NBS

352

The Viscosity and Thermal Conductivity

Coefficients of Dilute Neon, Krypton,

and Xenon

H. J. M. HANLE¥-A*ID G. E. CHILDS

/'tf*T OF

\

,i&

n

*"»f«u o«

'

I/) Q*

U.S DEPARTMENT OF COMMERCE

National Bureau of Standards
THE NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards1 provides measurement and technical information services

essential to the efficiency and effectiveness of the work of the Nation's scientists and engineers. The

Bureau serves also as a focal point in the Federal Government for assuring maximum application of the physical and engineering sciences to the advancement of technology in industry and commerce. To

accomplish this mission, the Bureau is organized into three institutes covering broad program areas of research and services: THE INSTITUTE FOR BASIC STANDARDS . . . provides the central basis within the United

States for a complete and consistent system of physical measurements, coordinates that system with the measurement systems of other nations, and furnishes essential services leading to accurate and uniform

physical measurements throughout the Nation's scientific community, industry, and commerce. This

Institute comprises a series of divisions, each serving a classical subject matter area: —Applied Mathematics—Electricity—Metrology—Mechanics—Heat—Atomic Physics—-Physical

Chemistry—Radiation Physics—Laboratory Astrophysics2—Radio Standards Laboratory,2 which

includes Radio Standards Physics and Radio Standards Engineering—Office of Standard Refer- ence Data. THE INSTITUTE FOR MATERIALS RESEARCH . . . conducts materials research and provides

associated materials services including mainly reference materials and data on the properties of materials. Beyond its direct interest to the Nation's scientists and engineers, this Institute yields services which are essential to the advancement of technology in industry and commerce. This Institute is or- ganized primarily by technical fields: —Analytical Chemistry—Metallurgy—Reactor Radiations—Polymers—Inorganic Materials—Cryogenics2—Materials Evaluation Laboratory—Office of Standard Reference Materials.

THE INSTITUTE FOR APPLIED TECHNOLOGY . . . provides technical services to promote the use of available technology and to facilitate technological innovation in industry and government. The

principal elements of this Institute are: —Building Research—Electronic Instrumentation—Textile and Apparel Technology Center

Technical Analysis—Center for Computer Sciences and Technology—Office of Weights and Measures—Office of Engineering Standards Services—Office of Invention and Innovation—Clearinghouse for Federal Scientific and Technical Information.3

1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D. C,

20234.

2 Located at Boulder, Colorado, 80302.

3 Located at 5285 Port Royal Road, Springfield, Virginia, 22151.
UNITED STATES DEPARTMENT OF COMMERCE • Alexander B. Trowbridge, Acting Secretary

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

NBS TECHNICAL NOTE 352

ISSUED MARCH 23, 1967

THE VISCOSITY AND THERMAL CONDUCTIVITY COEFFICIENTS

OF DILUTE NEON, KRYPTON, AND XENON

H. J. M. HANLEY AND G. E. CHILDS

Cryogenics Division

Institute for Materials Research

National Bureau of Standards

Boulder, Colorado

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 20402

Price: 25 cents

CONTENTS

List of Figures iv

List of Tables v Abstract 1

1. Introduction 1

2. The Potential Functions 5

3. Kinetic Theory Transport Expressions 6

4. Experimental Data 8

5. Method of Calculation and Results 8

5.1 Viscosity 8

5.1.1 Neon 9

5.1.2 Krypton and Xenon 10

5.2 Thermal Conductivity 12

6. Conclusion 12

7. Acknowledgment 13

8. References 21

in
LIST OF FIGURES

Argon percent deviation curves

Tl exp 'lc»l<

Tl ca lc x 100

Curve a is reproduced from Fig. 2 of Ref. 2 and was

calculated from the Kihara function with v = 0.1,

e/k= 139. 8 °K, and a = 3. 35A. Curve b was calculated with the m-6 function, m = 17, e/k = 151. 5°K, and

a = 3.31A.

•NT a. j •^j.- \ i lexp ~ 'loalc Neon percent deviation curve I — Tl ca 1 c x 100

calculated from the Kihara potential function with

Y = 0.1, e/k = 53.2°K, and a = 2. 67A. 11

Krypton and xenon percent deviation curves

rST[exp - Tl calo

Tl calc

X 100

calculated from the m-6 potential. For krypton,

m = 17, £ /k = 226. 0°K, and a = 3. 50a. For xenon,

m = 24, e/k= 382. 3°K, and a = 3.73A.

Neon percent deviation curve

^calc

X 100

calculated from the Kihara potential function,

Y = 0.1, e/k = 5 3. 2° K, and a = 2. 67A.

Krypton percent deviation curve

'"exp ~ ^calc

V X calc

X 100

calculated from the m-6 potential function,

m = 17, e/k = 226. 0°K, and a = 3. 50A .

