Calorillleters for Heat of 

Solution and Low-Temperature 

Heat Capacity Measurements 

GEOLOGICAL SURVEY PROFESSIONAL PAPER 755 

Calorimeters for Heat of 

Solution and Low-Temperature 

Heat Capacity Measurements 

By RICHARD A. ROBIE and BRUCE S. HEMINGWAY 

GEOLOGICAL SURVEY PROFESSIONAL PAPER 755 

A description of the construction and operation 

of a calorimeter for determining the heats of 

solution in aqueous HF or HCl and of a 

low-temperature heat capacity calorimeter for 

cp measurements between 10 and 380 kelvin 

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON 1972 
UNITED STATES DEPARTM.ENT OF THE INTERIOR 

ROGERS C. B. MORTON, Secretary 

GEOLOGICAL SURVEY 

V. E. McKelvey, Director 

Library of Congress catalog-card No. 72-600115 

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington, D.C. 20402 - Price 40 cents 

Stock Number 2401-2182. 
CONTENTS 

Abstract ___________________________________________ _ 

Introduction ________________________________________ _ 

Acknowledgments ___________________________________ _ 

Low-temperature heat capacity calorimeter _____________ _ 

Cryostat components ____________________________ _ 

Submarine _________________________________ _ 

Electrical lead wires _________________________ _ 

Heat station ________________________________ _ 

Helium reservoir ____________________________ _ 

Isothermal shield ____________________________ _ 

Helium economizer __________________________ _ 

Floating ring _______________________________ _ 

Vacuum elevator and heat switch _____________ _ 

Adiabatic shield _____________________________ _ 

Calorimeter ________________________________ _ 

Thermometer _______________________________ _ 

Heater _____________________________________ _ 

Cryostat hoist_ _____________________________ _ 

Vacuum systems ________________________________ _ 

Adiabatic shield controller ________________________ _ Assembly ______________________________________ _ 

Temperature-energy measurements circuit_ _________ _ 

Operation and data reduction _____________________ _ 

Heat capacity results for Calorimetry Conference benzoic acid _____________________________________________ _ 

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Heat of solution calorimeter __________________________ _ 

Components ____________________________________ _ 

Submarine _________________________________ _ 

Calorimeter vesseL __________________________ _ 

Calorimeter top and closure seal ______________ _ 

Thermometer _______________________________ _ 

Heater _____________________________________ _ 

Stirrer shaft and motor drive _________________ _ 

Puncture tube ______________________________ _ 

Sample holder and impeller assembly __________ _ 

Calorimeter support connecter ________________ _ 

Operation and data reduction _____________________ _ 

Corrections _________________________________________ _ 

Sources of heat exchange _________________________ _ 

ltadiation ______________________________________ _ 

Conduction through solid connections ______________ _ 

Conduction and convection through a gas __________ _ 

Corrections for heat exchange _____________________ _ 

Corrections for superheating of the electrical heater __ 

Calculation of heat of reaction ________________________ _ 

Heat of solution of Tris (C4HuNOa) ___________________ _ 

Conclusions and recommendations for future improve- ments ____________________________________________ _ 

References cited _____________________________________ _ 

ILLUSTRATIONS 

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FIGURE 1. Diagram showing cross section of helium cryostat for heat capacity measurements between 4 and 400 K_ _ _ _ _ _ _ _ _ _ 3 

2. Cutaway drawing of sample holder and heater bobbin-thermometer assembly_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 6 

3. Block diagram of adiabatic shield controller________________________________________________________________ 8 

4. Schematic diagram showing electrical measurements circuit for calorimetry _________________ .:.___________________ 10 

5. Temperature-time curve for a heat capacity measurement_ _________ .__________________________________________ 12 

6. Deviation plot of Cp for Calorimetry Conference sample of benzoic acid_______________________________________ 14 

7. Deviation plot of U.S. Geological Survey measurements of the Cp of the Calorimetry Conference sample of benzoic 

acid_______________________________________________________________________________________________ 16 

8. Cross section of HF solution calorimeter___________________________________________________________________ 18 

9. Drawing of sample holder and loading pedestaL____________________________________________________________ 20 

10. Temperature-time curve for the heat of solution of 4.6 g of hydromagnesite in 4 N HCL _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 21 

11. Coding sheet for heat of solution experiment_______________________________________________________________ 24 

12. Graph showing heat of solution of Standard Reference Material724, Tris, between 25° and 35°C_________________ 29 

TABLES 

Page 

TABLE 1. Time-voltage log of the heat capacity measurement shown in figure 5------------------------------------------ 12 

2. Least squares values for the heat capacity of the Calorimetry Conference sample of benzoic acid___________________ 15 

3. Observed heat capacities of Calorimetry Conference sample of benzoic acid_____________________________________ 15 

III 
IV CONTENTS 

Page 

TABLE 4. Printout of computer reduction____________________________________________________________________________ 22 

5. Fortran IV-G computer program for reducing heat of solution data ________________________ ---_- __ ------------- 23 

6. Thermal and electrical constants of solution calorimeter at 30°C_______________________________________________ 25 

7. Heat of solution of Tris (C4HnN03), in 0.1 N HCL---------------------------------------------------------- 30 
CALORIMETERS FOR HEAT OF SOLUTION AND 

LOW-TEMPERATURE HEAT CAPACITY 

MEASUREMENTS 

By RICHARD A. RoBIE and BRucE S. HEMINGWAY 

ABSTRACT 

This report describes the construction and operation of an 

aqueous-solution calorimeter for enthalpy of reaction measurements and a low-temperature calorimeter for measuring heat 

capacities between 10 and 380 K (kelvin). Heat capacity data 

are used to calculate the entropy from the third law of thermodynamics. 

The heat capacity calorimeter is of the adiabatically shielded 

type and uses precooling by solid nitrogen together with the use 

of helium gas (for heat exchange) to reach temperatures of 52 K. 

Liquid helium is used as the lowest temperature refrigerant. The 

calorimeter, a liquid-helium reservoir, a gas heat exchanger, and 

an automatically controlled adiabatic shield are suspended within 

a cryogenic vacuum submarine. The submarine is sealed with 

reusable soft aluminum gaskets and is supported within an 18.6-

liter metal Dewar flask. The operation of the calorimeter was 

tested by measuring the heat capacity of the Calorimetry Conference benzoic acid sample. Our results, between 29 and 300 K, 

are within 0.15 percent of the values obtained by six previous 

investigations on this same material. 

The vacuum-jacketed aqueous-solution calorimeter for heat of 

solution measurements in strong acids, including HF, is made of 

gold-plated copper and has a copper resistance thermometer 

wound on its outer surface, an internal heater, and a combined 

sample holder-stirrer. It may be operated either at constant 

pressure to obtain the enthalpy change, llH, or at a constant volume to obtain the change in the internal energy, !!U, at temperatures up to 100°C. It has a temperature sensitivity of ±0.00005°C. 

Heats of solution as small as 4 calories have been determined with 

a precision of ±0.05 cal. 

Our result for the heat of solution of U.S. National Bureau of 

Standards Standard Reference Material 724, Tris, C4HuNOa, 

in 0.1 N HCl at 25°C is: 

!lH = -7098.0±11 cal mole-1 

The temperature coefficient of the solution reaction is 

d!!H I dT = 42.7 cal mole-1 degree-1 

This value was obtained from 20 separate heat of solution measurements between 24 o and 36°C. The operation and methods of data 

reduction for these two calorimeters are discussed. 

INTRODUCTION 

In recent years earth scientists have become more 

aware of the usefulness of thermodynamic methods, 

and there has been an increasing demand for freeenergy data for minerals. Unfortunately there has not 

been an equivalent increase in the number of calorimetric studies of minerals, the principal source of freeenergy values. In the hope that we might attract others 

into the "business," we present a description of the 

construction and operation of two calorimeters used 

in laboratories of the U.S. Geological Survey for determining the enthalpy of formation, AH" and "Third 

Law" entropies, S, of minerals. These are a solution 

calorimeter for measuring heats of reaction and a heat 

capacity calorimeter capable of precise measurements 

in the range of 10 to 380,K (kelvin). 

The Gibbs free energy of formation, AG" is probably 

the single most useful thermodynamic property of a 

phase inasmuch as it provides a direct measure of the 

chemical stability of that phase. The Gibbs free energy 

of a phase may be determined from equilibrium data 

such as aqueous solubility and cell voltage or by calorimetric techniques from the relation 

(1) 

where AH1 is the enthalpy of formation and AS is the 

entropy change. 

Since the work of Julius Thomsen and Marcellin 

Berthelot in the 1880's, aqueous-solution calorimetry 

has been, and remains so today, the single most important technique for the precise determination of the 

heats of formation and reaction involving complex 

inorganic materials. 

The molar heat capacity at constant pressure, Cp, 

is the amount of heat necessary to raise the temperature 

of 1 formula weight (mole) of a material by 1 degree. 

The heat capacity is a function of temperature and 

goes to zero as the temperature approaches 0 K. 

Accurate heat capacity data permit calculation of the 

temperature coefficient of the enthalpy of a chemical 

reaction or of a phase transition from the relation: 

(2) 

The most important use for low-temperature Cp data 

1 
2 CALORIMETERS, HEAT OF SOLUTION AND LOW-TEMPERATURE HEAT CAPACITY MEASUREMENTS 

is, however, for determining the entropy, ST, utilizing 

the third law of thermodynamics: 

ST=So+ J.Tcp;T dT. (3) 

In relation 3, So is the entropy at 0 K, and for an 

ordered substance (that is, one which is in a state of 

internal equilibrium) So is zero. 

Besides its use for calculating Gibbs free energies 

from relation 1, the entropy can be used, together with 

the molar volume, V, to calculate the temperaturepressure variation of a chemical equilibrium from the 

Clapeyron equation, 

dP AS 

dT= AV. (4) 

For a solid the entropy at 298.15 K (25.0°C) is usually 

obtained from heat capacity measurements made from 

low temperatures ( :::;20 K) to above room temperature. 

If no anomalies exist below the lowest temperature at 

which CP is measured, entropies, accurate to 0.1 to 0.2 

percent, are readily obtained using modern calorimetric 

techniques. Precise measurements of heat capacities 

at low temperatures began with the work of W. F. 

Giauque and his students in the 1920's (for example, 

Gibson and Giauque, 1923). These studies provided 

a most elegant experimental confirmation of the third 

law of thermodynamics. 

Two types of calorimeters are in common use for 

the determination of heat capacities at .}ow temperatures. These are the isoperibol (commonly called 

"isothermal" but meaning constant-temperature environment, Kubaschewski and Hultgren, 1962) and 

the adiabatically shielded calorimeter; in this latter 

type the calorimeter surroundings are continuously 

maintained at very nearly the same temperature as 

the calorimeter. 

The design and operation of isoperibol-type calorimeters has been described by Giauque and Egan (1937) 

and by Cole, Hutchens, Robie, and Stout (1960). 

Adiabatically shielded calorimeters have been described 

by Southard and Andrews (1930), Scott, Meyers, 

Rands, Brickwedde, and Bekkedahl (1945), and 

Westrum (1962). Westrum, Furukawa, and McCullough (1968) have presented a comprehensive 

review of design and operation of adiabatic calorimeters. 

In designing calorimeters for either heat of solution 

or heat capacity measurements the following general 

requirements were considered: 

1. Minimal heat leak. 

2. Fast response to temperature changes. 

3. Calorimeter should contribute only a small fraction 

of the total heat capacity (calorimeter+solvent, 

or sample) measured. 

4. Sensitivity of 0.01 percent. 

5. Simplicity of operation and data reduction. 

6. Provision for eventual automatic data reduction. 

The additional specific requirements for the solution 

calorimeter were: 

1. Inertness to the widest variety of inorganic solvents 

including HF. 

2. Operable between oo and 150°C. 

3. Provision for rapid cooling without disturbing the 

calorimetric solvent. 

4. The use of gold plating instead of solid noble metal 

parts. 

5. Constant pressure and (or) constant volume operation (gas is evolved in the solution of carbonates 

or sulfides, and it is then preferable to operate 

with the calorimeter sealed). 

The design requirements that we felt were desirable 

for a low-temperature heat capacity calorimeter include: 

1. Use of liquid helium as the lowest temperature 

refrigerant for safety reasons. 

2. Ability to precool the calorimeter to near 50 K to 

economize on the amount of liquid helium used. 

3. Use of automatic regulation for temperature control 

of the adiabatic shield. 

A solution calorimeter which satisfied most of the 

above requirements was described by Robie (1965). 

Six years experience with this calorimeter (W aldbaum 

and Robie, 1966, 1972), including measurements with 

10 N HF at 70°C and 4 N HCl at 30°C and 3.5 atmospheres C02 pressure, suggested a number of improvements in the design, operation, and methods of 

data reduction which have been incorporated in the 

aparatus described in this report. 

A first version of the cryostat 1 used for the lowtemperature heat capacity measurements was built 

in 1959. The basic geometry of the cryostat is similar 

to one described by Morrison and Los (1950). 

ACKNOWLEDGMENTS 

We wish to express our appreciation to Rudolph 

Raspet, Raymond Trulli, W. H. Wilson, and Alex 

Herold, of the U.S. Geological Survey, and to Ralph 

Orwick, U.S. National Bureau of Standards, for help 

in the construction of the two calorimeters. We are 

also much indebted to Prof. Edgar F. Westrum, Jr., 

and Dr. Bruce D. Justice, Department of Chemistry, 

University of Michigan, for providing us with the 

1 A cryostat is a device used for maintaining and controlling temperatures below 

0°C. In this report we shall frequently use the abbreviations LN 2 and LHe to mean 

liquid nitrogen and liquid helium, respectively. LN2 boils at 77.3 K and LHe 

boils at 4.2 K. 
LOW TEMPERATURE HEAT CAPACITY CALORIMETER 3 

Fortran IV orthogonal polynomial curve fitting routine 

used at the Thermochemistry Laboratory of the University of Michigan, and to Walter Anderson of the U.S. 

Geological Survey for writing an early version of the 

X-Y plotter program. We thank Dr. D. W. Osborne 

and Prof. Edgar F. Westrum, Jr., for making their 

unpublished results on benzoic acid available to us. 

Dr. Stewart Gunn (University of California Lawrence 

Radiation Laboratory) called our attention to the 

transitions in Teflon near 25°C which had caused us 

many inexplicable problems prior to his help. The 

work described in this report was supported in part 

by National Aeronautics and Space Administration 

(NASA) contract T-75405. One of us (Hemingway) 

wishes to thank the National Science Foundation for 

partial support under grant G .A. 1651. 

LOW-TEMPERATURE HEAT CAPACITY 

CALORIMETER 

The calorimeter cryostat is shown in figure 1. The 

outer part of the cryostat is a commercial 0-ring 

flanged stainless steel Dewar flask (Minnesota Valley 

Engineering-F2A) 2 of 18.7 centimeters inside diameter, 

76 em internal depth, and 18.6 liter capacity (h). It 

is equipped with a Richards-type valve (Scott, 1959, 

p.182) for reevacuation if necessary. The upper plate 

of the cryostat seals against the 0-ring in the Dewar 

flange. This permits evacuation of the space over the 

LN 2 and eliminates the large outer jacket common to 

immersion-type cryostats operating below 77 K, such 

as those described by Giauque and Egan (1937), Cole, 

Hutchens, Robie, and Stout (1960), and Sterrett, 

Blackburn, Bestul, Chang, and Horman (1965). 

CRYOSTAT COMPONENTS 

SUBMARINE 

A vacuum submarine ( m) is supported within the 

Dewar by a thin-walled (0.064 em) stainless steel tube 

and is attached to a high-vacuum system by a rotatable 

0-ring flange (d). The submarine is constructed of 

2 Reference to specific manufacturers and model numbers is made to facilitate 

understanding and does not imply endorsement by the U.S. Geological Survey. 

FIGURE 1.-Cross section of helium cryostat for heat capacity 

measurements between 10 and 380 K. a,Twenty-eight pin electrical feed through, with protective aluminum cap; b, vacuum 

elevator for mechanical heat switch; c, connection for cryogenic 

vacuum pump; d, flange to vacuum system; e, filling tube for 

LN2;/, helium gas vent; g, filling tube for LHe; h, 0-ring flanged 

Dewar flask; i, aluminum gasket; j, copper heat station; k, 

electrical standoffs; l, helium economizer; m, cryogenic vacuum 

submarine; n, LHe reservoir; o, mechanical heat switch; p, 

floating ring; q, adiabatic shield; r, platinum resistance thermometer; s, heater-thermometer bobbin; t, calorimeter (sample 

container); u, isothermal shield. 

type 304 stainless steel, and all joints are fusion heliarc welded without the addition of filler rod using the 

(J) 

0:: 

LLJ 

1-

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z 

LLJ 

(.) 

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!:e 

'<t ;:!; 

~ 

8 

ID 

'<t 

0 

N 

0 

a 

b 

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d 

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f 

g 

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j 

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p 

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t 

u 
4 CALORIMETERS, HEAT OF SOLUTION AND LOW-TEMPERATURE HEAT CAPACITY MEASUREMENTS 

techniques of R. R. Orwick (U.S. National Bureau of 

Standards, 1968). It is 40.6 em deep, 13.97 em in 

diameter, and has a wall thickness of 0.13 em. The 

inner surface is nickel plated. The submarine is sealed 

with eight )i -20 bolts which compress an annealed 

aluminum gasket (i) against knife edges machined into 

the ·surfaces of the closure flanges. The knife-edge 

seal has proved to be highly reliable and will sustain a 

vacuum of 10-7 torr at 50 K. 3 To minimize heat transfer 

to the calorimeter by gaseous conduction and convection, the inside of the submarine is maintained at a 

pressure of 10-6 torr. Heat exchange by radiation is 

minimized by plating all metallic surfaces within the 

submarine with either nickel or gold (emissivity 

~0.03). A reservoir for LHe, a gas heat exchanger, 

the sample container (calorimeter), and its associated 

isothermal and adiabatic shields are supported within 

the submarine. 

