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Thermal Conductivity of

Selected Materials

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UNITED STATES DEPARTMENT OF COMMERCE • John T. Connor, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Thermal Conductivity of

Selected Materials

R. W. Powell,* C. Y. Ho,* and P. E. Liley*

* This report was prepared under contract at the

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-t * National Standard Reference Data SeriesNational Bureau of Standards—

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(Category 5—Thermodynamic and Transport Properties)

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For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C., 20402- Price $1.00
NATIONAL BUREAU OF STANDARDS

JUN 9 1970

GAYLORD
Foreword

The National Standard Reference Data System is a government-wide effort to give to the technical community of the United States optimum access to the quantitative data of physical science, critically

evaluated and compiled for convenience. This program was established in 1963 by the President’s

Office of Science and Technology, acting upon the recommendation of the Federal Council for Science

and Technology. The National Bureau of Standards has been assigned responsibility for administering

the effort. The general objective of the System is to coordinate and integrate existing data evaluation

and compilation activities into a systematic, comprehensive program, supplementing and expanding

technical coverage when necessary, establishing and maintaining standards for the output of the participating groups, and providing mechanisms for the dissemination of the output as required.

The NSRDS is conducted as a decentralized operation of nation-wide scope with central coordination by NBS. It comprises a complex of data centers and other activities, carried on in government

agencies, academic institutions, and nongovernmental laboratories. The independent operational status of existing critical data projects is maintained and encouraged. Data centers that are components

of the NSRDS produce compilations of critically evaluated data, critical reviews of the state of quantitative knowledge in specialized areas, and computations of useful functions derived from standard

reference data.

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

listed below. The data publications of the NSRDS, which may consist of monographs, loose-leaf sheets,

computer tapes, or any other useful product, will be classified as belonging to one or another of these

categories. An additional “General” category of NSRDS publications will include reports on detailed

classification schemes, lists of compilations considered to be Standard Reference Data, status reports,

and similar material. Thus, NSRDS publications will appear in the following eight categories:

Category Title

12

3

4

5

6

7

8

General

Nuclear Properties

Atomic and Molecular Properties

Solid State Properties

Thermodynamic and Transport Properties

Chemical Kinetics

Colloid and Surface Properties

Mechanical Properties of Materials

Within the National Bureau of Standards publication program a new series has been established,

called the National Standard Reference Data Series. The present report, which is in Category 5 of the

above list, is Number 8 of the new series and is designated NSRDS-NBS 8.

A. V. Astin, Director.

ill
PREFACE

The work presented in this report consists of the critical evaluation and analysis of the available thermal

conductivity data on eleven metals and nine nonmetals mainly for the solid state, on seven fluids for both the liquid

and gaseous states and on two for the liquid state only. The materials studied were selected primarily for their

potential applicability as reference standards or because of their technical importance. The temperature range for

which values are given often exceeds that for which these values are known with a'high degree of certainty. While

TPRC assumes full responsibility for the recommendations of these reference data, it also reserves the right to revise these recommendations in the light of better or more complete information that may become available subsequently.

Graphite was amongst the materials originally selected for study but is omitted from this report. While the

work on graphite has been completed and the data scrutinized, it has not been possible to arrive at a satisfactory

basis on which to recommend "most probable" standard reference values. This effort will continue into the second

year and it is hoped that further consideration of the problem will enable the formulation of appropriate recommendations.

The preparation of this report has aroused interest in several other materials for which similarly assessed

thermal conductivity values are required. These will receive detailed consideration in subsequent reports of this series.

As a result of this study, it has become possible to assess the state of adequacy of our knowledge on the

thermal conductivity of a selected group of materials. Unfortunately, the results are not encouraging in a large

number of the cases and serious new measurement effort and the establishment of improved capabilities are indicated. TPRC has taken active measures to contribute to this most urgent measurement program on a selective

basis, based on findings as discussed in this report.

The present work was greatly facilitated by the wide scope of knowledge previously collected and organized

at TPRC. In fact, without such extensive input, the scope of work generated during the first year could not have

been possible. The senior staff affiliated with this program consisted of Dr. R. W. Powell and Dr. C. Y. Ho

who collaborated on the sections comprising the metallic and nonmetallic solids and Dr. P. E. Liley who was

responsible for the sections on fluids. Dr. Y. S. Touloukian has served as coordinator and adviser to the program.

The senior authors are grateful for the cooperation and assistance they have received from Mr. George Wang and

his group and the staff of TPRC's Scientific Documentation Division, who have directly contributed to this program.

In order to give a greater degree of confidence to the recommendations set forth in this work, the preliminary report was distributed to some 54 active workers in this field for their comments and criticisms. The

authors wish to express their appreciation and sincere gratitude to all who responded so generously. Particular

acknowledgment is made for the valuable contributions of the following individuals: Dr. N. G. Backlund, Royal Institute of Technology, Stockholm, Sweden,

Dr. C. F. Bonilla, Columbia University, New York City, New York,

Dr. A. Cezairliyan, National Bureau of Standards, Washington, D. C. , Mr. G. L. Denman, Air Force Materials Laboratory, Wright -Patterson AFB, Ohio. , Dr. E. Deviatkova, Institute for Semiconductors, Leningrad, U. S. S. R. , Mr. D. R. Flynn, National Bureau of Standards, Washington, D. C. , Dr. P. E. Glaser, Arthur D. Little, Inc. , Cambridge, Mass. , Dr. D. T. Jamieson, National Engineering Laboratory, East Kilbride, Scotland, Dr. J. Kestin, Brown University, Providence, R. I. , Dr. P. G. Klemens, Research Center, Westinghouse Electric Corporation, Pittsburgh, Pa. , Dr. M. J. Laubitz, National Research Council, Ottawa, Canada,

Mr. C. F. Lucks and Mr. H. W. Deem, Battelle Memorial Institute, Columbus, Ohio.

IV
Dr. D. L. McElroy and his colleagues. Oak Ridge National Laboratory, Oak Ridge, Tennessee,

Mr. A. Missenard, Paris, France,

Mr. C. D. Pears, Southern Research Institute, Birmingham, Alabama,

Dr. W. A. Plummer, Corning Glass Works, Coming, N. Y. , Dr. H. Poltz, Physikalisch -Technische Bundesanstalt, Braunschweig, W. Germany,

Dr. R. L. Powell, National Bureau of Standards, Boulder, Colorado,

Dr. F Richter, Phoenix -Rheinrohr Ag. , Dusseldorf, W. Germany,

Dr. K. Schafer, University of Heidelberg, W. Germany,

Dr. G. A. Slack, General Electric Research Laboratory, Schenectady, N. Y. , Prof. N. B. Vargaftik, Moskovskii Aviatsionnyi Institut, Moscow, U. S. S. R. , Dr. R. G Vines, C. S. R. I. O. , Melbourne, Australia, Dr. G. K. White, National Standards Laboratory, C. S. I. R. O. , Chippendale, N. S. W. , Australia

It goes without saying that while the individuals mentioned above have read selected parts of the preliminary

report and given helpful comments and criticisms, this in no way commits them to the views expressed in this report for which the authors assume complete responsibility.

V
CONTENTS

Page

PREFACE jy

LIST OF FIGURES VII

LIST OF TABLES VIII

PART I - THERMAL CONDUCTIVITY OF METALS 1 A. INTRODUCTION 2

B. THERMAL CONDUCTIVITY OF A GROUP OF

SELECTED METALS 4

C. REFERENCES 60

PART H - THERMAL CONDUCTIVITY OF NONMETALLIC

SOLIDS 64

A. INTRODUCTION 65

B. THERMAL CONDUCTIVITY OF A GROUP OF

SELECTED NONMETALLIC SOLIDS 66

C. REFERENCES 113

PART HI - THERMAL CONDUCTIVITY OF LIQUIDS 114

A. INTRODUCTION 115

B. THERMAL CONDUCTIVITY OF A GROUP OF

SELECTED LIQUIDS 115

PART IV - THERMAL CONDUCTIVITY OF GASES 135

A. INTRODUCTION 136

B. THERMAL CONDUCTIVITY OF A GROUP OF

SELECTED GASES 136

VI
Figi

1

2

3i

314

5

6

7

8

9 10

11

12

13

14

15

16

1718

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

LIST OF FIGURES

Page

Recommended Thermal Conductivity of Metals at Low Temperatures 13 Recommended Thermal Conductivity of Metals at Moderate and High Temperatures .... 14

Thermal Conductivity of Aluminum 17 Thermal Conductivity of Aluminum (In liquid state) 18

Thermal Conductivity of Copper 22

Thermal Conductivity of Gold ' 29

Thermal Conductivity of Armco Iron 31

Thermal Conductivity of Iron 35

Thermal Conductivity of Manganin 39

Thermal Conductivity of Mercury 41

Thermal Conductivity of Platinum 45

Thermal Conductivity of Platinum (60%) + Rhodium (40%) Alloy 49

Thermal Conductivity of Silver 51

Thermal Conductivity of Tungsten 54

Recommended Thermal Conductivity of Nonmetallic Solids 71

Thermal Conductivity of Aluminum Oxide . .• 73

Thermal Conductivity of Beryllium Oxide 84

Thermal Conductivity of Corning Code 7740 Glass 89

Thermal Conductivity of Diamond 91

Thermal Conductivity of Magnesium Oxide 93

Thermal Conductivity of Pyroceram Brand Glass -Ceramic Code 9606 97

Thermal Conductivity of Quartz 99

Thermal Conductivity of Thorium Dioxide 107

Thermal Conductivity of Titanium Dioxide 109

Departure Plot for Thermal Conductivity of Liquid Argon 122

Departure Plot for Thermal Conductivity of Liquid Carbon Tetrachloride 123-124

Departure Plot for Thermal Conductivity of Liquid Diphenyl 125

Departure Plot for Thermal Conductivity of Liquid Helium 126

Departure Plot for Thermal Conductivity of Liquid Nitrogen 127

Departure Plot for Thermal Conductivity of Liquid m-Terphenyl 128

Departure Plot for Thermal Conductivity of Liquid p-Terphenyl 129

Departure Plot for Thermal Conductivity of Liquid Toluene 130-131

Departure Plot for Thermal Conductivity of Liquid Water 132-134

Departure Plot for Thermal Conductivity of Gaseous Argon 140-145

Departure Plot for Thermal Conductivity of Gaseous Carbon Tetrachloride 147

Departure Plot for Thermal Conductivity of Gaseous Helium 150-155

Departure Plot for Thermal Conductivity of Gaseous Nitrogen 157-162

Departure Plot for Thermal Conductivity of Gaseous Toluene 164

Departure Plot for Thermal Conductivity of Gaseous Water (Steam) 166-168

VII
34

5

6

7

8

9 10

11

12

1314

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

LIST OF TABLES

Page

Derived Values of f3 and Associated Constants for High-Purity Metals 12 Recommended Thermal Conductivity of Metals at Low Temperatures 15

Recommended Thermal Conductivity of Metals at Moderate and High Temperatures .... 16

Specifications of the Specimens of Aluminum 19-21

Specifications of the Specimens of Copper 23- 28

Specifications of the Specimens of Gold 30

Specifications of the Specimens of Armco Iron 32-34

Specifications of the Specimens of Iron 36-38

Specifications of the Specimens of Manganin 40

Specifications of the Specimens of Mercury 42-44

Specifications of the Specimens of Platinum 46-48

Specifications of the Specimens of Platinum (60%) + Rhodium (40%) Alloy 50 Specifications of the Specimens of Silver 52-53

Specifications of the Specimens of Tungsten 55-59

Recommended Thermal Conductivity of Nonmetallic Solids 72

Specifications of the Specimens of Aluminum Oxide 74-83

Specifications of the Specimens of Beryllium Oxide 85- 88

Specifications of the Specimens of Corning Code 7740 Glass 90

Specifications of the Specimens of Diamond 92

Specifications of the Specimens of Magnesium Oxide 94-96

Specifications of the Specimens of Pyrocram Brand Glass -Ceramic Code 9606 98

Specifications of the Specimens of Quartz 100-106

Specifications of the Specimens of Thorium Dioxide 108

Specifications of the Specimens of Titanium Dioxide 110-112

Thermal Conductivity of a Group of Selected Liquids 120-121

Thermal Conductivity of Gaseous Argon 139

Thermal Conductivity of Gaseous Carbon Tetrachloride 146

Thermal Conductivity of Gaseous Diphenyl 148

Thermal Conductivity of Gaseous Helium 149

Thermal Conductivity of Gaseous Nitrogen 156

Thermal Conductivity of Gaseous Toluene 163

Thermal Conductivity of Gaseous Water (Steam) 165

VIII
PART I THERMAL CONDUCTIVITY OF METALS

1

0
PART I - THERMAL CONDUCTIVITY OF METALS

A. Introduction

The metals studied in this report consist of aluminum (solid and liquid state), ' copper, gold, iron (Armco

and pure), manganin, mercury (liquid state), platinum, platinum alloyed with 40% rhodium, silver, and tungsten.

In order to provide as complete a background of available knowledge as possible, the TPRC data sheets for

each of the above materials have been thoroughly updated. In doing this, the original papers have been critically

reexamined and more complete specification tables have been prepared.

Earlier analytical work [l, 2, 3]* at the TPRC, had dealt in the main with the thermal conductivities of metals at low temperatures. This work showed that the available data for 22 metals, some 1, 000 points for 83

different samples, could be reduced to a single curve by plotting the reduced thermal conductivity against the re- duced temperature. At low temperatures the thermal conductivity of a metal has a maximum value, km, at a corresponding temperature, Tm. The reduced thermal conductivity, k‘ , has been defined as k/km, and the re- duced temperature , T

1', as T/Tm.

The standard deviation of the experimental points from the curve

l

1 . o 9 k* =

3 lT >

is calculated to be 0. 0320.

( 1)

It was further shown that in the low temperature region, 0<T<1. 5Tm, the thermal conductivity could

be calculated by the equation

where

k =

n

a* T + (2)

a

1

In this equation a"> a, m, and n are constants for a metal whereas (3 and a* are dependent on the purity and

perfection. Theoretically,

(3)

j3 - Po/ L0 (4) where p0 is the residual electrical resistivity and L0 is the theoretical value of the Lorenz function and equal to

2. 443 x 10-8 volt2 K

-2

. The parameter £

is also obtainable by fitting observed values of the thermal conductivity

at temperatures below Tm to Equation (2), and, for sufficiently low values of T, ft = T/k is a good approximation.

Hence, (3 can be calculated from either the residual electrical resistivity or the thermal conductivity at very low

temperatures. This quantity is a function of the net chemical purity and physical imperfection of the sample, becoming less than 0. 02 for highly pure metals. This form of equation indicates the very marked dependence of the

thermal conductivity in the region of Tm on the value of

f3, that is, on the degree of purity and perfection of the

sample.

In the present report the foregoing equations have been used to derive thermal conductivity values up to temperatures of about 1. 5 Tm. The values of the constants a", a, m and n for each metal are given in Table 1 together with the three parameters a' , f3, and the electrical resistivity ratio P273K/P4-2K which are functions of the degree of purity and perfection of the metal and hence differ from one specimen to another.

The values of 0, included in Table 1, column 9, are the lowest that have been obtained for each metal

from thermal conductivity measurements, and, in some instances, these values can be compared with those derived

for the same sample from electrical resistivity measurements, column 8. Where the {3 values derived in these

$ References appear under the heading REFERENCES for each of the parts.

2
two ways agree reasonably well, that obtained from the thermal conductivity measurements, has been the value

chosen for subsequent calculations. However, for iron and tungsten, where the agreement is poor, the value

derived from the electrical resistivity data has been used.

The values of P273K/P4. 2K °f column 6, relate to the purest samples for which low -temperature thermal

conductivity measurements have been reported, whereas the values of this ratio given in the last column of the

table are the highest that have been reported, so far. Comparison of the values in these two columns reveals very

large differences for all metals. This indicates that the much purer samples now becoming available will possess

correspondingly lower ft values according to Equation (4) and higher thermal conductivities, according to Equation

( 2).

At the present time, the choice exists of reporting for a pure metal in this low temperature range, either

the highest thermal conductivity values based on actual measurement of the property, or, the much higher thermal

conductivity values that would result when these much lower j3 values are inserted in Equation (2).

The low temperature thermal conductivities given in Table 2a and shown graphically in Figure 1 have

been obtained by the first of these two methods. The corresponding values of p0 and the chemical purity for each

pure metal are included in Table 2a These quantities specify each pure metal for which thermal conductivity val- ues are tabulated to about 1. 5Tm and, in the temperature interval from this limit to about 100 K, smoothly falling curves have been drawn to link on with the most probable curves proposed for the higher temperature range.

Because of the very strong dependence of the low -temperature thermal conductivity of a pure metal on the

physical perfection and on the degree of purity, it follows that a pure metal is not likely to be an ideal material for use as a thermal conductivity standard at low temperatures. In the high thermal conductivity region there will

probably be no alternative, but, when otherwise acceptable, a binary alloy is to be preferred. This should be composed of reasonably pure constituents, be metallurgically stable and insensitive to small compositional changes.

When a pure metal is used, a recommended procedure for a particular sample would be to measure pat room and

liquid helium temperatures, then to evaluate /J from Equation (4) and derive k from Equation (2). This should be

done after the sample is mounted in the thermal conductivity apparatus and when it is unlikely to be subjected to further strain.

In order to assist in determining the most probable thermal conductivity - temperature curve for each

metal in the higher temperature range, the available experimental data have been plotted with linear coordinates in Figures 3 to 13.

