on a single-crystal

sample of 99.999 percent purity. The first paper

[65] showed anomalies that were subsequently

attributed to deviations of the 1948 4 He temperature scale [112, 98] from the thermodynamic scale.

In the second paper [66] the authors showed that

when the 1948 4He scale was adjusted to conform

more nearly to the thermodynamic scale the

anomalies disappeared [38]. The values of y and

0D( 0) used in the analysis were from the latter

publication. The value of y is the highest among a cluster of values, while the value of #d( 0) is the

lowest among a cluster of values. Their values of

heat capacity are about 1.5 percent higher than the

selected values.

Three sets of measurements have been reported

by Hoare, Matthews, and Walling [57]; Hoare and

Yates [58]; and Dixon, Hoare, Holden, and Moody

[31]. No numerical values were given for silver in

the first paper [57]. In the second paper [58] y and

6G(0) obtained from measurements between 2 and

4.2 °K were reported, and the values of heat capacity

calculated from them deviate negatively from — 0.2

percent at 2 °K to —4.2 percent at 4.2 °K. In the

third paper [31] the results were reported on two

series of measurements on a spectrographically

pure sample. The 1958 4 He scale [14] was used.

The results of y and 6G(0) reported for the two series

of measurements do not quite overlap within the

precision figures given. The values of heat capacity

calculated from the y and 0d(O) agree with each

other within 0.7 percent and are within about 0.6

percent of the selected values.

Rayne [133] reported measurements on a sample

of 99.9+ percent purity from 0.2 to 1 °K. (See the

section on copper under reference [133] for a brief

description of the experimental method used.)

No numerical observations are given in the paper.

The lattice contribution was considered negligible

and the electronic coefficient of the heat capacity,

y, based on the observations between 0.2 and 0.65

°K is given. The value of y reported (0.669 ±0.063

mj °K-2 mol-1

) is higher than most of the recently

published values. The values of electronic heat

capacity based on the above value of y are higher

than the selected values based on both electronic

and lattice contributions below 0.4 °K but lower

above this temperature. This is to be expected since

the lattice contribution is significant at these temperatures. (The lattice contribution in the present

analysis has been found to be about 1 percent at 0.2 °K.)

Corak, Garfunkel, Satterthwaite, and Wexler

[28] made measurements from 1 to 5 °K on an annealed sample of 99.999+ percent purity. Cooling was done by helium exchange gas. The tem22
peratures were determined by means of a carbonresistance thermometer calibrated on the 1948

4 He scale [112, 98] and adjusted for the deviations

of the scale from the thermodynamic scale [38, 9],

Their value of y is the lowest of those published

and that of 0/40) is within a cluster of values published. Their values of heat capacity are in general

lower than the selected values, 5 percent lower at

1 °K and converging at 5 °K.

Rayne [94] measured from 1.5 to 4.2 °K a sample

of 99.99 percent purity using a mechanical heat

switch for cooling. A carbon-resistance thermometer was used that was calibrated on the 1948 4 He scale

[112, 98] with adjustments made for deviations from

the thermodynamic scale [38]. The value of y obtained is low but that of 0/4

0

) is in good agreement

with other published values. His values of heat

capacity are about 1 to 4 percent lower than the

selected values.

Ramanathan and Srinivasan [91] made measure- ments on an annealed sample of purity higher than

99.7 percent from 1.3 to 4.2 °K. A mechanical heat

switch was used for cooling. The values of y and

0/40) reported are relatively low. The 1948 4 He

scale [112, 98] was used. No weight was given to the measurements in the final evaluation of the best

values of heat capacity.

Filby and Martin [42] made three series of meas- urements from 0.4 to 1.5 °K on an annealed 99.9999

percent pure sample. The temperatures were based on 3 He vapor pressure reported by Sydoriak and

Roberts [107]. A superconducting Pb-wire heat

switch was used for cooling. The three values of y

obtained are among a cluster of recently published

values; one of the values of 0/40) lies within a cluster

of published values but the other two are located

outside the cluster. The values of heat capacity

from y = 0.652 mj °K~2 mol-1 and 0/40) = 226.5 °K

range from +0.2 to —0.1 percent of the selected

values. The values of heat capacity from the other

two sets of y and 0/40) are on the average about 1 percent lower than the selected values.

Another series of measurements was reported

by Martin [78] using a different calorimeter in the

range 3 to 30 °K on a sample of the same purity.

Germanium-resistance thermometers were used

that had been calibrated on the 1958 4 He scale [14], on the vapor pressure of hydrogen [116], a gas

thermometer [44], and the NBS-1955 provisional

scale [60, 46]. The cooling was achieved by circulating helium between the heat sink and the sample

through a separate small diameter tubing and subsequently removing the helium by pumping. The

average value of y reported earlier by Filby and

Martin [42] was used to calculate 6o( T) from the

experimental data. The reported value of 0/40),

estimated from the values of 0d(T), is in a cluster of

recently published values and is in close agreement

with the value reported earlier by Filby and Martin

[42] in the same cluster. Martin’s [78] values of

heat capacity are well within 0.8 percent of the

selected values.

DuChatenier and DeNobel [34, 35] reported

measurements from 1 to 30 °K on a polycrystalline

sample of 99.9999 percent purity. The only detectable impurities were 0.1 to 0.2 ppm of Cu, Pb, and

Bi. The temperatures were based on the 1958 4 He

scale [14] and the hydrogen vapor pressure work of

Hoge and Arnold [59]. Helium exchange gas was

used in cooling. The relatively high values of y and

0/40) reported are consistent with possible heat of

desorption effect of helium at the lower temperatures. Their smoothed values of heat capacity show

systematic “sinusoidal” deviations of + 3.5 to— 2.5

percent from the selected values. Similar deviations have been found with their data on copper

and gold [34, 35, 36].

Green and Culbert [53], Green and Valladares

[54], and Green [52], using the same or essentially

the same apparatus, have reported within a period

of little over a year four sets of measurements

between 2 and 4 °K on polycrystalline annealed

samples of 99.9999 percent purity. The sample

indicated as 99.9999 (II) by Green [52] was borrowed

from Isaacs and Massalski [62, 79] and was also

99.9999+ percent pure but from a different source

of manufacture than the other three samples [52,

53, 54]. The 1958 4 He scale [14] was used in the four

sets of measurements. (See the section on copper

for a description of the unique “adiabatic” technique used by Green et al. [24, 52, 53, 54, 115].)

Among the four reported values of 0/40) the maximum deviation is 0.4° in about 225 °K. The maximum deviation in the electronic heat-capacity

coefficient y is 0.008 in about 0.650 mj °K-2 mol-1

. Isaacs and Massalski [61, 79, 101] reported on sample 99.9999(11), y = 0.645±0.007 mj °K~2 mol-1 and 0/40) = 228.9 ±2.0 °K, based on the equation

C = yT + AT3 + BTh. The values of y and 0/40) obtained by Green [52] on his sample (99.9999(1)) are 0.652 mj °K-2 mol-1 and 225.4 °K, respectively, and

on the sample of Isaacs and Massalski [61, 79]

(99.9999(H)) are 0.651 mj °K“2 mob1 and 225.7 °K,

respectively. These results indicate that the two

samples, although they are from different sources

of manufacture, are pure enough that the heat

capacities are essentially the same within the capability of the experimental method. The values of

heat capacity obtained by Green et al. [52, 53, 54] are all within 0.7 percent of the selected values,

three sets being within 0.5 percent.

Massalski and Isaacs [61, 79, 101] made measure- ments between 1.6 and 4.2 °K on a polycrystalline

sample of 99.9999+ purity using a calorimeter with

a mechanical heat switch. A carbon-resistance

thermometer was used that was calibrated on the

1958 4 He scale [14]. Isaacs [61] showed that a heatcapacity equation of the form:

QT=y+ AT2 + BT4

represented his data on silver better. 1 he coefficient for the T

4 term obtained by the method of

23
least squares fitting of the observations to the equation is 0.00094 ± 0.00008 mj °K-6 mol-1 [61].

In a recent private communication, Isaacs [62]

showed a recalculation of the earlier data [61, 63,

79]. The equation obtained for silver is C/T= (6.45 ± 0.06) x 10~4 + (1.677 ± 0.006) x 10-4 T2

J °K“2 mol- 1

,

which no longer contains the T

A term. The values

of heat capacity calculated from the new equation

deviate on the average about —0.5 percent from the

selected values while the earlier values [61, 63]

deviate as much as +4.5 percent.

Shinozaki and Arrott [105] reported measure- ments between 2 and 4 °K on a silver sample for

which no information on purity or heat treatment

is given. Carbon-resistance thermometers calibrated against the 1958 4 He scale [14] were used.