ELECTRICAL LEAD WIRES 

Twenty-eight wires (25 copper and three constantan) 

enter the cryostat through a tubular multiheader 

connecter (a). A heavy walled aluminum cap covers the 

electrical junction. The copper leads, No. 32 American 

Wire Gage (Nylclad insulated) and No. 32 A WG 

constantan (double Formvar insulated), are wound 

into the grooves of a 28-lead screw thread (0.025 em 

deep) machined into the outer surface of the heat station (j) and are soldered to metal-ceramic electrical 

standoffs (Latronics 95 :0034) at the base (k) of the 

heat station. 

HEAT STATION 

The heat station (j), whose upper surface is in direct 

contact with the refrigerant in the Dewar flask, is a 

copper ring, welded to the top plate of the submarine. 

Its functions are to bring the electrical lead wires 

(at room temperature) to the temperature of the bath 

(LN 2) and thus minimize the heat conducted to the 

helium reservoir and to provide an isothermal junction 

for connecting the smaller diameter wires (No. 36 

AWG) which pass to the helium economizer, helium 

reservoir, floating ring, adiabatic shield, and finally 

the calorimeter. Fifty centimeters of each wire is 

wound onto the heat station and cemented in place 

with a thermosetting, polyvinyl phenolic varnish 

(General Electric-7031 glyptal); the varnish is baked 

at 150°C for 2 hours. Scott (1959, p. 127) has shown 

that this length of contact should bring the wire temper8 We have found that by coating the metal gaskets with a thin film of stopcock 

grease they can be reused as many as five times. In an earlier version of this cryostat· 

we used the solder cup joint described by Giauque and Egan (1937). This was later 

modified to use a commercial Teflon-coated metallic V-ring seal. Although both of 

these seals worked adequately, they are neither as reliable nor as convenient as the 

soft aluminum seal used in our present cryostat. 

ature to within 0.5 K of the heat-station temperature. 

Ginnings· and West (1968) gave a rigorous heat-flow 

analysis of the problem of heat-stationing electrical 

lead wires in calorimetry. At the heat station the wires 

are soldered to electrically insulated terminals. Smaller 

gage wires (No. 36 AWG) are also soldered to these 

terminals and are wound into the grooves of a 28-lead 

screw thread cut into the outer surfaces of the helium 

economizer (l), helium reservoir (n), and the floating 

ring (p). From the floating ring the wires pass to the 

adiabatic shield (q) to which they are similarly 

thermally anchored and thence to the calorimeter (t). 

HELIUM RESERVOIR 

The LHe reservoir (n) is constructed of copper. It 

has an external diameter of 12.7 em, a depth of 14.0 

em, and a wall thickness of 0.11 em. A 28-lead screw 

thread (one turn in 5 em by 0.025 em deep) is cut into 

the outer surface of the helium reservoir. Both the 

helium reservoir and economizer have a nickel-plated 

surface 0.0002 em thick. Twenty-five copper and three 

constantan wires are wound into these grooves on the 

outer surface of the economizer and helium reservoir 

and on the floating ring, and are cemented into place 

with GE-7031 baked at 150°C for 2 hours. The LHe 

reservoir has a capacity of 1,500 cm3• It is connected 

to the top of the cryostat and to the helium economizer 

through thin-walled (0.05 em) stainless steel (type 304) 

tubes. A 200-ohm resistance heater is wound about the 

lower one-fourth of the helium reservoir to permit 

rapid warmup when necessary. 

ISOTHERMAL SHIELD 

An isothermal shield ( u) is attached to the base of 

the helium reservoir and entirely surrounds the adiabatic shield and calorimeter. It is made of copper, is 

15.24 em long, and has an inside diameter of 9.84 em. 

The wall thickness is 0.064 em. Both inner and outer 

surfaces are nickel plated. The shield is attached to 

the base of the helium reservoir by six 4-40 screws. 

A thin film of stopcock grease (Apiezon T) is used to 

improve thermal c·ontact between the mating surfaces. 

HELIUM ECONOMIZER 

The effluent gas from the LHe reservoir (n) exits 

through a 10-plate heat exchanger (l), the purpose of 

which is to increase the refrigeration efficiency of the 

LHe by utilizing the high heat capacity of the helium 

gas to precool the electrical lead wires wound on the 

outer surface of the exchanger, before they reach the 

reservoir. Its design follows that of Westrum (1962). 

FLOATING RING 

A copper" floating ring" (p) is suspended immediately 
CRYOSTAT COMPONENTS 5 

beneath the LHe reservoir by three nylon rods (0.5 

em diameter and 3.2 em long). The electrical lead 

wires from the helium reservoir are wound into grooves 

on the outer surface of the ring and are thermally 

anchored to the ring with GE-7031 varnish baked at 

150°C. The function of the ring is to bring the electrical 

leads to a temperature intermediate between that of 

the LHe reservoir and the adiabatic shield. Twentyone metal-ceramic electrical terminals are soldered to 

the base of the ring to provide isothermal junctions for 

connecting the wires from the adiabatic shield. A 100- : 

ohm heater and one junction of a differential thermocouple are also attached to this tempering ring. The 

other end of the thermocouple is attached to the adiabatic shield. A controller, similar to that used with the 

adiabatic shield, is used to maintain any desired temperature differential between the floating ring and the 

shield. 

VACUUM ELEVATOR AND HEAT SWITCH 

The calorimeter is supported by a nylon line from 

the vacuum elevator. A modified commercial vacuum 

rotary feed through (b) (National Research Corp. 

1301) is used to raise or lower the calorimeter. In the 

fully raised position the conical closure plug at the top 

of the calorimeter meshes with a mating cone at the 

top of the adiabatic shield, which in turn contacts a 

mating conical surface (mechanical heat switch) at 

the base of the LHe reservoir (n). This permits the 

calorimeter and adiabatic shield to be cooled by conduction to the temperature of the LHe reservoir while 

operating in a high vacuum. After the calorimeter and 

adiabatic shield have cooled to below 10 K, the rotation 

of the winch (b) is reversed, thus separating them from 

thermal contact. 

To maximize heat transfer, the conical surfaces of 

the heat switch were lapped together prior to plating 

in order to maximize the surface contact area. About 

3 hours is required to cool the calorimeter and shield 

from 52 to '4.2 K~ 

ADIABATIC SHIELD 

The adiabatic shield (q) is supported by three nylon 

lines immediately beneath the floating ring (p). It 

completely surrounds the calorimeter (t), and is in 

turn surrounded by the isothermal shield ( u). The 

function of the adiabatic shield is to enclose the calorimeter (sample holder) with a surface of uniform temperature which can be continuously maintained at 

the same temperature as the sample holder. When this 

condition is satisfied, t::.T is zero and there is no heat 

exchange between·the calorimeter and. its surroundings. 

The adiabatic shield is constructed of copper and is 

made in three parts, top, bottom, and side. A double 

lead screw thread is machined into the outer surface 

of each part and both inside and outside surfaces are 

gold plated (0.0005 em thick). No. 30 AWG Lohm wire 

(W. B. Driver Co., double fiber-glass insulated) is 

wound noninductively into the thread grooves on each 

section of the shield to serve as heaters. The resistance 

of each of the three heater sections is, within about 10 

percent, in the same ratio as the mass of each part, 

and accordingly, thermal gradients between the three 

parts of the shield should be negligible. The heaters 

are connected in series, and only a single differential 

thermocouple is used to control the shield-calorimeter 

temperature difference. The electrical lead wires to the 

calorimeter are recessed into a deeper set of 20 grooves 

beneath the heater windings to equilibrate them 

thermally with the adiabatic shield. 

CALORIMETER 

The calorimeter (t) used in the present investigation 

was machined from copper rod. It· has an outside 

diameter of 4.76 em, a depth of 7.62 em, and a wall 

thickness of 0.038 em. The end caps are 0.064 em 

thick. The outside surface is electroplated with gold 

0.0005 em thick. The complete calorimeter assembly is 

shown in figure 2. Four 0.038-cm-thick fins are silver 

soldered axially to the central reentrant well to promote rapid temperature equilibration between the 

calorimeter and sample. The calorimeter is closed 

using a 0.95-cm-diameter tapered threaded plug 

(fig. 2, A) and a Teflon tape seal. A small tube (B) in 

the top of the calorimeter is used to replace the air in 

it with dry helium gas to speed up heat interchange 

between the sample and the calorimeter. It is sealed 

with a small amount of soft solder. The empty calorimeter, including thermometer (F) and heater bobbin 

(E), weighs 157.0 grams and has an internal volume of 

117.1 cm3• 

THERMOMETER 

Temperatures are determined using a four-lead 

strain-free platinum resistance thermometer (Meyers, 

1932), calibrated by the U.S. National Bureau of 

Standards. It has an ice-point resistance of 34.94 

ohms and a sensitivity at ooc of 0.14 ohm degree-1

• 

The original calibration was in terms of the International Practical Temperature Scale of 1948, IPTS48 (Stimson, 1961), and the provisional U.S. National 

Bureau of Standards scale, NBS-55, between 10 and 

90 K. 

In 1968 the International Practical Temperature 

Scale was completely revised to bring practical temperature measurements into better agreement with 

the true thermodynamic temperature (Comite International des Poids et Mesures, 1969). The new scale 
6 CALORIMETERS, HEAT OF SOLUTION AND LOW-TEMPERATURE HEAT CAPACITY MEASUREMENTS 

B 

E F 

c 

FIGURE 2.-Cutaway drawing of the sample holder and heater bobbin-thermometer assembly. A, Conical closure 

plug; B, filling tube for helium gas; C, calorimeter body; D, false bottom; E, copper heater bobbin (heater wire 

not shown); F, platinum resistance thermometer. 
ADIABATIC SHIELD CONTROLLER 7 

is designated IPTS-68. We converted our original 

thermometer calibration to IPTS-68 using the tables 

of Bedford, Durieux, M uijlwijk, and Barber (1969) 

for the range 13 to 90 K, and a new calibration calculated by the U.S. National Bureau of Standards for 

temperatures between 90 and 500 K. 4 Johnston and 

Lindberg (1968) have recently described miniature 

platinum thermometers having three times the sensitivity and only one-tenth of the mass of the standard 

Meyers (1932) design of thermometer. We have employed one of these miniature thermometers in a newer 

design of sample holder which weighs only 50 g and 

permits using samples as small as 30 g while retaining a 

precision of 0.05 percent. 

HEATER 

The calorimeter heater is a coil of No. 34 AWG 

Evanohm wire, double fiber-glass insulated, which is 

wound bifilarly on a copper bobbin (fig. 1, s) which 

also serves as the holder for the platinum thermometer. 

The heater wire is wound noninductively into a doublelead screw thread cut into the outer surface of the 

bobbin and is attached to the bobbin using several 

coats of polyester varnish baked at 150°C. The heater 

resistance, 175 ohms, changes by only 0.8 percent between 17 and 308 K (Furukawa and others, 1964). 

The copper bobbin, with the thermometer in place, 

slips within the reentrant well of the sample-holder 

(calorimeter) body and is brought into thermal contact 

using Apiezon T stopcock grease (Westrum and 

others, 1968). 

CRYOSTAT HOIST 

When assembling or dismantling the calorimeter, 

the cryostat may be raised or lowered through a vertical 

height of 90 em by means of a motor-driven hoist and 

rotated through approximately 120°. A bracket rigidly 

connects the main vertical tube of the cryostat with 

two linear-motion bearings which slide vertically on 

a hardened 1.90-cm-diameter steel rod anchored to 

the frame containing the vacuum system. The cryostat 

is raised using a ~{s-horsepower split-phase reversible 

motor operating at 24 rpm (revolutions per minute) 

and having 101.4 em-kilograms of torque. 

VACUUM SYSTEMS 

Two vacuum systems are used with the cryostat. 

4 The corrected resistance-temperature data were fitted by orthogonal polynomials of the form 

where X is the transformed resistance (Justice, 1969). The R versus T data on 

IPT8-68 were entered at one-kelvin intervals from 14 to 100 K, two-kelvin intervals from 100 to 200 K, and five-kelvin intervals from 200 to 350 K. The maximum 

deviation of the observed resistances to the fitted polynomial between 45 and 350 K 

was 3 X10-4 kelvin. 

The cryogenic vacuum system is used to evacuate the 

space above the LN 2 in the Dewar flask and thus 

lower the bath temperature to about 52 K 6 immediately 

prior to transferring LHe into the helium reservoir. 

It consists of a 3.8-liter-second-1 oil-sealed rotary pump 

(Kinney KC-8), a 2.5-cm bellows-sealed valve (Veeco 

SR-100), and a pressure-vacuum gauge which is connected to the top of the cryostat (fig. 1, c), with a 

2.5-cm-diameter flexible stainless steel bellows and 

quick-connect type fitting (Mason-Renshaw FTH-106). 

This system can reduce the calorimeter temperature 

from 77.3 to 52 K within 4 hours. 

The requirements for the vacuum system used to 

insulate the calorimeter from its surroundings are 

high pumping speed at pressures as low as 10-7 torr, 

compact size, and the capability of pumping gaseous 

helium. This last requirement precluded the use of 

ion pumps. We also wished to avoid use of water lines 

for cooling the diffusion pump. 

The system used to evacuate the submarine consists 

of a 150-liter-sec--'-1 6.35-cm-diameter air-cooled diffusion 

pump (Vactonic-150) trapped by a demountable 1.5-

liter LN 2 cold finger and backed by a 1-liter-sec-1 

rotary oil pump (Welch 1405). Pressures are read 

using a cold cathode Phillips gauge (Consolidated 

Vacuum Corp. P-100). 3.8-cm butterfly valves (Alpha 

Systems 1600) and 3.8-cm-diameter stainless steel 

tubing are used to give high conductance. A bypass 

line permits the cryogenic submarine to be evacuated 

(to 10-4 torr) directly with the rotary oil pump while 

the diffusion pump remains on. Silicone oil (Dow 

Corning-704) is used to minimize the oxidation of the 

diffusion pump fluid and to provide a lower ultimate 

pressure. During measurements the system continuously maintains a pressure of ~ 5 X 10-6 torr and 

effectively eliminates heat exchange by gaseous conduction and convection. 

A small high-pressure cylinder (113-liter-capacity 

lecture bottle) of purified helium gas, a two-stage gas 

regulator, and two ball valves are also connected to 

the high-vacuum side of the system. The cryostat, 

both vacuum systems, and the cryostat hoist are 

mounted on a frame 63.5 em wide by 106.7 em high by 

119.4 em long constructed of 14-gauge Unistrut metal 

framing. 

ADIABATIC SHIELD CONTROLLER 

The apparatus used to maintain the adiabatic shield 

at the same temperature as the calorimeter is essentially 

identical with the controller described by West and 

Ginnings (1957) and will be only briefly discussed. 

It consists of a stable low-noise d-e amplifier (Leeds & 

6 The vapor pressure of solid nitrogen at 52 K is 5.7 torr. 
8 CALORIMETERS, HEAT OF SOLUTION AND LOW-TEMPERATURE HEAT CAPACITY MEASUREMENTS 

Northrup 9829), a 10-millivolt recorder (Leeds & 

Northrup Speedomax W) equipped with a 100-percentcontrol slide wire, a three-mode (proportional, rate, 

reset) current-adjusting controller (Leeds & Northrup 

CAT-80), and a 50-watt d-e power amplifier (HewlettPackard 6824A). Figure 3 is a block diagram of the 

adiabatic-shield controller. 

A differential thermocouple (Au+2.1 percent Co 

versus Cu) senses any temperature difference between 

the adiabatic shield and the calorimeter. The thermocouple voltage is amplified by the d-e amplifier and is 

displayed on the chart recorder. Any deviation of this 

D-C 

AMPLIFIER CHART 

RECORDER 

voltage from the recorder set point causes the threemode controller to put out a direct current proportional 

to the deviation from the set point. This current, 0-5 

milliamperes, is insufficient to heat the adiabatic shield, 

and accordingly it is fed to the d-e power amplifier 

which in turn puts power into the shield heaters to 

reduce the temperature difference to zero. The thermocouple sensitivity is about 11 microvolts deg-1 at 10 K 

and 38'·JLV. deg...:i at 300 K (Fuschillo, 1957). 

Inasmuch as the preamplifier has a sensitivity of 

0.1 JLV, the shield controller can maintain a zero temperature difference between the calorimeter and adia3-MODE 

CONTROLLER 

D-C 

POWER 

AMPLIFIER 

D 

_j 

w 

D-C 

POWER 

SUPPLY 

0:: 

w 

1-

w 

~ 

0:: 

0 

_.J 

DIFFERENTIAL THERMOCOUPLE 

I 

CJ) 

w 

ou 

<( 

u 

---------

EXPLANATION 

COPPER 

--------

GOLD+ 2.1 PERCENT COBALT 

-----

FIGURE 3.-Block diagram of adiabatic shield controller. 

(/)~ (]) 

<( 

D 

<( 
TEMPERATURE-ENERGY MEASUREMENTS CIRCUIT 9 

batic shield to ±0.01 o at 10 K and ±0.004° at temperatures above 50 K. 