Following the figure for each metal is a specification table which provides the chemical composition and

other details for each specimen. In the tables, the code designations used for the experimental methods are as

follows:

C Comparative method

E Electrical method

F Forbes bar method

L Longitudinal heat flow method

P Periodic or transient heat flow method

R Radial heat flow method

T Thermoelectrical method

For curves listed in the specification table but not shown in the figure, particularly in the low temperature region, one is referred to the TPRC Data Book, Volume 1, Chapter 1 [4], in which complete numerical data tables are

also given.

Each figure includes a heavy broken line which is considered to represent the most probable curve of thermal conductivity versus temperature for a high purity sample of the metal. This curve has at times been based on

rather scanty information, and should therefore be accepted as an attempt to make the most of existing knowledge

and subject to modification in the light of further work. Guidance has at times been sought from electrical resistivity data, but these are often missing. Furthermore, the extent to which the Wiedemann-Franz-Lorenz law

3
can be used to evaluate thermal conductivities over a wide temperature range is a matter that still has to be more

fully investigated. Only as more thermal conductivity workers collaborate by including electrical resistivity

measurements whenever possible, will sufficient knowledge become available to determine just how the Lorenz

function varies with temperature for the different metals. At sufficiently high temperatures the Lorenz function

often tends to approximate to the theoretical value, but it seems that transition metals may present an exception.

At low temperatures, T<0, where 0 is the Debye temperature, two opposing effects become important and the

Lorenz function may either increase or decrease with decreasing temperature before finally returning to about the

theoretical value at near absolute zero. Some pertinent comments regarding the thermal conductivity of each metal for temperatures above 100 K

are given in the following section, and the recommended values are reported collectively in Table 2b and plotted in Figure 2. In the Tables 2a and 2b, the third significant figure is given only for the purpose of comparison and for

smoothness and is not indicative of the degree of accuracy.

B. Thermal Conductivity of a Group of Selected Metals

Aluminum

For aluminum additional measurements would be of interest at temperatures immediately above and below room temperature for a range of compositions including a sample of really high purity. Interest in this temperature region has been revived since Powell et al. [5] reported a minimum at about 220 K in the thermal conductivity

temperature curve for a sample of high purity aluminum (99. 993%). For another sample, Flynn [6] has since reported a minimum at about 240 K and, amongst older results, minima have been found at about 160 K and 145 K by

Lees [7] and Powers, Ziegler and Johnston [8] for samples of much lower purity (99% and 98. 17%). These four

results indicate the temperature of the minimum to increase with increase in thermal conductivity and presumably

with purity, and it is of interest to note that the measurements of Powers, Schwartz and Johnston [9] for a highly

pure (99. 99 +%) sample had decreased to a constant value at 237. 6 K, the upper limit of their experiment. At

temperatures above normal there are strong indications that the thermal conductivity increases to a gentle maximum and then decreases to the melting point, but so far, only one set of measurements, those reported by Flynn,

have covered a sufficient range to include both the minimum and the maximum. This explains the need for further

investigations to be made on a range of samples of aluminum.

The recommended curve follows the data of Powers, Schwartz and Johnston at 100 K, falls to a minimum

lying between their data and Flynn' s, rises to a maximum following the data of Powell et al. , then continues close

to the data of these latter workers.

Electrical resistivity values have been reported by Powell et al. [5] and by Mikryukov [10]. The values

derived for the Lorenz function by these workers agree to within 1 or 2 percent for all but the lowest temperatures,

but the electrical resistivities of the Russian work are up to 5 percent greater. These results support the conclusion of Powell et al. that the Lorenz function of aluminum is only weakly dependent on purity at temperatures above

normal and can serve as an aid in determining the thermal conductivity of a particular sample from a measurement

of its electrical resistivity. The Lorenz function can be assumed to be 2. 35 x 10

“ 8

, 2. 40 x 10

8

, and 2. 42 x 10 _8

volt2 K

-2 at 473, 673, and 873 K, respectively. The work of Powell et al. [11] would indicate very little change in the Lorenz function to occur on entering the liquid phase.

Figure 3b relates to the thermal conductivity of liquid aluminum and shows very diverse values to have been

obtained. Only Powell et al. included measurements of the electrical conductivity, and it is interesting to note that their values of the Lorenz function are close to the theoretical value, being respectively only about 0. 5% and 1. 5%

lower at 973 and 1223 K. Mention of this is made because Grosse [12] has recently assumed the theoretical value

of the Lorenz function to hold from the melting point to the critical point when deriving values for the thermal conductivity of aluminum over the entire liquid range. For the electrical conductivity of molten metals Grosse [13]

has proposed an equation of the form

4
where

(a* + b) ( 5) ( T

+ + b) = a

CT* = CTx/b'f ax i s the electrical conductivity of the molten metal at a temperature T between the melting point Tf and the

critical point Tc

, and af is the corresponding electrical conductivity at the melting point. T

+ is given by

(T - Tj)/(T C- Tf). The quantities a and b are constants. At Tc both a and k are assumed to be zero. Part of the curve derived in this way for the thermal conductivity of liquid aluminum is shown by the thin dash-dot line of Figure 3b. This curve has a maximum value of 1. 17 W cm-1 K

-1 at 2200 K.

The electrical conductivity values assumed by Grosse for liquid aluminum near the melting point were those

of Roll and Motz [14]. These values were some 6 percent higher than those of Powell et al. which accounts for

much of the difference between their thermal conductivity curves. The two curves are almost parallel, and the

present recommended curve is the heavy broken line shown between them, but biased toward the experimentally

determined thermal conductivity values. At about 950 K this line passes close to the values due to Konno [15]

which are the first such measurements made on liquid aluminum.

These recommended values indicate that on passing from the solid to the liquid state the thermal conductivity of aluminum decreases by a factor of about 2. 3.

The recommended values are thought to be accurate to within ±4 percent below room temperature and

±2 percent to ±3 percent above. For liquid aluminum the values are probably good to within ±5 percent.

More attention should also be directed to the determination of the electrical resistivity of liquid aluminum.

Copper

Well over a hundred separate determinations of the thermal conductivity of copper have appeared in the

literature. Despite this large number, there is the usual dearth of information in the immediate sub-normal temperature region and at high temperatures. Indeed, no measurements to high temperatures appear to have been made

for high -purity copper. Furthermore, relatively few workers have included measurements of the electrical resistivity of their samples. Of these, the data of Meissner [16], Jaeger and Diesselhorst [17], Schofield [18], Smith

and Palmer [19], Mikryukov and Rabotnov [20] and Powell and Tye [21] all yield values of the Lorenz function

which are in the range 2. 25 x 10

“

8 to 2. 42 x 10

" 8 volt2 K

-2

, that is below the theoretical value. Only the work of Mikryukov [10] yields values as high as 2. 50 x 10 -8

, suggesting that his thermal conductivity measurements for

copper may err on the high side. The earlier measurements of Mikryukov and Rabotnov [20] were made on a less

pure sample and at their highest temperatures of about 800 to 1000 K their thermal conductivity values agree with

those of Fieldhouse et al. [22] for a sample of electrolytic tough pitch copper to within 4 percent. Both of these curves are believed to be below the curve of high purity copper. The broken line proposed for the latter has been

derived by assuming the Lorenz function to increase from 2. 29 x 10

8 at 273 K to 2. 40 x 10

8 at 873 K and above.

The electrical resistivity values of Meechan and Eggleston [23] for a 99. 999 percent copper have been used.

Values for the thermal conductivity of liquid copper are available, but these have been shown [11, 24] to be

from 16 to 60 percent below the straight line

k = 0. 012 + 2. 32 x 10"8 —

P

which fits the experimental data for several molten metals and alloys. They are also below the curve derived by

Grosse [12] from electrical conductivity data [25]. Further measurements are thought to be necessary before any

firm recommendations can be made for copper in the liquid phase.

To proceed from 1. 5 Tm

to room temperature the recommended curve follows the data of White and

Tainsh [26] to 55 K and continues through about the mean of results of several workers including Lees [7],

Berman and MacDonald [27], White [28], Powell, Rogers and Coffin [29], and Powell, Roder and Hall [30] to

link on with the proposed higher temperature curve. The measurements by the last mentioned workers were on

5
one of the purest samples, yet from about 60 K upwards their curve tends to lie below the curves for samples of lower purity, and, at their upper temperature limit of 105 K their value is some 7. 5 percent below the present

recommendation. Clearly this is unsatisfactory, and further attention should be given to pure copper in the subnormal temperature region.

Owing to the dearth of data for high -purity copper, the recommended curve has a probable uncertainty of ±3 percent near room temperature increasing to ±5 percent at low and high temperatures.

Gold

Much more experimental work is required on gold before any firm recommendations can be made. Only

Mikryukov [10] has made determinations of the thermal conductivity of gold at temperatures above 373 K, and the

usual dearth of information in the immediate sub -normal temperature region also exists. The measurements of White [31] had extended from liquid helium temperatures to about 150 K and at the upper limit the curves for four

specimens had each passed through a minimum and had commenced to increase. Much of this effect was, however,

attributed by White to no correction being made for heat transfer by radiation and no definite claim had been made

that a true minimum had been obtained. Indeed, White [32] has suggested that the appropriate corrections for

specimen Au4 would amount to approximately -0. 15 ± 0. 03 W cm-1 K

_1 at 150 K, about -0. 08 at 125 K, and -0. 02

at 100 K. It will be seen that these corrections suffice to remove the minimum for this sample. The most probable curve has been drawn to closely satisfy these corrected values, but the values in this region should be regarded as very tentative and subject to modification.

At higher temperatures the measurements of Mikryukov over the range 330 to 963 K yield Lorenz functions

that are in good agreement with the theoretical value, but his electrical resistivity values appear to be high. At

his highest temperature Mikryukov’ s electrical resistivity is 11 percent greater than that of Meechan and Eggleston [23]. But this is not the only uncertainty. The resistivity at 273 K derived from Meechan and Eggleston'

s

value of 2. 35 x 10

6 ohm cm at 293 K is about 2. 19 x 106

. The Jaeger and Diesselhorst [17] value of 2. 42 x 10

6

at 291 K converts to 2. 27 x 10~6 at 273 K whilst other reported values at 273 K are: Kannuluik [33] 2. 13 x 10 -e

, Meissner [16] 2. 065 x 10

6

, Gruneisen and Goens [34] 2. 04 x 10

6 and Damon and Klemens [35] 2. 032 x 10 -6

. Thus the extreme difference in the values reported for the electrical resistivity of gold at 273 K amounts nearly to 12 percent. Unpublished measurements by R. W. Powell tend to confirm the lowest values. Therefore, in deriving the thermal conductivity values shown by the broken line use has been made of Powell' s resistivity values of 2.2, 3.71, 5.52, 7.47, 9.65, and 12. 64 /iohm cm at 293, 473, 673, 873, 1073, and 1273 K, respectively, and of assumed values for the Lorenz function which increase from 2. 37 x 10

8 volt2 K

-2 at 293 K to 2. 45 x 10 -8 at 573 K

and thereafter remain constant. It is clear that the values at present proposed have but little experimental support.

Yet gold might well prove to be an acceptable material for a reference standard. Gold is also a metal of theoretical interest, because, due to its low Debye temperature (0 about 170 K), measurements for the solid phase can be

made to the relatively high temperature of nearly 8 0. The lack of information on gold is surprising and further

investigations are highly desirable so that the uncertainties of from ± 3 percent in the present most probable values

at normal temperature, rising to about ±6 percent at higher and lower temperatures can be reduced.

Iron

* A commercial grade of iron known as Armco iron has been used extensively as a reference standard of thermal conductivity. Hence, recommended values for Armco iron are given separately from those for highpurity iron.

Typical weight percent composition of Armco iron; 0. 015 C, 0. 09 O; 0. 08 Cu, Ni each; <0. 05 Al, Cr, Mn, Mo

each; 0. 015 Ti, S, Si, V each; 0. 005 N, Peach; 0. 0001 H.

6
Armco Iron

In 1962, Powell [36], on the basis of some 17 sets of available data for the thermal conductivity of Armco

iron, produced a set of most probable values for the temperature range 273 to 1573 K. Since that time some roundrobin measurements have been made on a sample of Armco iron supplied by the Battelle Memorial Institute. The

values obtained by two laboratories for the thermal conductivity of this sample have been published [37, 38] and

those of three others have been available privately.

On comparing these five sets of values as given at 100 C intervals, with the suggested most probable values,

quite good agreement is obtained. No difference exceeds 4 percent and 38 percent of the new determinations agree

to within 1 percent with the proposed values. After taking the averages of the round-robin value at each temperature, differences from the earlier proposal [36] were noted to be + 1. 7% at 1273 K, + 1. 1% at 1173 K, and -1. 1%

at 973 K whilst all the other values agreed to better than 1 percent.

The values now proposed for the thermal conductivity of Armco iron from 273 to 773 K are the averages of Powell's most probable values and the mean of the five round-robin values. In the Curie temperature region and

the phase transformation region the curve has been lowered by up to 3 percent so as to conform with the data obtained by the Oak Ridge National Laboratory [39]. These workers have used the radial heat flow method. This

method, which uses smaller temperature differences, has allowed the fine structure of the curve to be derived in

this interesting temperature region. Furthermore, their results are known to agree closely with unpublished

measurements of the National Physical Laboratory. At 1059 K, about 16 K above the Curie temperature, the thermal conductivity ceases to fall and remains almost constant up to the alpha-to -gamma phase transformation where

a drop of about 4 percent occurs. In the gamma phase, the thermal conductivity of iron has a small positive temperature coefficient. These changes would have led to rather too high thermal conductivities being obtained in the

region of the Curie temperature by observers who based their results on a large temperature difference and this is thought to justify the treatment of the results that has been adopted.

Below room temperature the National Bureau of Standards and the National Physical Laboratory have obtained values that agree closely for this round-robin sample. Also available are results from the National Bureau

of Standards and the Battelle Memorial Institute for two different samples. Throughout the range 123 to 273 K

these four sets of values agree to within about 3 percent. At 273 K their arithmetic mean value is the same as that derived above, so it has been decided to use the average value from these four curves as the most probable value

for the thermal conductivity of Armco iron at sub -normal temperatures.

These recommendations are thought to have an accuracy of ± 3 percent below room temperature, ± 2 percent

to about 1000 K, the uncertainty probably increasing to about ± 8 percent at 1600 K.

Electrical resistivity determinations made on Armco iron before and after heating to 1653 K have shown

changes of as much as 3 percent at the ice point [40]. Similar changes may occur in the thermal conductivity and

it is clear that check measurements should be made after an Armco iron thermal conductivity standard has been

heated into the gamma-phase.

High Purity Iron

The thermal conductivity of high purity iron has been plotted separately in Figure 7. Except at low temperatures any real differences in the two grades of iron are so small that they tend to be masked by the experimental

inaccuracies. Fortunately, the Oak Ridge National Laboratory workers, Fulkerson, Moore and McElroy [41] have

used the same radial heat flow method for measurements on both Armco iron and an iron of high purity over the range 323 to 1273 K. From a linear plot of the thermal conductivity at 373 K against the equivalent carbon content

of the two irons they obtained a value for the thermal conductivity of an iron with no impurities. This seems a

7
reasonable procedure, and the values thought to be most probable for pure iron above 323 K have been obtained by

applying the same increase to the recommended values for Armco iron as the ORNL workers found when comparison was made with their own Armco iron results.

Partial independent confirmation for these ORNL values is furnished by some unpublished results obtained

at the NPL for another sample of high purity iron. The two sets of values are known to be in close agreement particularly in the 900 to 1200 K region. The ORNL data suggest a higher temperature coefficient for gamma iron of high purity, but this requires confirmation over a wider range of temperatures and has been largely ignored in making the present recommendations. The reliability of these recommendations is thought to be similar to those

for Armco iron.

In view of the scientific and technical importance of iron it is considered appropriate to include a brief discussion of the present state of knowledge regarding the thermal conductivity of liquid iron. This seems to be particularly desirable since the limited information available for the electrical resistivity of iron in the vicinity of the

melting point indicates iron to be unusual in having relatively little change on passing from the solid to the liquid

state. Powell [42] reported an increase in the resistivity of about 9 percent for the liquid state, and Mokrovskii

and Regel [25] reported a slightly larger decrease. In view of the close correspondence found for other metals

between the two conduction processes, it seems that only a small change is to be expected in the thermal conductivity of iron at the melting point. Near the melting point the thermal conductivity of liquid- iron is probably 0. 35 ±

0. 05 W cm-1 K

-1

. Grosse [12], by using only the electrical resistivity data of Mokrovskii and Regel, predicted a value of 0. 39 W cm-1 K

_1 at the melting point followed by a smooth curve rising to a maximum value of 0. 47 W

cm-1 K

-1 at 3000 K and falling to zero at 6750 K, the critical point. Iron is clearly another metal for which furth- er electrical conductivity measurements are required, particularly for the molten phase. The unusually small

change on melting should be an incentive, but, in addition, there is a difference of some 20 percent between the

values at present available which serves to limit the reliability of any derived thermal conductivity data for molten

iron.

For the thermal conductivity of high purity iron at temperatures below 1. 5 Tm, values were calculated as already explained in terms of a value of p0 « 3. 27 x 10 -8 ohm cm due to Arajs, Oliver and Dunmyre [43] who

appear to have worked with the purest iron so far studied. These workers also measured the thermal conductivity of this iron, and the results are given in Figure 7 and Table 7 by curves 34 and 35. These experimental curves

have not been used since the value of Tm appears to be displaced on the high side by several degrees, and, as is evident from Table 1, the jS value derived from the thermal conductivity data is much smaller than that derived

from p0

. Above 1. 5 Tm, the recommended curve continues smoothly, following the general trend, to join the

higher temperature curve at about 250 K.