A mechanical heat switch was used for cooling.

The heat capacities calculated using their reported

values of y and $d(0) are about 1 percent higher

than, the selected values.

Ahlers [4] reported measurements on a silver

sample of 99.9999 percent purity from 1.4 to 26 °K.

The germanium-resistance thermometer used was

calibrated against the 1958 4 He scale [14], another

germanium thermometer that was calibrated against

a gas thermometer [87], vapor pressure of H2 [116, 59], and the NBS-1955 scale [60, 46]. Contrary to the observations of Isaacs [61], the results

below 6 °K were shown to be representable, within

the root-mean-square deviation of 0.15 percent, by

C = AT+ BT3 form of equation. The Th term was

not needed. Ahler’s [4] values of heat capacity are very close to the selected values, on the average

within —0.2 percent.

24
Table 3. Sources of heat-capacity data on silver used in the analysis

Temper- Entropy at 298.15 °K Experimental method

ature range Purity of Electronic Debye 6 Year of heat specimen coefficient, y at 0 °K Refer- measure- Calo- Thermom- Temper- Cooling ences ments J °K 1 mol 1 cal 1 mol" 1 rimeter eter ature scale of mj °K 2 mol" 1 design sample

°K Weight % X HP °K

1914 158-371 99.99 (Measu 'ements were ma de at six temperatures) (T-l ' PRT 1 IPTS ‘‘ gas [120. 121.

122, 123|

1931 11-205 99.99 210 42.51 10.16 VI-1 Pb Pb. gas [40| vp-H,.

vp-O,.

gas, Pt

1932 2-20 ? 210 VI-I gas gas gas [129| 1932 1.4-20.3 99.95+ VI-I phosphor- vp-He, gas [69

1

bronze. vp-H,. constantan gas

1934 1. 7-4.9 99.95+ VI-I phosphor- vp-He, MHS [70| bronze, constantan

gas

1936 193-393 99.98+ GA-I TC. PRT ITS gas [16| 1936 325-925 99.99 VA-C TC ITS [83] 1941 15-298 99.99 (single 42.70 10.21 VI-I Au-Ag TC, gas [81

1

crystal) vp-H>. vp-02 . gas

1952 1. 2-4.2 99.999 (single 660 225 VI-I 1948 ‘He [65.661

crystal) 1955K 4 He

1953 10-20 spectroscopi- (No numerical data are given in the paper) VI-I PRT, con- vp-H-. gas [57| tally stand- ardized

stantan

1954 0.2-1 99.9+ 669 ± 63 " VI-I MS MS. gas. [133| 1948 4 He AD-MC

1955 1-5 99.98 (an- 610 ±5 " 225.3 ±0.2" VI-I C 1948W 'He gas [28| nealed) 1956 1.5-4.

2

99.99 613 ±5 a 226.2 ±0.3" VI-I C 1948R 4 He MHS [94| 1957 1. 3-4.2 99.7+ (an- 615 ±10 a 219.4 ±0.5" VI-I C 1948 ‘He MHS [91| nealed) 1957 2-4.2 spectroscopi- 690 ±30 “ 231 ±1 " VI-1 c 1955L 4 He cond [58| cally stand- ardized

1962 0.4- 1.5 99.9999 (an- 652 ±5 a 226.5 ±2.3" VI-I c SR‘He SHS [42| nealed) 638 ±7 a (Run 1) 223.4 ±3.2"

(Run 2) 649 ±8 a 229.0 ±4.5"

(Run 3) 1962 1-30 99.9999 682 226.2 VI-I c 1958 ‘He. gas [34. 35] vp- H > 1965 2-4 99.9999 (an- 646 ±5 a 225.5 ±0.5" VA-1 c 1958 ‘He MHS [53] nealed) 1965 1.2-4.

2

spectroscopi- 647 ±2 " 226.2 ±0.1 " VI-I c 1958 4 He MHS [31| cally pure 653 ±4 a (Run 1) 226.5 ±0.2"

(Run 2) 1965 1. 6-4.2 99.9999 + 645 ±7 " c 228.9 ±2.0"' c - d VI-I c 1958 ‘He MHS 179.61. 101.62|

1966 3-30 99.9999 (an- 646 ±4 a 226.6 ±1.0" VA-C Ge 1958 4 He, cond [78| nealed) vp-H,.

gas, NBS-1955

1966 2-4 99.9999 (an- 654 ±2 a 225.8 ±0.1" VA-I c 1958 ‘He MHS [54] nealed) 1966 2-4 99.9999 (I) 652 225.4 VA-I c 1958 ‘He MHS [52| 1966 2-4 99.9999 (II) 651 225.7 VA-I c 1958 4 He MHS [52| 1966 2-4 y 656 225.3 VI-I c 1958 4 He MHS [105] 1967 1.4-26 99.9999 645 226.0 VI-I Ge 1958 4 He, MHS [4] vp-H,, NBS-1955

gas

11 These figures prefixed with the ± symbols have been interpreted from the authors' description to indicate the precision of the values given. ''These figures prefixed with the ± symbols have been interpreted from the authors’ description to indicate the estimated uncertainties in the values

given.

I From the equation of the form: C = yT + AT' + BT’. where A = 127r‘R/5[f)/)((j)]'‘.

II Isaacs [62] recalculated the experimental observations and found silver to fit C=~yT + AT:' equation and y = 0.645 ± 0.006 mj K - mol ' and

0„(O) = 226.3 ±0.3 °K.

0 See section 2 for definitions of symbols and abbreviations used. 25
MILLI

JOULES

°K“

2

mol"

Figure 3. Comparison of the reported values of electronic coefficients of heat capacity, y, and Debye characteristic temperatures, 0D(O), of silver.

26
0.4

(±P/DP)‘AllDVdVD ±V3H JO 3AI±VAId3d 3Un±Vd 3dl/\l31

i'<"> oddco _

o

o

rO

o

inCO

o

o

CO

o

m

o

o

o

m

o

co o CO

I

° .. UJ

crZ>

t-<

crLd

CL5

UJIN0I1VIA3Q !N33d3d

O

27

Figure

4a.

Deviations

of

the

heat-capacity

data

of

the

literature

on

silver

from

the

selected

values

in

the

range

30

to

300

The

estimated

limit

of

accuracy

and

the

temperature

derivative,

dC/dT,

inJ

°K~

2

mol~

lof

the

selected

values.
o

UJ

cc3

I-<

ccLU

CL

UJ

IN0I1VIA3Q !N30d3d

28

f

I*’ 1

'RE

4b.

Deviations

of

the

heat-capacity

data

of

the

literature

on

silver

from

the

selected

values

in

the

range

0

to

30

°K

and

the

estimated

limit

of

accuracy

of

the

selected

values.
5

4

3

2

I

0

-I

-2

-3

4

5

TEMPERATURE, °K

4c. Deviations of the heat-capacity data of the literature on silver from the selected values in the range 0 to 5 °K and the estimated limit of accuracy of the selected values.