ASSEMBLY 

The empty calorimeter is weighed, filled with sample 

( -5+100 mesh powder), and closed using the threaded 

conical plug (fig. 2, A). Teflon tape, 0.007 em thick, is 

wrapped on the pipe threads of the closure plug to 

form a vacuum-tight seal. The calorimeter is weighed 

again and placed in a vacuum bell jar. It is evacuated to 

10-6 torr and the vacuum broken to a pressure of 1 

atmosphere using purified helium gas passed through an 

activated-charcoal trap cooled with LN 2· The bell 

jar is quickly removed and the helium-exchange-gas 

tube (fig. 2, B) immediately sealed with soft solder. 

The calorimeter is weighed again (to determine the 

mass of helium gas). The sealed calorimeter is supported 

within the adiabatic shield by the nylon line from 

the vacuum winch. The electrical leads to the platinum 

thermometer, the calorimeter heater, and the differential thermocouple (between the sample container 

and adiabatic shield) are connected at the calorimeter. 

The bottom of the adiabatic shield is attached and the 

isothermal shield is fastened to the base of the helium 

reservoir. The base of the submarine is attached with 

eight ~ -20 steel bolts. 

The submarine is next lowered into the Dewar flask 

using the motorized hoist and the Dewar sealed to 

the upper flange of the cryostat. 

Mter assembly, the cryostat is connected to the highvacuum system, and the rotary oil pump is turned on. 

After 10 minutes, the diffusion pump is turned on. 

Approximately 2 hours is required to evacuate the 

submarine to a pressure on the order of 5 Xl0-5 torr. 

After 24 hours of evacuation, the system reaches a 

limit of 8X10-7 torr. 

Preliminary heat capacity measurements are made 

at room temperature to ensure proper operation of the 

apparatus. The Dewar is then filled with LN 2· At this 

time the valve separating the submarine and the 

diffusion pump is closed and helium gas at about 1 

torr pressure admitted to the submarine from the 

helium lecture bottle. The helium gas serves to promote 

heat exchange between the refrigerant, LN 2, in the 

Dewar flask and the internal parts of the submarine. 

Approximately 90 min is required to cool the calorimeter, adiabatic shield, helium reservoir, economizer, 

and the floating ring to 77.3 K. LN 2 is then added to 

the Dewar, the boiloff vents sealed, the cryogenic 

vacuum pump turned on, and the valve to the large 

rotary pump opened. 

Three hours of evacuation by the vacuum pump 

(capacity 3.8 liters sec-1) reduces the temperature 

within the Dewar flask to about 52 K. The valve 

separating the submarine and diffusion pump is next 

opened and the helium exchange gas pumped out, 

thus thermally insulating the internal parts of the 

submarine, at 52 K, from their surroundings. The 

exchange gas can be pumped out to the order of 

8Xl0-6 torr within 45 min after opening the valves. 

Precooling the internal components of the cryostat to 

52 K rather than the usual 77.3 K results in a substantial saving in the amount of LHe used and in the time 

required for cooling to 4.2 K. 

The helium reservoir is then filled with LHe using a 

vacuum-jacketed transfer tube, and the adiabatic 

shield and calorimeter are brought into thermal contact with the base of the helium reservoir using the 

vacuum winch and heat switch. 

The capacity of the LHe reservoir, 1,500 cm3

, is 

sufficient to cool the calorimeter and adiabatic shield 

to 4.2 K and permit approximately 7 hours of measurements before the LHe has evaporated. Immediately 

after filling, the helium transfer tube is removed 

from the cryostat, the helium filling tube (fig. 1, g) is 

sealed, and the exhaust vent (fig. 1, f) is connected to 

an oil bubbler to prevent condensation of solid air 

within the reservoir. 

Mter the calorimeter and adiabatic shield have 

cooled to 10 K or lower, they are separated from thermal 

contact with the helium reservoir using the winch. 

The controllers for the adiabatic shield and the floating 

ring are then adjusted, and measurement of the heat 

capacity is begun. Between 5 and 50 K the increment of 

temperature rise for each measurement is made approximately 10 percent of the absolute temperaturethat is, ~T~1 kelvin at 10 K, 3 kelvins at 30 K-and 

above 50 K the temperature increment for each 

measurement is kept constant at about 5 to 7 kelvins. 

TEMPERATURE-ENERGY MEASUREMENTS CIRCUIT 

As part of our initial design requirements, we desired 

that the methods for measuring the temperature ,and 

energy input should be the same for both the heat 

capacity calorimeter and the heat of solution calorimeter. For both calorimeters, temperatures are determined using a four-lead resistance thermometer, 

and the energy input is by electrical heating using a 

four-lead resistance heater having a very small temperature coefficient of resistance. This type of arrangement 

allows us to determine both temperature and electrical 

power input from only voltage measurements by 

using potentiometric methods. 

The measuring circuit, shown schematically in figure 

4, consists of a five-position thermal-free ( ±0.01 p.V) 

selector switch (Guildline 9145A), a six-dial threerange potentiometer, and a d-e chopper amplifier-null 

detector (Keithley 147) having a sensitivity of ±0.003 
10 CALORIMETERS, HEAT OF SOLUTION AND LOW-TEMPERATURE HEAT CAPACITY MEASUREMENTS 

r-----rl I• 

STRIP- NULL 6-DIAL I -=->: CHART ,...--

DETECTOR POTENTIOMETER I ..:r- tO: RECORDER L----..1 --r STAN DARD 

HP 71018 

...L. 

KEITH LEY 147 GUI LDLINE 9160D ..:rDIGITAL 

VOLTMETER 

TRIPLETT 

4235-F 

I 

SWITCH GUILDLINE 9145A 

·~ 

r--------------------, 

: I I I I I I 

I I 

: ~~~ ~~~~;-~ 

L~----r-- r--- ------~ 

AAlAAAAA. -v v v-v v v vv 

500 49500 

n n 

CELL INC LOSURE 

GUILD LIN E M2A 

1.0 .Q GUILDLINE 9330 

-'\1"..-A 

100.0 

n ,---___:r-____ .,.AVA"vA~ GUI LDLINE v v 9330 RELAY PB JMI 105-13 

r ------- .. _ -------

CONSTANT 

VOLTAGE 

POWER SUPPLY 

NORTH HILLS 

TC 602 CR V.v.vY 

EVAN OHM 

HEATER 

--------------l----1--------- --------------r----l----- --- J 

V.v.vY 

PLATINUM 

RESISTANCE 

THERMOMETER 

FIGURE 4.-Electrical measurements circuit for calorimetry. 
OPERATION AND DATA REDUCTION 11 

JJ.V with less than 0.002 JJ.V hour-I drift. The potentiometer (Guildline 9160D) has a range of 0.01 JJ.V to 

2.11 v and a linearity of 0.0005 percent. 

The 1-v full-scale output of the null detector passes 

through a filter-attenuator network and is displayed 

on a 25-cm-strip-chart recorder (Hewlett-Packard 

7101B) with half-scale sensitivity of 1 or 10 JJ.V. The 

null-detector chart recorder was calibrated using the 

0.1-JJ.v steps of the potentiometer, and the calibration 

is incorporated into the computer program used to 

reduce the data. The unattenuated output of the null 

detector is simultaneously displayed on a digital voltmeter (Triplett 4235-F). The noise level of the system 

is ±0.02 JJ.V. 

Times are recorded from a digital clock. The coil of 

a mercury-wetted contact relay (Potter-Bromfield 

JM1 105-13) is connected in series with the input 

trigger of a six-digit universal counter and 6-v battery. 

The relay has a closure time of 0.004 sec and is assumed 

to be the same on opening. Elapsed times for the energy 

input (300 to 1,000 sec) are read to 0.001 sec from the 

counter and should be correct to ±0.002 percent. The 

wires supplying current to the thermometer are connected in series with either 12.4- or 18.6-v direct current 

(Willard DD5-3 batteries), a 6,140- or 9,100-ohm fixed 

resistor of very small temperature coefficient, and a 

100-ohm standard resistor (Guildline 9330). The function of the large series resistor is to provide a quasiconstant current for the platinum or copper resistance 

thermometer. The batteries and the 6,140- or 9,100-ohm 

resistor are enclosed in a thermally insulated and 

electrically shielded box. 

The current leads of the heater are series connected 

to a d-e power supply (0.001 percent stability) and a 

1.0-ohm standard resistor (Guildline 9330). The potential drop across the heater is attenuated by a 100 :1 

voltage divider before being read on the potentiometer. 

The potential drop across the 1.0- and 100.0-ohm standard resistors and the voltage across the resistance 

thermometer are read directly on the potentiometer 

without attenuation. The four sets of voltage leads 

are connected to the five positions of the selector 

switch which permits any of the four voltages to be 

connected across the potentiometer. The fifth position, 

Vo, is shorted by a copper bar and provides a measure 

of the electrical zero of the measuring circuit. 

If we call the voltage across the 100-ohm resistor VI, 

across the platinum (or copper) thermometer v2, across 

the 1.0-ohm resistor V3, and across the voltage-divider 

tap v 4 and the resistance of the calibrated shunts 

(standard resistors) R10o and RI, then the current 

through the thermometer is 

ltherm =vdRioo amps (5) 

and the thermometer resistance is 

Rtherm = (v2. Rioo) /VI ohms. (6) 

The current through the heater is 

lhtr = (v3/R1)- (v4/500.0) amps (7) 

where 500.0 ohms is the resistance of the voltagedivider tap. The term v 4/500.0 is the parallel current 

through the voltage divider. The voltage drop across 

the calorimeter heater is 

Vhtr =V4(v.d.f.) volts (8) 

where v.d.f. is the voltage divider factor. 

The electrical energy supplied to the calorimeter 

heater is 

(9) 

Because of the constancy of the power supply and the 

very low temperature coefficient of resistance for the 

Evanohm heater wire, the integral in equation 9 can 

be replaced by 

(10) 

where the barred quantities are the mean values of 

the heater voltage and current and t1 -ti is the elapsed 

time of power input. The elapsed time is obtained from 

the time .. interval meter reading directly to 0.001 sec. 

OPERATION AND DATA REDUCTION 

The heat capacity of a material is determined by 

measuring the energy necessary to raise the temperature of the substance by a certain number of degrees. 

An example of a temperature-time curve for a typical 

heat capacity measurement is shown in figure 5. The 

time-voltage log of the heat capacity run shown in 

figure 5 is listed in table 1. These data are read directly 

from the recorder trace, which provides a permanent 

record of the run, and are transferred to coding sheets 

prior to computer processing. The sample identification, 

number of measurements, sample mass, gram formula 

weight, and the difference in weights for the helium 

exchange gas, stopcock grease, and Teflon tape between 

the filled and empty sample holder are entered on the 

first two lines of the code sheets. The data on the code 

sheets may be converted to punched cards for batch 

processing or entered directly into a time-sharing 

computer using a remote terminal. 

During the time periods labeled "fore rating" or 

"after rating" (fig. 5), the change of temperature with 

time, dT I dt, is on the order of 10-4 deg min-1• The 

te1nperature rise, corrected for heat exchange, is obtained by extrapolating the fore- and after-period temperatures to the midtime of the energy-input period. 
12 CALORIMETERS, HEAT OF SOLUTION AND LOW-TEMPERATURE HEAT CAPACITY MEASUREMENTS 

U) 

z 

>s2 

_j 

w 

~ 

z 

wsl 

0:::: 

:::> 

I-

<( 

~60 

o_ 

~ 

w 

IFORE RATING 

I 

~HEATING 

581800 1810 1820 

TIME 

AFTER RATING 

1850 

FIGURE 5.-Temperature-time curve for a heat capacity 

measurement. The calorimeter was filled with 83.96 g of 

benzoic acid. 

TABLE 1.-Time-voltage log of the heat capacity 

measurement shown in figure 5 

[The switch positions 0 through 4 correspond to the voltages across the shorted 

electrical circuit, the thermometer current shunt, the resistance thermometer 

the heater current shunt, and the heater voltage divider, respectively) ' 

Time Switch Potentiometer Null 

hr min position dial setting detef't.or (v) (J,iv) 

Fore-rating period 

18 2 0 0.000000 -0.005 

4 1 .205850 .150 6 2 .078220 .470 

8 2 .078220 .460 

18 10 2 .078220 .450 

12 2 .078220 .440 

14 2 .078220 .430 

16 0 .000000 -.030 

18 1 .205850 .085 

18 20 2 .078220 .400 

Heating period 1 

21 3 0.535000 8.20 

22 3 .535000 5.80 

23 4 .932360 5.50 

24 4 .932360 3.90 

25 3 .535000 -2.00 

26 3 ;535000 -4.45 

27 4 .932360 -5.35 

28 4 .932360 -8.00 

After-rating period 

18 30 0 0.000000 -0.010 

32 1 .205825 .350 

34 2 .091515 .580 

36 2 .091515 .565 

38 2 .091515 .550 

18 40 2 .091515 .535 

42 2 .091515 .520 

44 2 .091515 .505 

46 1 .205825 .310 

48 0 .000000 -.030 

1 Power turned on at beginning and off at end of this period. Elapsed heating time, 480.029 sec. 

Stout (1968) gave a complete discussion of the calculations and general problems of correcting for heat 

exchange in low-temperature calorimeters. On page 25, 

we discuss in detail the sources of heat exchange and 

methods of correction for a solution calorimeter; since 

most of the development is directly applicable to the 

low-temperature measurements, we will defer further 

discussion of heat exchange until the later section. 

A computer program converts the raw data, table 1, 

into resistances and energies using equations 5 through 

10. The method of converting the resistances to temperatures depends upon the temperature range. Below 

45 K, temperatures are obtained from a stored resistance-temperature table by Lagrangian interpolation. 

Above 45 K, the polynomial expression (footnote 

4, p. 7) is used to calculate the temperature. 

During measurements the pressure on the solid 

sample in the calorimeter changes from 1 atmosphere 

at 300 K to 0.03 atmosphere at 10 K. The ~(pV) 

term for the sample is therefore negligible, and we 

may write 

Ej~Tcorr =~Hj ~Tcorr (11) 

where E is the electrical energy introduced into the 

sample container and ~H is the enthalpy change. 

The heat capacity differences for the helium exchange 

gas, soft solder, and Teflon tape seal are now subtracted from ~HI ~Tcorr· The heat capacity at constant 

volume, Cv, of the helium is assumed to be independent 

of temperature and to have the value 0.744 cal g-K-1 

(Guereca and others, 1967). The soft-solder difference 

correction is made using the heat capacities for tin and 

lead given by Hultgren, Orr, Anderson, and Kelley 

(1963). The correction for the stopcock grease is made 

using the heat capacity data on Apiezon T of E. F. 

Westrum, Jr. (written commun., Jan. 16, 1970), and 

that for Teflon tape from the data of Furukawa, 

McCoskey, and King (1952). 

Below 35 K, the observed ~HI ~T values are corrected for curvature using the relation 

c. =dHjdT~tJ.H/ t;T -tJ.'H/ aT{ 1:). . . (12) 

where H/ ~T2 is the second difference of the observed 

~HI ~T versus T curve (Osborne and others, 1925). 

Higher power terms are negligible. 

The heat capacity of the empty calorimeter is next 

subtracted from ~H/~Tsample+container and the result 

multiplied by the factor (formula weight/sample mass) 

to give molal heat capacities. 

Orthogonal polynomials (Justice, 1969) are then 

used to generate a least squares fit to the molarheat 

capacity data and obtain a smooth table of Cp versus 

temperature. Curve fitting is usually done in two parts 
HEAT OF SOLUTION CALORIMETER 13 

with a 10 kelvin overlap near that temperature at 

which the fUrvature of the heat capacity, d2CpjdT2, 

changes sign. The experimental data are plotted on an 

80-cm-wide X-Yplotter (Calcomp 763). This eliminates 

the tedium of hand plotting while retaining the accuracy 

(±0.006 em) of manual methods. A separate computer 

program uses the smoothed molarCP values to calculate 

the thermodynamic functions Sr, (Hr-Ho/T), and 

(Gr- H o) /T at integral values of the kelvin temperature between 0 and 350 K. 

HEAT CAPACITY RESULTS FOR CALORIMETRY 

CONFERENCE BENZOIC ACID 

At the request of the 1948 Calorimetry Conference, 

the U.S. National Bureau of Standards prepared 

uniform samples of a-Al203 (corundum), n-heptane 

(CHa(CH2)6CHa), and benzoic acid (C6HsCOOH) 

for the intercomparison of low-temperature heat 

capacity calorimeters. Benzoic acid has a high specific 

heat at low temperatures and is also used as a standard 

for acidimetry and for combustion calorimetry. Furukawa, McCoskey, and King (1951), Busey (1955), 

Osborne, Westrum, and Lohr (1955), Cole, Hutchens, 

Robie, and Stout (1960), Taylor and Smith (1962), 

E. F. Westrum, Jr. (written commun., 1970), and D. 

W. Osborne (written commun., 1970) have made 

measurements on the Calorimetry Conference benzoic 

acid sample using both adiabatically shielded and 

isothermal-type calorimeters. To check the performance 

of our calorimeter, we have measured the heat capacity 

of the Calorimetry Conference benzoic acid sample 

between 25 and 305 K. During the measurements, the 

calorimeter contained 83.960 g of sample. The weight 

of the empty calorimeter was 143.072 g. The sample 

accounted for 7 4 percent of the total observed heat 

capacity at 35 K and 65 percent at 300 K. 

Unfortunately, neither the Calorimetry Conference 

nor the U.S. National Bureau of Standards has yet 

reported recommended values for this material. In 

order to provide a best value curve for comparison with 

our results, we statistically smoothed the data of 

Furukawa, McCoskey, and King (1951), Busey (1955), 

Osborne, Westrum, and Lohr (1955), D. W. Osborne 

(written commun., 1970), Cole, Hutchens, Robie, 

and Stout (1960), and E. F. Westrum, Jr. (written 

commun., 1970) using orthogonal polynomial curve 

fitting (Justice, 1969). This was done in two parts with 

a 10 kelvin overlap at 45 K. In the smoothing, each 

point was given equal weight, and no attempt was made 

to correct all the data to the same temperature scale. 