Manganin (copper 84%, manganese 12%, nickel 4% by weight)

Relatively few determinations have been made on manganin and those of Lees [7] and of Jaeger and Diesselhorst [17] are old measurements. In spite of this, their values are thought to be acceptable, since these were

workers of high repute and it is only because of the low purity of the metals then available that some of their thermal conductivity values for metals have been replaced by later values. With a complex alloy such as manganin,

impurities in the constituent elements will be likely to have a reduced effect. The determinations to low temperatures were made by Zavaritskii and Zeldovich [44] to a reported accuracy of 5 percent on an alloy of slightly different composition (3% instead of 4% nickel). The effect of this is uncertain but should be small.

The three available sets of data are in good agreement and serve to give values for the thermal conductivity

of manganin for the range 3 to 373 K. Further information is required to provide values to higher temperatures.

8
Mikiyukov and Chou [45] however have studied from about 350 to 970 K a series of copper alloys, each containing 0. 9 percent of beryllium and with manganese contents of 3. 65, 5. 47, 7. 30, and 9. 12 percent, respectively.

Extrapolation of these values to a manganese content of 12 percent leads to a value at 373 K which is some 26 percent lower than the recommended curve. This indicates that the inclusion of a smaller weight percent of beryllium

than nickel causes a greater decrease in thermal conductivity. Similar treatment of the Russian data for higher

temperatures leads to a curve which from 373 to 600 K is parallel to that of Jaeger and Diesselhorst and then turns

up. This provides some justification for the extrapolated values that have been suggested for use at higher temperatures pending the availability of further experimental data for manganin. The values near room temperature

should be accurate to about ± 3 percent, the uncertainty increasing to nearly ± 10 percent at higher temperatures.

Mercury

Until recently the thermal conductivity of liquid mercury, even at room temperature, was very uncertain.

Recent work has, however, led to the availability of three sets of data [46, 47, 48] carried out in Great Britain,

the USSR and the USA, which agree to within about 10 percent at 350 K and more closely at higher temperatures.

In the case of liquid mercury it is again possible to refer to the predicted values of Grosse [12]. For this

metal the electrical conductivity has been determined by Birch [49] and decreases with increase of temperature

along a smooth curve to a value of about 10 ohm-1 cm-1 at the critical point of 1733 K indicated by this experiment.

In this instance, Grosse used a value of the Lorenz function of 2. 60 x 10 -8 V

2 K

-2 as found by others for the

range 373 to 570 K. He appears to have used this value together with the electrical conductivities of Birch right to the critical temperature. Part of Grosse' s thermal conductivity curve derived in this way is given in Figure 9. A

maximum value is indicated at about 760 K, followed by a fall at an increasing rate to meet the estimated saturated

vapor value of about 0. 001 W cm-1 K

-1 at about 1720 K.

The difference between Grosse 1 s predicted curve and the measured values at the highest temperature is about 8 percent. Whilst there are uncertainties regarding the true values of p and L, the general form of the curve derived by Grosse seems sound. Hence, the recommended curve has been drawn as the mean through the

experimental data of the three aforementioned groups of workers, which is seen to agree well with Grosse' s curve

in the extrapolated low-temperature region and up to about 600 K. However, from 600 to 800 K the recommended

curve has been increasingly biased toward that of Grosse. The probable uncertainty is ± 5 percent.

In the solid phase, mercury has a rhombohedral crystal structure and its thermal conductivity will be

dependent on the crystal orientation. This phase is not included in the present treatment.

Platinum

Platinum has been suggested by Powell and Tye [50] and Slack [51] as a promising material for consideration as a thermal conductivity reference standard, yet the determination of a curve that represents the true

variation with temperature of the thermal conductivity of this metal is proving unusuaUy difficult.

Most earlier determinations have followed that of Holm and Stormer [52] with a linear increase of nearly

30 percent from room temperature to 1000 C. Then came the measurements by Powell and Tye [50] on two highpurity (99. 999 +%) samples of 1/4 inch and 1/2 inch diameter that indicated the thermal conductivity to be almost

constant over this range of temperature. Their values could however be fitted by a very shallow concave curve and

later measurements by PoweU, Tye and Woodman [53] on the smaller rod have given a definite negative temperature coefficient from about 80 to 300 K, linking on well with the earlier measurements at the upper temperature

limit.

Thus a very gradual minimum occurs in the thermal conductivity of this sample at a temperature well above room temperature, say at about 520 K.

9
Very recent preliminary measurements by Flynn [54] at the National Bureau of Standards on another bar of platinum of lower purity (99. 98%) have given quite different results. The shallow minimum occurs at 223 K where

the NBS value is lower than that of the NPL by some 9 percent; at about 500 K the curves cross and at 1000 K the

NBS value exceeds that of the NPL by about 10 percent.

For a high purity (99. 999 +%) rod of platinum, Laubitz [55] has reported for the range 300 to 1000 K values

that agree with those derived for high purity (99. 999%) platinum by Martin and Sidles [56] from thermal diffusiyity

measurements. At that time Martin and Sidles made what seemed to be a surprising claim that the thermal conductivity of another sample of platinum of lower purity (99. 9%) was higher at high temperatures. Laubitz’

s

measurements were for one of the purest samples so far tested, yet at just above 300 K his experimental points are lower than those of Powell, Tye and Woodman by from 5 to 7. 5 percent and lofter than Flynn’ s by 0. 5 to 3 percent;

at about 1000 K his points are lower than Flynn' s by 3 to 5. 5 percent but higher than Powell and Tye' s by 5 to 7. 5 percent.

Of the indirect determinations that have been restricted to temperatures above 1200 K those of Hopkins and

Griffith [57] tend to support the measurements of Holm and Stormer whilst those of Wheeler [58] tend to support

Powell and Tye, but these two series of indirect determinations differ by nearly 20 percent.

The present situation is difficult to understand, particularly as the thermal conductivity differences do not seem to be reflected in similar electrical conductivity determinations that have been made. Either some, as yet

undetermined, variable is affecting the thermal conductivity of platinum or certain experimental uncertainties must

greatly exceed their estimated values. That these uncertainties persist near room temperature is most surprising.

Much more experimental work is clearly essential over the full temperature range and this should include

the interchange of specimens between different workers in the hope that this might help to determine whether the

differences are purely experimental or are related to particular specimens.

On the assumption that the differences are mainly experimental, a very tentative most probable curve has

been indicated by the broken line in Figure 10. This has a minimum value at about 520 K. By way of an independent indication of the need for clarification of this matter, the recent measurements of

Kobushko, Merisov and Khotkevich [59] might be mentioned. This group of Russian workers have proposed a variant of the electrically heated wire method for determining the thermal conductivity of metals to high temperatures,

and have selected platinum as the metal with which to check this method. The values which they obtained were

regarded as satisfactory since they agreed well with data reported for platinum by Vargaftig [60]. These would no

doubt be the original data of Holm and Stormer, and until the present uncertainties in the thermal conductivity of platinum have been resolved, platinum is hardly suitable for this type of test.

Platinum 60% -Rhodium 40% Alloy

Two sets of experimental data are available for this alloy at high temperatures and the agreement between

them is very poor.

The National Bureau of Standards is responsible for one of these sets of measurements [61] in which

electrical resistivity determinations were also included. Since these data have enabled values of the Lorenz function to be calculated and good agreement with the theoretical value is indicated, these thermal conductivity values

have been given preference. As reported, the Lorenz function follows a slightly wavy course with a minimum at 773 K and a maximum at 1173 K. Hence, in deciding on the recommended values a slight adjustment has been made

to give a Lorenz function which decreases smoothly with increase in temperature. Some extrapolation has been included at both ends of the reported temperature range. The values for the experimentally measured range should

be accurate to about ± 3 percent.

10
Silver

The situation in the case of silver is similar to that of gold in that surprisingly few determinations have been

made of its thermal conductivity at temperatures above 373 K.

Bailey [62] extended the measurements on Lees’ specimen to higher temperatures, but this sample was

clearly not of the highest purity. The minimum value obtained at 660 K is very questionable. The other two workers, Evans [63] and Mikryukov [10] obtained values which decreased steadily with increase in temperature at comparable rates. Whereas the purity of the sample studied by Evans was stated to be only 99. 4 percent, that of Mikryukov was 99. 99 percent. Moreover, the latter worker included electrical resistivity data which agree with

the values for high purity silver. From room temperature to 373 K other workers, including Lees [7] and Jaeger

and Diesselhorst [17] have obtained for silver Lorenz functions in the range 2. 31 x 10~8 to 2. 39 x 10 -8 whereas

Mikryukov' s value at 338 K is 2. 45 x 10 -8 volt2 K

-2

. This is why the recommended curve has been drawn below

that of Mikiyukov in this region. The recommended curve also agrees reasonably well with the data of the other

named workers after allowance has been made for the electrical conductivities of their samples being less than

that of pure silver. Here the uncertainty is about ± 2 percent increasing to about ± 5 percent at extreme temperatures.

Further measurements are considered desirable for pure silver.

Tungsten

The TPRC has located 103 sets of data for the thermal conductivity of tungsten, yet, ignoring the very low

values reported for some samples of low density, only three sets of measurements have been in the temperature

range 700 to 1100 K.

The values now recommended for the thermal conductivity of tungsten differ condsiderably, particularly at high temperatures, from the earlier TPRC recommended values. Measured values for tungsten in the region 80

to 110 K by deHaas and deNobel [64] and White and Woods [65] agree well and appear to relate to samples of high

purity. At the low temperature end the curve now recommended starts in the region of these values, agrees

closely with the values of Tye [66], Powell and Tye [21], and Moore, Graves, Fulkerson and McElroy [67] and

has been smoothly continued from 1273 to 3500 K. Over this later range it lies within ± 5 percent of measurements

by Wheeler [58], Osborn [68], Gumenyuk and Lebedev [69], Timrot and Poletskii [70], and the measurements of Platunov and Federov [71] made above 2100 K.

The methods used by these workers included variants of the electrically heated wire method, an electron

bombarded cylindrical rod method and a variable state method employing a modulated electron beam technique.

Thermal diffusivity was determined by Wheeler and the thermal conductivity was derived from it by using assumed

values for the density and heat capacity.

It will be seen that the results obtained by some other workers in this high temperature range show quite

large differences and their measurements have been disregarded as being less reliable.

Whereas for most of the metals dealt with in the foregoing paragraphs the Lorenz function is considered to tend toward the theoretical value of 2. 443 x 10 -8 volt2 K

-2 at high temperatures, for tungsten the high temperature

values of thermal conductivity now recommended yield Lorenz functions which are fairly constant but almost 20

percent in excess of the theoretical value. For a lattice component of thermal conductivity of this magnitude to persist to high temperatures is unusual, thus, whilst these present recommended values are thought to be within ± 3 to ±5 percent of the time values, further confirmatory work on tungsten still seems to be required.

11
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190

180

170

160

150

140

130

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110

100

90

80

70

60

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30

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TABLE

2

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15

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TABLE

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See

TPRC

Data

Book

Vol.

1,

Chapter

1,

References
TABLE

3.

SPECIFICATIONS

OF

THE

SPECIMENS

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253

Kemp,

WR.

G.,

Klemens,

P.

G.,

1959 L

7.

9-90

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to

the

above

specimen

except

2.4x

1.7

mm

cross-section,

and

Tainsh,

R.

J.

276

Weeks,

J.

L.

and

Seifert,

R.

L.

1953 C

343

Pure;

density

(25 C)=

7.8g

cm' 5 .

64

Hall,

E.H

1900 L

301,331

99.

93

pure;

0.

059

C.

98

Mendelssohn,

K.

and

Rosenberg,

H.

M.

1952 L

2.3-32

99.

99

pure;

annealed.
TABLE

7.

SPECIFICATIONS

OF

THE

SPECIMENS

OF

IRON

(continued) c ; cs o : v £ ' 3 d o a ' m -ih a w

et

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a5o

37

Private

communication
TABLE

7.

SPECIFICATIONS

OF

THE

SPECIMENS

OF

IRON

(continued)

- C g.2

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38

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TPRC

Data

Book

Vol.

1,

Chapter

1,

References

^Private

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Data

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Vol.

1,

Chapter

1,

References
THERMAL

CONDUCTIVITY,

Watt

cm"

TPRC TEMPERATURE, K
TABLE

9.

SPECIFICATIONS

OF

THE

SPECIMENS

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..

1,

Chapter

1,

References
TABLE

9.

SPECIFICATIONS

OF

THE

SPECIMENS

OF

MERCURY

(continued)

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Data

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Vol.

1,

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1,

References
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TABLE

10.

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OF

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11.

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OF

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TABLE

12.

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reference

standard.
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TPRC

TEMPERATURE,

K

—

FIG

13
TABLE

13.

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OF

THE

SPECIMENS

OF

TUNGSTEN

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See

TPRC

Data

Book

Vol.

1,

Chapter

1,

Referencest

Langmuir

and

Taylor

[87]

considered

these

temperatures

too

low

for

complete

annealing.
TABLE

13.

SPECIFICATIONS

OF

THE

SPECIMENS

OF

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(continued)

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TPRC

Data

Book

Vol.

1,

Chapter

1,

References
TABLE

13

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57

669

Platunov,

E.S.

and

Fedorov,

V.

B.

1964

L

1283-3223

Tungsten

rod;

photographic

recording

was

used

for

the

measurement

of

temperature

distribution

above

1500 C

.
TABLE

13.

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OF

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SPECIMENS

OF

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59

Private

communication,

Oct.

7,

1965
C. References

1. Cezairliyan, A. , "Prediction of Thermal Conductivity of Metallic Elements and Their Dilute Alloys at Cryogenic Temperatures", Purdue University, Thermophysical Properties Research Center, TPRC Rept.

14, 1-140, 1962.

2. Cezairliyan, A. , and Touloukian, Y. S. , "Generalization and Calculation of the Thermal Conductivity of Metals by means of the Law of Corresponding States", High Temperature, 3, 63-75, 1965; A translation of Teplofizika Vysokikh Temperatur, 3, 75-85, 1965.

3. Cezairliyan, A. , and Touloukian, Y. S. , "Correlation and Prediction of Thermal Conductivity of Metals

Through the Application of the Principle of Corresponding States", Advances in Thermophysical Properties

at Extreme Temperatures and Pressures , 3rd Symposium on Thermophysical Properties, A. S. M. E. , March 22-25, 1965, 301-313.

4. Touloukian, Y. S , Thermophysical Properties Research Center Data Book, Volume I. Metallic Elements

and Their Alloys, Chapter 1. Thermal Conductivity. Data sheets updated twice a year; 850 pages in Chapter 1 as of June 1965, 11" x 17".

5. Powell, R.W. , Tye, R. P. , and Woodman, Margaret J. , "The Thermal Conductivity of Pure and Alloyed

Aluminum: I. Solid Aluminum as a Reference Material", Advances in Thermophysical Properties at Extreme

Temperatures and Pressures, 3rd Symposium on Thermophysical Properties, ASME, March 22-25, 1965,

277-88.

6. Flynn, D. R. , National Bureau of Standards, Private communication, March, 1965.

7. Lees, C. H. , Bakerian Lexture - "The Effect of Temperature and Pressure on the Thermal Conductivities of

Solids. Part II. The Effect of Low Temperature on the Thermal and Electrical Conductivities of Certain

Approximately Pure Metals and Alloys" , Phil. Trans. Roy. Soc. London, A208 , 381-443, 1908.

8. Powers, R.W. , Ziegler, J. B. , and Johnston, H. L. , "The Thermal Conductivity of Metals and Alloys at Low Temperature. HI. Data for Aluminum Alloys between 25 and 300 K", Ohio State Univ. Columbus

Cryogenic Lab., ASTIA TR -264-7, ATI 105 924, 1-13, 1951.

9. Powers, R.W. , Schwartz, D. , and Johnston, H. L. , "The Thermal Conductivity of Metals and Alloys at Low

Temperatures. I. Apparatus for Measurements between 25 and 300 K. Data on Pure Aluminum, OFHC

Copper and L Nickel", Ohio State Univ. Columbus Cryogenic Lab. , USAF TR -264-5, 1-19.

10. Mikryukov, V. E. , "Thermal and Electrical Properties of Copper, Silver, Gold, Aluminum, and CopperBeryllium Alloys" , Vestnik Moskov. Univ., Ser. Mat., Mekh. , Astron. , Fiz. i Khim. , 12_(6), 57-67, 1957.

(English translation available from Clearinghouse for Federal Scientific and Technical Information, T T-65-

63678).

11. Powell, R. W. , Tye, R. P. , and Metcalf, S. C. , "The Thermal Conductivity of Pure and Alloyed Aluminum:

H. Molten Aluminum and Aluminum Alloys", Advances in Thermophysical Properties at Extreme Tempera - tures and Pressures , 3rd Symposium on Thermophysical Properties, ASME, March 22-25, 1965, 289-95.

12. Grosse, A V. , "Thermal Conductivity of Liquid Metals over the entire Liquid Range, i. e. , from the Melting

Point to Critical Point, in Relation to their Electrical Conductivities and the Fallacy of Dividing Metals into "Normal" and "Abnormal" Thermally Conducting Ones". The Research Institute of Temple University,

Philadelphia, Pa. , December 7, 1964, 71 pp.

13. Grosse, A. V , "Simple Relationship between Electrical Conductivity of Liquid Metals and Temperature over

their entire Liquid Temperature Range, i. e. , From the Melting Point to the Critical Point". The Research

Institute of Temple University, Philadelphia, Pa. , November 22, 1964, 40 pp.