29
Table 4. Thermodynamic Functions for Silver

Gram atomic wt.= 107.8700, T °K=273. 15+f °C, 1 cal=4. 1840J

T r°p

II o 1J o tl T

tl o (H°-H°)IT S° -(G°-H°)IT

°K J/deg-moI Jlmol J/deg-mol Jldeg-mol Jlmol Jldeg-mol

1.00 0.000818 0.000367 0.000367 0.000706 0.000339 0.000339

2.00 0.00265 0.00197 0.000987 0.00175 0.00152 0.000762

3.00 0.00650 0.00633 0.00211 0.00347 0.00406 0.00135

4.00 0.0134 0.0160 0.00399 0.00619 0.00879 0.00220

5.00 0.0243 0.0344 0.00689 0.0103 0.0169 0.00338

6.00 0.0403 0.0663 0.0110 0.0160 0.0299 0.00498

7.00 0.0626 0.117 0.0167 0.0238 0.0496 0.00709

8.00 0.0927 0.194 0.0243 0.0341 0.0783 0.00979

9.00 0.132 0.306 0.0340 0.0472 0.1 19 0.0132

10.00 0.183 0.462 0.0462 0.0636 0.174 0.0174

11.00 0.247 0.676 0.0614 0.0839 0.247 0.0225

12.00 0.325 0.961 0.0801 0.109 0.343 0.0286

13.00 0.421 1.332 0.102 0.138 0.466 0.0359

14.00 0.535 1.809 0.129 0.174 0.622 0.0444

15.00 0.670 2.409 0.161 0.215 0.815 0.0544

16.00 0.826 3.155 0.197 0.263 1.054 0.0659

17.00 1.002 4.067 0.239 0.318 1.344 0.0790

18.00 1.199 5.166 0.287 0.381 1.693 0.0940

19.00 1.414 6.471 0.341 0.452 2.109 0.1 1

1

20.00 1.647 8.001 0.400 0.530 2.599 0.130

25.00 3.066 19.62 0.785 1.043 6.446 0.258

30.00 4.774 39.14 1.305 1.750 13.35 0.445

35.00 6.612 67.58 1.931 2.623 24.22 0.692

40.00 8.419 105.2 2.630 3.625 39.79 0.995

45.00 10.1

1

151.6 3.368 4.715 60.61 1.347

50.00 11.66 206.1 4.121 5.862 87.04 1.741

55.00 13.04 267.9 4.871 7.040 119.3 2.169

60.00 14.27 336.2 5.604 8.228 157.5 2.624

65.00 15.35 410.4 6.313 9.414 201.6 3.101

70.00 16.30 489.5 6.993 10.59 251.6 3.594

75.00 17.14 573.2 7.642 1 1.74 307.4 4.099

80.00 17.87 660.7 8.259 12.87 368.9 4.612

85.00 18.53 751.8 8.844 13.97 436.1 5.130

90.00 19.11 845.9 9.399 15.05 508.6 5.652

95.00 19.63 942.8 9.924 16.10 586.5 6.174

100.00 20.10 1042. 10.42 17.12 669.6 6.696

105.00 20.52 1144. 10.89 18.1

1

757.7 7.216

110.00 20.89 1247. 1 1.34 19.07 850.6 7.733

115.00 21.23 1353. 1 1.76 20.01 948.3 8.246

120.00 21.54 1460. 12.16 20.92 1051. 8.755

125.00 21.82 1568. 12.54 21.80 1157. 9.260

130.00 22.07 1678. 12.91 22.66 1269. 9.759

135.00 22.31 1789. 13.25 23.50 1384. 10.25

140.00 22.52 1901. 13.58 24.32 1504. 10.74

145.00 22.72 2014. 13.89 25.1

1

1627. 1 1.22

150.00 22.90 2128. 14.19 25.88 1755. 1 1.70

155.00 23.07 2243. 14.47 26.64 1886. 12.17

160.00 23.22 2358. 14.74 27.37 2021. 12.63

165.00 23.37 2475. 15.00 28.09 2160. 13.09

170.00 23.50 2592. 15.25 28.79 2302. 13.54

30
Table 4. Thermodynamic Functions for Silver — Continued

Gram atomic wt.= 107.8700, T °K=273.

1

5+t °C, 1 cal=4. 1 8407

T c°c p

LJO no n r n o (H°t -H°0 )IT 5° -(G°-H°

)

-(G°t -H°0 )IT

°K J/deg-mol J/mol J/deg-mol Jldeg-mol Jlmol J/deg-mol

175.00 23.63 2710. 15.49 29.47 2448. 13.99

180.00 23.75 2828. 15.71 30.14 2597. 14.43

185.00 23.86 2947. 15.93 30.79 2749. 14.86

190.00 23.96 3067. 16.14 31.43 2904. 15.29

195.00 24.06 3187. 16.34 32.05 3063. 15.71

200.00 24.16 3308. 16.54 32.66 3225. 16.12

205.00 24.24 3429. 16.72 33.26 3390. 16.54

210.00 24.33 3550. 16.90 33.85 3558. 16.94

215.00 24.41 3672. 17.08 34.42 3728. 17.34

220.00 24.49 3794. 17.25 34.98 3902. 17.74

225.00 24.56 3917. 17.41 35.53 4078. 18.12

230.00 24.63 4040. 17.56 36.07 4257. 18.51

235.00 24.69 4163. 17.71 36.60 4439. 18.89

240.00 24.76 4287. 17.86 37.12 4623. 19.26

245.00 24.82 4411. 18.00 37.63 4810. 19.63

250.00 24.88 4535. 18.14 38.14 4999. 20.00

255.00 24.93 4659. 18.27 38.63 5191. 20.36

260.00 24.99 4784. 18.40 39.1

1

5386. 20.71

265.00 25.04 4909. 18.53 39.59 5582. 21.07

270.00 25.09 5035. 18.65 40.06 5782. 21.41

273.15 25.12 5114. 18.72 40.35 5908. 21.63

275.00 25.14 5160. 18.76 40.52 5983. 21.76

280.00 25.19 5286. 18.88 40.97 6187. 22.10

285.00 25.24 5412. 18.99 41.42 6393. 22.43

290.00 25.28 5538. 19.10 41.86 6601. 22.76

295.00 25.32 5665. 19.20 42.29 6811. 23.09

298.15 25.35 5745. 19.27 42.56 6945. 23.29

300.00 25.37 5792. 19.31 42.72 7024. 23.41

is the enthalpy of the solid at 0 °K and 1 atm pressure.

4.3. Cold (Au, 196.967), Assessment of the

Data Sources

Since the measurements by Clusius and Harteck [25] in 1928, about a quarter century elapsed

before Geballe and Giauque [48] made the next

study on gold in 1952. Since 1952, however, many

measurements have been reported, in particular

below 20 °K.

The final selected values of heat capacity between

30 and 300 °K were based largely on the data re- ported by Geballe and Giauque [48] and by Franzosini and Clusius [45]. The earber measurements of

Clusius and Harteck [25] were given very little weight. The average deviation from the selected

values of the data reported by Geballe and Giauque

[48] and by Franzosini and Clusius [45] is about 0.2

percent, while the average deviation of the data

reported by Clusius and Harteck [25] is about 1 percent.

Between 5 and 30 °K most weight was given to the data reported by Martin [78], the average deviation from the final selected values being less than

0.1 percent.

The equation of the form:

C = yT+AT3 + BT3

is a better representation of the heat-capacity data

for gold below 5 °K than the form C — yT + AT3

. Most weight was given to the values of heat capacity

corresponding to the three coefficients for the

equation reported by Isaacs [101] and by Will and

Green [115] and to those corresponding to the two

coefficients for the equation of the form:

C^yT+ AT3

reported by Martin [77, 78] for the measurements

between 0.4 and 1.5 °K. Very little weight was given

to papers in which the data between 1 and 5 °K

31
were fitted to the two-term equation. The values

of heat capacity calculated using the y and 0/>(O) obtained with the two-term equation deviate from

the selected values “parabolically”. In the discussions dealing with each data source, percent deviations are given for the ends of the temperature

range of measurements and at the “trough” of

the deviation.

Clusius and Harteck [25] reported measurements

between 15 and 212 °K on a sample described as “Feingold der Deutschen Goldscheideanstalt.”

Later Franzosini and Clusius [45] reported new

measurements between 13 and 273 °K on a 99.99

percent pure sample. Isothermal-shield calorimeters were used in both sets of measurements. Below

30 °K the deviations of the data of Clusius and

Harteck [25 ] from the selected values are within

+ 6.5 and —2.5 percent and above 30 °K within

+ 1.5 and —0.9 percent (average deviation = 1 percent). Below 30 °K the deviations of the data of

Franzosini and Clusius [45] from the selected values

are within +5 and —2.3 percent and above 30 °K

within +0.8 and —0.5 percent (average deviation =0.2 percent).

Geballe and Giauque [48] reported measurements

between 16 and 309 °K on a single crystal (2.5 kg)

of 99.99 percent purity. Analysis showed 0.001

percent each of Ag, Cu, and Fe. Gold-silver alloy

wire, calibrated against a copper-constantan thermocouple temperature scale [49, 50], was used for

temperature measurements. Their data were in- cluded in the selection of the best values of heat

capacity. Below 30 °K their values of heat capacity

do not deviate from the selected values by more

than +2.5 and —2.0 percent and above 30 °K by

more than +2 and —0.6 percent (average deviation =0.2 percent).

Corak, Garfunkel, Satterthwaite, and Wexler [28]

reported measurements from 1 to 5 °K on an an- nealed sample of 99.99+ percent purity. Cooling

was achieved by helium exchange gas. A carbonresistance thermometer was used that was cali- brated on the 1948 4He scale [112, 98] adjusted

for deviations from the thermodynamic scale [38, 9]. The values of y and 0d(O) reported are typical of

those published using the two-term heat-capacity

equation: C=yT + AT3

. The values of heat capacity

calculated from y and $o(0) deviate “parabolically”

from the selected values, with —0.2 and +2.2 percent

at the ends of the temperature range of measure- ments and —1.4 percent at the “trough” of the

deviation.