The correct statistical treatment would have included 

weighing each of the data in proportion to the sensitivity of the thermometer used and also to the ratio 

Cp sample/Cp sample+container· These data were not available for each set of measurements. Results for the molar 

heat capacity of the Calorimetry Conference sample of 

benzoic acid are shown in the form of the deviations, 

Cp(observed) -Cp(smooth), as a function of temperature in figure 6. The values of Cp from the least squares 

fit are given in table 2. 

Our measurements on this sample on the temperature 

scale IPTS-48/NBS-55, with 0°C =273.15 K, are 

listed in chronological order of measurement in table 3 

and are shown in a deviation plot in figure 7. The 

right-hand column of this table gives the deviation of 

our experimental observations from those of the best 

fit curve, table 2. With the exception of two points, 

our data are within 0.13 percent of the least squares 

curve. There is some indication that our results may be 

systematically low by as much as 0.1 percent at temperatures above 250 K. 

The benzoic acid data were also calculated using 

the IPTS-68 scale. As was anticipated, these results 

differed by as much as 0.1 percent from those calculated 

using the IPTS-48 /NBS-55 scale, and the largest 

differences occurred in the temperature range where 

the difference in the temperature scales is changing 

most rapidly. 

HEAT OF SOLUTION CALORIMETER 

The calorimeter and submarine assembly is shown in 

figure 8. In this calorimeter, heat interchange is minimized by surrounding the calorimeter with a high 

vacuum to eliminate heat transfer by both gaseous 

conduction and convection, by eliminating many of 

the direct thermal links between the calorimeter and 

the bath, and by constructing those remaining links of 

poorly conducting materials such as Teflon or stainless 

steel with small cross-sectional areas. The thermal 

response time of the calorimeter was made short by 

fabricating it of copper and by having a sharp, welldefined boundary between the calorimeter and its 

surroundings (Sunner and Wadso, 1959). 

COMPONENTS 

SUBMARINE 

The reaction vessel (calorimeter proper) is suspended 

within a vacuum jacket called a submarine (z). The 

submarine is rigidly supported by four 1.27 -em demountable steel rods connected at socket i in a 75-

liter constant-temperature water bath (Aminco 4-1585) 

held to ±0.01 °C. The top of the submarine is submerged to a depth of 10 em beneath the bath surface. 

The submarine is made of type 304 stainless steel, and 

the vertical tubes containing the electrical leads ahd 

the connection to the vacuum system are thin-walled 

stainless steel to minimize surface corrosion. The inner 

surface of the submarine is nickel plated, 0.0013 em 
0.11 1 1 1 I I I I I I I I I I I I I I 1 

(/) I C;. 

z 

~ + w C;. C;. 

~ + 0 C;. I 

0 C;. 0 X ..J 

+ 

X 

X 

xC!. X X 0 + C;. 0 0 0 + e;.O 0 

+ 

1 1 1 I I I I I I I I I I 

+ 

X X 

X XX 

X 

X 

XX 

+ 0 0 

+ 

<> X 

+ 

+ 

<> <> 

X 

X X 

X C;. 

X 

X 

0 0+0 + + ~ 0 0 + ,o.o C;. 

0 

0 0 

Oe;. 

0 

0 <> 

0 <> C;.~ ..J X 

C;. C;. oo 0 <( 0 \0 + 0 + <> u 0 0 0 <> C;. 

z 0 

- + + 0 oO C;. <> 6 <> 0 <I 

0 

C;. 

0 

C;. 

oO 

C;. C;. a+- 0 

0 

C;. <> 

C;. 

C;. 

0 

C;.o 0 

\ C;. 0 

-1.0 

percent 

-0.1' I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 

0 100 200 300 

TEMPERATURE, IN KELVINS 

FIGURE 6.-Deviation plot of the measured values for the heat capacity of the Calorimetry Conference sample of benzoic acid. The sources of the data are as fo1lows: 

0, Furukawa, McCoskey, and King (1951); b. and+, Busey (1955); X, E. F. Westrum, Jr. (written commun., 1970); 0, Cole, Hutchens, Robie, and Stout (1960); 

O, Osborne, Westrum, and Lohr (1955). 

~ """"" 

() 

> t-t 

0 

~ 

~ t:-:l 

t-3 

t:-:l 

~ 

sn 

::t: 

t:-:l 

> t-3 

0 

"%.:1 

U2 

0 

t-t 

q 

t-3 

~ 

0 

z 

> z 

t1 

t-t 

0 

~ t-3 

t:-:l 

a:: 

'i:l 

t:-:l 

~ 

> d 

~ 

t:-:l 

::t: 

t:-:l 

> t-3 

~ 'i:l 

> 9 

t-3 

~ 

a:: 

t:-:l 

> U2 

q 

~ 

t:-:l 

a:: 

t:-:l 

~ U2 
HEAT OF SOLUTION CALORIMETER 15 

TABLE 2.-Least squares values for the heat capacity of the 

Calorimetry Conference sample of benzoic acid 

Temperature 

(K) 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

32 

34 

36 

38 

40 

42 

44 

46 

48 

50 

55 

60 

65 

70 

75 

80 

85 

90 

95 

100 

105 

110 

115 

120 

125 

130 

135 

140 

145 

150 

155 

160 

165 

170 

175 

180 

185 

190 

195 

200 

205 

210 

215 

220 

225 

230 

235 

240 

245 

250 

255 

260 

265 

270 

275 

280 

285 

290 

295 

300 

305 

Cp (cal mole-1 K-1) 

0.482 

.815 

1.212 

1.654 

2.132 

2.637 

3.160 

3.693 

4.224 

4.748 

5.257 

5.752 

6.230 

6.694 

7.141 

7.568 

7.975 

8.363 

8.737 

9.098 

9.447 

10.239 

10.967 

11.628 

12.232 

12.802 

13.346 

13.880 

14.371 

14.824 

15.272 

15.722 

16.175 

16.630 

17.083 

17.535 

17.987 

18.439 

18.892 

19.348 

19.807 

20.269 

20.734 

21.202 

21.674 

22.149 

22.628 

23.111 

23.599 

24.091 

24.589 

25.091 

25.597 

26.108 

26.623 

27.141 

27.663 

28.189 

28.719 

29.254 

29.794 

30.338 

30.887 

31.439 

31.992 

32.546 

33.099 

33.651 

34.204 

34.760 

35.317 

35.865 

Cp (joules mole-1 K -1) 

2.019 

3.410 

5.069 

6.921 

8.919 

11.031 

13.222 

15.450 

17.675 

19.864 

21.996 

24.064 

26.067 

28.006 

29.876 

31.665 

33.367 

34.992 

36.555 

38.065 

39.526 

42.841 

45.888 

48.654 

51.178 

53.566 

55.841 

58.076 

60.127 

62.026 

63.898 

65.782 

67.678 

69.578 

71.476 

73.368 

75.258 

77.148 

79.045 

80.952 

82.871 

84.804 

86.750 

88.710 

90.684 

92.672 

94.676 

96.698 

98.738 

100.80 

102.88 

104.98 

107.10 

109.24 

111.39 

113.56 

115.74 

117.94 

120.16 

122.40 

124.66 

126.94 

129.23 

131.54 

133.86 

136.17 

138.48 

140.80 

143.11 

145.44 

147.77 

150.06 

TABLE 3.-0bserved heat capacities of Calorimetry 

Conference sample of benzoic acid 

[Temperature scale is IPTS-48/NBS-55. 0°C =273.15 K. t:..Cp is the difference 

between our measurement values and the least square values given in table 2] 

Temperature (K) 

54.51 

57.05 

60.80 

65.81 

Cp (cal mole-1 K-1) 

Series I 

10.184 

10.547 

11.007 

11.728 

+0.006 

+.002 

-.002 

.000 

TABLE 3.-0bserved heat capacities of Calorimetry 

Conference sample of benzoic acid-Continued 

Temperature 

(K) 

71.74 

77.87 

83.59 

89.26 

94.91 

54.57 

93.53 

99.23 

105.18 

111.14 

116.90 

122.45 

128.05 

133.70 

139.21 

144.57 

149.92 

155.39 

161.10 

166.88 

172.94 

29.11 

30.93 

39.44 

42.34 

45.14 

48.17 

52.07 

56.38 

169.27 

175.44 

181.84 

188.20 

194.53 

200.83 

207.10 

213.50 

219.92 

226.30 

232.75 

228.97 

235.42 

241.83 

248.48 

255.45 

262.28 

268.99 

275.58 

282.06 

288.43 

294.68 

300.84 

Cp (cal mole-1 K-1) 

Series 1-continued 

12.424 

13.105 

13.744 

14.312 

14.704 

Series II 

10.543 

14.704 

15.214 

15.748 

16.285 

16.806 

17.310 

17.821 

18.325 

18.825 

19.313 

19.804 

20.306 

20.817 

21.379 

21.941 

Series III 

5.025 

5.493 

7.485 

8.039 

8.583 

9.125 

9. 771 

10.435 

Series IV 

21.585 

22.179 

22.801 

23.408 

24.036 

24.661 

25.284 

25.929 

26.594 

27.253 

27.918 

Series V 

27.527 

28.210 

28.889 

29.611 

30.355 

31.096 

31.846 

32.579 

33.267 

33.973 

34.658 

35.357 

-.010 

-.011 

+.012 

+.017 

+.017 

-0.005 

+.012 

+.010 

+.008 

+.005 

+.005 

+.005 

+.010 

+.003 

+.005 

+.004 

+.005 

+.002 

-.019 

.000 

-.001 

-0.006 

+.004 

+.003 

-.005 

+.005 

-.004 

-.013 

-.011 

-0.020 

-.012 

-.005 

-.016 

-.009 

-.011 

-.020 

-.026 

-.021 

-.024 

-.034 

-0.028 

-.023 

-.026 

-.018 

-.032 

-.043 

-.035 

-.031 

-.059 

-.056 

-.067 

-.052 

thick. The submarine is sealed with a rubber 0-ring 

and is connected to a high-vacuum system with a 

rotatable 0-ring flanged seal (f). 

The vacuum system is identical with that used with 

the low-temperature heat capacity calorimeter. It 

provides a pumping capacity of 150 liters sec-1 at 10-5 

torr. It has a bypass line which permits the calorimeter 

to be taken apart, reloaded, and assembled while the 

diffusion pump remains on. On reassembly the submarine is evacuated directly by the roughing pump to 
0.1~~--~~--~--~~--~~--~--~~--~~--~~--~--~~--~~--~--~~--~--.--,--.--,--~--.--

(f) 

z 

-

> 

_J 

w (--- I & & A. ~ 

I 

w 

_J 

0 0.0 ~ 

-...... 

_j 

<! 

u 

z 

-

~ 

0.. 

0 

<J 

-0.1~~--~~--~~--~~--~~--~~--~~--~~--~~--~~--~~--~~--~~--~~--~~--~~ 

0 200 300 

TEMPERATURE, IN KELVINS 

FIGURE 7.-Deviation plot of U.S. Geological Survey measurements of the heat capacity of the Calorimetry Conference sample of benzoic acid. The data indicated by 

circles were reduced on the temperature scale IPTS-48/NBS-55. The points indicated by solid triangles were calculated on the basis of IPTS-68. 

1--l 

~ 

Cl 

> t""l 

0 

~ ~ 

~ 

I?:J 

t-3 

I?:J 

~ 

sn 

~ 

I?:J 

> t-3 

0 

~ 

r:n. 

0 

t""l 

q 

t-3 

0 

-

z 

> z 

tj 

s 

~ 

8 

I?:J 

~ 

1-0 

I?:J 

~ 

> d 

~ 

~ 

I?:J 

> t-3 

~ > Cl 

~ 

t-3 

~ 

== I?:J 

> UJ 

0 

~ 

~ r:n. 
HEAT OF SOLUTION CALORIMETER 17 

10-4 torr through the bypass line before opening to 

the diffusion pump. About 30 minutes is required for 

the submarine to reach about 5 X10- 6 torr. 

CALORIMETER VESSEL 

The body of the calorimeter (y) was spun from 0.635-

cm-thick copper plate on a steel mandrel. The external 

surface was machined to its final dimensions and the 

inner surface polished to an approximately 25 ~em rms 

(microcentimeter root mean square) finish using a 

flexible canvas lap loaded with 15-micron silicon 

carbide. 6 

The internal surface was electroplated with 0.004 

em of gold and then burnished with ball bearings as 

described by Robie (1965). A second layer of gold was 

then deposited to give a total thickness of 0.008 em. 

A 0.0005-cm gold plate was coated on the outer surface 

to minimize its emissivity. 

We have also used copper vessels coated with Teflon, 

0.013 em thick, deposited by flame spraying. This type 

of coating is quite satisfactory, does not cause any 

discernible delay in the thermal response of the calorimeter, and costs only about one-eighth as much as the 

heavy gold plating. Its only disadvantage is that, in 

the transition between 20° and 30°C, the thermal 

properties of the calorimeter vary nonlinearly, which 

complicates data reduction. For heat of solution studies 

of silicates in HF at temperatures above 30°C, this 

effect is not involved. 

CALORIMETER TOP AND CLOSURE SEAL 

The top of the calorimeter (q) was made from copper 

sheet 0.32 em thick. Both surfaces were lapped to a 

3-~cm-rms finish on a commercial lapping machine 

(Crane Lapmaster). A 4-40 flathead screw soldered to 

the upper surface serves the dual purpose of being the 

contact for the electrode during electroplating and 

afterward being a lug for attaching the electrical 

ground lead to the calorimeter. 

The two-piece closure ring (r) was made of aluminum 

and used a 3.9-threads-cm-1 modified acme thread for 

sealing. The bottom surface of the male part of the 

ring was flame sprayed with Teflon to prevent scratching of the gold-plated calorimeter top. The outer 

surface of the female part of the ring was plated with 

0.0005-cm-thick gold. A spanner wrench was used to 

tighten the top. 

& Both the steel mandrel upon which the calorimeter body is to be spun and the 

copper plate used to form the body should have a high surface finish. This eliminates 

much tedious polishing later and ensures a more satisfactory electroplate. Our 

experience has been that a corrosion-free surface may be obtained on either copper 

or aluminum, providing that the surface of the base metal is well polished ( ~25 

"em rms) prior to plating, that there are no sharp edges or bends (only smooth 

curves with a radius of curvature ( ~0.1 em), that the plating is burnished between 

successive deposits of gold, and that the gold has a total thickness of at least 

0.01 em. 

THERMOMETER 

A copper resistance thermometer ( u) similar to that 

described by Robie (1965) is wound bifilarly on the 

outside of the calorimeter body. It consists of No. 

34 AWG copper magnet wire (Nylclad insulation) 

which is cemented to the body of the reaction vessel 

with a polyester varnish (G. E. Glyptal 7031) and 

baked at 150°C for 2 hours. The thermometer has an 

ice-point resistance of 109.71 ohms and covers approximately 65 percent of the outer surface of the calorim~ 

eter. A gold-plated copper sleeve, 0.013 em thick 

( v), fits snugly over the resistance thermometer and is 

sealed to the calorimeter body with a thin fillet of 

epoxy resin. 

The thermometer was calibrated between 0° and 

80°C by comparison with both a quartz thermometer 

and a strain-free platinum resistance thermometer. 

The raw data were fitted by an equation of the type 

R(T) = Ro(1 +a(T) +b(T) 2) (13) 

where T is the temperature in oc and Ro is the thermometer resistance at 0°C. The temperature sensitivity 

of the thermometer is 0.47 ohms deg-1 or 940 ~v deg-1 

using a 0.0020-ampere thermometer current. 

HEATER 

In most aqueous-reaction calorimeters a heater 

within a protective well projects into the solution 

(Torgeson and Sahama, 1948; Kracek and others, 

1951; Gunn, 1958; Sunner and Wadso, 1959; Kilday 

and Prosen, 1964). It would seem a priori that this 

type of construction might lead to appreciable temperature differences between the heater wire and the 

solution. In an attempt to improve the temperature 

equilibration between the solvent and the heater 

while at the same time retaining both the chemical 

inertness and high electrical insulation necessary, we 

constructed the unit described below. 

A 305-cm piece of fiber-glass-insulated Evan ohm 

wire (No. 34 A WG) was butt silver soldered at both 

ends to 15-cm lengths of copper wire (No. 30 AWG). 

A 0.010-cm walled gold tube, 61 em long by 0.318 

em outside diameter, was welded shut at one end. 

The composite wire of Evanohm and copper was 

folded into the form of the letter "W" and inserted 

into this tube. The tube was then rolled flat into a 

rectangular cross section 0.5 by 0.063 em. The flattened 

tube was then wound into the form of a spiral (fig. 8, s) 

and brought out through the top of the calorimeter. 