14. Roll, A. and Motz, H. , "The Electrical Resistivity of Molten Metals", Z. Metallkde, 48, 272-280, 1957.

15. Konno, S. , "On the Variation of Thermal Conductivity during the Fusion of Metals", Sci. Reports Tohoku

Imp. Univ. , 8_, 169-179, 1919.

16. Meissner, W. , "Thermal and Electrical Conductivity of Several Metals between 20 and 373 K", Ann. Physik.,,

4, 47, 1001-58, 1915.

17. Jaeger, W. and Diesselhorst, H. , "Thermal Conductivity, Electrical Conductivity, Heat Capacity, and

Thermal Power of Some Metals", Wiss. Abhandl. Physik -tech. Reichsanstalt, 3^, 269-425, 1900.

18. Schofield, F.H. , "The Thermal and Electrical Conductivities of Some Pure Metals", Proc. Roy. Soc. (London), A107 , 206-27, 1925.

19. Smith, C S. and Palmer, E.W. , "Thermal and Electrical Conductivities of Copper Alloys", AIMME Tech.

Publ. No. 648, 1-19, 1935.

20. Mikryukov, V. E. and Rabotnov, S. N. , "Thermal and Electrical Conductivities of Mono- and Polycrystalline

Substances from 100 C to the Melting Point", Uchenye Zapiski Moskov. Ordena Lenina Gosudarst Univ. Mv

Lomonosova Fiz. , 7£, 167-79, 1944.

21. Powell, R.W. and Tye, R. P. , "New Measurements on Thermal Conductivity Reference Materials", In course

of pubHcation.

60
22. Fieldhouse, I. B. , Hedge, J. C. , Lang, J. I. , Takata, A. N. , and Waterman, T.E., "Measurements of Thermal Properties", WADC TR 55-495, Parti, 1-64, 1956.

23. Meechan, C. J. and Eggleston, R. R. , "Formation Energies of Vacancies in Copper and Gold", Acta Met. , 2, 680-3, 1954.

24. Powell, R. W. , "Correlation of Metallic Thermal and Electrical Conductivities for both Solid and Liquid

Phases", Intern. J. Heat Mass Transfer, 8., 1033-1045, 1965.

25. Mokrovskii, N. P. and Regel, A.R., "The Electrical Conductivity of Copper, Nickel, Cobalt, Iron and

Manganese in the Solid and Liquid States", J. Tech. Phys. , U. S. S. R. , 23, 2121-5, 1953.

26. White, G. K. and Tainsh, R. J. , "Lorenz Number for High-Purity Copper", Phys. Rev., 119 , 1869-71, 1960.

27. Berman, R. and MacDonald, D. K. C. , "The Thermal and Electrical Conductivity of Copper at Low Temperatures", Proc. Roy. Soc. (London), A211 , 122-8, 1952.

28. White, G. K. , "The Thermal and Electrical Conductivity of Copper at Low Temperatures", Austral. J. Phys. , 6, 397-404, 1953.

29. Powell, R. L. , Rogers, W. M. , and Coffin, D. O. , "An Apparatus for Measurement of Thermal Conductivity

of Solids at Low Temperatures", J. Res. NBS, 59 (5), 349-55, 1957.

30. Powell, R. L. , Roder, H. M. , and Hall, W. J. , "Low -Temperature Transport Properties of Copper and Its Dilute Alloys: Pure Copper, Annealed and Cold-Drawn", Phys. Rev., 115 (2), 314-23, 1959.

31. White, G. K. , "The Thermal Conductivity of Gold at Low Temperatures", Proc. Phys. Soc. (London), A66 , 559-64, 1953.

32. White, G. K. , Private communication, CSIRO, National Standards Laboratory, Australia, Nov. 30, 1965.

33. Kannuluik, W. G. , "On the Thermal Conductivity of Some Metal Wires", Proc. Roy. Soc. (London), A131 , 320-335, 1931.

34. Griineisen, E. and Goens, E. , "Investigations of Metal Crystals. V. Electrical and Thermal Conductivity

of Single and Polycrystalline Metals of the Cubic System", Z. Physik, 44, 615-642, 1927.

35. Damon, D. H. and Klemens, P. G. , "Electrical Resistivity of Some Gold Alloys; A Search for Effects Due to Local Modes", Phys. Rev., 138 (5A), A1390-A1394, 1965.

36. Powell, R. W. , "Armco Iron as a Thermal Conductivity Standard; Review of Published Data" Progress in International Research on Thermodynamic and Transport Properties , 2nd Symposium on Thermophysical

Properties, ASME, Jan. 24-26, 1962, Academic Press, 1962, 454-65.

37. Powell, R. W. , Hickman, M. J. , Tye, R. P. , and Woodman, M. J. , "Armco Iron as a Thermal Conductivity

Standard: New Determinations at the National Physical Laboratory", Ibid, 466-473.

38. Laubitz, M. J. , "The Unmatched Guard Method for Measuring Thermal Conductivity at High Temperatures",

Canadian Jnl. of Physics, 4^(10), 1663-78, 1963.

39. Godfrey, T. G. , Fulkerson, W. , Kollie, T. G. , Moore, J. P. , and McElroy, D. L. , "Thermal Conductivity of Uranium Dioxide and Armco Iron by an Improved Radial Heat Flow Technique", USAEC Rept. ORNL-3556,

1-67, 1964.

40. Flynn, D. R. , Robinson, H. E. , and Watson, T.W. , Heat Transfer Section, National Bureau of Standards

,

Private communication.

41. Fulkerson, W. , Moore, J. P. , and.McElroy, D. L. , "Comparison of the Thermal Conductivity, Electrical

Resistivity and Seebeck Coefficient of a High-Purity Iron and an Armco Iron to 1000 C", Accepted for

publication, J. Appl. Phys.

42. Powell, R.W. , "The Electrical Resistivity of Liquid Iron", Phil. Mag., 7, 4jl, 772-5, 1953.

43. Arajs, S. , Oliver, B. F. , and Dunmyre, G. R. , "Thermal Conductivity of High-Purity Iron at Low Temperatures", J. Appl. Phys., 36^(7), 2210-2, 1965.

44. Zavaritskii, N. V. and Zeldovich, A. G. , "Thermal Conductivity of Technical Materials at Low Temperatures", Soviet Phys. Tech. Phys. , 1, 1970-1974, 1956.

45. Mikryukov, V. E. and Chou, S. C. , "Heat, Electrical, and Mechanical Properties of the Alloys Copper - Beryllium - Manganese", Vestnik Moskov. Univ. , Ser. Mat., Mekh. , Astron. , Fiz. i Khim. , 13 (3), 129-38, 1958.

46. Powell, R.W. and Tye, R. P. , "The Thermal and Electrical Conductivity of Liquid Mercury", International

Developments in Heat Transfer, Part IV, ASME Symposium, 856-62, 1961.

47. Vel'tishcheva, V. A. , Kalakutskaya, N. A. , and Nikol' skii, N. A. , "The Heat conductivity of Mercury",

Teploenergetika, IT, 80-2, 1958; and Nikol' skii, N. A. , Kalakutskaya, N. A. , Pchelkin, I. M. , Klassen,

T. V. , and Vel'tishcheva, V. A. , "Thermophysical Properties of Some Metals and Alloys in a Molten State",

Voprosy Teploobmena, Akad. Nauk SSSR, Energet. Inst. im. G. M. Krzhizharovoskogo , 11-45, 1959.

48. Ewing. C.T. , Seebold, R.E., Grand, J. A. , and Miller, R.R. , "Thermal Conductivity of Mercury",

NRL-4506, 1-11, 1955.

61
49. Birch, F. , "The Electrical Resistance and the Critical Point of Mercury", Phys. Rev. , jM, 641-648, 1932.

50. Powell, R. W. and Tye, R. P. , "The Promise of Platinum as a High -Temperature Thermal Conductivity

Reference Material", Brit. J. Appl. Phys., 14 (10), 662-6, 1963.

51. Slack, G. A. , "Platinum as a Thermal Conductivity Standard", J. Appl. Phys., 35., 339-44, 1964.

52. Holm, R. and Stormer, R. , "Measurement of the Thermal Conductivity of a Platinum Probe in the Temperature Range 19-1020 C", Wiss veroffentl. Siemens -Konzern, 9 (2), 312-322, 1930.

53. Powell, R.W. , Tye, R. P. , and Woodman, Margaret J. , "The Thermal Conductivity and Electrical Resistivity and Electrical Resistivity of Polycrystalline Metals of the Platinum Group and of Single Crystals of Ruthenium", In course of publication.

54. Flynn, D. R. , "Thermal Conductivity of a 2-cm diam. Bar of Engelhard E-2 Grade Platinum", National

Bureau of Standards, Washington, D’C., U. S. A. , Private communication, Jan. 20, 1966.

55. Laubitz, M. J. , "The Thermal Conductivity of Platinum from 300 to 1000 K", Division of Applied Physics,

National Research Council, Ottawa, Ontario, Canada, Private communication, Oct. 1965.

56. Martin, J. J. and Sidles, P. H. , "Thermal Diffusivity of Platinum from 300 to 1300 K", Iowa State Univ. , Ames Laboratory Contribution No. 1614, 1964.

57. Hopkins, M. R. and Griffith, R. L. , "The Determination of the Lorenz Number at High Temperatures",

Z. Physik. , 150, 325-31, 1958.

58. Wheeler, M. J. , "Thermal Diffusivity at Incandescent Temperature by a Modulated Electron Beam Technique",

Brit. J. Appl. Phys., 16^(3), 365-76, 1965.

59. Kobushko, V. S. , Merisov, B.A. , and Khotkevich, V. I. , "A Method of Determining the Thermal Conductivity

of Metals at High Temperature", Inzhenemo-Fizicheskii Zhumal, 8.(1), 58-63, 1965. Translated in International Chemical Engineering, j5(3), 485-488, 1965; and J. Eng. Phys., S>(1), 43-6, 1965.

60. Vargaftik, N. B. , "Teplofizicheskie Svoistova Veshchestv" Gosenergoizdat, 1-368, 1956.

61. Flynn, D. R. , "Thermal Conductivity of Semiconductive Solids, Method for Steady -State Measurements on

Small Disk Reference Samples", NBS Rept. 7740, 1-41, 1962.

62. Bailey, L. C. , "The Thermal Conductivities of Certain Approximately Pure Metals and Alloys at High

Temperatures", Proc. Roy. Soc. (London), A134, 57-76, 1931.

63. Evans, J. E. , Jr. , "Thermal Conductivity of 14 Metals and Alloys up to 1100 F [595 C]", NACA Research

Memo. E50L07, 1-15, 1951.

64. deHaas, W. J. and deNobel, J. B. , "The Thermal and the Electrical Resistance of a Tungsten Single Crystal

at Low Temperatures and in Magnetic Fields", Physica, 5.(5), 449-63, 1938.

65. White, G. K. and Woods, S. B. , "Low -Temperature Resistivity of the Transition Elements: Cobalt, Tungsten,

Rhenium", Can. J. Phys. , 3_5, 656-65, 1957.

66. Tye, R. P. , "Preliminary Measurements of the Thermal and Electrical Conductivities of Molybdenum,

Niobium, Tantalum and Tungsten", J. Less-Common Metals, 3^, 13-18, 1961.

67. Moore, J. P. , Graves, R. S. , Fulkerson, W. and McElroy, D. L. , "The Physical Properties of Tungsten",

Metals and Ceramics Div. , Oak Ridge National Laboratory, Private communication, 1965.

68. Osborn, R. H. , "Thermal Conductivities of Tungsten and Molybdenum at Incandescent Temperatures", J. Optical Soc. Am. , 31, 428-32, 1941.

69. Gumenyuk, V. S. and Lebedev, V. V. , "Investigation of the Thermal and Electrical Conductivity of Tungsten

and Graphite at High Temperatures", Phys. Metals and Metallog. USSR, 11 (1), 30-5, 1961.

70. Timrot, D. L. and Poletskii, V. E. , "Use of Heating by Electron Bombardment to Investigate the Coefficient

of Heat Conductivity in High-Melting-point Alloys and Compounds", High Temperature, USSR, 1(2), 147-51,

1963.

71. Platunov, E. S. and Federov, V. B. , "Use of Photographic Pyrometiy in Thermal Studies", High Temperature, 2, 568-572, 1964.

72. Revel, G. , "Aluminum of High Purity obtained by Zone Melting", Compt. Rend., 259 , 4031-3, 1964.

73. Gniewek, J. J. and Clark, A. F. , "Preparation of Copper Crystals with Low Electrical Resistivity", J. Appl.

Phys., 36 (10), 3358-9, 1965.

74. Schmidt, P. H. , "Purification and Crystal Growth of Gold", J. of Electrochemical Soc. , 112 (6), 631-2,

1965.

75. Isin, A. and Coleman, R. V. , "Magnetoresistance of Iron Whiskers", Phys. Rev., 137 (5A), A1609-13,

1965.

76. Jackson, J. J. , Argonne National Lab. , Private communication to T. F. Connolly, Research Materials

Information Center, ORNL, June, 1965.

62
'

77. Coleman, R V., Private communication to D. C. Lawson and B. T. Boiko, cited as Ref. 11 in Appl. Phys.

Letters, 5 ( 8), 155-6, 1964.

78. Appel, J. C. , Chambers, R. H. , and Trozera, T. A. , "A Program of Basic Research on Mechanical Properties of Reactor Materials", General Atomic, Quarterly Progress Rept. on Contract AT (04-3)-167 for the period ending Jan. 31, 1965, 1-28, 1965.

'

| \
PART II

THERMAL CONDUCTIVITY OF NONMETALLIC SOLIDS

64
PART II - THERMAL CONDUCTIVITY OF NONMETALLIC SOLIDS

A. Introduction

The nonmetallic solids treated in this part include aluminum oxide, beryllium oxide, Corning code 7740

glass, diamond, magnesium oxide, Pyroceram brand glass-ceramic code 9606, quartz, thorium dioxide, and ti- tanium dioxide. The thermal conductivities of these solids cover a fairly wide range. A thorough literature search was conducted for the thermal conductivities of these solids. The available

experimental data are collected and shown in Figures 15 to 23. Each figure is followed by a specification table

giving information on the specimens corresponding to the respective curves in the figure. For curves listed in the

specification table but not shown in the figure, particularly in the low temperature region, one is referred to the

TPRC Data Book Volume HI, Chapter 1 [1], in which complete numerical data tables are also given. The heavy

broken line shown in the figure represents the recommended curve of thermal conductivity versus temperature.

For each of the oxides, except quartz, the recommended curve is for a 99. 5% pure, 98% dense polycrystalline

specimen. In all the oxide single crystals, only the data for quartz single crystals are analyzed at this time.

The recommended values are the results of critical analysis of available data from all sources. The analysis procedure involves careful evaluation of the validity of available data and related information, resolution and

reconciliation of the disagreements of conflicting data, correlation of data with affecting parameters, comparison

of the resulting values with theoretical predictions and so forth.

According to theory, the thermal conductivity of nonmetallic crystals is determined both by the specific

heat aqd the mean free path of the phonons. At temperatures close to absolute zero the phonons are scattered by

the boundaries: the thermal conductivity varies as T3 and is size dependent. As the temperature is increased,

other scattering mechanisms become effective: scattering of phonons by static imperfections (impurities, isotopes

and all kinds of defects) and scattering of phonons by other phonons (Umklapp processes). The last mentioned process increases rapidly with temperature, until the mean free path decreases more rapidly with temperature than

the specific heat increases. At this point, still at very low temperatures (usually below 0/20), the thermal conductivity passes through a maximum, and then decreases again, in some perfect crystals exponentially. Around

the Debye temperature and above, it should vary as T

-1

.

However, experimental thermal conductivity data measured at high temperatures show numerous exceptions to this T

-1 rule. In some cases the thermal conductivity varies more slowly than T

_1

. This can be ascribed

to scattering by imperfections. At high temperatures the resistance due to Umklapp processes varies as T, that due to imperfections is more or less independent of temperature, and the combined resistance has an intermediate

variation, hence the conductivity varies more slowly than T

-1

. This is particularly pronounced in mixed crystals

and in highly disordered crystals. Furthermore, in the extreme case of disorder such as in glasses and in vitre- ous materials, the disorder determines the phonon mean free path which consequently becomes constant at high

temperatures. Hence the thermal conductivity increases with temperature, being roughly proportional to the

specific heat of the material.

Other cases of departure from the theoretical behavior may be explained in terms of a radiative component

of heat transfer. In porous materials, a radiative heat transfer across the pores acts as a shunt. In some cases

the crystals are at least partly transparent to infrared radiation, and there is an internal radiation component.

In either case the additional thermal conductivity is proportional to the specific heat of the radiation component

(proportional to T

3

) and the mean free path of the photons. In some cases this mean free path is governed by internal absorption and scattering processes; the radiation component is then an intrinsic property of the material.

In other cases the material is transparent, and the photons traverse the specimen. The corresponding componeqt

of heat transfer is thus dependent on the dimensions of the specimen, analogous to the case of phonon heat transport near absolute zero. Finally, it may happen that photons move from the heat source in the measuring apparatus to the heat sink, partly going through the specimen and partly through free space. In this case it seems diffi65
cult to separate radiative measurement error from internal radiative heat transport. To compound the conceptual

difficulty, since the internal absorption and scattering probabilities depend on photon frequency, it may happen that

part of the radiative conductivity is intrinsic and part dependent on specimen dimensions. To sum up, the

radiative component of the thermal conductivity can be extremely complex, is generally not well understood, and

often increases rapidly with temperature, though in principle it may also decrease over some range of temperatures, depending on the photon absorption coefficient.