Ramanathan and Srinivasan [92] reported meas- urements between 1.3 and 4.2 °K on a sample of 99.97

percent purity. The values of y and 0p{0) reported

are also typical of values published on gold using

the two-term equation to represent the data. The

1955L 4He scale [111] was used. The calculated

heat capacity deviate “parabolically” from the

selected values, with +0.5 and 2.0 percent at the

ends of the temperature range of measurements

and —0.2 percent at the “trough” of the deviation.

Budworth, Hoare, and Preston [17] reported

measurements from 1.8 to 4.2 °K on a material that

was described as spectroscopically standardized

in which individual impurities were of the order

of 2 to 3 ppm. Cooling of the sample was achieved

by condensing helium in a small chamber attached

to the sample vessel and subsequently removing

the helium by pumping. A carbon-resistance thermometer calibrated on the 1955L 4He scale [111]

was used. The reported values of y and 0d(O) based

on the equation: C — yT + AT3 are the highest of

the published values. The values of heat capacity

calculated from y and 0d(O) deviate “parabolically”

with +2.0 and —0.6 percent at the ends of the

temperature range of measurements and —1.2

percent at the “trough” of the deviation.

DuChatenier and DeNobel [34] and DuChatenier,

DeNobel, and Boerstoel [36] have reported measure- ments between 1 and 30 °K on an annealed polycrystalline sample of 99.9999 percent purity. The

analysis is stated, however, to be 2 ppm Na and less

than 1 ppm Ag and Cu. No transition metals were

detected. The temperatures, measured by means

of a carbon-resistance thermometer, were based

on the 1958 4 He scale [14] and the hydrogen vapor

pressure work of Hoge and Arnold [59]. Helium

exchange gas was used in cooling. The values of

y and 9p{0) reported are typical of those values

published on gold. The smoothed values of heat

capacity that were reported [36] exhibit an almost

“sinusoidal” deviation from the selected values

with a maximum of about ±3 percent. This same

type of deviation has been found with their data on copper and silver [34, 35].

Crane [29] reported measurements from 1.2 to 5 °K on “pure gold” but gave no numerical values.

Zimmerman and Crane [117] reported measurements

on a polycrystalline sample of 99.999+ percent

purity and on a single crystal of 99.99+ percent

purity. The values of 6d(0) reported for the two

specimens are essentially the same, but the y value

for the single crystal is 3 to 4 percent higher than

that of the polycrystalline sample. They fitted their

data to the two-term equation. The values of heat

capacity calculated from the y and dpi0) reported

for the polycrystalline sample deviate “parabolically” with —0.7 and +2.0 percent at the ends

of the temperature range of measurement and —0.8

at the “trough” of the deviation. For the single

crystal sample the corresponding deviations are + 0.5, + 1.9, and 0 percent.

Martin [77, 78] reported measurements in the

ranges 0.4 to 1.5 °K and 3 to 30 °K on an annealed

sample of 99.9999 percent purity. The measure- ments between 0.4 and 1.5 °K were made in a calorimeter in which the sample was cooled by

means of a superconducting Pb-wire heat switch.

A carbon-resistance thermometer calibrated on the

1962 3 He scale [104] was used. In the range 3 to 30 °K another calorimeter was used in which the

cooling was achieved by circulation of helium gas

between the heat sink and calorimeter. A ger32
manium thermometer was used that had been cali- brated on the 1958 4He scale [15], with the vapor

pressure of hydrogen [116], a gas thermometer

[44], and the NBS 1955 provisional scale [60, 46].

Values of y and 0d(O) obtained from the measure- ments between 0.4 and 1.5 °K are the lowest of

those published. The data reported by Martin

[77, 78] were included in the selection of the best

values. The values of heat capacity of Martin [77,

78] in general fall well within ±0.1 percent of the

selected values.

Isaacs [61] reported measurements from 1.5 to 4.2 °K on a sample of 99.9999+ percent purity. A

mechanical heat switch was used in cooling the

sample. A carbon-resistance thermometer cali- brated on the 1958 4 He scale [14] was used. Isaacs

[61] showed that his data can be represented better

by an equation of the form: C — yT f-AT3 + BT5

, the

coefficient for the T5 term was found to be negative

(B = - 0.00048 ±0.00025 mj °K-6 mol- 1 ). Isaacs

[101] subsequently recalculated the observations

and obtained somewhat different results for 0£>(O) and essentially the same y. The coefficient of the

T5 term was again found to be negative (B = — 0.0016

±0.0003 mj °K-6 mol-1

). The values of heat capacity based on the new coefficients are in better

agreement with the final selected values, the deviations of the values of heat capacity calculated using

the new values of y, #d( 0), and B range from 0 to — 1.3 percent and those using the old values range

from— 0.2 to + 2.1 percent.

Will and Green [115] reported measurements from

2 to 4 °K on an annealed polycrystalline sample of

99.9999 percent purity. A mechanical heat switch was used in cooling. (See the section on copper for a description of the unique adiabatic method used

[24, 52, 53, 54, 115].) The values of y and 0o(O) re- ported are among the lower group of values published on gold. Will and Green [115] used the heatcapacity equation of the form C = yT + AT3 + BT5 to fit their data, the coefficient of the T5 term

being found to be negative {B- — 0.00108 + 0.00007

mj °K-6 mol-1

) similar to that reported by Isaacs

[61, 101]. Will and Green [115] found Martin’s re- sults [78] to fit the three-term equation. The values

of heat capacity calculated using the y, 6d(0), and

B reported deviate from the selected values about

+ 0.1 to +0.6 percent.

Table 5. Sources of heat-capacity data on gold used in the analysis

Temper- Entropy at 298.15 °K Experimental method

ature range Purity of Electronic Debye 6 Year of heat specimen coefficient, y at 0 °K Refer- measure- Calo- Thermom- Temper- Cooling ences ments J “K 1 mol 1 cal “Kr1 mol -1 rimeter eter ature scale of mj °K~2 mol-1 design sample

°K Weight % X 103 °K

1928 15-212 fine gold Vl-I* Pb e Pb, PRT,e gas e [25] gas, vp-Ho, vp-02 1952 16-309 99.99 (single 47.30 ±0.08 b 11.30 ±0.02 b VI-I Au-Ag TC, vp-H2 , gas [48] crystal

)

vp-02 , vp-N2 , gas

1955 1-5 99.99+ (an- 743 ±14 a 164.57 ±0.14 a VI-I C 1948W 4 He gas [28] nealed) 1959 1.3-4.

2

99.97 764 ±29 a 164.2 ±0.5 a VI-I C 1948 4 He MHS [92] 1960 1. 8-4.2 spectroscopi- 870 ±26 a 166.6 ±1.0 a VI-I c 1955L 4 He cond [17] cally stand- ardized

1962 1-30 99.9999 740 165.2 VI-I c 1958 4 He, gas [34, 36] vp-H2 1962 1.2-5 “pure” (No numerical data are given in the paper) VI-I c vp-4 He MHS [29] 1962 1.5-4.

2

99.999+ 740 ±10 a 164.0 ±1.0 a VI-I c 1958 4 He MHS [117] 1962 1. 5-4.2 99.99+ (single 767 ±13 a 164.2 ±1.2 a VI-I c 1958 4 He gas [117] crystal) 1963 12-273 99.99 165 47.57 ±0.13 b 11.37 ±0.03 b VI-I Pb Pb. gas [45] vp-H2 , Vp-O-2, gas, Pt

1964 0.4- 1.5 99.9999 (an- 728 ±18 a 162.4 ±2.0 a VI-I c 1962 3 He SHS [77, 78] nealed) 1964 3-30 99.9999 (an- VA-C Ge 1958 4 He, cond [77, 78] nealed) vp-H2 , gas, NBS- 1955

1965 1.5-4.

2

99.9999+ 729 ±18 a ' c,d 162.8 ±1.5 b ' c,<1 VI-I C 1958 4 He MHS [61.62] 1966 2-4 99.9999 730 ±7 a ’ c 162.5 ±0.4 a - c VA-I C 1958 4 He MHS [115]

a These figures prefixed with the ± symbols have been interpreted from the authors’ description to indicate the precision of the values given.

b These figures prefixed with the ± symbols have been interpreted from the authors’ description to indicate the estimated uncertainties in the values

given.

c From the equation of the form: C = yT + AT3 + BTh

, where A = 127r4 R/5[0/)(O)]3

. d Isaacs [62] recalculated the experimental observations and found slightly different values: y = 0. 731 ±0.020 mj °K~2 mol 0i,(O)= 162.4 ±0.6 °K; = — 0.0016 ± 0.0003 mj °K-6 mol-'.

c See section 2 for definitions of symbols and abbreviations used.