STIRRER SHAFT AND STIRRER MOTOR 

The two-piece hollow stirrer shaft (j, t) is seated in 

ball bearings at (d) and also in an 0-ring sealed needle 
18 CALORIMETERS, HEAT OF SOLUTION AND LOW-TEMPERATURE HEAT CAPACITY MEASUREMENTS 

a 

FIGURE 8.-Cross section of HF solution 

calorimeter. a, Thrust bearing; b, spring 

return; c, retainer guide for puncture 

tube; d, stirring-tube bearings and retainer ring; e, electrical feed through; J, 

rotatable 0-ring flange to vacuum system; 

g, stirrer motor (72 rpm/25 oz.-in. torque); 

h, timing belt drive (2: 1); i, support-rod 

connection socket; j, stirrer drive tube; 

k, hollow puncture tube; l, electrical 

standoff and lead wires; m, needle bearing; 

n ,0-ring seals for stirrer; o, Teflon calorimeter support flange; p, Teflon connecterseparator for stirrer drive; q, calorimeter 

top; r, calorimeter closure ring and 0-ring 

seal; s, calorimeter heater; t, gold stirrer 

tube; u, Copper resistance thermometer; 

v, gold-plated radiation shield; w, gold 

foil seal; x, Teflon sample holder-impeller 

with pop-out plug; y, calorimeter (reaction 

vessel); z, submarine. 
HEAT OF SOLUTION CALORIMETER 19 

bearing (m) just above the point of entrance to the 

calorimeter. The upper part of the stirrer shaft is a 

stainless steel tube. The lower part of the stirrer shaft 

(t), in direct contact with the solvent, is constructed 

of gold. It is connected to the upper part by a Teflon 

connecter (p) to avoid direct metal-to-metal contact 

and to reduce heat transfer. The connecter contains 

an 0-ring which forms a pressure-tight seal against the 

puncture tube (k). The outside diameter of the stirrer 

rod is sealed at the top of the calorimeter by two surface-flourinated (Lubrin) 0-rings to form a gas-tight 

rotatable seal capable of holding 3.5 atmospheres 

internal pressure. These 0-rings are removed when 

the calorimeter is operated at constant pressure. 

A capacitor reversible synchronous motor (g, Superior 

SS 25, 72 rpm/1.8 em-kg torque) is rigidly mounted 

on a bracket integral with the main vertical tube of 

the submarine. It drives the stirrer at 144 rpm through 

a toothed timing belt drive (h) and thus eliminates 

possible variation in the stirring rate due to belt 

slippage. 

PUNCTURE TUBE 

The puncture device (k) is a round-bottomed alumina 

tube having a 0.08-cm wall.7 The sample is brought 

into contact with the solvent by a sharp downward 

thrust on the shaft of the plunger. This ruptures the 

gold seal and pushes . out the Teflon plug, thus permitting the sample to react with the solvent. A springloaded thrust bearing (a) in a retaining cage (c) is 

attached to the puncture tube. The retaining cage 

prevents the puncture tube from being expelled from 

the calorimeter when a gas-producing reaction, such as 

the solution of a carbonate in HCl, takes place. 

The hollow construction permits the solution to be 

cooled in place without disassembling the calorimeter. 

A small amount of LN 2 is squirted into the puncture 

tube for cooling. This allows one to make the solution 

measurements over the same temperature interval as 

the electrical calibration, if desired (Gunn, 1958). 

(See fig. 10.) 

SAMPLE HOLDER AND IMPELLER ASSEMBLY 

The sample holder-impeller assembly (x) was machined from Teflon rod. The combined internal sample 

holder-impeller was designed to eliminate most of the 

inconvenience inherent in the methods of sample 

introduction used with the type of HF calorimeter 

described by Torgeson and Sahama (1948). Teflon was 

used because of its chemical inertness, ease of fabrica7 We have experimented with gold-plated and Teflon-coated hollow tubes with 

limited success. Eventually the abrasive nature of the samples scratched through 

the inert coating and permitted the acid to attack the base metal (stainless steel). 

tion, and low cost. Mter filling 8 and weighing, the 

sample holder is screwed onto the lower end of the gold 

end of the stirrer tube. A breakable gold foil seal ( w) 

0.003-cm thick at the top and a pop-out Teflon plug at 

the bottom of the sample holder separate the sample 

from the solvent prior to the initiation of the solution 

reaction. 

CALORIMETER SUPPORT CONNECTER 

The calorimeter is supported from the top plate of 

the submarine by a double-flanged Teflon tube (o). 

The support tube seals against the top plate of the 

submarine and against the calorimeter top (q) with 

rubber 0-rings. A double 0-ring seal (n) on the inner 

surface of the support tube seals the stirrer tube. 

OPERATION AND DATA REDUCTION 

The Teflon sample holder (C), figure 9, with the gold 

foil gasket (D) in place, is screwed onto an aluminum 

pedestal (E) for convenience in loading. The sample, 

-50-mesh powder, is poured into the holder, compressed lightly with a Teflon or polished stainless steel 

rod, and weighed. The bottom plug (A) is pressed into 

place to seal the holder and the entire assembly is 

inverted. The aluminum pedestal is removed and the 

filled sample holder is screwed onto the base of the 

stirring tube. A more complete description of this 

type of sample holder is given in Waldbaum and Robie 

(1970). The calorimeter, filled with a weighed amount of 

solvent, is then connected to the calorimeter top using 

the closure ring, the thermometer leads are soldered 

to their terminals, and the base of the submarine is 

attached. The complete assembly is mounted in the 

constant-temperature bath and locked into position 

using the support rods. The assembly is then connected 

to the vacuum system, the vacuum pumps are started, 

and the stirrer motor is turned on. Assembling the system requires approximately 15 minutes, and it takes 

about 30 minutes for the vacuum to reach 5 X 10-6 

torr. The calorimeter is then heated rapidly to the 

starting temperature of the initial calibration period 

and allowed to come to thermal equilibrium for 10 

minutes before measurements are begun. 

A heat of solution experiment consists of measuring 

the amount of electrical energy required to raise the 

temperature of the calorimeter a certain number of 

degrees (calibration) and observing the temperature 

change caused by the solution of a specified amount of 

sample in the calorimeter solvent (reaction). The heat 

s We have found a Parr pellet press very useful for increasing the amount of 

sample that can be contained in the sample holder. The original press dies were re- placed with ones made of hardened type 416 stainless steel with an inside diameter 

about 0.01 em less than the inside diameter of the sample holder. After compaction 

the sample can be pressed directly from the die into the sample holder. 
20 CALORIMETERS, HEAT OF SOLUTION AND LOW-TEMPERATURE HEAT CAPACITY MEASUREMENTS 

of solution, in calories per gram, is derived from these 

two measurements after correcting for heat exchange 

with the surroundings. 

A complete temperature-time curve is shown in 

figure 10. Because of the very low heat leak for this 

calorimeter, the temperature-time curves during a 

20-minute rating period are linear within the sensitivity 

of our temperature measurements. During a run the 

time, potentiometer-dial setting, selector-switch poA 

--B 

~c 

D 

0 

E 

FIGURE 9.-Sample holder and loading pedestal. A, Teflon 

sealing plug; B, powdered sample; C, sample holder-impeller 

body; D, gold foil seal; E, aluminum loading pedestal. 

sition, null-detector reading, and elapsed time of power 

input are noted on the recorder trace and are also entered on a preprinted code sheet, figure 11. 

Approximately 20 seconds before the start of the 

solution reaction, the null-detector range is changed 

from 10 J.LV to 100 or 300 J.LV and the voltage drop across 

the thermometer monitored continuously on the 

recorder. Mter the temperature rise has reached about 

90 percent of completion, the range is reset to 10 J.LV 

for added sensitivity in the tailing-off part of the 

temperature change and beginning of the after-rating 

period. 

The code sheets serve as guides for card punching 

or for entering data via a remote terminal for computer 

processing. The voltage-time data from the code sheets 

(fig. 11) are converted into resistances, temperatures, 

and energy using a Fortran computer program. Resistances are converted into temperatures from the 

thermometer equation using the Newton-Raphson 

iteration method (Margenau and Murphy, 1956, p. 

492). The program makes the necessary corrections for 

heat exchange and generates values of the isothermal 

heat of solution at the reference temperature, usually 

25° or 30°C. The printout of the program is shown in 

table 4. 

The Fortran IV -G source program is listed in 

table 5. With very minor modification we also use 

this program in a batch-processing mode. We use a 

time-shared IBM 360/65 computer and a remote 

terminal (IBM 27 41) for the computations. The individual t::.H values at various temperatures are fitted 

by least squares to determine the best value for the 

temperature coefficient, d(t::.H)/dT, of the solution 

reaction. This value is then used to adjust the individual values to the reference temperature (usually 

25°C). The standard error of estimate, thermochemical 

uncertainty (Rossini, 1956), is obtained from these 

values extrapolated to the reference temperature. 

CORRECTIONS 

The observational data (temperature-time and energy) must be corrected for heat exchange and for 

superheating of the heater during an electrical calibration, converted from constant volume (t::.U) to 

constant pressure (t::.H) (if the calorimeter was operated 

sealed), and corrected to the reference temperature to 

obtain the isothermal heat of solution AH sotn at the 

reference temperature. These corrections are discussed 

in the following sections. 

SOURCES OF HEAT EXCHANGE 

The observed temperature changes for a calorimeter 

surrounded by a constant-temperature heat sink 

(an isoperibolic calorimeter) must be corrected for 
CORRECTIONS 21 

heat exchange between the calorimeter and the constant-temperature bath. The total rate of heat transfer 

between the calorimeter and the surrounding bath 

can be expressed as 

surrounding submarine and upon the emissivities of 

the outer surface of the calorimeter and inner surface 

of the submarine, and it is proportional to the difference 

in the fourth powers of the absolute temperatures of 

the calorimeter and submarine. dQjdt=BN(Tc-TB) cal min-1 (14) 

where B N is the thermal conductance, in calories 

degrees-1 minutes-1; Q is heat, in calories; t is time; 

and T c and T B are the absolute temperatures of the 

calorimeter and bath. Heat exchange between the 

calorimeter and the bath takes place by four separate 

mechanisms: radiation, conduction through solid connections, and convection and conduction through a gas. 

dQ I dt = o-A cF ( T c 4 - T 8 

4). (15) 

In the above relation T s is the temperature of the 

submarine and is identical with T B, the bath temperature, o- is the Steffan-Boltzman constant, Ac is the 

surface area of the calorimeter, and F is the shape 

factor. The shape factor (Scott, 1959) is 

F =e. ·e,;(e.+ ~:(1-e,) e.) (16) RADIATION 

Heat exchange due to radiation depends upon the 

ratio of the surface areas of the calorimeter and the 

where A 8 is the area of the inner wall of the submarine 

and es and ec are the surface emissivities of the sub32.0 RUN H-10 

HYDROMAGNESITE IN 4 N HCI 

- 0.000518 deg min-I 124.8 

124.6 

31 ·

5 1----11NITIAL CALIBRATION--_______,.~REACTION PERIOO--,-J 

u 31.0 0 

z 

w .. a:: 

~30.5 <( 

a:: 

w 

a.. 

:!!: 

w 

1-

30.0 

-0.000098 deg min-I 

en 

:!!: 

124.4 ~ 

z 

I LL.i 

! u I I 124.2 ~ 

___ !__C!?Ll!!_~!lS!L____ ______ _ ______________________ _ 

FINAL CA~IBR~TION--~ ~ 

! ! u; I I W 

! ! a:: 

! ! 124.0 a:: 

I I w I I II I W 

I I ~ I I 0 

I I ~ ! ! I i i 123.8 a:: ~------------------------~-----------------------------:-------------------------:-----:-----------~------- w 

! ! I I I ~ I I ! ! ! I I I I I 

I I ! l ! I l I I I 

I I I I I 

l ! l l i 

i ! i ! ! 

r--HEATER ON i ! HEATER ON --4 r--

! ! ! i i 

T bath --------------~---------

_ 0.000745 de min-I 123.6 

123.4 I l \ l l 29'~1L0-0----~112L0--~--Iul4_0 ______ 1~16-0~----~~18_0 ______ !?~.0-0~----~2~2-0----~~2~4-0~----~2~6-0~ 

TIME 

FIGURE 10.-Temperature-time curve for the heat of solution of 4.6 g of hydromagnesite in 4 N HCl (run H-10). The shaded areas 

are 

i

t, 

(Too-T)dt deg min. 

t; 

For the initial calibration period this integral is positive, and for the final calibration period it is negative. The temperaturetime changes are indicated for the rating periods. 
22 CALORIMETERS, HEAT OF SOLUTION AND LOW-TEMPERATURE HEAT CAPACITY MEASUREMENTS 

TABLE 4.-Printout of computer reduction 

HEAT EXCHANGE CALCULATIONS FOR SOLUTION CALORIMETRY, DATE IS 1 0/111/1971 

RUN H 1 0 DATE-21 NOV., 1966 BOOK II PAGE 86•87 SAMPLE TE COALINGA, CAL. 

VACUUM(INITIAL-3.5E-5 FINAL-3.2E-5) BATH TEMPERATURE 28 .• 85 

TIME THERMOMETER EMF THERMOMETER CURRENT RESIST]\NCE TEMPERATURE DRIFT 

HR MIN MINUTES DIALS NULL ZERO SUM DIALS NULL ZERO SUM OHMS (C) DEG/MIN 

18.30.0 1110.000 132640. -1.35 0.05 132638.60 107335. 2.53 0.05 107337.48 123.571561 29.4511944 

18.48.0 1128.000 132640. 5.32 0.05 132645.27 107335. 2.39 o.os 107337.34 123.577934 29.468441 0.0007498 

HEATING PERIOD 1 

18.50.0 1130.000 29.469941 TI 

357712. 2.05 o.o 357714.05 18441111. 0.112 o.o 18114114.42 29.472941 TI 1 

35.769079 VOLTS 0.18325211 AMPS 195.1905114 30.312501 TF' 

18.58.0 1138.000 30.313656 TF 

TIME 480.060 SEC ENERGY 752.0740 CAL HEAT CAPACITY 895.105844 CAL/DEG MEAN TEMP. 29.892721 

19. o.o 1140.000 133075. -4.32 o.o 133070.68 107332. 2.68 o.o 107334.68 123.971338 30.314233 

19.27.0 1167.000 133075. -0.53 0.05 133074.42 107332. 2.56 0.05 107334.51 123.981019 30.322028 0.0002887 

SOLUTION PERIOD 

19.28.0 1168.000 30.322317 TI 

30.322333 TI 1 

19.30.0 1170.000 133491. 0.63 o.o 133491.62 107332.07 124.372542 31.150987 

DICKINSON TEMP 30.740732 OCCURS 0.06 MIN AFTER INITIAL TIME 31.159131 TF' 

20. 5.0 1205.000 ElAPSED TIME 37.00 31.155604 TF 

20. 6.0 1206.000 133492. 1. 77 o.o 133493.77 107330. 1.96 o.o 107331.96 124.374677 31.155509 

20.36.0 1236.000 133492. 0.14 0.01 133492.13 107330. 1.81 0.01 107331.80 124.373324 31.)52644 -0.0000955 

HEATING PERIOD 2 

20.37.0 1237.000 31.152549 TI 

357110. 0.12 o.o 357710.12 184436. 0.60 o.o 184436.60 31.152167 TI 1 

35.768687 VOLTS 0.18324431 AMPS 195.196715 31.989766 TF 1 

20.45.0 1245.000 31.987694 TF 

TIME 480.070 SEC ENERGY 752.0494 CAL HEAT CAPACITY 897.172306 CAL/DEG MEAN TEMP. 31.570966 

20.47.0 1247.000 133904. 8.04 o.o 1339,2.04 107328. 1.44 o.o 107329.44 124.767301 31.986658 

21. s.o 1265.000 133904. 3.14 o.o 133907.14 107328. 1.30 o.o 107329.30 124.762897 31.977338 -0.0005178 

SUMMARY 

CALIBRATION 1 CALIBRATION 2 SOLUTION 

DELTA T OBS. 