Xenon percent deviation curve V

^exp ~ ^calc

calc

X 100

14

15

16

calculated from the m-6 potential function, m = 24,

e/k= 382. 3°K, and a = 3. 73A . 17

IV
LIST OF TABLES

I. Best values of the Lennard- Jones parameters

obtained for neon, krypton, and xenon 9

II. Best functions and the parameters for

neon, krypton, and xenon 10

III. Viscosity and thermal conductivity of

gaseous neon 18

IV. Viscosity and thermal conductivity of

gaseous krypton 19

V. Viscosity and thermal conductivity of

gaseous xenon 20

THE VISCOSITY AND THERMAL CONDUCTIVITY COEFFICIENTS

OF DILUTE NEON, KRYPTON, AND XENON

H. J. M. Hanley and G. E„ Childs

The coefficients of viscosity and thermal conductivity for dilute

neon, krypton, and xenon were examined by a method already proved

successful for dilute argon, oxygen, and nitrogen. This method selects

a suitable potential function, and its parameters, which is then used to

correlate theory with experimental data, given the kinetic theory expressions for the transport coefficients. The method has recently been ex- panded and generalized and the results of this general study are applied

in this note. The potential functions examined were members of the

m-6, Kihara, Exp: 6, and Morse families. It was found that the Kihara

was most suitable for neon, and the m-6, with m = 17 and m = 24, was

most suitable for krypton and xenon, respectively. Viscosity and thermal conductivities were calculated from these functions and tables are

given between 100 and 1000°K.

Key Words: dilute gases, neon, krypton, xenon, transport

coefficients, correlations, m-6, Kihara, Exp: 6,

Morse, potential functions.

1. INTRODUCTION

In this note we correlate transport coefficients of dilute neon,

krypton, and xenon by applying a method which has been discussed and

t shown to be successful in previous publications for argon [l, Z] and

for oxygen and nitrogen [3] . Experimental transport coefficients for

these gases were correlated by means of the rigorous kinetic theory

expressions and a suitable intermolecular potential function. Recently

this method has been considerably expanded and can now be generalized

for any given potential function and for any property [4] , provided that

theoretical tables for the potential and the property can be calculated.

t Numbers in brackets refer to references,
(Specifically, the properties second virial coefficient, Joule -Thomson

coefficient, viscosity and diffusion coefficients; and the families m-6,

Kihara, Exp: 6, and Morse were considered). The general study is

not yet complete but three conclusions have resulted from it which are

relevent to this note because they enable the correlation procedure to be

considerably simplified,, The conclusions are taken to be correct.

We first define a reduced temperature T by the relation T = T/(e/k), where T is the absolute temperature, e is the value of the

maximum energy of attraction between two molecules for a given

potential function, and k is Boltzmann' s constant. We frequently

refer to the temperature reduced with respect to the 12-6 (LennardJones) potential, T12-6 ; this choice is a matter of convenience

because values of (e/k)i2_6 are known for most common substances,

at least to a first approximation.

The conclusions from the general study can be stated;

1. It appears impossible to distinguish between one reasonable intermolecular potential function and another in the reduced temperature

range of about 2. < T12_6 < 5. .

2. If a potential function of one family correlates data in a particular

manner, it appears that a member of another family can always be

chosen that will correlate the data in a similar manner. This is

especially true for the temperature range 1. 5 < Ti2_6 < 10. 0. This

conclusion obviously includes the result of conclusion 1 above.

By "reasonable" we mean that the function is based on a model

believed to approximate the real situation. The conclusions,

therefore, may not be valid for such relatively simple models

as the square well, triangular well, and so on.
3. It seems that it is impossible to find a three -parameter function

that will satisfactorily correlate transport data over the temperature

range of approximately 1.0 < T12-6 < 20.0. This is a very wide range;

for argon, for example, it is 12 5 < T°K< 2, 500.

Also, preliminary calculations have indicated that the ability

to distinguish between one function and another, which is already negligible between 2. < Ti3_6 < 5.0, is further reduced

over a wider temperature range if the data have a random

error of about 0. 5% or more.

It is not intended to discuss the general validity of these conclusions in this article, but we indicate the validity of 1 and 2 for

transport processes by considering results from our previous investigations [l, 2, 3] „ Consider first conclusion 2 for the special case of

argon. Curve a, Fig. 1, shows the deviation curve obtained when the

viscosity coefficient was correlated with the Kihara function [l] . We have now found that this deviation curve is essentially duplicated

when a member of the m-6 family was used, m = 17 in this case

(curve b). Undoubtedly a similar curve would have been obtained

with a member of the Exp: 6 family. In other words, there most

probably exists a value of & (the characteristic parameter of the

Exp: 6 family) which will enable argon to be correlated in a similar

manner; however, the necessary theoretical calculations for the

Exp: 6 family are not yet complete.

With regard to conclusion 1 we can clearly demonstrate [Fig. 1 shown here; Fig. 2 of Ref. 1, and Figs. 5, 6, and 7 of Ref. 3] that in

the range 2. < I12-6 < 5.0, the m-6, Kihara, Exp: 6, and Morse

functions all satisfactorily, and in like manner, correlate the data for

argon, oxygen, and nitrogen.

The point we wish to emphasize is that in the range 1. 5 < Ti2_6 < 10.0, there is a lack of uniqueness in the choice of the three-parameter function investigated [4] . So before starting to investigate
<

> -I

UJo

KIHARA A - [14]

9 - [15] • - [16]

- [17]

H - [18]

O - [19]

D - [20] X - [21]

o

X• o DDD -X 2f X X- H

A

xA A* H

CC

m -6

X• o aoa

*P X x

-H- at. a

-i

-2

=«* °A A

A

200 400 600 800

TEMPERATURE, °K

1000 1200

Fig. 1. Argon percent deviation curves V

Mexp " Mcali

^lcalc

x 100 \ Curve a

is reproduced from Fig. 2 of Ref. 2 and was calculated from the

Kihara function with v = 0. 1, e/k = 139. 8°K and a = 3. 35A.