33
MILLI

JOULES

°K"

2

mol

0.90

0.85

0.80

0.75

0.70

Figure 5.

ELECTRONIC

COEFFICIENT OF

HEAT CAPACITY

7

DEBYE

CHARACTERISTIC

TEMPERATURE

® D (0)

167

17

17

166

SELECTED VALUES

7 = 0.729 ±0.010 mj °K~ 2 mol

-1 ©D

(0) = 162.5 ± 1.5 °K 34

45

28

117,92

117 164

117 92

28

34,117

61

115 62 ,77

163

162

Comparison of the reported values of electronic coefficients of heat capacity, y, and Debye characteristic temperatures, 0D(O)i of gold.

34
(IP/DP) ‘AllDVdVD _LV3H 30 3AllVAId3Q 3dniV83dlAI31

sT ro c\j — o o o o

35

50

100

150

200

250

300

TEMPERATURE,

°K

Figure

6a.

Deviations

of

the

heat-capacity

data

of

the

literature

on

gold

from

the

selected

values

in

the

range

30

to

300

°K.

The

estimated

limit

of

accuracy

and

tne

temperature

derivative,

dC/dT,

inJ

°K~

2

mol~'

of

the

selected

values.
oUJ

crz><

cru

CL

UJ

hNOI1VIA30 _LN3DU3d

<r> 3

e

oonO

-Q

c

5o

©

c:©s

3

s

3

©O

3

-©

•c

W5©©

O

-Q

sCW

cc3

u.

36
5

4

3

2

I

0

-I

2

3

4

5

SYMBOL REF. NO. B 36

© 78

TEMPERATURE, °K

£ 6c. Deviations of the heat-capacity data of the literature on gold from the selected values in the range 0 to 5 °K and the estimated limit of accuracy of the selected values.

37
Table 6. Thermodynamic Functions for Gold

Gram atomic wt.= 196.9670, T °K=273. 15+r °C, 1 cal=4. 18407

T C° II ° II

o

ti T

/i 0 (H°t ~H°)IT s° -(G°-H°0 )IT

°K Jldeg-mol J/mol Jldeg-mol Jldeg-mol Jlmol Jldeg-mol

1.00 0.00118 0.000478 0.000478 0.000880 0.000402 0.000402

2.00 0.00504 0.00326 0.00163 0.00266 0.00206 0.00103

3.00 0.0141 0.0123 0.00410 0.00620 0.00631 0.00210

4.00 0.0306 0.0340 0.00849 0.0123 0.0153 0.00383

5.00 0.0570 0.0768 0.0154 0.0218 0.0321 0.00641

6.00 0.0955 0.152 0.0253 0.0354 0.0603 0.0100

7.00 0.149 0.273 0.0390 0.0539 0.104 0.0149

8.00 0.220 0.456 0.0570 0.0782 0.170 0.0212

9.00 0.313 0.720 0.0800 0.109 0.263 0.0292

10.00 0.431 1.090 0.109 0.148 0.391 0.0391

11.00 0.577 1.592 0.145 0.196 0.562 0.0511

12.00 0.755 2.255 0.188 0.253 0.786 0.0655

13.00 0.963 3.112 0.239 0.322 1.073 0.0825

14.00 1.203 4.193 0.299 0.402 1.434 0.102

15.00 1.474 5.529 0.369 0.494 1.880 0.125

16.00 1.772 7.149 0.447 0.598 2.426 0.152

17.00 2.096 9.081 0.534 0.715 3.081 0.181

18.00 2.442 1 1.35 0.630 0.845 3.861 0.214

19.00 2.807 13.97 0.735 0.987 4.775 0.251

20.00 3.187 16.97 0.848 1.140 5.838 0.292

25.00 5.245 37.97 1.519 2.069 13.76 0.550

30.00 7.375 69.53 2.318 3.214 26.89 0.896

35.00 9.395 1 1 1.5 3.186 4.505 46.14 1.318

40.00 11.22 163.2 4.079 5.881 72.08 1.802

45.00 12.86 223.4 4.965 7.299 105.0 2.334

50.00 14.29 291.4 5.828 8.729 145.1 2.902

55.00 15.52 366.0 6.654 10.15 192.3 3.496

60.00 16.59 446.3 7.438 1 1.55 246.5 4.109

65.00 17.51 531.6 8.179 12.91 307.7 4.734

70.00 18.31 621.2 8.874 14.24 375.6 5.366

75.00 19.01 714.6 9.528 15.53 450.0 6.001

80.00 19.63 811.2 10.14 16.78 530.8 6.635

85.00 20.17 910.7 10.71 17.98 617.7 7.267

90.00 20.64 1013. 11.25 19.15 710.6 7.895

95.00 21.06 1117. 11.76 20.28 809.1 8.517

100.00 21.44 1223. 12.23 21.37 913.3 9.133

105.00 21.77 1331. 12.68 22.42 1023. 9.740

110.00 22.06 1441. 13.10 23.44 1137. 10.34

115.00 22.33 1552. 13.49 24.43 1257. 10.93

120.00 22.56 1664. 13.87 25.38 1382. 1 1.51

125.00 22.78 1777. 14.22 26.31 1511. 12.09

130.00 22.97 1892. 14.55 27.20 1645. 12.65

135.00 23.15 2007. 14.87 28.07 1783. 13.21

140.00 23.31 2123. 15.17 28.92 1925. 13.75

145.00 23.45 2240. 15.45 29.74 2072. 14.29

150.00 23.59 2358. 15.72 30.54 2223. 14.82

155.00 23.70 2476. 15.97 31.31 2377. 15.34

160.00 23.81 2595. 16.22 32.07 2536. 15.85

165.00 23.91 2714. 16.45 32.80 2698. 16.35

170.00 24.00 2834. 16.67 33.52 2864. 16.85

38
Table 6. Thermodynamic Functions for Gold— Continued

Gram atomic wt.= 196.9670, T °K=273.

1

5+t °C, 1 cal=4.1840J

T ^c°p

11 O 11 o n T n o

o

o Ias o 5E-

, s° -(G°-H°0) -(G°t-h°0 )IT

°K J/deg-mol J/mol Jldeg-mol J/deg-mol Jlmol J/deg-mol

175.00 24.08 2954. 16.88 34.21 3033. 17.33

180.00 24.15 3075. 17.08 34.89 3206. 17.81

185.00 24.22 3196. 17.27 35.55 3382. 18.28

190.00 24.29 3317. 17.46 36.20 3561. 18.74

195.00 24.35 3438. 17.63 36.83 3744. 19.20

200.00 24.41 3560. 17.80 37.45 3930. 19.65

205.00 24.48 3683. 17.96 38.05 4118. 20.09

210.00 24.54 3805. 18.12 38.64 4310. 20.52

215.00 24.60 3928. 18.27 39.22 4505. 20.95

220.00 24.65 4051. 18.41 39.79 4702. 21.37

225.00 24.71 4174. 18.55 40.34 4903. 21.79

230.00 24.76 4298. 18.69 40.89 5106. 22.20

235.00 24.82 4422. 18.82 41.42 5312. 22.60

240.00 24.87 4546. 18.94 41.94 5520. 23.00

245.00 24.92 4671. 19.06 42.46 5731. 23.39

250.00 24.97 4796. 19.18 42.96 5945. 23.78

255.00 25.02 4921. 19.30 43.46 6161. 24.16

260.00 25.07 5046. 19.41 43.94 6379. 24.53

265.00 25.12 5171. 19.51 44.42 6600. 24.91

270.00 25.17 5297. 19.62 44.89 6823. 25.27

273.15 25.20 5376. 19.68 45.18 6965. 25.50

275.00 25.21 5423. 19.72 45.35 7049. 25.63

280.00 25.26 5549. 19.82 45.81 7277. 25.99

285.00 25.31 5676. 19.91 46.25 7507. 26.34

290.00 25.35 5802. 20.01 46.69 7739. 26.69

295.00 25.39 5929. 20.10 47.13 7974. 27.03

298.15 25.42 6009. 20.15 47.40 8123. 27.24

300.00 25.43 6056. 20.19 47.56 8211. 27.37

Ho is the enthalpy of the solid at 0 °K and 1 atm pressure.

39
UJQ

Z>h-< o a: in Lu — CL

cp o

<f St

(\J

in

rOro O

ro

OJ m

OJ

OJ O

OJ

OJ m

OJ oOJ m

O

OJ OO

OJ

O

N-rO O

CD

ro O

in

ro O

ro O

roro O

OJro »o(l) Q© ‘3amva3dlAI31 3llSia31DVdVHD 3A93Q

o

ro o

o

ro

40

f-KiURE

7.