TEMPERATURE CORRECTION 

CORRECTED DELTA T 

CONVERGENCE TEMP 

ALPHA (*10000) 

BN 

HEAT OF STIRRING 

POWER 

OBS HEAT CAPACITY 

C EXTRAP. TO T(M,SOLN) 

DELTA II PER GRAM 

0.843715 

-0.004155 

0.839560 

30.838117 

5.492662 

0.491651 

0.000543 

6.554759 

895.105844 

895.7090 

-164.162.7 

DELTA U PER HOL -76843.5173 

0.835145 

0.002453 

0.837599 

30.962815 

5.042173 

0.452370 

0.000561 

6.554408 

897.172306 

896.6390 

-163.9924 

-76942.7314 

0.833287 

0.003511 

0.836798 

30.962815 

5.042173 

0.452370 

0.000561 

marine and calorimeter respectively. If we call the 

fraction of the thermal conductance caused by radiation 

BR, then 

(17) 

CONDUCTION THROUGH SOLID CONNECTIONS 

The heat leak due to conduction through each of the 

solid connections is proportional to T c- T B, the thermal 

conductivity, ki, and the cross-sectional area, ai, and 

is inversely proportional to the length of the heat 

path, l i· The total is 

dQjdt=~kt{},\Tc-TB) (18) 

i=l li 

DEG C 

DEG C 

DEG C 

DEG C 

1/MIN 

CAL/DEG/MIN 

DEG/MIN 

WATTS 

CAL/DEG 

CAL/DEG 

CAL 

CAL 

SAMPLE WEIGHT 

SAMPLE MASS 

FORMULA WEIGHT 

4.5688 GRAMS 

4.5705 GRAMS 

467.6740 GRAMS 

INTEGRAL (E/DT) 4939190.0100 M-VOLT-MIN 

(T(INF)-TM) -6.9624 DEG-MIN 

D(DELTA Q)/DT 0.2035 CAL/DEG-GM 

D(DELTA H)/DT 95.1631 CAL/DEG-MOL 

DELTA QAT 30.000 -164.4161 CAL/GRAM 

DELTA HAT 30.000 -76893.1244 CAL/MOL 

where the summation indicates the contributions due 

to the two Teflon connecters, the eight copper lead 

wires, and the puncture tube. The thermal conductance 

due to solid conduction is thus 

k1a1 k2a2 Bk=T+---z;-+···· (19) 

CONDUCTION AND CONVECTION THROUGH A GAS 

Heat transfer by convection and conduction through 

a gas varies with pressure. The theory is complicated, 

but the significant point is that at pressures below 5 

X 10-6 torr the mean free path of the gas molecules is 

large compared with the separation of the calorimeter 
CORRECTIONS 

TABLE 5.-Fortran IV-G computer program for reducing heat of solution data 

L.0001 /JOB GO 

L.0002 C HEA'l'-EXCIIAIIGE COMPUTATIONS FOR SOWTION CALORIMETRY 03/23/1970 

L. 0003 C I!"'RT IV - G OOUBLE PRECISION ARI'l'IIMETIC 

L. 0004 IMPLICIT REAL'S (A-H,D-Z) 

L.0005 DIMENSION E(20,4) ,C(20,4) ,TE(20,4) ,T(40) ,RK(6) ,R(20) ,A(85), 

L. 0006 1"1'8( 50) ,DELTKS(10) ,8(50) ,DRIFT(4) ,DELT(J) ,DELTEU) ,EM(10) ,CM(10), 

L.0007 2BETA(3) ,DELTK(J) ,ALPHA(J) ,CV(4) ,POWER(J) ,SP( 10) ,ES( 10) ,TS ( 10), 

L.0008 3G(30) 

L. 0009 C INITIAL ENTRY CARDS 1. (THERIIOIIETER CONSTANTS) 

L.0010 C 2. (GP'W,CP(T) CONSTANTS,DELTA H(T)) 

!;;"0011 C 3. (DATE OF CALCULATION), SUPERHBATING CORRECTION 

L.0012 80 READ(5,1) (RK(I) ,I•1, 3) ,GPW,DCDT1,DCDT2,DHDT,'l'MO,DAY ,YEAR,SP(1) 

L.0013 1 I!"'IUIAT(JD12. 7/U12.0/A2,A2,A4,1X,F10.0) 

L.OOU C READ THIRTEEN DATA CARDS I!"'R EACH RUN 

L.0015 328 READ(S,J) G(15),G(16),(A(N),N-2,12) 

L.0016 3 I!"'RIIAT ·(2(FJ.0),6X,11A6) 

~:~~~~ ~~g·-~~~D~NF~~TS~ ~U~~/~~~ :0~ ~:~!IAL ENTRIES 

L.0019 IF(G(15) - 100.) 611,1402,611 

L.0020 611 IF(G(15h·250.)3J,80,33 

L. 0021 BOOK-PAGE REl'BRENCE, BATH 'l"EliPERATURE, VACUUM, IIEIGHT, 

L. 00 2 2 REFERENCE 'l'EIIPERATURE AND VACUUM CORRECTION 

L.0023 33 READ(5,35) (A(N) ,N•25,29) ,T(20) ,A(J1) ,A(32) ,A (52) ,T(21) ,VACORR 

L.0024 35 FORMAT (SA6,F6.3,2A6,F8.4,F6.J,F10.8) 

L.0025 DO 177 L-1,8 

L.0026 READ (5,4) TE(L,1),TE(L,2),(E(L,M),M•1,J),C(L,1),C(L,2) 

L.0027 177 CONTINUE 

L. 0028 READ (5, 4) TE ( 9,1) ,TE (9, 2), (E (9,H) ,H-1, 3) ,C (9,1) ,C (9,2) ,TE (12,1), 

L. 0029 ITE( 12 ,2) ,TE ( 13,1) ,TE ( 13 ,2) ,A(Q6) 

L. 0030 READ (5, 4) TE (1 0,1) ,TE( 1 0,2), (E (1 O,M) ,H-1, 3) ,C (10,1) ,C (1 0, 2), 

L.OOJI ITE( 16,1) ,TE( 16,2) ,TE( 17,1) ,TE( 17 ,2) ,A(60) 

L.OOJ2 READ(S,4) TE(11,1) ,TE(11,2), (E(11,M) ,H-1,3) ,C(11,1) ,C(11,2), 

L. 0033 ITE( U,1) ,TE( 14, 2) ,TE(15,1) ,TE (1 S, 2) ,A (51) 

L. 003~ ~ I!"'RIIAT (F2.0,FS. 3,F7. O,P'7. 2 ,P'S. 2 ,FI 0.0 ,F7. 2,F3. O,F4. 1,F3.0,F~. 1, 

L.0035 1F15. 3) 

L. 0036 CALCULATIONS 

L.0037 INITIAL CONVERSION OF INPUT DATA 

L.0038 DO 17 L-1,11 

L.0039 TE(L,J) • TE(L,2) + 6.D1'TE(L,1) 

L. 0040 17 CONTINUE 

L.0041 DO 117 L-1,11 

L.0042 C(L,J) • E(L,J) 

L.0043 E(L,2) • E(L,2)•1.01J 

L.OOU C(L,2) • C(L,2)•1.01J 

L.0045 E(L,4) • E(L,1) + E(L,2) - E(L,3) 

L.0046 C(L,4) • C(L,I) + CIL,2) - C(L,J) 

L. 0047 117 CONTINUE 

L.OOU C CALCULATION or I, R, AND TAT AVERAGE TIME or SOLUTION RUN 

L.0049 DIDTI • (C(4,4) - CI3,4))/(TE(4,3) - TE(J,3)) 

L.OOSO DIDTF • (C(6,4) - CI5,4))/(TE(6,3) - TE(S,3)) 

L.0051 E(11,4) • A(S1)/(TE(15,3) - TE(U,3)) 

L.0052 DIFC • (C(4,4) + DIDTI*(TE(11,J)-TE(4,3)))-(C(5,4)+DIDTF*(TE(11,3) 

L.OOSJ 1-TE(5,3))) 

L.0054 DJIDfi • (B(4,4) - E(3,4))/(TE(4,3) • TB(J,l)) 

L.OOSS DBDTF • (E(7,4) - E(S,4))/(TB(6,3) • TB(S,J)) 

L.0056 BBI • DEDTI• (TE(U,J)•TB(4,J)) + B(4,4) 

L.0057 BBF • DBDTFO(TB(15,3)•TE(5,l)) + 1(5,4) 

L.OOS8 RATIO • (B(11,4) • BBI)/(BBF- BBI) 

L.OOS9 C(11,4) • C(4,4)+DIDTI•(TE(11,3)·TB(4,l))•DIFC*RATIO 

L. 0060 TEMPERATURE CONVERSION USING IIBifTON•IIAPBSOII MB'l'ROD OP ITERATION 

L.0061 STARTING TEMPERATURE I!"'R NBI!'l'OII-IIAPHJ'SON ITERATION IS T(21), THE 

L. 0062 REl'BRBIICE TEMPERATURE. 

L.0063 DO 19 L-1,11 L.0064 IP(L-9) 100,19,83 

L.0065 83 IP(L-10) 1t,19,100 

L.0066 100 R(L) • I.D.:IOB(L,4)/C(L,4) 

L. 0067 TB( 1) •T (21)- (RK( I)+ (RK(2)+RJC( 3) *T(21)) OT(21) -R(L)) / (RK(2) +2.DO• 

L.0068 IRK(J)OT(21)) 

L.0069 DO 678 I•2,50 

L. 0070 TB(I) •TS(I-1)- (RIC( 1) + (Rlt(2)+RJC( 3) •TB( I-1)) •TB (I-1) -R (L)) / 

L.0071 1 (RK(2)+2.DO'RK(J) *TB(I-1)) 

L.0072 TABS • DABS(TB(I-1) - TB(I)) 

L.0073 IF (TABS - 2.D-7) 679,679,678 

L. 007~ 678 CONTINUE 

L.0075 679 T(L) • TB(I) 

L.0076 19 CONTINUE 

L.0077 DRDT • RK(2) + 2.DO•RK(J)*T(11) 

L.0078 C COMPUTATION OF DRIFT RATES AND INITIAL AND PINAL TEMPERATURES 

L.0079 DO 18 L-1,4 

L.OOSO DRIFT(L) • (T(2'L)-T(2•L-I))/(TE(20L,3)-TE(20L-1,J)) 

L.0081 18 CONTINUE 

L.0082 T(l2) • (TE(I2,3) - TE(2,3))*DRIFT(1) 

L.0083 T(13) • (TE(13,3) - TE(J,J))*DRIFT(2) 

L.0084 T(14) • (TE(14,3) - TE(4,J))•DRIFT(2) 

L.0085 T(15) • (TE(15,3) - TE(5,J))*DRIFT(3) 

L.U086 T(16) • (TE(I6,3) - TE(6,3))•DRIFT(3) 

L. 0087 T ( 11) • (TE( 17, 3) - TE (7, 3)) •DRIFT (4) 

L.0088 DELT(I) • (T(IJ)-T(12)) 

L.0089 DELT(2) • (T(I5)-T(14)) 

L.0090 DELT(J) • (T(I7)-T(16)) 

+ T(2) 

+ T(J) 

+ T(4) 

+ T(5) 

+ T(6) 

+ T(7) 

L.0091 A(44) • -(DRIFT(!) + DRIFT(2))*A(46)/1.2D2 

L.0092 A(45) • -(DRIFT(J) + DRIFT(4))'A(60)/1.2D2 

L.0093 DELTK(I) • DELT(1) + A(44) 

L.0094 DELTK(J) • DELT(J) + A(45) 

L.0095 ALPHA(!) • (DRIFT(1) - DRIFT(2))/DELTK(1) 

L.0096 ALPHA(2) • (DRIFT(2) - DRIFT(3))/DELT(2) 

L.0097 ALPIIA(3) • (DRIFT(3) - DRIFT(4JJ/DELTK(l) 

L.0098 C CONVERGENCE TEMPERATURE 

L.0099 T(30) • T(12) + DRIFT(1)'A(46)/1.2D2 

L.OIOO T(JI) • T(13) - DRIPT(2)'A(46)/1.2D2 

L.0101 T(34) • T(16) + DRIFT(J)OA(60)/1.2D2 

L.0102 Tl35) • T(11) - DRIFT(4)0A(60)/1.2D2 

L.0103 T(J7) • T(JO) + DELTK(I)/2.00 

L.0104 T(39) • T(J4) + DELTK(J)/2.00 

L.OIOS T(18) • T(30) + DRIFT(I)/ALPHA(I) 

L.0106 T(19) • T(34) + DRIFT(3)/ALPHA(J) 

L. 01 Q7 DELTK (2) • DELT (2)-ALPHA(3) 0 (T (19) -T( 11)) • (TE( 15, 3)-TE( 14, 3)) 

L.0108 C BETA -MODULUS OF STIRRING 

L.0109 C T(20) • TEMPERATURE or THE BATH 

L.0110 BETA(!) • ALPHA(!) O .(T(18) - T(20)) 

L.0111 BETA(2) • ALPHA(J) • (T(19)-T(20)) 

L.0112 C HEAT CAPACITY OF THE CALORIMETER 

L.0113 DO 34 L-9,10 

L.0114 EM(L) • E(L,4)•0.999935D0/1.D4 

L.0115 CM(L) • C(L,4)/1.D6-EM(L)/3.D4 

L.0116 R(L) • EM(L)/CM(L) 

L. 0117 34 CONTINUE 

L.0118 TXT • TE(15,3) - TE(14,3) 

L.0119 TX• ( (ALPHA(l) o (T( 11 )-T(19)) 'TXT)+ (DRIFT(J) 0(TE(15,3)•TE(14, 3)))) 

L.0120 TX•TX/(DRIFT(J)-DRIFT(2)) 

L.0121 DTX•TX 

L. 0122 TX-TX+TE ( 14, 3) 

L. 0123 T ( 32) •T( 14)+DRIFT(2) o (TX-TE ( 1Q, 3)) 

L. 0124 T (33)-T( 15)+DRIFT (3) • (TX-TE( 15,3) l 

L.0125 TS(10)-T(33)-T(32) 

L.0126 "1'5(7)• T(32)+(TS(10)/2.DO) 

L.0127 DELTE(I) • EM(9)/4.1UD00CM(9)'A(Q6) 

L.0128 DELTE(2) • EM(10)/4.18QDO•CM(IO)•A(60) 

t:m~ ~!~l : g:~i:m~g~~~m L.0131 CV(I) • TS(S)•SP(I) 

L.0132 CV(2) • TS(6)•SP(1) 

L.OIJJ CV (3) • CV (1) + DCDTI • (TS (7) - T(37)) 

L.0134 CV(4) • CV(2) + (TS(7) - T()9))'DCDT2 

L.0135 322 POWER( 1) • EM(9) •CH(9) 

L.0136 POWER(2) • EM(10)'CH(10) 

L.0137 BNI • ALPHA(!) • CV(I) 

L.0138 BN2 • ALPHA(l) O CV(2) 

L.0139 C BEGIN SUMMARY COMPUTATION OF SOWTION ENTHALPY 

L.OUO 701 A(61) • (T(19) - T(11))0(TE(15,3) - TE(14,3)) 

L.OUI A(62) • -A(61)'A..PIIA(l) 

L.0142 DELTK(2) • A(62) + DELT(2) 

L.~143 CORRECTION OF SMIPLE WEIGHT TO VACUUM" RHO AIR • 0.001185: 

L.014~ RIIO PERHAS • 7.8, CF. NBS CIRC. 547 

L.014'i A(84) • A(52) 

L.0146 A(52) • A(52)•VACORR 

L.0147 C FIRST ORDER HEAT OF SOLUTION 

L.OU8 A(66) • -L'V(3) 'DELTK(2)/A(52) 

L.OU9 A(69) • -CV(4)•DELTK(2)/A(52) 

L.0150 C MOLAR HEAT OF SOLUTION 

L.0151 A(75) • GFW'A(66) 

L.0152 A(81) • GP'W0 A(69) 

L.0153 C Q(CHEMICAL) CORRECTED TO REFERENCE TEMPERATURE 

L.0154 A(70) • DHDT • (T(21) -T(32)) + A(69) 

L.0155 A(71) • DHDT O (T(21) - T(Jl)) + A(66) 

L.0156 A(54) • (A(70) + A(71))/2.DO 

L.0157 C MOLAR HEAT OF SOLUTION AT REFERENCE TEMPERATURE 

L.0158 A(83) • A(70)'GP'W 

L. 0159 A(72) • A(71) o GP'W 

L. 0160 ALP AI • ALPIIA(I) •I.DQ 

L.0161 ALPAJ • ALPHA()) •1.D4 

L.0162 A(85) • A(54)0GP'W 

L.0163 DQDT • (A(66) - A(69))/DELTK(2) 

L.0164 A(55) • DQDT'GP'W 

L.0165 C PRINT OUT 

L.0166 READ(9,9222) 

L. 0167 WRITE(6, 9234) 

L. 0168 9234 P'ORMAT(/ /) 

L. 0169 23 WRITE(6, 5) 'l'HO,DAY, YEAR, (A(N) ,N•25, 29), (A(N) ,N•l, 11) ,A (31) ,A (32), 

L.0170 1T(20) 

L. 0171 5 FORMAT ( ' HEAT EXCHANGE CALCULATIONS I!"'R SOLUTION CALORIMETRY, D 

L.0172 lATE IS ',A2,'/',A2,'/',A4// 

L.0173 25H RUN ,A6,6H DATE-,2A6 ,5H IJOOK,A6,6H PAGE ,A6,3X,'SAHPLE ', 

L.0174 39A6/' VACUUM(INITIAL-',A6,' FINAL-',116,') BATH TEMPERATURE', 

L.0175 4F6.2/) 

L.0176 WRITE(6,2009) 

L.0177 2009 FORHAT(5X,'TIHE',19X,'THERMOMETER EMP',11X,'TIIERMOMETER CURRENT' 

L. 0178 1, 9X, 'RESISTANCE' , JX, 'TEMPERATURE' , 4X, 'DRIFT'/' HR MIN MINUTES 

L. 0179 2IALS NULL ZERO SUM DIALS NULL ZERO SUM 

L.0180 3HHS (C) DEG/HIN'/J 

L.0181 KZ • 1 

L.0182 KY • 46 

L.0183 KXX • 37 

L. OIBQ NY •30 

L.0185 KX • 12 

L. 0186 KK • 9 

L.0187 DO 9221 L-2,8,2 

L. 0188 WRITE (6, 9222) (TE(L-1 ,H) ,H•I, 3), (E (L-I,H) ,H•I, 4), (C (L-I,H) ,M•I, 4), 

L.0189 IR(L-I),T(L-1) 

L. 0190 KP • L/2 

L. 0191 WRITE (6, 9222) (TE (L,H) ,1~•1, 3), (E (L,H) ,H•l, 4), (C (L,H) ,H-1, 4) ,R (L), 

L.0192 2T(L) ,DRIFT(KP) 

L.0193 IF(KP-2) 9223,9224,9225 

L. 0194 9223 WRITE (6,1 O)KZ, (TE(KX,H) ,H•l, 3) ,T (KX), (E (KK,H) ,H•I, Q), (C (KK,H) ,H-1, 

L. 0195 14) ,T (NY) ,F.II (KK) ,CM (KK) ,R (KK), T(NY+I), (TE (KX+I,H) ,H•I, 3) ,T(KX+I), 

L. 0196 2A(KY) ,DELTE(KZ) ,CV (KZ) ,T(KXX) 

I..QW _.G..• ntl. L. 0198 KY • 60 

L. 0199 KXX = 39 

L. 0200 NY •34 

L.0201 KK • KK+2 

L.0202 KX = 14 

L.0203 GO TO 9221 

L. 0204 9224 WRITE(6, 11) (TE(KX,H) ,11=1, 3), T(J(X), T ( 32), (TE (KK,H) ,11•1, 3), (E (KK,M), 

L.0205 1M• I,~) ,C (KK, 4) ,R (KK) ,T ( 11 l, TS ( 7) ,DTX,T()3), (TE (KX+1 ,II), 

L.0206 2H-1,J),TXT,T(KX+1) 

r ... o)o·, r.x = 1r. 