Curve b was calculated with the m-6 function, m = 17,

e/k = 151. 5° K and a = 3. 31 A.
neon, krypton, or xenon, we can say that should we find that a particular potential function satisfactorily correlates the transport data

in the temperature range 1. 5 < T12--6 < 10. 0, we can be reasonably

sure that this function is as suitable as any other function we might

select. As mentioned above, this statement is based on studies of the

m-6, Kihara, Exp: 6, and Morse functions —about all the common

three-parameter functions in use at the present time.

The comment on the experimental requirements reinforces the

decision made previously that it is best to study experimental viscosity

data in order to determine a potential function and its parameters.

Any attempt to select a potential function from experimental thermal

conductivity data is not likely to be successful because thermal conductivity data are known to be less accurate.

2. THE POTENTIAL FUNCTIONS

The discussion in this note is restricted to the functions of four

families: the m-6, the Kihara, the Exp: 6, and the Morse. The Kihara,

in particular, has received much attention in the literature recently [5,

6, 7] , as has the Morse function which has been described by several

authors [8, 9] . The usage of the m-6 family is not as common as the

others (although it contains the Lennard- Jones function) because of the

difficulties in obtaining the tables of the collision integrals. Recently,

however, these tables have become available [10] .

If U(r) is the interaction potential of two molecules separated by

a distance r, and e is the maximum energy of attraction, or energy

minimum, the potentials of the families are written:

m-o

m

" a m

c°

A

( ° 17 ^ 1 / rr

&

N\m-6 \m-6

\•» r J V r . J J / _ V m ^

/ ^ m -) U(r) = e /

where a is the value of r at U(r) = 0.

(1)
Kihara

U(r) = 4e [C r - a

12

r - a > (2)

U(r) = ro

, r < a;

here the finite size of the molecule is taken into consideration

by including a core diameter, a. The reduced parameter Y>

defined as a/a, is the parameter characteristic of this family.

Exp: 6

U(r) =

1 - 6/a

6

ea(l-r/rm) _ (rm/r)

6

(3)

where r is the value of r at the energy minimum, and a the family m

parameter which represents the steepness of the repulsive part of

the function.

Morse

U(r) = e {eXp[- 2 Q)(r-rm)]-2exp[-(|)(r.rm)]}, (4)

where c is related to the curvature of the potential at r = r , m

and is the family parameter in this case.

3. KINETIC THEORY EXPRESSIONS FOR THE VISCOSITY

AND THERMAL CONDUCTIVITY COEFFICIENTS

The kinetic theory for a dilute gas is formally complete[ 11, 12] ; the Chapman- Enskog treatment of the Boltzmann equation gives the

viscosity and thermal conductivity coefficients in terms of collision

integrals which are functions of the gas dynamics and thus of the inter-
molecular potential. It is the lack of knowledge of the latter which

restricts the applicability of the kinetic theory expressions. These

expressions are:

Viscosity (r\)

,6 26.693 (MT)2 n 10

s , — "^

UZLLL f gem-1

sec" 1

, (5)

Thermal Conductivity (X)

l

. - 832.24 (T/M)2

, _ -i -i , -i .,, X 10 = i—

f— f, J cm sec deg , (o)

R

3 Q<2 ' 3

>'"(T*)

where: M = molecular weight. (M = 20. 183 for neon,

M = 83. 80 for krypton, M = 131. 30 for xenon.

R = a distance parameter, i. e. , R - <J for the m-6,

Kihara and Morse; and R = r for the Exp: 6. m

T = the absolute temperature, °K.

q(2,2) ^ j _ t ^e recjuced collision integrals (reduced

by dividing by the integrals for the rigid sphere

case) at the reduced temperature T , where

T' = T/(e/k) with k the Boltzmann constant.

The terms f and f. account for higher mathematical approximations to r\ and X and are slowly varying functions of T which seldom

differ from unity by more than about 0. 5%. To be consistent with the

accuracy of the experimental viscosity and thermal conductivity data

especially at extreme temperatures, the terms can be omitted from

Eqs (5) and (6) without significant error.

Appropriate tables of the collision integrals as a function of T

for each of the families were taken from Refs. 7, 10, 12, and 13. The

numerical values of the integrals depend on the method of integration
which varies from one procedure to another, but it was verified that

the choice of any particular set of tables made no significant difference

to the results presented here.

4. EXPERIMENTAL DATA FOR NEON, KRYPTON, AND XENON

The experimental data were taken from the following references:

Neon, viscosity, Refs. 16, 17, 20, 22-26;

temperature range 80 - 1100°K.

Krypton, viscosity, Refs. 22, 25, 27, 28;

temperature range 283 - 972°K.

Xenon, viscosity, Refs. 22, 25, 28-30;

temperature range 288 - 972°K.

Neon, thermal conductivity, Refs. 31-37;

temperature range 90 - 579°K.

Krypton, thermal conductivity, Refs. 32, 33, 38;

temperature range 171 - 579°K.

Xenon, thermal conductivity, Refs. 30, 32, 33, 38;

temperature range 155 - 579 °K.