Comparison

of

the

Debye

characteristic

temperatures

,

0„(T),

of

the

selected

vat

ties

of

heat

capacity

of

copper,

silver,

and

paid

in

the

ranpe

0

to

300

°K.

The

values

#!>( T)

were

calculated

from

the

relations

C

v

=

C,,

—

yT

—

AQfT

and

D(0/T)—

C

V

/3R. (

See

the

text

for

further

details.)

I

he

vertical

lines

at

60

°K

and

above

correspond

to

0.1

percent

of

the

heat

capacity

and

those

below

60

°K1

percent

of

the

heat

capacity.
5. References

[1] Ahlers, G., Some Properties of Solid Hydrogen at Small

Molar Volumes, Thesis — UCRL-10757, 133 pp. (1963), U.S. Atomic Energy Comm. Contract No. W-7405-

eng-48, University of California, Lawrence Radiation

Laboratory, Berkeley, Calif.

[2] Ahlers, G., Lattice heat capacity of solid hydrogen, J. Chem. Phys. 41, 86-94 (1964).

[3| Ahlers, G., Heat capacity of copper. Rev. Sci. Instr. 37,

477-480 (1966).

[4] Ahlers, G., The heat capacity of silver below 26 °K, J. Phys. Chem. Solids 28, 525-527 (1967).

[5] Aoyama, S., and Kanda, E., Specific heats of nickel and

cobalt at low temperature, Nippon Kagaku Zasshi 62,

312-315 (1941).

[6] Barber, C. R., The establishment of a practical scale of temperature for the range 10—90 °K, Brit. J. Appl. Phys.

13, 235-241 (1962).

[7] Barber, C. R., and Hayes, J. G., The derivation of the provisional reference table CCT 64, T = f(W) for platinum

resistance thermometers for the range from 12 to 273.15 °K. Part II. The derivation of the table for the range from 90 to 273.15 °K, Metrologia 2, 11-13 (1966).

[8] Barber, C. R., and Horsford, A., Differences between the thermodynamic scale and the International Practical Scale of Temperature from 0 °C to — 183 °C, Metrologia

I, 75-80 (1965).

[9] Berman. R., and Swenson, C. A., Absolute temperature

scale between 4.2° and 5.2 °K, Phys. Rev. 95, 311-314

(1954).

[10J Blakemore, J. S., Schultz, J. W., and Myers, J. G., Measurements on gallium-doped germanium thermometers,

Rev. Sci. Instr. 33, 545-551 (1962).

[11] Bleaney, B., and Hull, R. A., The determination of the vapour-pressure curve of liquid helium below 1.6 °K

using a magnetic thermometer, Proc. Roy. Soc. (London)

178A, 74-85 (1941).

[12] Bleaney, B., and Simon, F., The vapour pressure curve of

liquid helium below the A-point, Trans. Faraday Soc. 35,

1205-1214 (1939).

[131 Borovick-Ramanov, A. S., Strelkov, P. G., Orlova, M. P., and Astrov, D. N., “The I.M.P.R. Temperature Scale from the 10 to 90 °K Region” in American Institute of Physics, Temperature, Its Measurement and Control in Science and Industry 3, Pt. 1, pp. 113-128 (Reinhold

Publishing Corp., New York, 1962).

[14] Brickwedde, F. G., van Dijk, H., Durieux, M., Clement,

J. R., and Logan, J. K., The “1958 He4 Scale of Temperatures,” J. Res. NBS 64A (Phys. and Chem.), No. 1, 1-17

(1960).

[15] Bronson, H. L., Chisholm, H. M., and Dockerty, S. M., On

the specific heats of tungsten, molybdenum, and copper. Can. J. Res. 8, 282-303 (1933).

[16] Bronson, H. L., and Wilson, A. J. C., The heat capacities

of silver, nickel, zinc, cadmium and lead from —80° to 120 °C, Can. J. Res. 14A, 181-193 (1936).

[17] Budworth, D. W., Hoare, F. E., and Preston, J., The ther- mal and magnetic properties of some transition element

alloys, Proc. Roy. Soc. (London) 257A, 250-262 (1960).

[18| Burk. D. L., Estermann, I., and Friedberg. S. A., The low temperature specific heats of titanium, zirconium, and

hafnium, Z. Physik. Chem. (Frankfurt) 16, 183-193

(1958).

[19] Busey, R. H., The heat capacity of rhenium heptoxide

from 15 to 300 °K. Entropy and free energy, J. Am.

Chem. Soc. 78, 3263-3266 (1956).

[20] Cameron, A. E., and Wichers, E., Report of the Inter- national Commission on Atomic Weights (1961), J. Am.

Chem. Soc. 84, 4175-4197 (1962).

[21] Cataland, G., and PI umb, H., Isotherms determined by the National Bureau of Standards acoustical thermometer

in the liquid helium temperature range, J. Res. NBS 69A

(Phys. and Chem.), No. 6, 531-534 (1965).

[22] Clement, J. R., Logan, J. K., and Gaffney, J., Liquid helium

vapor pressure equation, Phys. Rev. 100, 743-744

(1955).

[23] Clement, J. R., Logan, J. K., and Gaffney, J., Une equation pour la pression de la vapeur saturee de Fhelium liquide, Proc. Conf. de Phys. des Basses Temp., Paris, 2—8

Sept. 1955, 601-604 (Suppl. Bull. Inst. Intern. Froid

Paris, Annexe 1955-3).

[24] Clune, L. C., and Green, B. A., Jr., Low-temperature specific heats of a-CuSn and a-CuZn alloys, Phys. Rev. 144.

525-528 (1966).

[25] Clusius, K., and Harteck, P., Uber die spezifischen Warmen

einiger fester Korper bei tiefen Temperaturen, Z. Physik. Chem. (Leipzig) 134, 243-263 (1928).

[26] Clusius, K., and Vaughen, J. V., Zur Temperaturmessung

unterhalb von 80° absolut mittels des Bleithermometers,

Z. Ges. Kalte-Ind. 36, 215-221 (1929).

[27] Cole, A. G., Hutchens, J. O., Robie, R. A., and Stout,

J. W., Apparatus and methods for low temperature heat capacity measurements. The heat capacity of standard

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Gram atomic wt. =63. 5400, T °K=273.15+t °C, 1 cal=4.1840J