In analysing the available data, attempts were made to consider all parameters likely to affect the thermal conductivity, such as purity, crystal imperfection, crystal axes orientation, density (or porosity), thermal

history, microstructure, etc. However, it is very unfortunate that in the majority of cases the authors do not report all necessary pertinent information to fully characterize the materials for which their data are reported.

Data for unspecified materials are of little utility. The recommended values have therefore at times been_based on

scanty information and should be accepted as an attempt to make the most of existing knowledge and subject to modification in the light of further work.

For a material to be used as a reference standard, the chemical and physical stability is a major requirement. The stability of a material is very much dependent on the environment in which heating to high temperatures

takes place. For instance, the stoichiometric composition of titanium dioxide is affected by heating to high temperatures in reducing environment and consequently its thermal conductivity is likely to change after such heating.

Therefore, selection of a suitable environment is important in using a reference material.

Some pertinent comments regarding the thermal conductivity of each solid are given in the following section, and the recommended values are reported collectively in Table 14 and in Figure 14. In the table, the third

significant figure is given only for the purpose of comparison and for smoothness and is not indicative of the degree of accuracy. The recommended values for most of these materials do not cover the low temperature region.

This is because either there are no experimental data available in the low temperature region for some of the

materials or the pertinent information on specimen characterization is inadequate. It is noted that in the low temperature region the thermal conductivity of a crystal is very strongly dependent on its purity and perfection,

among other parameters, and therefore knowledge of the sample characterization is particularly important at low

temperatures.

B. Thermal Conductivity of A Group of Selected Nonmetallic Solids

Aluminum Oxide. - There are 169 sets of experimental thermal conductivity data available for aluminum oxide,

of which 34 sets are for single crystals and the remaining 135 sets are mostly for polycrystalline specimens and

for some alumina powder. Despite these large numbers, the specimen purity and density (or porosity) are known

for only one set of data for the single crystals, and for only 25 sets of data for the polycrystalline specimens.

It is indeed a waste of effort to make such extensive measurements on specimens whose major specification and

characterization are not known.

The available data for polycrystalline specimens cover the temperature range from 2. 5 to 2030 K. There

are four sets of data below room temperature. One set of data (curve 130) bridges the gap and covers the low,

normal, and moderately high temperature regions. However, the latter appeared to be not of the correct trend.

All the remaining data are above room temperature. They spread into a wide band, as shown in Figure 15, over

the entire temperature range where data are available. The spreading of the curves is mainly due to the differ- ences in purity and density of the specimens measured, and therefore effectively each curve represents a different

material. It should be noted here that, because of the nature of these different curves, an average curve obtained

through some form of statistical fit of all these data points would have little meaning.

From the inadequate information available on specimen specification and characterization, the analysis of thermal conductivity data can be based only on porosity and purity. The thermal conductivity values of various curves at each of several selected temperatures were read off a large working-graph, and were used to determine

66
the relationship between thermal conductivity versus porosity and purity by means of an iteration technique. The

procedure used was as follows.

The thermal conductivity values were first plotted against porosity of the specimens neglecting at first the differences in specimen purity. A preliminary curve was thus obtained at each temperature representing the tentative relationship between thermal conductivity and porosity. Using this preliminary result the thermal conductivity

values were adjusted to zero porosity, and the resulting zero-porosity thermal conductivity values were plotted

against specimen purity. Thus a second generation preliminary curve was obtained at each temperature representing the tentative relationship between thermal conductivity and purity. Again using this second generation preliminary result the thermal conductivity values were adjusted to zero impurity, and the resulting zero- impurity

thermal conductivity values were plotted against porosity. By repeating this procedure, two final curves were

obtained representing the relationships between thermal conductivity versus purity and porosity. It must be

pointed out that the resulting relationships are still very preliminary in nature due to the inadequacy of available

information.

The relationship between thermal conductivity and porosity derived from experimental data is found in closer agreement with the relationship derived by Euler [2] from the theoretical model of Maxwell [3] than with

the simplified relation derived by Loeb [4, 5].

Using the above correlation procedure, at each of the several selected temperatures, a point was obtained

corresponding to the thermal conductivity of a 99. 5% pure, 98% dense polycrystalline specimen. A mean curve was subsequently drawn through these points to serve as the recommended curve.

The recommended curve has a minimum at about 1700 K, in agreement with the general trend of the ex- perimental data. Above 1700 K it turns up probably mainly due to the increasing contribution of the radiation

component. The uncertainty of the recommended values should be within ± 8% at temperatures from 500 to 1000 K

and increases to about ± 15% below 250 K and above 1800 K.

Beryllium Oxide . - The thermal conductivity of beryllium oxide is exceptionally high, in fact, higher than that

of most refractory materials. At temperatures below about 500 K it exceeds the thermal conductivity of beryllium.

There are 58 sets of data available for polycrystalline beryllia. No data are available for single crystals.

Four sets of data are below room temperature and the rest are above. Out of the 58 sets of available data, only 15

sets are for specimens of known purity and density ( or porosity) . The purity and density of most specimens are

low.

In the measurements of the thermal conductivity of five specimens of beryllium oxide of different density,

Powell [6] found that, within the temperature range studied ( 325 to 825 K) , the thermal conductivity of beryllia

varies approximately inversely as the absolute temperature and, at any one temperature, varies approximately

linearly with the density.

The thermal conductivity data were correlated with porosity and purity. Several points corresponding to a

99. 5% pure, 98% dense polycrystalline specimen were obtained at several selected temperatures. The recom- mended curve, as shown in Figure 16, has been drawn through these points. It has a minimum at about 2100 K

and turns up above this temperature. This trend of the thermal conductivity curve has been investigated and

confirmed experimentally by several workers including Taylor [7].

The uncertainty of the recommended values is thought to be within ±8% at temperatures from 500 to 1000 K

and increases to ± 15% below 300 K and above 1800 K. Beryllium oxide has a phase transformation at about 2370

K. This may limit the use of beryllia as a high- temperature thermal conductivity standard.

Corning Code 7740 Glass. - This glass is produced by Corning Glass Works and is a particular kind of borosilicate glass, commercially known as Pyrex glass. It is composed approximately of 80. 6% Si02, 13% B2O3,

4. 3% Na20, and 2. 1% A1203 , which is the average of the compositions reported for four of the specimens measured.

67
The spreading of the thermal conductivity curves as shown in Figure 17 is probably mainly due to experimental errors since small variations of chemical composition or microstructure.in different specimens of this

glass are unlikely to cause very large differences in thermal conductivity .

There are 12 sets of thermal conductivity data available for this glass. The specimen measured by Birch

and Clark [8] (Curve 10) was stated as No. 774 Pyrex glass from Corning Glass Works instead of No. 7740, but was actually the same kind of glass, since No. 774 was the old designation. The data of curves 2 and 6, which

spread out the most, were derived from thermal diffusivity measurements and appear to be in error. The recommended curve has been drawn through the mean of the remaining 10 curves.

The recommendations are thought to be accurate to within ± 5% at moderate temperatures and within ± 10%

below 200 K and above 700 K.

Diamond. - Despite its high cost, diamond is, from a theoretical standpoint, the obvious choice for a reference

standard due to the fact that it forms a monatomic, isotropic crystal lattice, reasonably free from defects and

most close to the simple crystalline model on which the theory of thermal conductivity is based. Furthermore,

diamond retains rather well its geometry and degree of perfection. At room and moderate temperatures diamond

has the highest thermal conductivity of all materials.

The water-white diamonds are divided into types I and II, according to whether the ultraviolet absorption by

the diamond is pronounced at wavelengths near 3000 X or 2200 X, respectively [9, 10]. Type II diamonds are in turn subdivided into two kinds: type Ila which refers to the insulating variety and type lib to the good conductors

of electricity.

There are 14 sets of data available for diamond as shown in Figure 18. It can be seen that only for type I does more than one experimental curve exist. Moreover, most of the measurements have come from the

Clarendon Laboratory, Oxford [ 11, 12], and for type I the workers concerned regarded the newer measurements

(curve 14) as being more accurate. Therefore, there is no comparison or choice that can be made from the

existing data for diamond. It is very tentatively recommended that the values represented by the three smooth

curves for the three types of diamond, in the temperature range from 150 to 400 K, be provisionally accepted as most probable values pending the availability of further experimental data. Until further data are available an

attempt to estimate the accuracy of the present values does not seem justified.

Magnesium Oxide. - Fifty-two sets of experimental data are available, in which six sets are for single crystals

and the remaining 46 sets are mostly for polycrystalline specimens and for some magnesia powder. All data

available for polycrystalline specimens are at temperatures above room temperature. Out of the 52 sets of available data, only 13 sets are for specimens of known purity and density (or porosity). The purity and density of most specimens are low.

Charvat and Kingery [5] have investigated the effect of purity, porosity, and microstructure on the thermal conductivity of magnesium oxide among other materials. They give fairly complete information on the

specification and characterization of their specimens, which many other workers fail to do. However, their data

appear to be high and the inclusion of their data in the correlation of thermal conductivity with purity and porosity

would probably lead to high results.

The recommended curve as shown in Figure 19 is for a 99. 5% pure, 98% dense polycrystalline specimen,

and is the result of the correlation of thermal conductivity with purity and porosity. This curve has a minimum at about 1650 K and turns up at higher temperatures. The uncertainty of the recommended values is thought to be

within ± 8% at temperatures from 500 to 1000 K and increases to ± 15% below 300 K and from 1650 to 2000 K.

The uncertainty increases to about ± 20% above 2100 K.

-#Dr. P. G. Klemens (private communication) suggests that even at ordinary temperatures the thermal conductivity of glass is governed by the mean free path of relatively long wave phonons, and that this mean free path may

be sensitive to the occurrence of very small crystallites. This may be a greater source of variability in the

thermal conductivity than chemical composition.

68
Pyroceram Brand Glass-Ceramic Code 9606. - This is a microcrystalline material composed of silicon dioxide,

aluminum oxide, magnesium oxide, and a small amount of titanium dioxide, and is produced by Corning Glass

Works.

There are eight sets of experimental data available. As shown in Figure 20, six curves are in the temperature range from 93 to 1433 K. Of these six curves only two( curves 1 and 2) were obtained by direct measurements

of thermal conductivity. The other four curves were derived from thermal diffusivity data. In view of the fact that these curves were obtained by completely different methods, the agreement of the data with one another

is rather good.

Curves 1 and 2 were produced by Robinson and Flynn [13] and their experimental data are usually reliable.

The recommended curve has been drawn closely following these two curves. At temperatures above 500 K the

recommended curve deviates slightly from curve 1 to follow the general trend of all the curves, since at temperatures above 600 K curve 1 is essentially a straight line which is deemed not very likely. Flieger [14] observed a small jump in his thermal diffusivity data. This jump is ignored at this time pending further confirmation.

The recommended values should be accurate to within ±5% at temperatures from 200 to 1000 K. The uncertainty increases to ± 10% at 100 K and 1400 KQuartz. - There are 45 sets of experimental thermal conductivity data available for quartz single crystals, of which 13 sets, 22 sets, and one set are, respectively, for single crystals measured with the heat flow direction

parallel, perpendicular, and at 45 degrees to the e-axis of the crystal, and nine sets for single crystals of unknown

axis orientation. Four sets of data are available for quartz powder and 7 8 sets of data available for fused quartz,

which is called by various commercial names such as fused quartz quartz glass, fused silica, vitreous silica,

silica glass etc. It is surprising to note that out of these 127 sets of data only one set is for a specimen whose

purity and density are both known. The specimen purity is known for only two other curves and the specimen

density is known for only 28 other curves.

The available data and pertinent information were studied, critically evaluated, and selected. The recom- mended curve as shown in Figure 21 for a high-purity ( 99. 99

+ %) quartz single crystal measured with the heat flow

direction parallel to the c-axis has been drawn as the mean of curves 39, 14, 49, 51, 24, and 54. The recommended

curve for a high-purity ( 99. 99+ %) quartz single crystal measured with the heat flow direction perpendicular to the c-axis has been drawn as the mean of curves 6, 15, 50, 53, 23, 17, 3, 2, and 55. The recommended curve for highpurity ( 99. 99+ %) clear fused quartz has been drawn as the mean of curves 45, 46, 47, 48, 110, 12, 13, 11, 16, 111, 120,

66,67,68,30, 84, and 29. The above curve numbers are listed in such an order that the curves commence at in- creasing temperatures.

Quartz crystal has a phase transformation which occurs at about 848 K. Experimental specific heat data

[15, 16, 17] and thermal expansion data [18] indicate a pronounced discontinuity at the transition temperature.

The effect of this phase transformation on the thermal conductivity of quartz crystal is not known, since no measurement has ever been made above 750 K.

The uncertainty of the recommended values for quartz single crystal is thought to be within ±5% at temperatures from 300 to 500 K and increases at lower and higher temperatures up to ± 10% at 40 and 800 K. The

uncertainty of the recommended values for fused quartz should be within ±4% at temperatures from 200 to 500 K. and increases to ± 8% at 50 K and 900 K and up to ± 15% below 10 K and at 1400 K.

Thorium Dioxide . - There are only six sets of experimental thermal conductivity data available for thorium

dioxide over the temperature range from 304 to 379 K and from 527 to 1821 K. No data are available below room

temperature and between 379 and 527 K. Furthermore, all the available data are for polycrystalline specimens

and no measurements have yet been made on thoria single crystal.

From the available inadequate information, the specimen purity and density are known for only one set of

data, and density is known for the other curves. Below 380 K the only two available curves, 1 and 2, were

69
produced by the same author on the same specimen. The difference in the experimental results was attributed by

the author to the difference in the coatings used on the end faces of the cylindrical specimen in separate runs, and

he pointed out that the data obtained during the second run ( curve 2) using a platinum alloy glaze on the faces of

the cylinder were more accurate than those obtained during the first run (curve 1) in which a gold coating was used. The recommended values at the lower temperatures are therefore based on curve 2.

Several points, each at one of the several selected temperatures, were derived from the available meager

information to correspond to a 99. 5% pure, 98% dense polycrystalline specimen, and the recommended curve has

been drawn through these points. The uncertainty of the recommended values is thought to be within ± 15% at temperatures from 350 to 1000 K and increases at lower and higher temperatures up to ± 20% at 250 K and ±25% at 1900 K.

Titanium Dioxide. - There are 36 sets of experimental thermal conductivity data available for titanium dioxide,

of which 21 sets are for single crystals, 13 sets for polycrystalline specimens and 2 sets are for an unspecified

specimen measured before and after irradiation. The specimen purity and density ( or porosity) are both known

for only six sets of data.

For the polycrystalline titania all available data are at temperatures above 350 K, and it is interesting to note that all curves except two were produced by workers of the same institution. Their later results [5] were

10% to 50% higher than earlier ones, which was attributed partially to the use of dense high-purity specimens and

partially to the improved design of the thermal conductivity apparatus used in their later measurements. However,

on comparison of their results with the recently published data for extremely high-purity titania single crystals

[19]| their later results [5] appear to be somewhat too high. On account of this fact, adjustments and modifications have been made in deriving the recommended values from their data.

The recommended values are for a 99. 5% pure, 98% dense polycrystalline specimen. The uncertainty of the recommended values should be within ± 10% at temperatures from 400 to 1000 K and increases to ± 15% at 250

K and 1400 K.

70
THERMAL

CONDUCTIVITY,

Watt

cm'
TABLE

14.

RECOMMENDED

THERMAL

CONDUCTIVITY

OF

NONMETALLIC

SOLIDS

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OF

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15.

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15.

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OF

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TPRC

Data

Book

Vol.

3,

Chapter

1,

References
TABLE

15.

SPECIFICATIONS

OF

THE

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TABLE

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Vol.

3,

Chapter

1,

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TABLE

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TABLE

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Data

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Vol.

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TABLE

16.

SPECIFICATIONS

OF

THE

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21

131

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TPRC

Data

Book

Vol.

3,

Chapter

1,

References

TABLE

20.

SPECIFICATIONS

OF

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Unpublished

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THERMAL

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3,

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References
TABLE

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Chapter 1,

References
TABLE

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112

See

TPRC

Data

Book

Vol.

3,

Chapter

1,

References
C. References

1. Touloukian, Y.S. , Thermophysical Properties Research Center Data Book, Volume IE. Nonmetallic Elements, Compounds and Mixtures ( in Solid State at Normal Temperature and Pressure) , Chapter 1. Thermal

Conductivity. Data sheets updated twice a year; 390 pages in Chapter 1 as of June 1965, 11 in. x 17 in.

2. Euler, F. , "Simple Geometric Model for the Effect of Porosity on Material Constants", J. Appl. Phys. , 28

( 11) , 1342-5, 1957.

3. Maxwell, J.C., "A Treatise on Electricity and Magnetism", Dover Edition (republication of the third edition

of 1891) , Vol. 1, 1954, 440-1.

4. Loeb, A. L. , "Thermal Conductivity: VIII, A Theory of Thermal Conductivity of Porous Materials", J. Am.

Ceram. Soc. ,_37(2), Part II, 96-9, 1954.

5. Charvat, F.R. and Kingery, W. D. , "Thermal Conductivity: XIII, Effect of Microstructure on Conductivity

of Single-Phase Ceramics", J. Am. Ceram. Soc., 40 ( 9) , 306-15, 1957.

6. Powell, R. W. , "The Thermal Conductivity of Beryllia", Trans. Brit. Ceram. Soc., 53^(7), 389-97, 1954.

7. Taylor, R. E. "Thermal Conductivity and Thermal Expansion of BeO at Elevated Temperatures" , USAEC

Rept. NAA-SR-4905, 1-19, 1960.

8. Birch, F. and Clark, H. , "The Thermal Conductivity of Rocks and its Dependence upon Temperature and

Composition", Am. J. Sci. , 238, 529-58, 1940.