5. METHOD OF CALCULATION AND RESULTS

5. 1 VISCOSITY

The method for selecting a function and its parameters which will

suitably correlate experimental data in conjunction with Eq (5) has been

explained in detail in Refs. 1, 2, and 3. We investigated a particular

function by first observing the variation of e/k with T at a fixed R, then

observing any subsequent changes caused by varying R. To do this,

experimental values of T] and the corresponding temperatures for a given

gas were substituted in Eq (5) together with a sensible value for R,

hence obtaining Q ' as a function of T. An interpolation computer

routine then generated T by inserting the calculated Ct

' into a

given set of (T ) for the function. From T and the expression

e/k = T/T , e/k was then computed as a function of T. This procedure
was repeated for several values of R, varying R by about 10% overall.

The same experimental data were used for all functions of the four

families. The procedure was repeated for all the gases.

The best value of R was that value associated with the curve having

the least variation of e/k over the widest temperature range, allowing

for the approximate 1% experimental and interpolation error. Values

of e/k were chosen to obtain agreement at 293°K for neon[ 20] and krypton[25] and 298 °K for xenon[25] . We estimated e/k to about 1% and R

to about 0. 2% for neon, but for krypton and xenon the estimation is about

2% and 1%, for e/k and R, respectively. The higher possibility for error

is due to the lack of data for these two gases. Table I gives the values

of the Lennard- Jones parameters for each gas.

TABLE I Best values of the Lennard- Jones parameters obtained

for neon, krypton, and xenon

Gas e/k, °K a, A

neon 47.0 2.72

krypton 182.8 3.62

xenon 249.5 3.96

We report that the variation of e/k and R obtained here for neon,

krypton, and xenon was essentially the same as that obtained in Refs. 1 and 3. We also report a marked lack of sensitivity in choosing a function in the temperature range 2. < T12 -s < 5. for all gases which is

as it should be in view of conclusion 1 in the introductory remarks.

5.1.1 NEON

The experimental data are in the range 80 < T °K< 1100 which is

equivalent to a reduced range of 1. 7 < T;i_2_ 6 < 23. 4. We repeat that a marked lack of sensitivity characterized the choice of a potential func-
a , A

2. 67

3. 50

3. 73

tion in the range 2. 3 < T12 _ 6 < 5.0, where all functions essentially behave similarly. However, the functions behaved differently and gave

different results in the range 5.0< T12 _ 6 < 27.0, but in view of conclusion

3 we did not expect to find a function that resulted in good agreement

between experiment and theory over the entire temperature range. It was felt that the Kihara function with y - 0. 1 (Table II) was the best

possible. The deviation curve is plotted in Fig. 2.

TABLE II

Best functions and the parameters for neon, krypton, and xenon

Gas Function e/k, °K

neon Kihara (y = 0.1) 53.2

krypton m-6 (m = 17) 226.0

xenon m-6 (m = 24) 382. 3

It is assumed that functions of the m-6, Exp: 6, and possibly the

Morse families also exist that could be used to obtain a similar deviation curve. At present we do not have complete tables of collision

integrals for the values of a (Exp: 6) or c (Morse) that can completely

verify this point, but application of the 16-6 member of the m-6 family

(e/k= 68.4°K, a = 2. 60 A) gives a deviation curve which is practically

identical with Fig. 2.

5.1.2 KRYPTON AND XENON

For these gases the experimental viscosity data lie between 280

and 975°K. In terms of reduced temperatures, therefore, the range for

krypton is 1. 5 < Ti'a-e < 5. 3, and for xenon 1. 1 < Ti' 2 _ 6 < 3. 9. It is at

once clear that the problem is not so much the choice of a function

which correlates the data, because we have an embarassment of choices,

but rather to find a function that can predict data outside the present

10
coh-OcMro>tf-inc0 — — CMCMCMCMCMCM

i i i i « O <3 > B

T

%

>EKD

B

"*W1P

ro cm — O

N0I1VIA3Q !N30U3d

o

oCM

o

o

00

UJ

° *z

CD <

UJ

Q.

UJ

o

o

o

oCNJ

CM

I

o

o

o

X

>

ao

CD

o

ti

•i-i

•

nb

I*< o

• CO

LT>

II

o) *

J> r-H o

II J >

-t->

oo

o

ft

J-i d

•H

11
experimental range. The problem can be simplified because (conclusion

3) if a suitable function of a particular family can be found, then it is

unlikely that the correlation can be satisfactorily improved upon considering another family from those for which collision integrals are

available. Thus it is only really necessary to work with one family and

the m-6 was selected for this purpose. We have shown that m = 16 is a

suitable parameter for neon, and m = 17 for argon. If it is assumed

that m increases with molecular weight, it can be expected that a value

of at least m = 17 would be required for krypton and a higher value for

xenon. From the collision integral tables available we selected m = 17

for krypton and m = 24 for xenon. Deviation curves are plotted in Fig. 3.

5.2 THERMAL CONDUCTIVITY

Thermal conductivities were calculated from Eq (6) using the

functions and parameters determined from viscosity data as outlined

above. Deviation curves are given in Figs. 4, 5, and 6 for neon, krypton,

and xenon, respectively. It is well known that the scatter in experimental thermal conductivity coefficients between the results of different

workers is large (about 5%) and the graphs indicate that the correlation

is satisfactory.