L.0208 KK • KK-1 

L.0209 GO TO 9221 

L.0210 9225 IF(KP-4) 9223,9221,9221 

L. 0211 9221 CONTINUE 

L. 0212 9222 I!"'RHAT( IX,Fl. 0 ,F4. 1,F9. 3, 2 (F9. 0, 21'6. 2 ,FI 0, 2), 21'13. 6,1'11. 7 l 

L.0213 11 I!"'RHAT(/51X,'SOLUTION PERIOD' /1X,I'l.O,F4.1,F9.3,75X,P'13.6,' TI'/ 

L. 0214 192X,F13. 6, 411 TI '/IX,P'l.O ,F4 .1,F9. 3,F9. 0, 2F6. 2 ,Fl 0. 2, 21X,F1 0. 2, 

L.0215 22F13.6/25X,' DICKII;SON TEMP',F10.6,' OCCURS ', ' 

L.0216 31!"7.2,' MIN AFTER INITIAL TIM•: ',1'13.6,~H Tl''/ 

L.0217 41X,F3.0,F4.1,1'9.J,' ELAPSED TIME', P'8.2,53X,F13.o,' TF'/) 

L.0218 10 FDIUIAT(/51X, 'HEATING PERIOD ',I1/1X,FJ.0,1'4.1,P'9. 3, 75X,F13.6,' TI' 

L. 0219 1/17X, 2 (F9. 0, 2F6. 2 ,FI 0. 2) ,13X,F13 .6 ,411 TI '/34X,F'10. 6,' VOLTS', 15X, 

L.0220 2F10.8,' AHPS',F12.6,F13.6,4H TF'/1X,F3.0,F4.1,F9.3,75X,F13.6,' TF' 

L.0221 3//' TIME ',1'8.3,' SEC ENERGY',F10.4,' CAL ·HEAT CAPACITY',Fil. 

L.0222 46,' CAL/DEG MEAN TEMP. ',F11.6/) 

L. 0223 WRITE(6, 9248) 

L.0224 9248 FORMAT(/) 

L. 0225 WRITE (6, 71 0) DELT( 1) ,DELT( 3) ,UELT(2) ,A (84) ,A~~~) ,A (~5) ,A (62) ,A (52), 

L. 0226 1 DEL'rK ( 1) ,DELTK (3) ,DELTK (2i ,GI'W, T( 18 l ,T ( 19), T( 19) ,AI.!' A 1,ALFA3 ,ALFA3 

L.0227 2,A (51 l ,BN1,all2,BN2,A (61) ,BETA (1) ,BETA (2) ,BETA 12) ,POWER II) ,POWER 12) 

L.0228 J,DQDT ,CV (1) ,cv (2 l ,A (55) ,CV (3 l ,CV (4) ,A (69) ,A (66), T 121) ,A (54) ,A (83), 

L.0229 4A(72) ,T(21) ,A(85) 

L.0230 710 I'ORHAT(55X,'SUHIIARY'//21X,'CALIBRATION 1 CALIBRATION 2 SOLUTIO 

L.0231 IN'//' DELTA T OBS.',7X,P'15.6,F15.6,F11.6,' !lEG C',8X,'SAHPLE WEIG 

L. 0232 2HT', 9X, F9. 4,' GRAMS'/' TEMPERATURE CORRECTION', F12. 6 ,FIS. 6 ,Fil. 6, 

L.0233 3 1 DF.G C',BX, 1 SAMPU: MASS 1 ,11X,F9.ll,' GRAMS'/' CORRECTED DELTA T' 

L.0234 4,SX,F12.6,F15.6,F11.6,' DEG C1 ,8X, 1 FORMULA WEIGHT 1 ,8X,F9.11., 1 GRA 

L.0235 5MS'/' CONVERGc'NCF. TEMP',7X,F11.6,F15.6,F11.6,' DEG C'/' ALPHA (01 

L.0236 60000)',10X,F10.6,F15.6,F11.6,' 1/IUN',8X,'INTEGRAL (E/DT) ',F15.4 

L.0237 7,' H-VOLT-HIN'/ 0 BN' ,17X,F15.6,F15.6,F'11.6,' CAL/DEG/HW',11X,' I L.0238 8T(INF)-TH)',F11.4,' DEG-HIN'/' IIEAT OF STIRRWG',3X,F15.6,F1S.6, 

L.0239 9F11. 6,' DEG/HIN' /' POWER', 1 4X, F15. 6 ,F15. 6, IJX, 'WATTS', 8X, 'D (DELTA 

L.0240 1 Q) /DT', 6X,F'12. 4,' CAL/DEG-GM' /' OBS HEAT CAPACITY ',F15.6 ,F15 .6 

L.0241 2,1JX,'CAL/DEG',6X,'D(DELTA H)/DT',6X,F12.~,' CAL/DEG-MOL'/' C EXT 

L.02~2 JIIAP. TO T(H,SOLN) ',FlO. 4,F15. 4,1 5X, 'CAL/DEG' /' DELTA H PER GRAM', 

L.0243 46X,F10.4,5X,F10.4,15X, 0CAL',10X,'OELTA Q AT 0 ,F7.3,F14.4,' CAL/GHA 

L.02Q4 SM'/' DELTA H PER MOL 1 ,SX,F12.4,F1S.li,15X, 1CAL',10X, 1 DELTA H AT',F7 

L.0245 6.3,FU.4,' CAL/MOL') 

L. 0246 KJX•I 

L. 024 7 TIHEN•TE ( 9, 3) 

L.0248 TIHEM• (TE( 12, l)+TE( 13, 3)) /2.UO 

L. 0249 GO TO 85 

L.0250 88 TIHEII•TE(10,3) 

L.0251 TIMEH• (TE( 16, l)+TE( 17, 3)) /2.ll0 

L. 0252 KJX•2 

L.0253 85 IF(TIMEM-TIIIEN)87,86,87 

L.0254 86 IF(KJX-1)88,88,89 

L. 0255 87 WRITE ( 6, 90) 

L.0256 90 I!"'RHAT(' MEAN TIME WRONG ') 

L.0257 89 WRITE(6,91) 

L. 0258 91 I!"'IUIAT(/ /) 

L. 0259 GO TO 328 

L.0260 U02 STOP 

L.0261 END 

L. 0262 /DATA 

23 
Vacorr. 

/I. 1()10,013171 

• L_~~~~~~~~~_L_L_L_L_L_L_L_L_L_L_L_L~ 

)ftVJ!,,!'W"I•I I t•yr••••l-1 I !I!W,.....tvl I I•'V'V' 1!1'-II"I'V'Vi"'' I .,.,_, I I I I '" 1..-..L__i_--'--'--'--'--'--'---'---'----'----'----'-.-l..---'----'----l..---l..---1.---1.---l..---i 

l••v• ,,,.,-, , , •• ,.,..-•--•-•••-• , ¥",.,.,..,_.., , •••vr>,~• ,, ._, .. ,,........,..~-· , ·.-- -· L.-'--'--'--'--' 

3 1/~'I!~.Ol • I I ,, :0:1 3~ 21 l : ::z o &,sj : • _. -~ L__l__1_ -"--'----'---'--L___L_____L__L__j___L....L.....L.._j___L__L._l--L.....J_LJ.......l_...L...L_L_~~ 

41,~ol..,~-,l I I I I/~~~~ i\7'~ 1- I l;'tl ll;l?l I I 1\~~ -~~ l/oi33.2l_l : :2. 6~ :-~-~-~~-~l__i .L_L_jl_____j----'----'-_l_ 

- 5 

• •• ~~~~~L-L-L-L-L-L-L_L_L__L___L__~~i_~i_~~~ 

6 

I I .1 I I I I I I I 

7 - -- .I I " •• 1 I i . ~·--~~~~~~~==~ 

al'/ I !"I~! I I I l/~'~'q'/)'ll1 I I ·~I I //\1 I I •/ll/\1 -~_L lt:o:z:3:2:sl I : I. 2 &'1-~---~--~-'-~' ,_L_l__L___L__L_L_L-L-L-L-L---l..---l.._~~___.J._J_ 

ti tf 

91/oll\di · I · l:~'"'-1-1,·,1 I · " ·/\·,1 I /\·~ -'---' · l/i~44ifM I . o.l/-!IIL slSaJ.: I l(it5:HI.: I~~ 