9. Robertson, R. , Fox, J.G. , and Martin, A. E. , "Two Types of Diamond", Phil. Trans. Roy. Soc., A232 , 463-536, 1934.

10. Champion, F.C., "Some Physical Properties of Diamonds", Advances in Phys. , £(20), 383- 411, 195 6.

11. Berman, R. , Simon, F.E.

,

and Ziman, J.M. , "The Thermal Conductivity of Diamond at Low Temperatures", Proc. Roy. Soc. (London), A220 , 171-83, 1953.

12. Berman, R. , Foster, E. L. , and Ziman, J. M. , "The Thermal Conductivity of Dielectric Crystals: The Effect of Isotopes", Proc. Roy. Soc. (London), A237, 344-54, 1956.

13. Robinson, H. E. and Flynn, D.R., National Bureau of Standards, Washington, D.C., private communication.

14. Flieger, H.W. , Jr., National Bureau of Standards, Washington, D.C., unpublished data.

15. Moser, H. , "Measurement of True Specific Heat of Silver, Nickel, j3- Brass, Quartz and Vitreous Silica between 50 and 700 C by a Refined Method", Physik. Z. , 37, 737-53, 1936.

16. Mosesman, M.A. and Pitzer, K.S., "Thermodynamic Properties of the Crystalline Forms of Silica",

J. Am. Chem. Soc. , (33, 2348-56, 1941.

17. Sinel'nikov, N.N.

,

"A Vacuum Adiabatic Calorimeter and Some New Data on thea-/3 Transition for Quartz",

Doklady Akad. Nauk SSSR, 92, 369-72, 1953.

18. Rosenholtz, J. L. and Smith, D. T. , "Linear Thermal Expansion and Inversions of Quartz, Various Rock

Crystal", Am. Mineralogist, 26_, 103-9, 1941.

19. Thurber, W. R. and Mante, A.J.H., "Thermal Conductivity and Thermoelectric Power of Rutile (Ti02 )", Phys. Rev., 139 ( 5A) , A1655-65, 1965.

113
PART III

THERMAL CONDUCTIVITY OF LIQUIDS

114
PART m - THERMAL CONDUCTIVITY OF LIQUIDS

A. Introduction

Nine liquids were selected for examination. Four of these liquids have previously been analyzed by Makita

and constitute part of TPRC Data Book Volume, II, Chapter 1. The results of his analysis have been compared with

further work in the present study and are discussed below.

B. Thermal Conductivity of a Group of Selected Liquids

Argon . -Three experimental works are available on the thermal conductivity of liquid argon. Keyes [192^ made

measurements in a coaxial -cylinder apparatus near saturation conditions at three temperatures from 86. 9 K to 111.9 K. The extensive measurements of Uhlir [353] were made in a coaxial-cylinder apparatus using the gas

thermometer, covering temperatures from 86 to 150 K and pressures up to 96 atm. The uncertainty in the measurements was reported to be from 0.5 to 2. 5 percent. Other measurements for the liquid and gaseous phases were

carried out in a coaxial-cylinder apparatus with an accuracy of two percent, by Ziebland- Burton [57,413], over the temperature range from 93 up to 150.7 K for the liquid phase under various pressures up to 120 atm. From the standpoint of the experimental method and procedure, all the above measurements are considered to be reliable.

In this analysis, the values under saturated vapor pressures are obtained from the graphical extrapolation of the data of both Uhlir and Ziebland- Burton. No correction was made for the values of Keyes. The three sets of data for the saturated liquid are given equal weight and are fitted to a quadratic equation represented by

106k (cgsu) = 516.609 - 2.32178 T - 0.00255768 T

2 (T in K).

+

In arriving at this formula, the values at the critical point are excluded because the uncertainty in the measurements

and the graphical extrapolation would increase. Therefore, the above equation should be valid in the temperature

range from 80 to 148 K. This equation is found to fit the above enumerated values with a mean deviation of 0.61 percent and a maximum of 1.9 percent. The recommended values (Table 24) are generated from the above

formula, and the values at all temperatures should be correct within two percent.

In the departure plot (Figure 24), the departures of the data near the critical point of curves 1 and 2 are

calculated beyond the limit of the above equation.

Carbon Tetrachloride . -Makita considered 20 experimental measurements in the literature on the thermal

conductivity of liquid carbon tetrachloride. The extensive measurements of Challoner-Powell [434], Filippov [442],

Mason [475], Riedel [279,486], Schmidt - Leidenfrost [492] were considered to be reliable from the standpoint of

their experimental methods and procedures, and were given weight in this analysis. Furthermore, the single point

values of Frontas'ev-Gusakov [447,448], Riedel [483,484] and Van de Held-Van Drunen [507] were also considered

reliable and were used for the estimation of the most probable correlation. Although there were several other

extensive measurements [427-29, 437, 517], these were considered to be less reliable, and therefore, were given

no weight in his analysis.

The correlation formula obtained was

l0®k (cgsu) = 384.690-0.457184 T (T in K).

This equation was found to fit the above enumerated measurements with a mean deviation ol 1.4 peicent and a maximum of 4. 9 percent.

* Reference numbers used in the text, tables and figures of Parts III and IV of this repoit icfei to the section of References in Volume II, Chapter I of TPRC Data Book.

^ No attempt has been made to round-off computer results for equation coefficients, which are gi\en to nioie places

then are physically significant. They have been left in the original form to eliminate eiroi geneiated b\ using an equation with rounded coefficients for interpolation.

115
The recommended values were calculated from the above equation and were considered to be substantially correct in the range from 255 K to 378 K.

Subsequently, some further sources of values have been compared with Makita' s correlation. The result of

this comparison ( shown in Figure 25) is to indicate agreement to within four percent in the worst case and to about

two percent as an average. As some measurements disagreed with the original correlation to as much as twelve

percent, it can be concluded that, the further sources are in satisfactory agreement with Makita' s correlation and

that the latter can be considered as a satisfactory basis for generating the recommended values.

The recommended values were therefore generated from Makita' s correlation equation above and then converted into the tabulated units (watts cm- 1 K

-

*) using the appropriate conversion factor. The values so obtained are given in Table 24, while Figure 25 is a departure plot of the references which were compared. As stated

above, a probable error of two percent appears realistic.

Diphenyl. - Three sets of experimental data are available for the thermal conductivity of liquid Diphenyl.

Analysis of these data showed that, to within the experimental uncertainty, it was possible to represent these as a

linear function of temperature. The recommended values were read from a large scale plot and checked by dif- ferencing. They should be accurate to two percent for the entire range of the tabulation ( 330-600 K) . The values are given in Table 24 while Figure 26 is the departure plot for this substance.

Helium. - A number of experimental works has been reported on the thermal conductivity of liquid helium from

the standpoint of the interest in low temperature physics. As is well known, a thermodynamic transition in the

liquid phase of helium takes place at a temperature near 2. 17 K, referred to as the "lambda point". At temperatures above the lambda point, the liquid is called helium-I and below this point it is called helium-II. Helium-I is not particularly remarkable, but helium-II has a number of interesting properties especially flow and conduction

properties due to the quantum nature of this liquid.

The thermal conductivity of liquid helium-I was first measured by Keesom - Keesom [547], and it was

found that the value is of the same order of magnitude as that of gases at ordinary temperatures. Grenier [133,

545,546] made measurements in a parallel-plate apparatus within the uncertainty of 10 percent, covering the temperature range from 2. 2 to 4. 2 K, and found that the thermal conductivity of helium-I decreases with decreasing

temperature and exhibits a minimum near 2. 4 K. He concluded that helium-I behaves more like a gas than a nor- mal liquid. Bowers [48,49] also measured it in a longitudinal capillary apparatus. Although his measurements were not a precise absolute evaluation of the thermal conductivity, he obtained a linear relation down to the lambda

point with considerable scattering. More recently, Fairbank - Lee [544] obtained more accurate values at temperatures from 2. 3 to 3. 9 K under saturated vapor pressures, using a capillary method. As their results are considered to be the most reliable to date, all their reported points are given equal weight in this analysis and are

fitted to a quadratic equation, represented by

10% ( cgsu) = 99. 5614 - 43. 8934 T + 8.94877 T2

( T in K) .

This equation should be valid at temperature above 2. 2 K. The above equation is found to fit the data of Fairbank - Lee with a mean deviation of 1. 7 percent and a maximum of 3. 7 percent. The recommended values of Table 24

are generated from this equation, and the values should be substantially correct within two percent. Figure 27 is a departure plot for this substance.

On the other hand, of all the physical properties of helium-H, the most remarkable is the extraordinarily

high transport of heat. Preliminary measurements by Keesom - Keesom [547] at 1. 4 and 1. 75 K gave values of the thermal conductivity of about 190 cal cm- 1 sec

- 1 K" 1

. It may be noted that this value is about 200 times that of

copper at ordinary temperatures. In their further measurements [548, 560,561], it was found that the thermal

conductivity as a function of temperature has a very pronounced maximum near 1. 92 K, and under some condition, a thermal conductivity as high as 810 cal-1 cm-1 sec -1 K

-1 was observed. Hence, liquid helium-II is by far the best

heat conducting substance known. A number of investigations have been carried out on the super-heat-conduction

116
of liquid helium-II [198, 231, 548—567], The mechanism of heat transport in liquid helium-II is quite different

from that in helium-I or other liquids due to its extreme fluidity and the associated transport of energy by virtue of convective currents. Under these circumstances it is not possible to observe a "true" thermal conductivity as a transport property. Therefore, observed thermal conductivity values are found to depend markedly on the conditions of measurement, that is, the heat current density, the temperature gradient, and the dimensions of the test

cell used. It is considered to be impossible to treat the heat conduction in helium-II in the same way as in other

liquids. Therefore, no correlation is attempted in this analysis.

Nitrogen. - There exist eight available experimental works on the thermal conductivity of liquid nitrogen.

The extensive measurements of both Uhlir [353] and Ziebland - Burton [57,413] are considered to be the most reliable from the standpoint of the experimental method and procedure. As they did not give the values for the

saturated liquid, a graphical extrapolation is used to obtain the values at the saturated vapor pressures. All of the values thus obtained are given equal weight. Another set of recommended values reported by Powers, et al. [276,531] is also partly used in this analysis. On the other hand, two sets of data reported by Borovik [42,46]

deviate considerably, and the values of Hammann [139] and Prosad [535] are too high. Therefore, no weight is given to these sets of data.

The correlation formula is determined from the reliable values described above, excluding those at the

critical point because the values near the critical point are considered to be less reliable. The correlation formula is given by

10®k ( cgsu) = 695. 957 - 5. 15493 T + 0. 00504635 T

2

( T in K) .

This equation should be valid between 60 and 123 K. It is found that this equation fits the above enumerated values

with a mean deviation of 0. 8 percent and a maximum of 2.2 percent. The recommended values of Table 24 are

calculated from the above equation and the data above -320 F should be substantially correct within two percent.

In the departure plot ( Figure 2 8) , the values near the critical point of curve 1, 6, and 8 are plotted beyond the limit of validity of the above formula. A single point value which was obtained at 33 atm by Ziebland - Burton [412] is plotted without any extrapolation to the saturated liquid. Furthermore, only a part of the results

of Hamman ( curve 3) is plotted for the sake of clarity in this figure.

m-Terphenyl, - Only two sets of experimental values were available for the thermal conductivity of liquid

m-Terphenyl, the results of Horrocks and McLaughlin [637] from 355 to 407 K and of Reiter [639] from 373 to 623 K. Graphical plotting of these data revealed a difference in the two sets of about three percent. There was

also a difference in the temperature derivative of thermal conductivity.

In preparing the recommended values, a smooth curve was drawn through the higher temperature Reiter

data and midway between the two sets of data for the lower temperatures. Values, read off this curve and checked

by differencing for even increments of temperature, are given in Table 24. Figure 29 is the departure plot for

this substance. The reliability of the recommended values can be assessed as about two percent.

p-Terphenyl. - Experimental measurements of the thermal conductivity of p-Terphenyl have been reported by

Horrocks and McLaughlin [637] and Reiter [639], for temperature ranges of 488-520 and 523-623 K, respectively,

these data appear to be in reasonably good concordance. The recommended values of Table 24 were obtained from

a smooth curve drawn through the experimental data and should be accurate to within one-half percent between 490

and 620 K and one percent for all other temperatures tabulated. Figure 30 is the departure plot for this substance.

Toluene. - Makita analyzed twenty-four experimental works on the thermal conductivity of liquid toluene. The discrepancy between the reported values of different investigators was found to be extremely large. The results of several extensive measurements fall into two groups, one group being about twelve percent to eighteen

percent higher than the other. The results of Abas-Zade [l, 2], who used the hot-wire method, and those of Bridgman [431], Markwood-Benning [238], and Smith [500], who used the coaxial-cylinder method, all fall in

the higher set. On the other hand, recent results of Calloner- Powell [434], Filippov [100, 441 j, McCready [47 l].

117
Os' minin [478], Riedel [486], Schmidt-Leidenfrost [492], Vargaftik [508] and Ziebland [519] fall within the

lower group. From the standpoint of the experimental method and procedure, the latter set of data were felt to be more reliable. Therefore, the eight sets of extensive data mentioned above were given equal weight in his analysis, and the single point values of Frontas' ev-Gusakov [447,448] and Riedel [483,484] were also included in the

estimation of the post probable values.

The correlation formula obtained was

10%: ( cgsu) - 502.540 - 0.607275 T (Tin K) .

This equation was found to fit the experimental values of the above-enumerated investigators with a mean deviation

of 1. 2 percent and a maximum of 3. 9 percent.

The above equation was used for the calculation of the recommended values. The values should be correct

in the temperature range between 189 K and 389 K.

Although Abas-Zade [2] made measurements up to the critical point and Filippov [100, 441] also measured

up to 511 K under saturation pressures, no correlation was attempted in the region where the vapor pressure is higher than one atmosphere.

It can be concluded that Makita' s recommended values were accurate to about four percent.

In the present work, experimental measurements made subsequent to Makita' s correlation and other

measurements not utilized by him have been compared with his correlated values. The results of both comparisons are given in the departure plot of Figure 31. From this, it might be deduced that the correlation is satisfactory at 265 K and high by one or two percent at about 375 K. As the uncertainty in these figures is less than the

uncertainty in the bulk of the newer data ( of about three percent) and in the data compared by Makita (of about

four percent) , the original Makita correlation is felt to be satisfactory and there is felt to be no rational basis

for a change in the correlation at this time. The recommended values of Table 24 were obtained by interpolation

of the Makita tabulation. They should be accurate to four percent.

Water . - More than sixty experimental works are available on the thermal conductivity of liquid water.

With two exceptions [217,488], experimental results show that the thermal conductivity of water increases with

increasing temperature from the normal melting point to the normal boiling point and reaches a maximum near

400 K. Beyond this temperature the thermal conductivity first decreases gradually and at a faster rate near the

critical point. The extensive results of Timrot - Vargaftik [339] and Schmidt - Sellschopp [494] have long been

considered to be most reliable and were cited in review papers [258, 465, 498, 520] and many handbooks. Subsequently, more careful measurements were reported by Powell-Challoner [434,480], Riedel [279,485,486,487],

Schmidt- Leidenfrost [301,492,493], Vargaftik-Oleshchuk [509,510], Wright [518], and some other investigators.

Furthermore, Powell [479] made a study and recommended the most probable values.

This analysis is divided into the following three parts:

(a) The supercooled state — below the normal melting point.

There is only one set of data reported by Riedel [485], who extrapolated the values of various salt solutions to zero concentration, and covered temperatures down to 233. 16 K. The reported values are exactly linear

with temperature. However, his value at the normal melting point is about one percent higher than the most

probable value of the normal state at the same temperature. Therefore, Riedel' s data were adjusted by a parallel displacement and the final correlation formula is

10% ( cgsu) = 273. 778 + 3. 90000 T ( T in K) .

This equation should be valid in the temperature range from 233. 16 to 273. 16 K, and should be accurate within one

percent. The recommended values from 250 to 265 K were calculated from this equation.

(b) The normal liquid state — from the normal melting point to the thermal conductivity maxima.

118
Seven sets of data [279, 479, 480, 487, 493, 510, 518] were selected as the most reliable and were given equal

weight. The correlation formula obtained is

10®k ( cgsu) = -1390.53+ 15. 1937 T - 0.0190398 T2

( T in K)

.

This equation should be valid between 273. 16 and 413. 16 K. It is found that this equation fits the above-mentioned

data with a mean deviation of 0. 24 percent and a maximum of 0. 82 percent. This equation was used to generate the recommended values from 265 to 410 K.

( c) The higher vapor pressure state — from near the thermal conductivity maxima up to the critical point.

The values of Vargaftik - Oleshchuk [509,510] are considered to be more reliable than the older data of Timrot - Vargaftik [339]. Therefore, the weight given in this analysis is two to the former and one to the latter. The correlation formula obtained is

10®k (cgsu! = -339. 838 + 9. 86669 T - 0. 0123045 T2

( T in K) .

This equation should be valid in the temperature range from 413. 16 to 613. 16 K, and is found to fit the experimental data of Vargaftik - Oleshchuk with a mean deviation of 0. 39 percent and a maximum of 1. 4 percent. No further

extrapolation is recommended since the deviation becomes extremely large beyond 613. 16 K. The tabulated val- ues from 420 to 610 K are calculated from this formula.

For the sake of clarity, the departure curves are presented on three plots ( Figure 32) . The first plot

consists of 16 sets of data up to 3 80 K. The second plot represents 26 other works in the same temperature

range. The third plot depicts three sets of data at vapor pressures higher than one atm.