T C° TJ o TJO tl T

tl o CH°-H°)IT -(C°-//°) -(G°r-H°0 )/T

°K Cal/deg-mol Cal/mol Cal/deg-mol Cal/deg-mol Cal/mol Cal/deg-mol

1.00 0.000177 0.000086 0.000086 0.000258 0.000165 0.000165

2.00 0.000423 0.000378 0.000189 0.000451 0.000516 0.000258

3.00 0.000805 0.000978 0.000326 0.000689 0.00108 0.000360

4.00 0.00139 0.00206 0.000514 0.000995 0.00192 0.000479

5.00 0.00225 0.00385 0.000771 0.00139 0.00310 0.000620

6.00 0.00346 0.00668 0.001 1

1

0.00190 0.00474 0.000790

7.00 0.00508 0.0109 0.00156 0.00255 0.00695 0.000994

8.00 0.00720 0.0170 0.00213 0.00336 0.00990 0.00124

9.00 0.00990 0.0255 0.00283 0.00436 0.0137 0.00153

10.00 0.0133 0.0370 0.00370 0.00557 0.0187 0.00187

11.00 0.0174 0.0523 0.00475 0.00702 0.0250 0.00227

12.00 0.0224 0.0721 0.00601 0.00874 0.0328 0.00274

13.00 0.0284 0.0974 0.00749 0.0108 0.0426 0.00327

14.00 0.0355 0.129 0.00923 0.0131 0.0545 0.00389

15.00 0.0439 0.169 0.01 13 0.0159 0.0689 0.00459

16.00 0.0538 0.218 0.0136 0.0190 0.0863 0.00539

17.00 0.0651 0.277 0.0163 0.0226 0.107 0.00630

18.00 0.0783 0.348 0.0194 0.0267 0.132 0.00731

19.00 0.0933 0.434 0.0228 0.0313 0.161 0.00845

20.00 0.1 10 0.536 0.0268 0.0365 0.194 0.00972

25.00 0.230 1.363 0.0545 0.0729 0.460 0.0184

30.00 0.405 2.928 0.0976 0.130 0.958 0.0319

35.00 0.631 5.496 0.157 0.208 1.792 0.0512

40.00 0.894 9.296 0.232 0.309 3.077 0.0769

45.00 1.178 14.47 0.322 0.431 4.920 0.109

50.00 1.471 21.09 0.422 0.570 7.415 0.148

55.00 1.765 29.18 0.531 0.724 10.65 0.194

60.00 2.054 38.73 0.646 0.890 14.68 0.245

65.00 2.332 49.70 0.765 1.066 19.56 0.301

70.00 2.596 62.03 0.886 1.248 25.34 0.362

75.00 2.843 75.63 1.008 1.436 32.05 0.427

80.00 3.072 90.43 1.130 1.627 39.71 0.496

85.00 3.285 106.3 1.251 1.819 48.32 0.568

90.00 3.480 123.2 1.369 2.013 57.90 0.643

95.00 3.660 141.1 1.485 2.206 68.45 0.721

100.00 3.825 159.8 1.598 2.398 79.96 0.800

105.00 3.977 179.3 1.708 2.588 92.43 0.880

1 10.00 4.1 16 199.6 1.814 2.776 105.8 0.962

1 15.00 4.244 220.5 1.917 2.962 120.2 1.045

120.00 4.362 242.0 2.017 3.145 135.5 1.129

125.00 4.470 264.1 2.1 13 3.326 151.6 1.213

130.00 4.571 286.7 2.205 3.503 168.7 1.298

135.00 4.663 309.8 2.295 3.677 186.7 1.383

140.00 4.749 333.3 2.381 3.848 205.5 1.468

145.00 4.828 357.2 2.464 4.016 225.1 1.553

44
Appendix 1. Thermodynamic Functions for Copper —Continued

Gram atomic wt =63.5400, T °K=273. 1 5+/ °C, I cal=4.1840y

T c° n

rjo U°

T

ti 0 -(G°t-H°0)/T

°K Cal/deg-mol Cal/mol Cal/deg-mol Cal/deg-mol Cal/mol Cal/deg-mol

150.00 4.901 381.6 2.544 4.181 245.6 1.638

155.00 4.969 406.3 2.621 4.343 266.9 1.722

160.00 5.032 431.3 2.695 4.502 289.1 1.807

165.00 5.090 456.6 2.767 4.658 312.0 1.891

170.00 5.145 482.2 2.836 4.81 1 335.6 1.974

175.00 5.196 508.0 2.903 4.960 360.1 2.058

180.00 5.244 534.1 2.967 5.107 385.2 2.140

185.00 5.289 560.4 3.029 5.252 411.1 2.222

190.00 5.331 587.0 3.089 5.393 437.7 2.304

195.00 5.371 613.8 3.147 5.532 465.1 2.385

200.00 5.408 640.7 3.203 5.669 493.1 2.465

205.00 5.443 667.8 3.258 5.803 521.7 2.545

210.00 5.476 695.1 3.310 5.934 551.1 2.624

215.00 5.507 722.6 3.361 6.064 581.1 2.703

220.00 5.537 750.2 3.410 6.191 61 1.7 2.781

225.00 5.565 778.0 3.458 6.315 643.0 2.858

230.00 5.591 805.8 3.504 6.438 674.9 2.934

235.00 5.616 833.9 3.548 6.558 707.4 3.010

240.00 5.640 862.0 3.592 6.677 740.5 3.085

245.00 5.663 890.3 3.634 6.793 774.1 3.160

250.00 5.684 918.6 3.675 6.908 808.4 3.234

255.00 5.704 947.1 3.714 7.021 843.2 3.307

260.00 5.722 975.7 3.753 7.132 878.6 3.379

265.00 5.740 1004. 3.790 7.241 914.5 3.451

270.00 5.757 1033. 3.826 7.348 951.0 3.522

273.15 5.767 1051. 3.848 7.415 974.2 3.567

275.00 5.773 1062. 3.861 7.454 988.0 3.593

280.00 5.788 1091. 3.896 7.558 1026. 3.663

285.00 5.803 1120. 3.929 7.661 1064. 3.732

290.00 5.818 1 149. 3.961 7.762 1 102. 3.800

295.00 5.832 1178. 3.993 7.862 1141. 3.868

298.15 5.840 1 196. 4.013 7.923 1166. 3.911

300.00 5.845 1207. 4.024 7.960 1181. 3.936

Ho is the enthalpy of the solid at 0 °K and 1 atm pressure.

45
Appendix 2 . Thermodynamic Functions for Silver

Gram atomic wt.= 107.8700, T °K=273.