10 I;{Olf/: .. 1 I 1:1:>.-l7,/.a 1 I .o.r1.11 1 .•. olo1-~-- _i/K.4lf3~ [ 0.691 

I/D7332II .92ll19lZKl. r lz:olosl.: II : : :4'1:3:c;,r:~:o:.:a:J: I : :S~Iut:ion: : : I 

~~~~+-~~~~~~~~-'-~-'--'--'--'--'--'-~~~-'-~~~-L-L-L-L--'--L~--'---'----'-~~--~~----~~~-'--'---'-~---'--L----'-.-l..---'----'--_L---L...__L_---l..---l..---L---l..---l..---L_J_J_J_J~~~~L-L-L-L-~ 

FIGURE 11.-Coding sheet for heat of solution experiment. The sheet serves as a guide for card punching the time, potentiometer-dial setting, null-detector reading, and 

elapsed time necessary for reducing a complete heat of solution measurement. 

1:'1:) 

~ 

0 

> 

~ 

0 

~ Jo.-4 

~ t_:l:j 

1-3 

t_:l:j 

~ 

.rn 

::z:: 

t_:l:j 

> 1-3 

0 

":rj 

00 

0 

~ 

§ 

0 

z 

> z 

1:::1 

~ 

~ 1-3 

t_:l:j 

~ 1-tj 

t_:l:j 

~ 

> 1-3 

~ 

~ 

::z:: 

t_:l:j 

> 1-3 

(") 

~ > 9 

1-3 

~ 

~ t_:l:j 

> 00 

~ 

~ ~ t_:l:j 

~ 00 
CORRECTIONS 25 

and submarine wall and heat transfer by these mechanisms is negligible. Ginnings and West (1968) gave an 

extended treatment of the theory. For our calorimeter, 

operating in a vacuum of 10-5 torr, the mean free path 

is about 10 meters, and gaseous conduction and convection are effectively absent. This is in agreement 

with our experimental observation that the relaxation 

time 9 between the calorimeter and the constanttemperature bath is essentially independent of pressure 

below 5 X10-5 torr. 

If we substitute the appropriate numerical values for 

the emissivities dimensions and temperature in equations 16 and 17, we find that BR~0.32 cal deg-I min-I. 

Similiarly using the conductivities of Teflon, copper, 

and stainless steel and the dimensions of the connecter 

and copper wires, we get from equation 19 that Bk 

~0.03 cal deg-I min-I and 

BN =BR+Bk~0.35 cal deg-I min-I. (20) 

The values of B N observed in an actual calorimetric 

experiment range from 0.4 to 0.55 cal deg-I min-I in 

good agreement with the theoretical calculation. At 

25°C, 90 percent of the thermal conductance is due to 

radiation. Inasmuch as B R in equation 17 is proportional to the third power of the absolute temperature 

(Stout, 1968), BN, the total conductance, will also 

vary approximately as T3• The thermal and electrical 

constants of our calorimeter are listed in table 6. 

We point out that the thermal conductance of the 

calorimeter described in this report is near the lower 

limit possible for an isoperibolic-type calorimeter 

operating near 25°C without adding intermediate 

floating shields (Ginnings and West, 1968). Calorimeters in which the submarine is air filled (Torgeson 

and Sahama, 1948; Kracek and others, 1951) have 

thermal conductances nearly four times greater than 

our calorimeter and accordingly the corrections for 

heat exchange become much more significant. 

TABLE 6.-Thermal and electrical constants of solution 

calorimeter at 30°C 

Thermal-leakage modulus, a_____________ 0.00048 min-1 

Thermal conductance, B N _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 0.43 cal deg-1 min-I 

Temperature drift due to heat of stirring, 

13' =dT /dL _ _ _ ______ __ __ _ _ _____ _ _ _ _ _ _ 0.0004 deg min-1 

Temperature drift due to 0.002-ampere 

thermometer current, {j" =dT /dL _ _ _ _ _ _ 0.000007 deg min-I 

Temperature sensitivity_________________ 0.00005 deg 

CORRECTIONS FOR HEAT EXCHANGE 

bath, the temperature change caused by the electrical 

energy introduced by the heater (calibration) or by 

the chemical reaction (solution) must be corrected for 

the loss or gain of heat from the bath to obtain the true 

temperature change. These corrections are made using 

the observed temperature drifts, dT I dt, of the calorimeter. These corrections are developed in the next 

section. Alternate treatments have been given by Coops, 

Jessup, and Van Nes (1956), Coughlin (1962), and 

Wadso (1966). The following symbols and definitions 

will be used in the derivation of the corrections for 

heat exchange: 

Symbol and definition Unit 

T =temperature________________________________ Deg 

t =time______________________________________ Min 

C=heat capacity_______________________________ Cal deg-1 

electrical power {j' c Deg min-1 

heat of stirring rate 

{j" c Deg min-1 

{j = {j' + {j" _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Deg min-1 

E =electrical energy_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Cal 

Q=heat of a chemical reaction___________________ Cal 

a =BN /C =(relaxation time)-1 _ _ __ _ _ _ _ __ _ _ _ _ _ _ _ _ _ Min-1 

TB=bath temperature (a constant)________________ Deg 

Too =convergence temperature ____________ -- ____ -_ Deg 

Ti=temperature at the start of electrical heating or 

of the chemical reaction___________________ Deg 

T1 =temperature at the end of electrical heating or 

at completion of the chemical reaction_______ Deg 

ti =time at the start of energy input or of chemical 

reaction at ti, T = Ti- _____________ ---- _--- Min 

t

1 =time at the end of energy input or at completion 

of chemical reaction at t

1, T = T1____ _ _ _ _ _ _ _ _ Min 

The change of temperature with time for a calorimeter surroundea by a constant-temperature bath is 

given by Newton's law of cooling 

(21) 

where T is the temperature of the calorimeter. At 

infinite time, dT I dt = 0 since the heat generated by 

the stirrer and the thermometer current will be exactly 

balanced by the heat lost to the bath. Then at t = oo, 

Because of the finite thermal conductance, BN, 

between the calorimeter and the constant-temperature and (22) 

9 The relaxation time is the time necessary for the initial temperature difference 

between the calorimeter and the bath (T0 -TB) to decrease to 1/e =0.868 of its 

initial value (e =2.718 •.• ). 

(23) 

Too is usually called the adiabatic or convergence 
26 CALORIMETERS, HEAT OF SOLUTION AND LOW-TEMPERATURE HEAT CAPACITY MEASUREMENTS 

temperature. Substituting equation 23 into equation 

21, we get 

dT ldt =a(T 00 -T) 

which has the solution 

(24) 

(25) 

where To is the temperature at the time t 0• For our 

calorimeter a~0.0005 min-1 (see eq 27) and (T 0 - T 00 ) 

never exceeds 3°C. Consequently the actual exponential 

temperature changes can be replaced by linear changes 

over the length of a rating period (approx 20 min) 

within the sensitivity of our measurements, ±0.00005 

deg. Equation 24 can be rewritten in the form 

(26) 

If we indicate the fore- and after-rating-period temperatures linearly extrapolated to the midtime of the 

energy-input period by T /and T/, then by substituting 

into equation 26 and rearranging we can evaluate 

a from 

a= [dT ddt -dT1Idt]/(T/- T /). (27) 

This is actually a mean value of a between T /and T/. 

In principle it would be possible to obtain a from 

equation 21 by observing dT I dt of the calorimeter with 

the stirrer motor turned off, that is to say, with {j~O. 

This condition would, however, lead to thermal gradients within the calorimeter and a less precise value of 

a than that obtained using equation 27. a is the reciprocal of the relaxation time between the calorimeter and 

its surroundings and has the dimensions minutes-t. 

For comparing the thermal isolation of different designs 

of calorimeters, the appropriate quantity is the thermal 

conductance, BN, which is given by 

BN = aC cal deg-1 min-I (28) 

(see also eq 15 through 20). The correction to the observed temperature rise during either an electricalcalibration or chemical-reaction period Is 

(29) 

The correction can be either positive or negative depending upon whether the mean temperature of the 

calorimeter was above or below the convergence 

temperature T w The integrals are shown graphically 

in figure 10. The two types of cross hatching indicate 

the sign, positive or negative, of the integral in equation 

29. If the starting temperature of the run had been 

approximately 0.15°C lower, the positive and negative 

parts of the integral for the solution period would 

have been nearly equal and the heat-exchange correction for the chemical-reaction period would have 

been very nearly zero. In general the heat-exchange 

corrections for this calorimeter are less than 2 percent 

of the observed temperature rise. 

In operation the thermometer current and the stirrer 

are on continuously. During the energy-input period 

of an electrical calibration, the temperature of the 

calorimeter varies linearly with time. Accordingly, 

we may rewrite equation 29 as 

and substituting equations 25 and 26 into 29 gives 

aT= -[(dT;/dt)~(dTJ!dt)} -t;) (Sl) 

which is more convenient for calculation. The temperature rise corrected for heat exchange during the 

electrical calibration is thus 

T -T -T·-[(dTddt)+(dT!Idt)J( _ ·) .1. corr - f ~ 2 tf t ~ • (32) 

Alternatively the temperatures of the fore- and afterrating periods of an electrical calibration may be 

extrapolated to the midtime of the energy input as in 

equation 27, and the corrected temperature rise is 

.1Tcorr = T/-T /, (33) 

which is mathematically the same as equation 32, for 

linear temperature changes. For the case where the 

rating-period temperatures change nonlinearly, quadratic or higher order extrapolations are required to 

evaluate T / and T/. This is most conveniently done 

by plotting the data on log paper. The corrections 

necessary to obtain the corrected temperature rise for 

an isoperibolic calorimeter with nonlinear temperature 

drifts have been given by Cole, Hutchens, Robie, 

and Stout (1960). The heat capacity (electrical calibration) is 

C = (E- ~E) I .1.T corr cal deg-1 (34) 

and is assigned to the mean temperature of the electrical 

calibration 

The term ~E is a small correction to the electrical 

energy, E, due to superheating of the heater wire. 

This correction is discussed on page 27. 

During the solution . period the temperature varies 

nonlinearly with time, and it is necessary to evaluate 

the integral in equation 29 by numerical integration 

of the temperature-time curve. The correction for heat 
CORRECTIONS 27 

exchange during the solution period may be obtained 

directly from the observed variation of the thermometer 

voltage v(t) without conversion to temperature. From 

the initial and final times of the solution period and 

the observed v(t) curve, we get an average voltage v 

from the mean-value theorem 

(36) 

where the integral is evaluated numerically from the 

recorder trace. We then use the v(t) curve to obtain 

the time, t, at which the voltage has the value. v. 

The thermometer current will also change nonlinearly 

during the solution period, but the change will be very 

much smaller in magnitude than the voltage change. 

The small linear variation of the thermometer current 

with time in the rating periods is used to extrapolate 

the initial and final currents to the time 'l:. If we denote 

these linearly extrapolated currents by primes and 

recall that the current varies inversely with the voltage 

as the resistance thermometer warms up, then we may 

write 

(1 /-i)/(1 / -//) = (v -vi)/(v1 -vi) (37) 

which can be solved for i. From v and i we get the 

value of the resistance and thence the temperature 

T at f. The heat-exchange correction for the solution 

period can now be written as 

(38) 

and 

The values of a and Too used in calculating the heat 

exchange for the solution period are those calculated 

from the final electrical calibration. This is because 

stirring of the calorimeter changes kinematically at 

the time that the sample-holder seals are ruptured to 

initiate the reaction. This method of correcting for 

heat exchange is sometimes called the RegnaultPfaundler method (Coops and others, 1956). An alternate approach is the graphical method suggested 

by Dickinson (1915). Dickinson showed that a mean 

time, tm, exists such that the following relation holds: 

dT,jdt(tm-t,)+dTJ!dt(tf-tm) ~a f 1(T00 -T)dt. 

This is equivalent to 

(40) 

(41) 

If we linearly extrapolate the fore- and after-ratingperiod temperatures to tm and denote these temperatures by double primes, it can be shown that the 

corrected temperature rise is 

i

t, 

.D. T corr, so In = T /' - T /' = T 1 - T i-a ( T 00 - T)dt t. 

(42) 

and the mean temperature of the solution period to 

which the electrical calibrations must be extrapolated 

and to which the heat of solution is assigned is 

T m = (T /' +T/')/2. (43) 

The use of Dickinson's method requires a trial-anderror approach to obtain the time tm that satisfies equation 40. In practice we calculate the corrected temperature change for the reaction from equation 39 and 

then obtain tm by substitution in equation 40. Dickinson 

also pointed out that, if the temperature change during 

the reaction period was truly exponential, then tm 

would occur at that time when the temperature change 

had reached 63 percent of T 1 - T i, namely (1 -1 I e) 

(T1 - Ti), and the corrected temperature rise could be 

calculated from the difference of the rating-period 

temperatures as extrapolated to the time at which 63 

percent of the total temperature change had occurred. 

For a solution reaction which is completed in 5 minutes 

or less, this approximate method of correction is good 

to ±0.02 percent. However, for a slow reaction such 

as the solution of a feldspar in 10 N HF at 50°C, 

which may take as much as 70 min to dissolve, the 

difference between the corrected temperature rise 

obtained from equation 39 and this approximate 

method can result in an error as large as 0.1 percent. 

CORRECTIONS FOR SUPERHEATING OF THE 

ELECTRICAL HEATER 

To check the precision of the energy measurements, 

a plot was made of the heater resistance (measured 

during the energy-input period) as a function of the 

calorimeter temperature. The data showed a larger 

scatter than the accuracy of the measurements system 

warranted. Examination of the data indicated that, 

for a fixed calorimeter temperature, the heater resistance varied with the applied voltage, implying that 

the heater wire was not at the same temperature as 

the calorimeter during the energy-input period. To 

check this the following experiment was performed. 

The calorimeter was loaded with crushed ice and 

distilled water and assembled within the submarine, 

and the outer bath was also filled with crushed ice and 

water. The submarine was evacuated to 2X10-5 torr, 

and the resistance of the heater was determined at 

d-e voltages of 10, 20, 30, 40, 50, and 55, using the 

procedures of a normal electrical calibration. 

The resistance of the heater varied linearly with 

the square of the voltage ( ±0.0005 percent). Inasmuch 

as the experiment was performed under isothermal 

conditions, at the ice point, the heater wire was superheated with respect to the equilibrium temperature 
28 CALORIMETERS, HEAT OF SOLUTION AND LOW-TEMPERATURE HEAT CAPACITY MEASUREMENTS 

of the calorimeter. Using the temperature coefficient of 

resistivity for Evanohm, the results were converted 

to a linear variation of (T w-T c) as a function of the 

square of the voltage, where T w is the heater-wire 

temperature. 

Assuming that the copper lead wires from the heater 

are at the temperature of the bath, T B, at point l 

(fig. 8), the correction, oE, to the electrical energy 

introduced into the calorimeter is 

BE={(ka/l) .C<T~-TB)dt] (44) 

where k, a, and l are the conductivity, cross-sectional 

area, and length of the copper wires and the basis of 

the factor 4 is that there are two current and two voltage 

leads connected to the heater. The wire temperature, 

T w, is calculated from 

(45) 

where the constant K is evaluated from the superheating experiment described above and T M is the 

mean temperature of the calorimeter (see eq 35). 

The corrected energy input is thus 

Ecorr=E-oE. (46) 

The magnitude of K depends upon the length and crosssectional area of the copper lead wires in direct contact 

with the solution. For the most recent version of our 

heater, the correction, oE, amounts to approximately 

0.02 percent of Ecorr· 

From our experience and similar results by Gunn 

(1964) and Ingemar Wadso, 10 we believe that a systematic error may be present in many heat of solution 

results obtained with calorimeters where the heater 

is in a reentrant well. We recommend that this experiment be repeated in other calorimeters. For a calorimeter using a heater wound on its external surface 

(Robie, 1965), the correction due to superheating can 

be measured directly during a heating period (Giauque 

and Wiebe, 1928; Waldbaum, 1966; and Stout, 1968). 

CALCULATION OF HEAT OF REACTION 

From the preceding discussion, figure 10, and table 

4, it is seen that the corrected electrical calibrations 

of the initial (sample separated from solvent) and 

final system (sample in solution) are assigned to different temperatures. 

To convert the corrected temperature change for 

the chemical reaction into an enthalpy or internalenergy change, the electrical calibrations must first be 

extrapolated to T.m, so in. 

1 0 Ingemar Wadso (written commun., 1968) observed a variation of 18 cal 

mole-1 in the heat of solution of Tris, depending upon the degree of thermal contact 

between the heater wire and calorimeter. 

The temperature variation of the heat capacities 

dC I dT of both the initial and final systems are determined in a separate series of electrical calibration 

(.~T~0.5°C) over a range about 5 degrees above and 

below 'Tm, soln· The heat capacities are extrapolated 

to the mean temperature of the solution reaction, 

Tm, so!n, using the dCidT data. 

If we denote the extrapolated values of the heat 

capacities at T m, soln as C /and C/, then the isothermal 

heat of solution, Q, at Tm, soln is 

Q ilTcorr·(C/+C/)12 l ca g-1 

sample mass 

(47) 

and the temperature coefficient of the heat of reaction is 

(C I -C/) dQidT 1 cal g-1 deg-1• (48) sample mass 

A more precise temperature coefficient is obtained by 

measuring heats of solution at temperatures 5 to 10 

degrees apart. The agreement between the value of 

dQ I dT obtained from equation 48 with temperature 

changes of 0.2 degree and the value based on measurements 5 to 10 degrees apart is an excellent measure of 

the precision available with this calorimeter. This is 

shown graphically in figure 12. The temperature 

coefficient is used to adjust the heat of solution data 

to the reference temperature, usually 25°C. 

If the measurements were made with the calorimeter 

open to the atmosphere, the Q values are equal to the 

change in enthalpy, ilH. If the calorimeter was operated 

sea~d, the observed heats are at constant volume 

(Qv) and are equal to JlU, the change in the internal 

energy. To obtain the enthalpy change 11H, Qp, it is 

necessary to correct for the 11 (p V) term using the 

relation 

11H = ilU +Pil V + V ilp. (49) 

Details of this correctioJ;l and also minor corrections 

for condensation and evaporation were given by Gunn 

(1965) and E. J. Prosen.U Our values for the heat of 

solution of U.S. National Bureau of Standards Standard 

Reference Material 724, Tris, were corrected for 

evaporation and condensation using the relations 

given by Prosen. 

HEAT OF SOLUTION OF TRIS (C4H 11N03 ) 

As a result of suggestions by Irving and Wadso (1964) 

and Gunn (1965), the Standards Committee of the 

Calorimetry Conference requested the U.S. National 

Bureau· of Standards to prepare a large uniform sample 

of Tris (C 4H 11NO 3) for the intercomparison of solution 

u Prosen, E. J., May 1967, Recommendations for investigations of Tham [Tris] as a reference substance for solution calorimetry: Mimeographed notes accompany- ing U.S. National Bureau of Standards Standard Reference Material 724. 
HEAT OF SOLUTION OF TRIS (C4HuNOa) 29 

55.0 

~ 

<( 

0: 56.0 <.9 

.......... 

_J 

<( 

u 

z 

r 

c 

0 57.0 C.fl 

I 

<] 

I 

58.0 

~ / 

59.0 

25.0 3Q.O 

TEMPERATURE, IN °C 

35.0 

FIGURE 12.-Heat of solution of Standard Reference Material 724, Tris, between 25° and 35°C. t.H at T/' shown by 0. t.H at T1n 

shown by A. Solid line is the least squares fit to all the data. The short line segments represent the individual temperature 

coefficients of the heat of solution. 

calorimeters by means of the reaction of Tris with 

0.1 N HCI. In September 1967, this material was made 

available as Standard Reference Material 724 through 

the U.S. National Bureau of Standards to about 20 

different laboratories. 

We have made measurements on a commercial sample 

of Tris (Fisher, T -395) and on Standard Reference 

Material 724, at temperatures between 25° and 35°C. 

Our results, uncorrected for vaporization and condensation, are listed in table 7. When converted to molar 

values using 121.1372 as the formula weight and making 

the correction for vaporization and condensation 

(approx 1 cal mole-1), the result is -7098.0±11 cal 

mole-1 at 25.0°C. The temperature coefficient, 

d(llH)jdT, obtained from these data is 42.7 cal mole-1 

deg-1• The uncertainty associated with the heat of 

solution result is that recommended by Rossini (1956), 

that is, twice the standard error. 

Hill, Ojelund, and Wadso (1969) obtained -7109 ± 1 

cal mole-I, and Gunn (1970) found -7107 ±0.6 cal 

mole-1 for the heat of solution of Standard Reference 

Material 724 in 0.1 N HCl at 25°C. Both of these 

investigations used calorimeters having internal thermometers and reentrant well heaters, in contrast 

with the calorimeter used in our studies. 
30 CALORIMETERS, HEAT OF SOLUTION AND LOW-TEMPERATURE HEAT CAPACITY MEASUREMENTS 

TABLE 7.-Heat of solution of Tris (C4HuNOa) in 0.1 N HCl 

[T;' and Tr' are defined on page 26] 

Run Initial 

temperature 

of reaction 

(OC) 

Solution 

enthalpy at T;' 

(cal g-1) 

Final 

temperature 

of reaction 

(OC) 

Solution 

enthalpy at Tr' 

(cal g-1) 

Temperature 

coefficient 

of solution enthalpy (cal g-1 deg-1) 

Solution 

enthalpy 

at 25°C 

(cal g-1) 

U.S. National Bureau of Standards Standard Reference Material 724 

NBS 3 ___________ 24.84 -58.6743 25.10 -58.5157 -0.6118 -58.5844 4 ___________ 24.85 -58.6367 25.11 -58.5365 -.3870 -58.5795 5 ___________ 24.83 -58.5097 25.09 -58.4107 -.3832 -58.4461 

1 ___________ 29.87 -56.8254 30.12 -56.7703 -.2197 -58.5617 2 ___________ 29.86 -57.1127 30.11 -57.0438 -.2737 -58.8386 6 ___________ 29.59 -57.3554 29.84 -57.2902 -.2578 -58.9878 7 ___________ 29.66 -56.8994 29.91 -56.8056 -.3736 -58.5422 10 ___________ 29.87 -56.5767 30.12 -56.4577 -.4768 -58.2810 

g ___________ 34.91 -55.0465 35.15 -55.0048 -.1715 -58.5675 11 ___________ 34.90 -55.0071 35.15 -54.8676 -.5747 -58.4774 

Average ____________________________________ - --- - ___ - - - - - - - --- - - - - -- - -- - - - - ---- - ------ --- ---- --- -58.5866±.091 

Eastman reagent (Fisher T-395) 

[These measurements are not of the highest precision but were made primarily to evaluate design changes in the heater and support tube] 

T 2--------------- 29.91 -57.0444 3 _______________ 29.86 -56.9386 4 _______________ 30.25 -56.7629 5 _______________ 30.25 -56.9455 67-1 ____________ 30.11 -56.9664 

67-2 ____________ 31.13 -57.2067 67-3 ____________ 31.31 -56.6665 67-4 ____________ 31.25 -56.7252 

67-5 ___ --------- 31.27 -56.7709 67-6 ____________ 30.95 -56.9137 

67-7------------ 30.19 -57.0220 67-8 ____________ 30.52 -56.8229 67-9 ____________ 30.45 -57.0940 68-4 ____________ 29.56 -57.3043 

67-10 ___________ 35.30 -55.1609 67-11 ___________ 35.41 -55.0780 67-12 ___________ 35.31 -55.5002 

68-1 ____ - ------- 35.76 -54.8842 68-2 ____________ 36.18 -55.1073 

68-3 ____________ 36.40 -54.6930 

CONCLUSIONS AND RECOMMENDATIONS 

FOR FUTURE IMPROVEMENTS 

30.16 

30.11 

30.50 

30.50 

30.37 

31.39 

31.56 

31.50 

31.51 

31.20 

30.44 

30.77 

30.70 

29.82 

35.55 

35.65 

35.62 

36.00 

36.43 

36.65 

The solution calorimeter discussed in this report has 

a number of improvements over previously described 

isoperibol-type calorimeters. It has a smaller heat 

leak than earlier calorimeters and can be used either at 

constant pressure to measure dH or at constant volume 

to measure d U. It has a very fast response time and is 

routinely used with HF at 80°C. Its surface thermometer records the true surface temperature, not an 

internal temperature requiring correction (Cole and 

others, 1960). 

Six years of experience with this calorimet~r has 

suggested certain improvements that could b,e incorporated in future models. The calorimeter v6lume 

could be reduced to 500 ml, and the sample holder to 

2 ml. For measurements at 25°C the Teflon sample 

holder-impeller assembly could be replaced by one of 

gold to avoid the small anomaly caused by the 27°Cphase transition in Teflon. If the calorimeter is used 

only above 30°C, this is not necessary. The calorimeter 

can readily be converted to adiabatic operation by 

-56.9577 -0.3454 -58.7812 

-56.9216 -.0674 -58.6926 

-56.6699 -.3721 -58.6168 

-56.8081 -.5492 -58.7772 

-56.9186 -.1904 -58.7952 

-57.1033 -.4102 -59.3684 

-56.5980 -.2740 -58.9074 

-56.6895 -.1429 -58.9614 

-56.4834 -1.1557 -58.8864 

-56.9942 .3217 -59.1018 

-56.8788 -.5725 -58.8296 

-56.7769 -.1839 -58.7958 

-57.0976 .0143 -59.0669 

-57.2839 -.0808 -58.9524 

-55.0714 -.3672 -58.8020 

-54.9451 -.5463 -58.7346 

-55.4028 -.3977 -59.1622 

-54.7523 -.5446 -58.6650 

-55.0153 -.3769 -59.0584 

-54.6628 -.1245 -58.7532 

the addition of an appropriate shield between the 

calorimeter and submarine wall. 

Instruments have recently become available that will 

permit automatic measurement of both temperature 

and electrical power with the same precision attainable 

using the potentiometric circuit shown in figure 4. 

The direct determination of electrical power to ±0.001 

percent using an integrating digital voltmeter has been 

described by Furukawa (1965) and Martin (1967). 

Martin (1967) has also discussed an automatically 

balanced a-c bridge for platinum resistance thermometry having a temperature sensitivity of ±0.0001 

degree. An improved version of this bridge, having 

output in the binary coded decimal (BCD) mode, is 

now commercia1ly available. When combined with a 

digital coupler that can sequentially interrogate several 

digital devices at preset times and output the data 

serially to either magnetic or paper tape, these instruments can provide a completely automatic dataacquisition system for calorimetry. 

Small two-stage cryogenic refrigerators, originally 

developed for cooling infrared detectors, can produce 1 

watt of cooling at 20 K and an ultimate temperature 
REFERENCES CITED 31 

of 13 K. They should be readily adaptable to lowtemperature calorimetry and have the advantages of 

eliminating the need for LHe with its attendant inconvenience. Although their initial cost is high, the 

savings in the cost of LHe and LN 2 (no longer required) 

could pay for the device within 3 years. 

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U.S. GOVERNMENT PRINTING OFFICE: 1972 Q-471-717