Seven sets of data [217, 450, 461, 471, 472, 473, 488] which yield departures greater than 10 percent, and

older data [429, 430, 453, 454, 455, 456, 511, 512, 513, 514, 516] which were published in the 19th century, are not shown af all. The recommended values appear in Table 24.

119
TABLE 24. THERMAL CONDUCTIVITY OF A GROUP OF SELECTED LIQUIDS

( mw. cm-1 K

-1

} T

(K) Helium Nitrogen Argon

2.4 0.192

2.6 0.193

2.8 0.197

3.0 0.204

3.2 0.214

3.4 0.227

3.6 0.241

3.8 0.260

4.0 0.282

4.2 0.307

4.4 (0.335)*

4.6 (0.366)*

4.8 (0.400)*

5.0 (0.437)*

5.2 (0.477)*

6065

70

1. 692*

1.598

1. 504

Carbon

tetra- Diphenyl m-Terphenyl Toluene Water

chloride

75

80

8590

95

1.411

1.320* 1.315*

1.229* 1.258

1.140* 1.200*

1.051+ 1.141*

100

105

110

115

120

0.965* 1 . 082*

0. 879* 1 . 023*

0.794* 0 . 963*

0.710* 0 . 903*

0.627* 0 . 842*

125

130

135

140

145

0.544* 0.780*

0. 717*

0. 654*

0. 591*

0. 527*

150 0.463* (1.719)*

160 ( 1. 694) * 170 ( 1. 669) * 180 1. 644

190 1. 619

200 1.594

210 1.569

220 1.543

230 ( 1. 169) * 1.518

240 ( 1. 150)* 1.492

250 1. 131 1.467 5.22*

260 1. 112 1.442 5.39*

270 1. 093 1.416 5.55*

280 1. 074 1.391 5.74

290 1. 055 1. 365 5.92

300 1. 036 1.340 6.09

310 1. 017 1.315 6.23

320 0. 997 1.289 6.37

330 0. 978 ( 1. 402) * 1.264 6.48

340 0. 959 ( 1.387) * 1.238 6.59

350 0. 940 1.373 ( 1. 361)* 1.213 6.68

360 (0.921) 1.359 ( 1. 356)* 1. 188 6.75

370 (0.902) 1.345 1. 351 1. 162 6. 80 380 ( 0. 882) 1. 331 1. 346 1. 137 6. 84*

390 ( 0. 863) 1.316 1. 341 ( 1. 112) *6. 86*

120
TABLE 24. THERMAL CONDUCTIVITY OF A GROUP OF SELECTED LIQUIDS

( mw . cm

- 1 K

"

*) ( continued)

T Carbon

(K) tetra- Diphenyl m-Terphenyl p-Terphenyl Toluene Water

chloride

400 ( 0. 844) 1.302 1.335 ( 1. 086)* 6. 86* 410 ( 0. 825) 1.288 1.329 f 1.061)* 6. 86* 420 (0. 806) 1.274 1.323 ( 1. 036)* 6. 84* 430 ( 0.787) 1.259 1.317 ( 1. 013)* 6. 81* 440 ( 0. 768) 1.245 1.310 (0. 985V 6.7 8* 450 ( 0. 749) 1.231 1.304 1. 320* ( 0. 959)* 6.73*

460 1.217 1.297 1.310* ( 0. 933)* 6.67*

470 1.202 1.290 1. 300* (0.908)* 6.61*

480 1. 188 1.283 1. 289* ( 0. 885)* 6.53*

490 1. 174 1.276 1. 278 ( 0. 862)* 6.45*

500 1. 160 1.268 1. 267 ( 0. 839)* 6.35*

510 1. 146 1.261 1. 256 6.24*

520 1. 131 1.254 1. 244 6. 12* 530 1. 117* 1.246 1.232 5.99*

540 1. 103* 1.238 1. 220 5. 86* 550 1.089* 1.230 1. 208 5.71*

560 1.074* 1.222 1. 196 5.55*

570 1.060* 1.213 1. 184 5.39*

580 1. 046* 1.205 1. 172 5.20*

590 1. 032* 1. 197 1. 159 5.01*

600 1.018* 1. 188 1. 143 4. 81* 610 1. 180 1. 129 4.60*

620 1. 172 1. 113 4.40*

630 1. 163 1. 097 (4.20)*

640 1. 155* 1. 079 (4.01)*

650 1. 146* 1. 062

* Extrapolated for the supercooled liquid. [Approximate n. m. p. in K: N2 , 63; A, 84; CC14 , 250; C 12H 10 , 342; m-C 18H 14 , 361; p-C 18H 14 , 486; C7 H 10 , 178; H20, 273. 1].

*Under saturation vapor pressure [Approximate n.b. p. in K: He, 4.3; N2 , 77; A, 88; CC14 , 350; C 12H 10> 528; m-C 18H 14 , 637; p-C 18H 14 , 658; C7 H 10 , 384; H20, 373].

121
FIGURE

24.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

LIQUID

ARGON

Curve

Reference
FIGURE

25.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

LIQUID

CARBON

TETRACHLORIDE

U

cr3

<

<r

UJ

a.

Q

)

O

C

Q)

Sha;o«

W ^ 05 0 N

CO oo t> 00 05

CSJ ^

0)&

3O

H 05 CO Tf in

<uo

a

<Du

a>

<D Oh

CN csj COTf Tf rt

(1) £

3o HOJWTpm0t*coo5o

442

16

497

447,

448

17

503

450

18

504,

505

458

19

507

475

20

517
FIGURE

25.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

LIQUID

CARBON

TETRACHLORIDE

(continued)

O

u.

Lda:35

ccUJ

CLs

UJHoZ©O

PSo©>so

<N CO ^ lO

632 633 634 634 635
FIGURE

26.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

LIQUID

DIPHENYL

O

639 640
FIGURE

27.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

LIQUID

HELIUM

133,

545,

546

547
FIGURE

28.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

LIQUID

NITROGEN

535 353 412

57,

413
FIGURE

29.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

O

Curve

No.

Reference

No.

TEMPERATURE

1

637

2

639
FIGURE

30.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

LIQUID

p-TERPHENYL

O

639
FIGURE

31.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

LIQUID

TOLUENE

Ui

tr

z>H

<

cr

UJ

o.5

UJ

I-

<uo

c

tu

tu

<U «

tuto

0)o

a0

Sh0

u-t0«

O

ooooNw^cDNinc^ooooi W^00000000050)0)OOH

co^io(Ot»ooo)OH(Nc»:^ HHHHHHHlNNNNN

5:^

co

co

COCOCOCOOTfLOCOCOO

H(N«TfW 0 C»®a)OHM

iN3oy 3d *3aniavd3a
FIGURE

31.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

LIQUID

TOLUENE

(continued)

O

00 H CO

CO ^ ^

CD CD CD

h cq co ^ lO CD t637 632 633 642
FIGURE

32.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

LIQUID

WATER

(A)

LUor3

I-<

GCbJ

Q.5

bJ

IVod

<»OK

<o o0oa

0)00«0&3O

<N

05

OrHLO HC0^1005D-0500 00505C5COOO»H

050H(NWt}<IOCO

oajrt o)in«DD»

00 00

O 00 00 00 ^ ^ (N ^ -«t TjHCSJOOt^IOCOOOO
FIGURE

32.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

LIQUID

WATER

(B)

(continued)

CDO

c

<D

<D

CD «

^fl)O^OC* 0005 ONWl/5 t^

cdt

DO

oCO HlNC0TfinCDt>00J3OH(N cococococococococo^t^^

to

Tf

<Do

a

<d

CD

«*-< CD K

CD

<N

lO oCD ilflOOHWOOO)«^0C'COJ> ic^cNcocococorrrrrpLomin

CDtu

t-ccaioHNcoifiniot'cocD HHHNNNNNNNNNN
no

0) IooU

03WH<£0

30O'a

pMO

>"H—I >HO

3oQ£OU

<!W

33H

P3o

pmHs

Phw

03

33H

03C

ftWQW

03

30O

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CDoa

<u

Mi

CD

M-C0) 03

0)£o

C3 05 05 CO O ^ CO in

TEMPERATURE
PART IV

THERMAL CONDUCTIVITY OF GASES

135
PAET IV - THERMAL CONDUCTIVITY OF GASES

A. Introduction

Recent developments have resulted in more accurate experimental and theoretical methods of determining

the conductivity of gases at high temperatures. Despite such developments, the reliability of the data is still, in some cases, doubtful. In the analyses which follow, preference has been given to experimental data over theoretical or, where only theoretical values exist, to those which are derived from the most reliable basis.

B. Thermal Conductivity of a Group of Selected Gases

Argon

Experimental measurements have been reported for the thermal conductivity of gaseous argon for temperatures between about 90 and 1373 K and many correlations and calculations have appeared, the more recent extending to temperatures will above 15, 000 K. At atmospheric pressure, the ionization is of the order of one, five and

ten percent at temperatures of 9400, 10, 900 and 11, 750 K, respectively. Hence, the tabulation of recommended

values only extends to 10, 000 K so that these values may, without serious error, be said to refer to neutral argon. As shown by the departure plots (Figure 33) most experimental, correlated and calculated values are in reasonable accord and the accuracy of the recommended values of Table 25, derived by drawing a smooth curve

through these sources, can be assessed as about one percent for temperatures between 100 and 500 K, five percent

for temperatures below 100 K and between 500 and 1500 K and ten percent between 1500 and 10, 000 K.

Carbon Tetrachloride

Surprisingly few experimental measurements of the thermal conductivity of gaseous carbon tetrachloride

appear to have been made. The most recent data are those of Masia and co-workers [571, 578] and earlier measurements were made by Eucken [97] and Moser [51, 254, 416]. Two correlations have appeared by Lenoir [223]

and Vargaftik [601, 602] in addition to several nomograms which were not considered in this analysis.

As will be noted from the departure plot (Figure 34) a five percent difference exists between the Masia and

Moser values. The Lenoir correlation, given without source references, was evidently based on the Moser data

while that of Vargaftik evidently considered only the Eucken and Moser data. The recommended values here presented in Table 26 were based on the Eucken and Masia data for temperatures from 273 to 373 K and the trend for

higher temperatures was adjusted to approach the Vargaftik value at about 573 K.

In view of the disagreement between the Masia and Moser data, the tabulation of recommended values only

extends from 250 to 500 K and the values must be regarded as only being accurate to five percent. If further experimentation shows the Masia data to be accurate, this error estimate can be reduced to one or two percent.

Diphenyl

The only information available to TPRC concerning the thermal conductivity of gaseous diphenyl is contained

in an AEC Report by Ellard et al. [644]. These workers tabulate values from 340 to 820 K without information as

to the source. The values of Table 27 are the result of smoothing the above table. No departure plot is given due

to the complete absence of other source information and the values must be considered definitely provisional until such time when experimental data becomes known.

Reference numbers used in Parts HI and IV of this report refer to the section of References in Volume II, Chapter 1 of TPRC Data Book.

136
Helium

Helium is one of the few gases where quantum effects become significant at low temperatures. In addition

to the experimental data of Ubbink and deHaas [251] calculated values have been made for very low temperatures

and the recommended values for such temperatures were deduced from a curve drawn through both calculated and

experimental values. The usual increment of 10 K for the tabulation of recommended values is inadequate for

helium at low temperatures and appropriate increments have been chosen in the tabulation.

No experimental data were found below about 2 K and gaps exist between 4 to 14 K, 21 to 73 K and above

2000 K. Some discrepancies exist between the measurements of different workers. The trend of the Johnston and

Grilly data [168] and some previous correlations [147, 187, 223,' 521, 570, 630, 631] is to produce values lower

than the Kannuluik and Carmen [173] data. The values were selected so as to agree with the higher temperature

data of the latter workers. This selection agrees with the trend of the considerably higher temperature data of Blais and Mann [569] and of Petersen and Bonilla [628].

Certain conclusions can be reached concerning previous analyses. The calculated values of Amdur [10]

and the recommended tables of Chelton and Mann [81] should be disregarded below 100 K. The tables of Lenoir

[223] agree to within about one percent between 20 and 450 K while the NBS tables [147] only agree to the same

accuracy between about 205 and 415 K. Many correlations [147, 187, 223, 521, 630, 631] fail above about 600 K. Of the seventeen different values

found in the literature for the thermal conductivity at the ice point (273. 15 K), thirteen agree to within two percent

with the recommended value of this report. Further experimental measurements are desirable for temperatures

below 100 K and above 600 K. Below 100 K the recommended values of Table 28 should be accurate to within five percent, from 100 to 400 K the accuracy should be one percent, from 400 to 700 K five percent, from 700 to 2000 K ten percent and

above 2000 K as much as twenty -five percent. The departure plots appear in Figure 35.

Nitrogen

Many experimental, theoretical and correlated sets of values are available for : .he thermal conductivity of gaseous nitrogen. In view of- this fact, it is surprising that the departure plots show the degree of disagreement

between these different values to be larger than would be expected.

As will be observed from the departure plots, the recommended values, obtained by drawing a smooth

curve through the experimental data, are somewhat lower than most previous correlations for temperatures between about 250 and 700 K and, for the Keyes [187] and NBS [146] correlations, for higher temperatures.. It seems that the more recent measurements justify this change.

While measurements up to about 1200 K appear in reasonable agreement, for higher temperatures the trend

of the experimental and theoretical values differs. The recommended values were selected to occur midway between the experimental values at 1200 K and to approach the theoretical estimates at about 2500 K. Theoretical

estimates for temperatures above about 3500 K differ according to whether consideration is given to the influence

of dissociation on the thermal conductivity. Even supposedly similar calculations differ increasingly at higher

temperatures. Due to this reason, the tabulation of recommended values was only undertaken for temperatures to 3500 K, at which temperature the reaction contribution of some two percent is less than the uncertainty in the re- commended values. The recommended values can thus be considered as applying to both the equilibrium and the frozen gas.

The accuracy of the recommended values of Table 29 can be assessed as two percent for temperatures

below about 350 K, five percent for temperatures from 350 to 1200 K and ten percent above 1200 K. Further ex- periments are to be desired for the entire temperature range if accuracy better than two percent is desired. More

137
accurate calculations are also required, possibly for temperatures from 1000 to about 4000 K and certainly for

higher temperatures. The departure plots appear in Figure 36.

m-Terphenyl

No values have been found for the thermal conductivity of gaseous m-Terphenyl.

p-Terphenyl

No values have been found for the thermal conductivity of gaseous p-Terphenyl.

Toluene

Data on the thermal conductivity of gaseous toluene have been reported by Abas-Zade [2] for temperatures

between 273 and 594 K. Examination of these data showed that between 373 and 573 K a linear variation of thermal

conductivity with temperatures apparently occurs. The value quoted at the highest temperature appears anomalously high unless decomposition of the vapor occurred. In the preparation of the table of recommended values a smooth curve was drawn through the experimental points except for the value at 594 K. The recommended values

of Table 30 were obtained from this curve which was assumed to be linear above 373 K. The trend of the data with

temperature is in need of rechecking by new measurements. Provisionally, the accuracy can be assessed at two

precent below 530 K and ten percent for the higher temperatures. The departure plot appears in Figure 37.

Water (Steam)

In preparing tables of recommended values for the thermal conductivity of water vapor a more complete

collection of tabulations based upon correlating equations, etc. , was made than usual. This was done because

severe disagreement exists between different sets of data for this substance. Many users of tabulated values have

been unaware of the primary data upon which their tables were based and of the fact that such primary data were

subject to large errors. Recent measurements have shown that at least one set of primary data are in considerable error and hence also many tabulations.

Examination of the departure plots (Figure 38) reveals that there now exist a large number of experimental

data which agree with the recommended values to within some three percent. In severe disagreement are the

measurements of Keyes, reported by himself [187] and with Sandell [195]. These show a systematic trend with

temperature in disagreement with others and also with more recent measurements and should be disregarded. A

large number of tabulations have wholly or in part been based upon the Keyes data. Those of Lenoir [223], Keyes

[187], Nusselt [263, see also 201], Keenan and Keyes [594], Jakob [593], van Iterson [592] and Grober and Erk

[591], are unsatisfactory above about 373 K and only moderately accurate for the few cases [201, 223, 263, 594]

where they extend to lower temperatures. In addition to the recommended values, the tabulations of Koch and

Fritz [201], the recalulated values of Keyes and Sandell [360, 365, 366] and the Russian data cited by Keyes [596] are reasonably accurate for all temperatures as are those of Keyes and Vines [590] for temperatures above 420 K.

Still in severe disagreement are the high temperature data of Geier and Schafer [587] and Vargaftik et al. [360,

365, 366]. For this reason, the tabulation of recommended values has been curtailed to 900 K.

The accuracy of the recommended values of Table 31 can be estimated as being within two percent from 320

to 700 K, and five percent from 250 to 310 K and 710 to 900 K. The uncertainty at the higher temperatures is produced by the problem of estimating the radiation error in the vapor. Due to the high boiling point of water as compared to most fluids, pressure effects are significant to higher temperatures than usual and hence influence

the recommended values to about 600 K. More precise recommended values for temperatures below 600 K will

require a detailed consideration to be made of the pressure effect and has thus limited the suggested accuracy to two percent rather than a closer tolerance. Further experimentation is to be desired for all temperatures and

pressures so that the uncertainties due to pressure, radiation, and accomodation effects can be reduced.