6. CONCLUSION

The deviation curves verify that the kinetic theory expressions

adequately correlate the experimental data available above 100 °K,

allowing for the estimated error in the data. The data for krypton and

xenon are in a temperature range which does not allow us to choose a

potential function that can be proved to be satisfactory over the complete temperature range considered, 100 to 1000 °K. Although a sensible

guess was made when selecting the function used for these latter gases,

there must, of course, be some uncertainty in the theoretical transport

coefficients calculated for temperatures outside the range of the data.

12
Tables of the viscosity and thermal conductivity in the temperature

range 100 to 1000°K were computed for all gases, and they are given

in Tables III, IV, and V for neon, krypton, and xenon, respectively.

The viscosity tables are estimated to be accurate to 2% and the thermal

conductivity tables accurate to 5%.

7. ACKNOWLEDGMENT

We would like to thank Dr. Max Klein for valuable discussions.

This work was supported by a grant from NASA, Contract Number

R-06-006-046.

13
1

l~~l l~~l 1^1 f"~l

1 1

1 1

I—• I—I l—I I—I »TJ

1

N IO N 00 CVJ lO CO o> o

CM CJ CVJ CM N N cj (vi ro

i—i i_j ij i—i _! 1—I •—1 — I I 1 I X X o > X

X

X

o x • «

X

X

X X

1

X

< X

X

5* X

x

X

g IP § CD -0. i X ^ 1 X

E x 5 E X

H: x \ • 5

X **

X • X — • —

X > X o

X| " o> •1 W< o

1 1 1 1 1

1

UJ

<T o

CD <

g

UJ

a.

UJ

CM — CM CM — O i i N0I1VIA3Q !N3Dd3d

CM CO

14
- CM IO -* IO (0 N

ro ro to ro ro ro ro — i i i > • O < <

<b%>

CM

O

OO

O

O

CD

UJ

° 2

CO <

tr

UJ

Q_

UJ

Io

o

O

c\J

ro cm — O —

i N0I1VIA3Q !N30U3d

CM

i

O

o

r—

(V]

II

t> T)

1 c1 (0 c o

r~- oo X

• CO

II o

,*

o!O

^***'*

i o

Of

05

O i—

Pi ^ o o o

1 1

11 >-

>

+->a

cuu

u

<DO*

PIo

(I) Z

+-> oa

a}

15
cm ro co 10 ro ro

i i i • D

O

CM

o

o

o

o

o

00

o

4

(0

UJ

(Z3

o ho <

cc

UJ

a.2

UJ

o

o

O

o

CM

CM CM

i

um

T3 •

<D *«sj O

i—

i

IT) d o o en

i—

i

rt II u b

i 1 T3 o a o d

I—

1

H X

o

o o vO

d (VJ a o fM r< —4

1 S

II

P. ^ X X •^^^ a CO

,<; ^ **

1 i £i—

i

<L>

ii

Jr- a

Z

p el c1 o

•r" •iH +-> +-> (t u

1" fl >a <S x r-

-i- rt p' S a Pi c1 5

f- +->

a,1 O

a a

p vD

c1 1 u a

>s

f- 2i *

in

•i-i

N0I1VIA30 lN30U3d

16
O cvj ro oo

ro ro ro ro

<

i i • D

u ^

•

CVJ

O

00

o

UJ

a:

o r- o

to <

2

UJ

Q.

UJ

Io

o

o

oCM

in sr ro cm — o

N0I1VIA3Q !N30U3d

o

u

O

o

o

X

<<

-a!co

4 CO

II b

oCO

ro" 00

CO

2.*

a) ^^ ^

>

o

o

sr1 (NJ

o

+-> o

I—

>

X)

a>o

f-l

a ' o

(1) X

OX) •H

<u

+-> o

ft

0)

17
TABLE III VISCOSITY AND THERMAL CONDUCTIVITY OF GASEOUS NEONt

TEMPERATURE VISCOSITY THERMAL TEMPERATURE VISCOSITY THERMAL CONDUCTIVITY CONDUCTIVITY

K 6/CM-SEC J/CM-SEC-OEG K 6/CM-SEC J/CM-SEc-DECS

7JI0* X 10 *

TJ 1 6 Mo6

50O 441 8 682, 6 510 447 5 691, 3 520 453 1 699, 9 530 458 7 708, 5 540 464 1 716, 9

550 469 6 725 4 560 475 733 8 570 480 4 742 1 580 485 ,7 750 4 590 491 1 758 6

100 140 6 217 2 600 496 4 766. 8 no 152 2 235 1 610 501 6 774, 9 120 163 3 252 3 620 506 8 783 n 130 174 268 i 630 512 791, 140 184 4 284 8 640 517 2 798, 9

150 194 3 300 2 650 522 ,2 806 7 160 204 315 1 660 527 4 814, 7 170 213 3 329 4 670 532 4 822 5 180 222 4 343 5 680 537 4 830 2 190 231 2 357 2 690 542 ,4 837 9

£00 239 8 370 4 700 547 ,4 845 6 210 248 2 383 4 710 552 ,3 853 3 220 256 4 396 1 720 557 ,3 860 9 ?30 264 5 408 6 730 562 ,2 868 4 240 272 4 420 a 740 567 876

25G 280 1 432 6 750 571 ,8 883 4 260 287 6 444 4 760 576 .6 890 7 270 295 455 7 770 581 ,5 898 2 280 302 4 467 1 786 586 ,2 905 6