1

5 + t °C, 1 cal=4. 18407

T r

° ^ p (H°t -H°0 )IT s° -(G°t -H°0 ) -(G°-H°)IT

°K Calldeg-mol Cal/mol Calldeg-mol Calldeg-mol Cal/mol Cal/deg-mol

1.00 0.000196 0.000088 0.000088 0.000251 0.000156 0.000156

2.00 0.000633 0.000472 0.000236 0.000500 0.000522 0.000261

3.00 0.00155 0.00151 0.000505 0.00091

1

0.00121 0.000404

4.00 0.00320 0.00382 0.000955 0.00156 0.00242 0.000606

5.00 0.00581 0.00823 0.00165 0.00254 0.00444 0.000889

6.00 0.00964 0.0158 0.00264 0.00391 0.00763 0.00127

7.00 0.0150 0.0280 0.00400 0.00578 0.0124 0.00178

8.00 0.0222 0.0464 0.00580 0.00822 0.0194 0.00242

9.00 0.0316 0.0731 0.00812 0.0114 0.0291 0.00323

10.00 0.0437 0.110 0.0110 0.0153 0.0423 0.00423

11.00 0.0590 0.162 0.0147 0.0201 0.0600 0.00545

12.00 0.0778 0.230 0.0191 0.0260 0.0830 0.00691

13.00 0.101 0.318 0.0245 0.0331 0.112 0.00865

14.00 0.128 0.432 0.0309 0.0416 0.150 0.0107

15.00 0.160 0.576 0.0384 0.0515 0.196 0.0131

16.00 0.197 0.754 0.0471 0.0630 0.253 0.0158

17.00 0.240 0.972 0.0572 0.0762 0.323 0.0190

18.00 0.287 1.235 0.0686 0.0912 0.406 0.0226

19.00 0.338 1.547 0.0814 0.108 0.506 0.0266

20.00 0.394 1.912 0.0956 0.127 0.623 0.0311

25.00 0.733 4.689 0.188 0.249 1.543 0.0617

30.00 1.141 9.354 0.312 0.418 3.193 0.106

35.00 1.580 16.15 0.461 0.627 5.791 0.165

40.00 2.012 25.14 0.629 0.866 9.514 0.238

45.00 2.417 36.23 0.805 1.127 14.49 0.322

50.00 2.786 49.25 0.985 1.401 20.81 0.416

55.00 3.117 64.03 1.164 1.683 28.51 0.518

60.00 3.411 80.36 1.339 1.967 37.64 0.627

65.00 3.669 98.08 1.509 2.250 48.18 0.741

70,00 3.896 117.0 1.671 2.530 60.13 0.859

75.00 4.096 137.0 1.827 2.806 73.48 0.980

80.00 4.272 157.9 1.974 3.076 88.19 1.102

85.00 4.429 179.7 2.114 3.340 104.2 1.226

90.00 4.568 202.2 2.246 3.597 121.6 1.351

95.00 4.692 225.3 2.372 3.848 140.2 1.476

100.00 4.804 249.1 2.491 4.091 160.0 1.600

105.00 4.904 273.4 2.603 4.328 181.1 1.725

110.00 4.994 298.1 2.710 4.558 203.3 1.848

115.00 5.075 323.3 2.811 4.782 226.7 1.971

120.00 5.148 348.8 2.907 5.000 251.1 2.093

125.00 5.215 374.7 2.998 5.211 276.7 2.213

130.00 5.276 401.0 3.084 5.417 303.2 2.332

135.00 5.331 427.5 3.167 5.617 330.8 2.450

140.00 5.382 454.3 3.245 5.812 359.4 2.567

145.00 5.429 481.3 3.319 6.002 388.9 2.682

150.00 5.473 508.6 3.390 6.186 419.4 2.796

155.00 5.513 536.0 3.458 6.367 450.8 2.908

160.00 5.550 563.7 3.523 6.542 483.1 3.019

165.00 5.585 591.5 3.585 6.713 516.2 3.128

170.00 5.617 619.5 3.644 6.881 550.2 3.236

46
Appendix 2. Thermodynamic Functions for Silver —Continued

Gram atomic wt.= 107.8700, T °K = 273-15+t °C, 1 cal=4. 1 8407

T L F

IT ° JJ O n T Ho (H°-H°0 )/T s° —(G°— //°) -(.G°-H°)/T

°K Cal/deg-mol Cal/mol Cal/deg-mol Cal/deg-mol Cal/mol Cal/deg-mol

175.00 5.647 647.7 3.701 7.044 585.0 3.343

180.00 5.676 676.0 3.756 7.203 620.6 3.448

185.00 5.702 704.5 3.808 7.359 657.0 3.551

190.00 5.727 733.0 3.858 7.512 694.2 3.654

195.00 5.751 761.7 3.906 7.661 732.1 3.755

200.00 5.773 790.5 3.953 7.807 770.8 3.854

205.00 5.795 819.5 3.997 7.949 810.2 3.952

210.00 5.815 848.5 4.040 8.089 850.3 4.049

215.00 5.834 877.6 4.082 8.226 891.1 4.145

220.00 5.852 906.8 4.122 8.361 932.5 4.239

225.00 5.870 936.1 4.161 8.492 974.7 4.332

230.00 5.886 965.5 4.198 8.622 1017. 4.424

235.00 5.902 995.0 4.234 8.748 1061. 4.514

240.00 5.917 1025. 4.269 8.873 1 105. 4.604

245.00 5.932 1054. 4.303 8.995 1 150. 4.692

250.00 5.946 1084. 4.335 9.115 1195. 4.780

255.00 5.959 1 1 14. 4.367 9.233 1241. 4.866

260.00 5.973 1143. 4.398 9.349 1287. 4.951

265.00 5.985 1173. 4.428 9.463 1334. 5.035

270.00 5.997 1203. 4.457 9.575 1382. 5.118

273.15 6.005 1222. 4.474 9.644 1412. 5.170

275.00 6.009 1233. 4.485 9.685 1430. 5.200

280.00 6.020 1263. 4.512 9.793 1479. 5.281

285.00 6.032 1294. 4.539 9.900 1528. 5.361

290.00 6.042 1324. 4.564 10.00 1578. 5.440

295.00 6.053 1354. 4.590 10.1

1

1628. 5.519

298.15 6.059 1373. 4.605 10.17 1660. 5.567

300.00 6.063 1384. 4.614 10.21 1679. 5.596

H„ is the enthalpy of the solid at 0 °K and 1 atm pressure.

47
Appendix 3. Thermodynamic Functions for Gold

Gram atomic wt.= 196.9670, T °K=273.15+r °C, 1 cal=4. 18407

T C°^ p TJO TJO ti T

/i o S°T -(G°-H°0 )IT

°K Calldeg-mol Callmol Calldeg-mol Calldeg-mol Cal/mo! Calldeg-mol

1.00 0.000282 0.000114 0.000114 0.000303 0.000181 0.000181

2.00 0.00121 0.000779 0.000390 0.000728 0.000669 0.000335

3.00 0.00337 0.00294 0.000980 0.00158 0.00178 0.000593

4.00 0.00732 0.00811 0.00203 0.00304 0.00402 0.00101

5.00 0.0136 0.0184 0.00367 0.00530 0.00812 0.00162

6.00 0.0228 0.0363 0.00605 0.00854 0.0149 0.00249

7.00 0.0356 0.0652 0.00931 0.0130 0.0256 0.00366

8.00 0.0526 0.109 0.0136 0.0188 0.0414 0.00517

9.00 0.0748 0.172 0.0191 0.0262 0.0637 0.00708

10.00 0.103 0.261 0.0261 0.0355 0.0944 0.00944

11.00 0.138 0.380 0.0346 0.0469 0.135 0.0123

12.00 0.180 0.539 0.0449 0.0607 0.189 0.0157

13.00 0.230 0.744 0.0572 0.0770 0.258 0.0198

14.00 0.288 1.002 0.0716 0.0961 0.344 0.0246

15.00 0.352 1.321 0.0881 0.118 0.451 0.0301

16.00 0.424 1.709 0.107 0.143 0.581 0.0363

17.00 0.501 2.170 0.128 0.171 0.738 0.0434

18.00 0.584 2.712 0.151 0.202 0.924 0.0514

19.00 0.671 3.339 0.176 0.236 1.143 0.0602

20.00 0.762 4.055 0.203 0.273 1.397 0.0699

25.00 1.254 9.074 0.363 0.495 3.290 0.132

30.00 1.763 16.62 0.554 0.768 6.429 0.214

35.00 2.246 26.66 0.762 1.077 11.03 0.315

40.00 2.682 38.99 0.975 1.406 17.23 0.431

45.00 3.073 53.40 1.187 1.745 25.10 0.558

50.00 3.415 69.64 1.393 2.086 34.68 0.694

55.00 3.709 87.47 1.590 2.426 45.96 0.836

60.00 3.964 106.7 1.778 2.760 58.93 0.982

65.00 4.185 127.1 1.955 3.086 73.55 1.132

70.00 4.377 148.5 2.121 3.404 89.78 1.283

75.00 4.544 170.8 2.277 3.711 107.6 1.434

80.00 4.691 193.9 2.424 4.009 126.9 1.586

85.00 4.820 217.7 2.561 4.298 147.6 1.737

90.00 4.934 242.1 2.689 4.577 169.8 1.887

95.00 5.034 267.0 2.810 4.846 193.4 2.036

100.00 5.123 292.4 2.924 5.107 218.3 2.183

105.00 5.202 318.2 3.030 5.359 244.5 2.328

110.00 5.273 344.4 3.131 5.602 271.9 2.471

115.00 5.336 370.9 3.225 5.838 300.5 2.613

120.00 5.393 397.7 3.314 6.066 330.2 2.752

125.00 5.444 424.8 3.399 6.288 361.1 2.889

130.00 5.490 452.2 3.478 6.502 393.1 3.024

135.00 5.533 479.7 3.554 6.710 426.1 3.156

140.00 5.571 507.5 3.625 6.912 460.2 3.287

145.00 5.606 535.4 3.693 7.108 495.2 3.415

150.00 5.637 563.5 3.757 7.299 531.2 3.542

155.00 5.665 591.8 3.818 7.484 568.2 3.666

160.00 5.691 620.2 3.876 7.664 606.1 3.788

165.00 5.714 648.7 3.932 7.840 644.8 3.908

170.00 5.735 677.3 3.984 8.01

1

684.5 4.026

48
Appendix 3. Thermodynamic Functions for Gold —Continued

Gram atomic wt.= 196.9670, T °K=273. 15+/ °C, 1 cal=4. 18407

T c°^ p

LJO two n T

ti 0 ch°t -h°)/t 5°

°K Cal/deg-mol Callmol Calldeg-mol Calldeg-mol Callmol Calldeg-mol

175.00 5.754 706.0 4.035 8.177 724.9 4.142

180.00 5.772 734.9 4.083 8.339 766.2 4.257

185.00 5.789 763.8 4.128 8.498 808.3 4.369

190.00 5.805 792.7 4.172 8.652 851.2 4.480

195.00 5.820 821.8 4.214 8.803 894.8 4.589

200.00 5.835 850.9 4.255 8.951 939.2 4.696

205.00 5.850 880.2 4.293 9.095 984.3 4.802

210.00 5.864 909.4 4.331 9.236 1030. 4.906

215.00 5.878 938.8 4.367 9.374 1077. 5.008

220.00 5.892 968.2 4.401 9.510 1124. 5.109

225.00 5.906 997.7 4.434 9.642 1172. 5.208

230.00 5.919 1027. 4.466 9.772 1220. 5.306

235.00 5.932 1057. 4.497 9.900 1270. 5.402

240.00 5.944 1087. 4.528 10.02 1319. 5.497

245.00 5.956 1116. 4.557 10.15 1370. 5.591

250.00 5.968 1146. 4.585 10.27 1421. 5.683

255.00 5.980 1176. 4.612 10.39 1472. 5.774

260.00 5.992 1206. 4.638 10.50 1525. 5.864

265.00 6.004 1236. 4.664 10.62 1577. 5.953

270.00 6.015 1266. 4.689 10.73 1631. 6.040

273.15 6.022 1285. 4.704 10.80 1665. 6.095

275.00 6.026 1296. 4.713 10.84 1685. 6.126

280.00 6.037 1326. 4.737 10.95 1739. 6.211

285.00 6.048 1356. 4.760 11.06 1794. 6.296

290.00 6.059 1387. 4.782 11.16 1850. 6.378

295.00 6.069 1417. 4.804 11.26 1906. 6.460

298.15 6.075 1436. 4.817 11.33 1941. 6.511

300.00 6.079 1447. 4.825 11.37 1962. 6.541

Hq is the enthalpy of the solid at 0 °K and 1 atm pressure.

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