138
TABLE 25. THERMAL CONDUCTIVITY OF GASEOUS ARGON (mw. cm" 1 K

_1

) T (K) k T (K) k T (K) k

50 (0. 0326)*

(0. 0392)*

650 0. 319 2500 0. 815

60 660 0. 322 2600 0. 839

70 (0. 0457)*

(0. 0522)*

670 0. 326 2700 0. 864

80 680 0. 329 2800 0. 888

90 0. 0587 690 0. 333 2900 0. 913

100 0. 0652 700 0. 336 3000 0. 938

110 0. 0716 710 0. 339 3100 0. 962

120 0. 0779 720 0. 343 3200 0. 987

130 0. 0839 730 0. 346 3300 1. Oil

140 0. 0898 740 0. 349 3400 1. 036

150 0. 0957 750 0. 353 3500 1. 060

160 0. 1016 760 0. 356 3600 1. 084

170 0. 1074 770 0. 359 3700 1. 109

180 0. 1131 780 0. 362 3800 1. 133

190 0. 1188 790 0. 366 3900 1. 158

200 0. 1244 800 0. 369 4000 1. 182

210 0. 1300 810 0. 372 4100 1. 207

220 0. 1355 820 0. 375 4200 1. 231

230 0. 1409 830 0. 378 4300 1. 256

240 0. 1462 840 0. 381 4400 1. 281

250 0. 1515 850 0. 384 4500 1. 305

260 0. 1567 860 0. 387 4600 1. 330

270 0. 1619 870 0. 390 4700 1. 354

280 0. 1671 880 0. 393 4800 1. 379

290 0. 1722 890 0. 396 4900 1. 404

300 0. 1772 900 0. 398 5000 1. 429

310 0. 1822 910 0. 401 5200 1.478

320 0. 1871 920 0. 404 5400 1. 526

330 0. 1919 930 0. 407 5600 1. 575

340 0. 1966 940 0. 410 5800 1. 624

350 0. 2013 950 0. 413 6000 1. 673

360 0. 2059 960 0. 416 6200 1. 722

370 0. 2103 970 0. 418 6400 1. 771

380 0. 2147 980 0. 421 6600 1. 821

390 0. 2190 990 0. 424 6800 1. 881

400 0. 2233 1000 0. 427 7000 1. 950

410 0. 2276 1050 0. 441 7200 2. 03

420 0. 2318 1100 0. 454 7400 2. 12 430 0. 2359 1150 0. 468 7600 2. 23

440 0. 2400 1200 0. 481 7800 2. 35

450 0. 2441 1250 0. 495 8000 2.48

460 0. 2481 1300 0. 508 8200 2. 63

470 0. 2520 1350 0. 521 8400 2. 80

480 0. 2559 1400 0. 535 8600 2. 99

490 0. 2599 1450 0. 548 8800 3. 18

500 0. 2638 1500 0. 561 9000 3. 39

510 0. 268 1550 0. 575 9200 3. 61

520 0. 272 1600 0. 588 9400 3. 83

530 0. 276 1650 0. 602 9600 4. 07

540 0. 280 1700 0. 615 9800 4. 31

550 0. 283 1750 0. 628 10000 4. 56 560 0. 287 1800 0. 641

570 0. 290 1850 0. 654

580 0. 294 1900 0. 667

590 0. 297 1950 0. 680

600 0. 301 2000 0. 692

610 0. 305 2100 0. 717

620 0. 308 2200 0. 741

630 0. 311 2300 0. 766

640 0. 315 2400 0. 790

Extrapolated

139
FIGURE

33

DEPARTURE

CURVE

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

ARGON

UJ

<rZ>6

ocUJ

O.

UJH

a>oav

<0

<U OS%u

a>oa

0)Fh

0) <4-1 a)

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CM 05

00 CM <OrHHlO^COC0CM~°O

05000CMI>t^a005CM ^ W H H CM CD

CMCO^0t>OOO5OW cocooococococo^^

ID

00CO CMHCJ^t^OJOOWCO 0505^Ht-I>HLOlO fHHCMCDHCOCMCOrH

HtMCO^CONQOOH

CMCMCMCMCMCMCMCOCO

ID 00 CD CM T*t>00t>OCMCMlD05 COHHOOOOHrlOO COCOHCM^HCOW

OHCMW^COf-OOO HHHrlrHHrtH CQ
FIGURE

33

DEPARTURE

CURVE

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

ARGON

(continued)

OO U_

CO (r3s o a: o uj

h- 0-Z

UJH

Oo

tooo

lOoo

<3- O

roOO

OJOO

CMOO

rOO

M-

(Uoa

<u

t-i <U

<L> QS

a>tao

ID OS

<u>

S3 u

n 3 h

h

(N

H 00 05H

(M ^ rH

O) IO 05 in

H

H

N

N C*3 ^ H Tf lO to to

OJ r*H r-H ^ r-H lO CD CD H CO

lT5CDI>CX)Oif-HOJlO

603 617 618 105
FIGURE

33

DEPARTURE

CURVE

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

ARGON

(continued)

CO

05

<N

<N 00

05 <N

<N CO © CO

lO 00 CO <N oo o’

t£)

HH CO 00

CO CO rH (M

q

H

N

M ^

rH rH Tf LO CO H M H H r}< CO LO CO CD H H ^ lO Ifl t>

LO 05 O CO CO CO

00 o *H <N

CO CO

»H o

CO CO

00 05
FIGURE

33.

DEPARTURE

CURVE

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

ARGON

(continued)

o

•H ^ Tf H N H

CO lO CO

h m co r- o

615 146

292,

293
FIGURE

33.

DEPARTURE

CURVE

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

ARGON

(continued)

00

CM

ro

CM O
DEPARTURE

CURVE

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

ARGON

(continued)

O

O

<no

a

<o

OJ hnh rH i-H i-H

(5 50 CO CO Ph

u

614 620
TABLE 26. THERMAL CONDUCTIVITY OF

GASEOUS CARBON TETRACHLORIDE (raw. era

-1 K_1

) T (K) k

250 0. 0528

260 0. 0555

270 0. 0583

280

' 0. 0612

290 0. 0642

300 0. 0673

310 0. 0705

320 0. 0738

330 0. 0770

340 0. 0803

350 0. 0835

360 0. 0866

370 0. 0897

380 0. 0928

390 0. 0959

400 0. 0989

410 0. 1019

420 0. 1049

430 0. 1079

440 0. 1108

450 0. 1136

460 0. 1163

470 0. 1189

480 0. 1214

490 0. 1238

500 0. 1261

146
FIGURE

34

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

CARBON

TETRACHLORIDE

Q)Oc

<D

Q)

<D cc

oo

t>io

r-T t>

t> 05

LO cZ

0)>o

>H CM CO lO

51,

254

601,

602

223
TABLE 27. THERMAL CONDUCTIVITY OF GASEOUS DIPHENYL (mw. cm-1 K

-1

) T (K) k T (K) k

300 0. 075 600 0. 304

310 0. 082 610 0. 312

320 0. 089 620 0. 321

330 0. 095 630 0. 330

340 0. 102 640 0. 338

350 0. 109 650 0. 347

360 0. 116 660 0. 356

370 0. 123 670 0. 364

380 0. 130 680 0. 373

390 0. 137 690 0. 382

400 0. 144 700 0. 391

410 0. 151 710 0. 400

420 0. 159 720 0.408

430 0. 166 730 0.418

440 0. 173 740 0.426

450 0. 181 750 0.436

460 0. 188 760 0.445

470 0. 196 770 0.454

480 0. 203 780 0.463

490 0. 211 790 0. 472

500 0. 220 800 0.481

510 0. 228 810 0. 490

520 0. 236 820 0.499

530 0. 244 830 0. 508

540 0. 253 840 0. 518

550 0. 261 850 0. 527

560 0. 269

570 0. 278

580 0. 287

590 0. 295

148
TABLE 28. THERMAL CONDUCTIVITY OF GASEOUS HELIUM (mw. cm -1 K"1

) T (K) k T (K) k T (K) k T (K) k

0. 08 0. 00044 150 0. 950 650 2. 64 1750 5. 57

0. 09 0. 00053 160 0. 992 660 2. 67 1800 5. 70

0. 10 0. 00064 170 1. 033 6^0 2. 69 1850 5. 83

0. 15 0. 00130 180 1. 072 680 2. 72 1900 5. 96

0. 20 0. 00231 190 1. 112 6^0 2. 75 1950 6. 08

0. 25 0. 0039 200 1. 151 700 2. 78 2000 6. 20

0. 30 0. 0062 210 1. 190 710 2. 81 2100 6. 44

0. 35 0. 0089 220 1. 228 720 2. 84 2200 6. 69

0.40 0. 0120 230 1. 266 730 2. 87 2300 6. 93

0.45 0. 0154 240 1. 304 740 2. 90 2400 7. 16

0. 5 0. 0187 250 1. 338 750 2. 92 2500 7. 39

0. 6 0. 0231 260 1. 372 760 2. 95 2600 7. 62

0. 7 0. 0252 270 1.405 770 2. 98 2700 7. 85

0. 8 0. 0262 280 1.437 780 3. 01 2800 8. 07

0. 9 0. 0266 290 1.468 790 3. 04 2900 8. 29

1. 0 0. 0269 300 1. 499 800 3. 07 3000 8. 51

1. 25 0. 0281 310 1. 530 810 3. 09 3100 8. 72

1. 5 0. 0306 320 1. 560 820 3. 12 3200 8. 95

2. 0 0. 0393 330 1. 590 830 3. 15 3300 9. 16

2. 5 0. 0502 340 1. 619 840 3. 18 3400 9. 37

3. 0 0. 0607 350 1. 649 850 3. 21 3500 9. 58

3. 5 0. 0732 360 1. 678 860 3. 23 3600 9. 79

4. 0 0. 0803 370 1. 708 870 3. 26 3700 10. 00

4. 5 0. 0879 380 1. 737 880 3. 29 3800 10. 22

5. 0 0. 0962 390 1. 766 890 3. 32 3900 10.43

6 0. 1113 400 1. 795 900 3. 35 4000 10. 64

7 0. 1247 410 1. 824 910 3. 37 4100 10. 85

8 0. 1393 420 1. 853 920 3. 40 4200 11. 06

9 0. 1523 430 1. 882 930 3. 43 4300 11. 27

10 0. 1640 440 1. 914 940 3. 46 4400 11.48

12 0. 1866 450 1. 947 950 3.49 4500 11. 69

14 0. 2067 460 1. 980 960 3. 52 4600 11. 90

16 0. 2259 470 2. 013 970 3. 54 4700 12. 11

18 0. 2435 480 2. 046 980 3. 57 4800 12. 31

20 0. 2582 490 2. 080 990 3. 60 4900 12. 51

25 0. 2962 500 2. 114 1000 3. 63 5000 12. 71

30 0. 3330 510 2. 15 1050 3. 76

35 0. 3669 520 2. 18 1100 3. 89

40 0.4000 530 2. 22 1150 4. 03

45 0. 4314 540 2. 25 1200 4. 16

50 0. 4623 550 2. 29 1250 4. 29

60 0. 521 560 2.33 1300 4. 43

70 0. 578 570 2. 36 1350 4. 55

80 0. 631 580 2. 40 1400 4. 69

90 0. 679 590 2. 43 1450 4. 82

100 0. 730 600 2.47 1500 4. 94

110 0. 776 610 2. 51 1550 5. 07

120 0. 819 620 2. 54 1600 5. 21

130 0. 863 630 2. 58 1650 5. 33

140 0. 907 640 2. 61 1700 5.45

149
FIGURE

35.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

HELIUM

lN30U3d 4 3dnidVd3Q

LlJ cc3

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DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

HELIUM

(Continued)

521 630 631 611 616
FIGURE

35.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

HELIUM

(continued)

<do

d

Q) COOOO-HO-H-HOO to 05

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FOR

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OF

GASEOUS

HELIUM

(

continued)

0) o0

CDU

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in

^ CO ^ lO CO 05 3

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630 631 611 569
FIGURE

35

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

HELIUM

(continued) oo

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FIGURE

35.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

HELIUM

(continued)

6700

6900

7100

7300

7500

7700

7900

8100

8300

8500

8700

8900

TEMPERATURE,

Curve

Reference

33

521

36

611
TABLE 29. THERMAL CONDUCTIVITY OF GASEOUS NITROGEN (mw. cm-1 K

_1

)

T (K) k T (K) k T (K) k

50 (0. 0485)! 500 0. 3864 950 0. 609

60 (0. 0578)1 510 0.392 960 0. 613

70 (0. 0670] 520 0. 398 970 0. 618

80 0. 0762 530 0.403 980 0. 622

90 0. 0852 540 0. 408 990 0. 626

100 0. 0941 550 0.414 1000 0. 631

110 0. 1030 560 0. 420 1050 0. 651

120 0. 1119 570 0.425 1100 0. 672

130 0. 1208 580 0. 431 1150 0. 693

140 0. 1296 590 0. 436 1200 0. 713

150 0. 1385 600 0.441 1250 0. 733

160 0. 1474 610 0. 446 1300 0. 754

170 0. 1562 620 0. 452 1350 0. 775

180 0. 1651 630 0.457 1400 0. 797

190 0. 1739 640 0. 462 1450 0. 819

200 0. 1826 650 0. 467 1500 0. 842

210 0. 1908 660 0. 472 1550 0. 867

220 0. 1989 670 0. 478 1600 0. 893

230 0. 2067 680 0. 483 1650 0. 921

240 0. 2145 690 0.488 1700 0. 950

250 0. 2222 700 0. 493 1750 0. 981

260 0. 2298 710 0. 498 1800 1. 013

270 0. 2374 720 0. 503 1850 1. 046

280 0. 2449 730 0. 508 1900 1. 080

290 0. 2524 740 0. 513 1950 1. 113

300 0. 2598 750 0. 517 2000 1. 146

310 0. 2671 760 0. 522 2100 1. 207

320 0. 2741 770 0. 526 2200 1..263 330 0. 2808 780 0. 531 2300 1. 314

340 0. 2874 790 0. 536 2400 1. 361

350 0. 2939 800 0. 541 2500 1. 406

360 0. 3002 810 0. 546 2600 1. 449

370 0. 3065 820 0. 551 2700 1. 494

380 0. 3127 830 0. 555 2800 1. 542

390 0. 3189 840 0. 559 2900 1. 590

400 0. 3252 850 0. 564 3000 1. 640

410 0.3314 860 0. 569 3100 1. 691

420 0. 3376 870 0. 574 3200 1. 743

430 0. 3438 880 0. 578 3300 1. 795

440 0. 3501 890 0. 583 3400 1. 853

450 0. 3564 900 0. 587 3500 1. 915

460 0. 3626 910 0. 592

470 0.3688 920 0. 596

480 0.3749 930 0.600

490 0. 3808 940 0. 605 Extrapolated

156
FIGURE

36

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

NITROGEN
FIGURE

36

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

NITROGEN

(continued)
FIGURE

36.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

NITROGEN

(continued)

CO

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CM

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CM CD to 00

CD CM CD CM

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FIGURE

36.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

NITROGEN

(continued)

CD

tHCDCO

I CO CO ID 05 »H t- fH ONNNOiOflO N CD CD CD CD (M N

oo 05 CO <N CO ^ ID N (N CO ^ ^ ^
CONDUCTIVITY

OF

GASEOUS

NITROGEN

(continued) <§aWaHaoaHawaaHa<awp

CD

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DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

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(continued)

^ in

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CM CO

CO CO
TABLE 30. THERMAL CONDUCTIVITY OF

GASEOUS TOLUENE (mw. cm"1 K"1

) T (K)

250

260

270

280

290

300

310

320

330

340

350

360

370

380

390

400

410

420

430

440

450

460

470

480

490

500

510

520

530

540

550

560

570

580

590

600

k

0. 116

0. 121

0. 126

0. 133

0. 139

0. 146

0. 154

0. 162

0. 170

0. 180

0. 189

0. 198

0. 208

0. 219

0. 230

0. 240

0. 251

0. 262

0. 273

0. 284

0. 295

0. 305

0.316

0.327

0. 338

0.349

0. 360

0. 371

0. 382

0. 393

0.405

0. 416

0.427

0.439

0. 450

0.461

163
FIGURE

37.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

TOLUENE

Curve

Reference
TABLE 31. THERMAL CONDUCTIVITY OF GASEOUS WATER (STEAM) (raw. cm"1 K"1

) T (K) k T (K) k

250 (0. 140)* 600 0.464

260 (°. 148)' 610 0.475

270 (0. 156) 620 0.486

280 0. 164 630 0.497

290 0. 172 640 0. 508

300 0. 181 650 0. 518

310 0. 189 660 0. 529

320 0. 197 670 0. 540

330 0. 205 680 0. 551

340 0. 214 690 0. 562

350 0. 222 700 0. 572

360 0. 231 710 0. 58

370 0. 239 720 0. 59

380 0. 248 730 0. 60

390 0. 256 740 0.62

400 0. 264 750 0. 63

410 0. 273 760 0. 64

420 0. 282 770 0. 65

430 0. 291 780 0. 66 440 0. 300 790 0. 67

450 0. 307 800 0. 68

460 0. 317 810 0. 69

470 0. 327 820 0. 70

480 0. 337 830 0. 71

490 0. 347 840 0. 72 500 0. 357 850 0. 73

510 0. 368 860 0. 74

520 0. 378 870 0. 75

530 0. 389 880 0. 76

540 0.400 890 0. 77 550 0. 411 900 0. 78

560 0.422

570 0.432

580 0. 443

Extrapolated 590 0.454

165
DEPARTURE

CURVE

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

WATER

(

STEAM)

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38.

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CONDUCTIVITY

OF

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WATER

(STEAM)

(continued)

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FIGURE

38.

DEPARTURE

CURVE

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

WATER

(STEAM)

(continued)

\

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S H to CO o H CO

r i i i o

TjH LO 05 rH H H H M

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