<?90 309 5 478 2 790 590 ,9 912 9

300 31^ 7 489 2 80O 595 7 920 2 M0 323 7 500 810 600 4 927 4 320 330 6 510 7 820 605 934 7 330 337 4 521 i 830 609 .7 941 9 3*0 344 1 531 5 840 614 3 949

I5y 350 7 541 7 850 619 956 ?. 360 357 2 551 9 860 623 5 963 ? 370 363 7 561 •i 870 628 970 2 380 370 571 6 880 632 7 977 3 190 376 4 581 4 890 637 2 984 3

"00 382 ,6 591 .1 900 641 ,7 991 3 410 388 .8 600 .6 910 646 ,2 998 ,3 420 394 ,9 610 1 920 650 7 1005 2 430 401 .0 619 ,4 930 655 ,? 1012 1 440 407 .0 628 ,7 940 659 .6 1018 9

450 412 .9 637 ,9 950 664 .0 1025 8 460 418 .8 647 .0 966 668 ,4 1032 6 470 424 .7 656 .0 970 672 7 1039 2

4fi0 430 ,4 664 ,9 980 677 .1 1045 9 490 436 ,2 673 .8 99o 681 ,5 1052 7

1000 684.9 1058.0

t Calculated for the dilute gas by the Kihara potential with

Y = 0. 1, a = 2.67 A, e/k = 53. 2°K.

18
TABLE IV

VISCOSITY AND THERMAL CONDUCTIVITY OF GASEOUS KRYPTONt

TEMPERATURE VISCOSITY thermal conductivityTEMPERATURE VISCOSITY THERMAL CONDUCTIVITY

K G/CM-SEC

TJ 1 6 J/CM-SEC-DEG

\I06 K G/CM-SEC

,IO«

J/CM-SEC-OEG

XlO6

500

510

520

53540

392.6

398.

B

404.9

411.0

417.0

146.1 148.4

150.7 152.9

155.1

550

560

570 580

590

422.9 428.8

434.6

440.4

446.1

157.3 159.5

161.7 163.8

166.0

100*

110*

120*

130*

140*

90.3

98.6

106.9 115.2

123.6

33.6

36.7 39.8 42.8

46.0

600

610 620

630

640

451.8 457.4

463.0 468.5

473.9

168.1 170.?

172.?

174.3 176.3

150*

160* 170* ISO* 190*

132.1 140.5

148.

9

157.4

165.8

49.1 52.3

55.4

58.6

61.7

650

660 670

680 690

479.4 484.9

90.2 495.5

500.8

178.4

180.4

182.4

184.4 186.3

POO*

210* 220* 230* 2*0*

174.2 182.6

191.0 199.2 207.3

64. a 67.9

71.0

74.1 77.1

700

710 720

730

740

506.1 511.3 516.5

521.5

526.7

188.3 190.2

192.1 194.0

196.0

250*

?60*

270

2fl0 290

215.4

223.-4 231.4

239.3

247.1

80.1

83.1 86.1 89.0

91.9

750

760

770

789

790

531.8 536.8

541.8

546.7

551.7

197.8

199.7 201*6

203.4

205.2

300

?10

320

330

440

254.9

262.5

270.1 277.5

284.9

94.8

97.7

100.5

103.2

106.0

800

810 820

830

840

556.6

561.4

566.3

571.1 575.9

207.1 208.9

210.7 212.5

214.3

350

360 370

380

390

292.2

299.4

306.5

313.6 320.5

106.7

111.4

114.0 116.7

119.3

850

860

870

880

890

580.6

585.4

590.0

594.7 599.4

216.0

217.8

219.5

221.3

223.0

400 410

420 430

440

327.5 334.3

341.0 347.7 354.4

121.8

124.4

126.9 129.4

131.8

900 910

920

930

940

604.0 608.5

613.0 617.7 622.2

224.7

226.4

228.1 229.8 231.5

450

460

470 480

490

360.9

367.4

373.8 380.2

386.5

134.3

136.7

139.1 141.4

143.8

950

960 970 980*

990*

626.7

631.1 635.6 640.0

644.4

233.2

234.8

236.5

238.1 239.8

1000* 647.7 241.0 t Calculated for the dilute gas by the m-6 potential with

m= 17, a = 3. 50A, e/k= 226. 0°K.

* There is some uncertainty in these transport coefficients because

they have been extrapolated outside the range of the experimental

data.

19
TABLE V

VISCOSITY AND THERMAL CONDUCTIVITY OF GASEOUS XENONt

TEMPERATURE VISCOSITY THERMAL CONDUCTIVITY

TEMPERATURF VISCOSITY THERMAL CONDUCTIVITY

K G/CM-SEC J/CM-SEC-DEG K G/CM-SEC J/CM-SEC-DEG

7IO6 XlO6

17 10

6 \I06

500 367.3 87.2

510 373.6 88.7 520 379.9 90.2

530 386.1 91.7 540 392.3 93.?

550 398.5 94.6

560 404.7 96.1 570 410.8 97.5

580 416.8 99.0

590 422.8 100.4

100* 89.4 21.2 600 428.7 101.8 110* 96.7 23.0 610 434.6 103.2

120* 103.9 24.7 620 440.4 104.6

130* 111.1 26.4 630 446.2 106.0

1*0* 118.2 28.1 640 452.0 107.3

150* 125.2 29.7 650 457.7 108.7

160* 132.4 31.4 660 463.4 110.0

170* 139.5 33.1 670 469.0 111.4

180* 146.6 34.8 6P0 474.7 112.7 190* 153.7 36.5 690 466.2 114.0

200* 160.9 38.2 700 485,8 115.3

210* 168.0 39.9 710 491.2 116.7

220* 175.2 41.6 720 496.7 116.0

230* 182.4 43.3 730 502.1 119.2 240* 189.5 45.0 740 507.5 120.5

250* 196.6 46.7 750 512.9 121.8 260* 203.8 48.4 760 518.

2

123.1 270* 211.0 50.1 770 523.5 124.3

?80 218.2 51.

a

780 528.

8

125.6

29fl 225.3 53.5 790 534.0 126.8

300 232.4 55.2 800 539.2 128.0

310 239.4 56.8 810 544.3 129.3

320 246.4 58.5 820 549.5 130.5

330 253.5 60.2 830 554.6 131.7

340 260.5 61.9 840 559.7 132.9

350 267.4 63.5 850 564.6 134.1

360 274.3 65.1 860 569.7 135.3

370 281.3 66.8 870 574.7 136.5

380 288.1 68.4 880 579.6 137.6

390 295.0 70.0 890 584.6 138.8

400 301.8 71.7 900 569.5 140.0

410 308.6 73.3 910 594.3 141.1

»20 315.3 74.9 920 599.1 142.3

430 321.9 76.4 930 604.0 143.4

440 328.5 78.0 94Q 608.7 144.5

450 335.1 79.6 950 613.5 145.7

460 341.6 81.1 960 616.2 146.8

470 348.1 82.7 "70 622.9 147.9

480 354.5 84.2 980* 627.6 149.0

490 360.9 85.7 990* 632.2 150.1

1000* 635.4 150.9 t Calculated for the dilute gas by the m-6 potential with

m = 24, a = 3.73A, e/k= 382. 3°K.

* There is some uncertainty in these transport coefficients because

they have been extrapolated outside the range of the experimental

data.

20
8. REFERENCES

1. H. J. M. Hanley, Comparison of the Lennard- Jones, Exp: 6, and

Kihara Potential Functions from Viscosity Data of Dilute Argon,

J. Chem. Phys 44, 4219-22 (1966).

2. H. J. M. Hanley, The Viscosity and Thermal Conductivity Coefficients of Dilute Argon between 100 and 2000 °K, Natl. Bur. Std.

Tech. Note No. 333 (March 1966).

3. G. E. Childs and H. J. M. Hanley, The Viscosity and Thermal

Conductivity Coefficients of Dilute Nitrogen and Oxygen, Natl.

Bur. Std. Tech. Note No. 350 (October 1966).

4. M. Klein, Determination of Intermolecular Potential Functions

from Macroscopic Measurements, J. Res. Nat. Bur. Std. 70A,

No. 3, 259-269 (1966); M. Klein and H„ J. M. Hanley, to be

published.

5. J. A. Barker, W. Fock, and F. Smith, Calculation of Gas Transport Properties and the Interaction of Argon Atoms, Phys. Fluids

7, 897-903 (1964).

6. J. S. Rowlinson, A Test of Kihara' s Intermolecular Potential,

Mol. Phys. 9, No. 2, 197-98 (1965).

7. J. P. O1 Connell and J. M. Prausnitz, Applications of the Kihara

Potential to Thermodynamic and Transport Properties of Gases,

ADVANCES IN THERMOPHYSICAL PROPERTIES AT EXTREME

TEMPERATURES AND PRESSURES, 19-31, Am. Soc. Mech.

Engr., New York (1965).

8. S. E. Lovell and J. O. Hirschfelder, Tables of Collision Integrals

for Gases Obeying the Morse Potential, University of Wisconsin

Theoretical Chemistry Laboratory, WIS-AF-21 (June 1962), Contr.

No. AF 33(657)-7311.

9. D. D. Konowalow and S. Carra, Determination and Assessment of

Morse Potential Functions for Some Nonpolar Gases, Phys.

Fluids 8, 1585-89(1965).

10. M. Klein and F. J. Smith, to be published.

21
11. S. Chapman and T. G. Cowling, THE MATHEMATICAL THEORY

OF NON UNIFORM GASES, Cambridge (1964) 7th Printing.

12. J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, MOLECULAR

THEORY OF GASES AND LIQUIDS, John Wiley & Sons, New York

(1964) Second Printing.

13. E. A. Mason and W. E. Rice. The Intermolecular Potentials for

Some Simple Non-polar Molecules, J. Chem. Phys. 22, 843-51

(1954).

14. A. Michels, A. Botzen, and W. Schuurman, The Viscosity of

Argon at Pressures up to 2000 Atmospheres, Physica 20, 1141-

48 (1954).

15. A. Van Itterbeek and O. Van Paemel, Measurements on the Viscosity of Argon Gas at Room Temperature and Between 90° and

55°K, Physica J5, 1009-11(1938).

Id. H. L. Johnston and E. R. Grilly, Viscosities of Carbon Monoxide,

Helium, Neon, and Argon Between 80° and 300 C K, Coefficients of

Viscosity, J. Phys. Chem. 46, 948-63 (1942).

17. M. Trautz and R. Zink, Die Reibung, Warmeleitung und Diffusion

in Gasmischungen. XII. Gasreibung bei hoheren Temperaturen,

(The Viscosity, Heat Conduction and Diffusion of Gas Mixtures.

XII. The Viscosity of Gases at Higher Temperatures), Ann.

Physik 7^ 427-52 (1930).

18. V. Vasilesco, Recherches Experimental s sur la Viscosite des

Gaz aux Temperatures Elevees, (Experimental Research on the

Viscosity of Gas at Elevated Temperatures), Ann. Phys. (Paris)

jiO, 137-76 (1945).

19. G. P. Filippova and I. P. Ishkin, The Viscosity of Air, Nitrogen,

and Argon at Low Temperatures and at Pressures up to 150 Atmospheres, Inzh. Fiz. Zh. Akad. Nauk Belorussk SSR 4, 105-09

(1961).

20. R. Wobser and F. Muller, Die innere Reibung von Gasen und

Dampfen und ihre Messung im Hoppler-Viskosimeter, (The Viscosity of Gases and Vapors and their Measurement with the

Hoppler Viscometer), Kolloid-Beih. 52, 165-276 (1941).

22
21. F. G. Keyes, The Heat Conductivity, Viscosity, Specific Heat

and Prandtl Numbers for Thirteen Gases, Mass. Inst, of Technol.,

Proj. Squid, Tech. Rept. No. 37 (1952), DDC ATI 167 173.

22. A. O. Rankine, Uber die Anderung der inneren Reibung der Gase

der Argongruppe mit der Temperatur, (On the Variation with

Temperature of the Viscosities of the Gases of the Argon Group),

Physik. Z. _U, 745-52 (1910).

23. R. S. Edwards, The Effect of Temperature on the Viscosity of

Neon, Proc. Roy. Soc. (London) A 119 , 578-90(1928).

24. M. Trautz and H. E. Binkele, Die Reibung, Warmeleitung und

Diffusion in Gasmischungen. VIII. Die Reibung des Hg , He, Ne,

Ar und ihrer binaren Gemische, (The Viscosity, Heat Conduction

and Diffusion in Gas Mixtures. VIII. The Viscosity of Ha , He,

Ne, Ar and their Binary Mixtures), Ann. Physik 5, 561-80 (1930).

25. J. Kestin and W„ Leidenfrost, An Absolute Determination of the

Viscosity of Eleven Gases over a Range of Pressures, Physica

_25, 1033-62 (1959).

26. N. J. Trappeniers, A. Botzen, H. R. Van den Berg and J. Van

Oosten, The Viscosity of Neon Between 25°C and 75°C at Pressures up to 1800 Atmospheres. Corresponding States for the

Viscosity of the Noble Gases up to High Densities, Physica 30,

985-96 (May 1964).

27. A. Nasini and C. Rossi, Viscosita di miscele di gas rari, (Viscosity of Rare Gas Mixtures), Gazz. Chim. Ital. 58, 898-912

(1928).

28. M. Rigby and E. B. Smith, Viscosities of the Inert Gases, Trans.

Faraday Soc. 62, 54-58 (1966).

29. M. Trautz and R. Heberling, Die Reibung, Warmeleitung und

Diffusion in Gasmischungen. XXV. Die Inhere Reibung von

Xenon und Seinen Gemischen mit Wasserstoff und Helium,

(The Viscosity, Thermal Conductivity and Diffusion in Gas

Mixtures. XXV. The Viscosity of Xenon and its Mixtures with

Hydrogen and Helium), Ann. Physik 20, 118-20(1934).

23
30. E. Thornton, Viscosity and Thermal Conductivity of Binary Gas

Mixtures: Xenon -Krypton, Xenon-Argon, Xenon-Neon and XenonHelium, Proc. Phys. Soc (London) 76, 104-12 (I960).

31. S. Weber, Uber die Warmeleitfahigkeit der Gase, (The Thermal

Conductivity of Gas), Ann. Physik 82, 479-503 (1927).

32. M. Curie and A. Lepape, Conductibilite thermique des gaz rares,

(Thermal Conductivity of Rare Gases), J. Phys. Radium 2_, 392-

97 (1931).

33. W. G. Kannuluik and E. H. Carman, The Thermal Conductivity

of Rare Gases, Proc. Phys. Soc. (London) B65, 701-09 (1952).

34. F. G. Keyes, Thermal Conductivity of Gases, Trans. ASME 76,

809-16 (1954).

35. L. B. Thomas and R. C. Golike, A Comparative Study of Accommodation Coefficients by the Temperature Jump and Low-Pressure Methods and Thermal Conductivities of He, Ne, and C02 , J. Chem. Phys. 22, 300-05 (1954).

36. B. N. Srivastava and A. K. Barua, Thermal Conductivity of

Binary Mixtures of Diatomic and Monatomic Gases, J. Chem.

Phys. 3_2, 427-35 (I960).

37. J. V. Sengers, W. T. Bolk, and C. J. Stigter, The Thermal

Conductivity of Neon Between 25° C and 75° C at Pressures up to

2600 Atmospheres, Physica 30, 1018-26(1964).

38. F. G. Keyes, Thermal Conductivity of Gases, Trans. ASME 77,

1395-96 (1955).

24 GPO 834-786

U.S. DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20230

POSTAGE AND FEES PAID

U.S. DEPARTMENT OF COMMERCE

OFFICIAL BUSINESS

H