jras

'.:

:

: .:' .<; »

^rf' ' » * ^ 1 l\l 1

350

The Viscosity and Thermal Conductivity

Coefficients of Dilute Nitrogen

and Oxygen

G. E. CHI LDS AND H. J. M. HANLEY

*** ° F Cf

Z

»*

\

,&': n

*"*CA U O? '

(A

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards
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NBS TECHNICAL NOTE 350

ISSUED OCTOBER 31, 1966

THE VI SCOSI TY AND THERMAL CONDUCTIVI TY

COEFFI CI ENTS OF Dl LUTE Nl TROGEN AND OXYGEN

G. E. CHI LDS AND H. J. M. HANLEY

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

2„ Potential Functions -----——-—-—-——- ——-— • _____ 2

3o Kinetic Theory Transport Expressions--------------------- 3

4 Experimental Data ---• _________<._..=, = ,=, = _________ = .,.._____ 4

5.1 Nitrogen ____________ _____________ 5

6. Thermal Conductivity ------------------------------------- 15

8 . Acknowledgment ______„.,< --,.—>_,.__.____—_>.__ __.,,.___ 19

9. References ,_______. ,_____„___. ,___„______________ 22

III
LIST OF FIGURES

1. Variation of e /k versus T (both in degrees Kelvin) for

selected values of a using the Lennard- Jones potential

function for nitrogen.

2. Best values of o for various values of y for the Kihara

potential function for nitrogen. 9

3. Best values of rm for various values of a for the Exp: 6

potential function for nitrogen. 10

4. (a) Best values of o for three values of c for the Morse

potential function, (b) Variation of o for a given value

of c. Nitrogen. 11

5. Nitrogen percent deviation curves ( —i-^ ——- )x 100 LV T] calc y J

of experimental and calculated viscosity coefficients for

three potential functions using the best values selected by

the method explained in the text. 12

6. Nitrogen and oxygen deviation curves calculated from the

Kihara functions (for nitrogen Y =0.2, for oxygen y = 0. 1).

These functions were selected as the best. 13

7. Oxygen percent deviation curves for three functions 14

Percent deviation curves

^•e x p - A-c a 1 c ^c a 1 c

") x lOo]

for the thermal conductivity of nitrogen and oxygen. 16

9. Percent deviation curves of selected experimental thermal

conductivity data calculated from Eqs (8) and (9). 17

IV
LIST OF TABLES

I. Best values of the parameters obtained from each potential

function for nitrogen. 6

II. Best values of the parameters obtained from each potential

function for oxygen. 7

III. Viscosity and Thermal Conductivity of Gaseous Nitrogen. 20

IV. Viscosity and Thermal Conductivity of Gaseous Oxygen. 21

THE VISCOSITY AND THERMAL CONDUCTIVITY COEFFICIENTS

OF DILUTE NITROGEN AND OXYGEN

G. E. Childs and H. J. M. Hartley

The coefficients of viscosity and thermal conductivity for dilute

nitrogen and oxygen were examined using a method proved suitable for

argon. Given the kinetic theory expressions for the transport coefficients, this method indicates a selection of a potential function and its

parameters to correlate theory with experimental data. The potential

functions chosen were the Lennard- Jones, Kihara, Exp: 6, and the

Morse. It was found that the Kihara was most suitable and theoretical

viscosity coefficients were computed with this function. The usual

correction to the kinetic theory equation for thermal conductivity, the

Eucken correction, was found not to be sufficient and it was decided

to use an empirical polynomial equation to correlate the thermal conductivity coefficients. Tables of the transport coefficients for both

gases are given between 100 and 1000°K.

Key Words: Dilute gases, Nitrogen, Oxygen, Transport coefficients, Lennard-Jones, Kihara, Exp: 6, Morse

potential functions, Eucken correction, Correlation.

1. INTRODUCTION

The viscosity and thermal conductivity coefficients of dilute nitrogen and oxygen can be calculated from the Chapman-Enskog kinetic

theory expressions [l] *. As these expressions are known to be satisfactory, the problem, as for all dilute gases, is that of choosing a

suitable potential function and the best force constants for that function.

The method of selection used here is the same as that proved successful

for dilute argon [2, 3] . The kinetic theory thermal conductivity equation

is not applicable for polyatomic gases and the usual procedure is to

apply the Eucken correction [l] . However, it was found that this did

not give satisfactory results and it was necessary to use a polynomial

expression.

^Numbers in brackets refer to references.
2. THE POTENTIAL FUNCTIONS

The discussion was restricted to the four most commonly used

functions: the Lennard-Jones, the Kihara, the Exp: 6, and the Morse.

The Kihara, in particular, has received much attention in the literature

recently [4, 5, 6]. The Morse function has also been described by several authors [7, 8]. As the functions are well known and have been fully

discussed, it is necessary only to outline them here. If U(r) is the

interaction potential of two molecules separated by distance r, and £

is the maximum energy of attraction, or energy minimum, the potentials

are written:

Lennard-Jones

r U(r) =4e

|_ (o7r) lrf - (a/r) b J

,

where cr is the value of rat U(r) =0.

Kihara

(i)

U(r) = M - a \;

_ v. r - a J

° - a \l2 { G - a V r - a r> a (2)

U(r) r ^ a,

Here the finite size of the molecule is taken into

consideration by including a core diameter, a. (For

the Lennard-Jones, a = 0.) A reduced parameter Y is

defined as a/(7.

Exp: 6

°<')-T^s[!-

a(1 - ,/ ^

: .^/')'].

where r ffl is the value of r at the energy minimum and cc a parameter which represents the steepness of the repulsive

part of the function.

(3)
Morse

U(r) =e{exp [-2 (f )

(r-rB )] -2 exp [- (f )(r-r.)]

} ^ (4)

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

3. KINETIC THEORY EXPRESSIONS FOR THE VISCOSITY AND

THERMAL CONDUCTIVITY COEFFICIENTS

The kinetic theory for a dilute gas is formally complete [1]; 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 intermolecular potential. It is the lack of knowledge of the latter -which

restricts the applicability of the kinetic theory expressions. These

expressions are:

Viscosity (r\)

mn? 266.93 (MT) V3

r _x -i

rjlO = J—

f g cm sec , (5)

R

2

fi (3 ' 2) *(T*) ^

Thermal Conductivity (A.)

lin 7 8322.4 (T/M) 1/; _i _i _ a .,, A10 = f, J cm sec deg , (6)

R

2 Q( 2 ' 3):,;

( T ^) K

where: M = molecular weight. (M = 28 . 134 for nitrogen

M =31.9988 for oxygen)

R = a distance parameter, i.e. , R - (J for the

Lennard-Jones, Kihara, and Morse; and R = r m for the Exp: 6.

T = the absolute temperature, °K.
(3 2 ^

*'* Q (T#) = the reduced 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 v\ 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 at

extreme temperatures, they can be omitted from Eqs (5) and (6) without significant error.

Tables of the collision integrals as a function of T* for each of

the potentials were taken from Refs . 1, 6, 7, and 9. The numerical

values of the integrals depend on the method of integration, but it was

verified that the choice of any particular set of tables made no significant difference to the results presented here.

For polyatomic gases the Eucken correction modifies Eq (6) to:

X - X

(

' — — + - ^ Eucken dilute V 15 ft + sJ ' (7)

where X is the Chapman- Enskog value (Eq (6)), Cv is

dilute ° the specific heat of the gas at constant volume and ^ the gas

constant. The Eucken factor contributes 0.25% at low temperature and 0. 4% at high temperature to the total conductivity.

4. EXPERIMENTAL DATA

The experimental data were taken from the following references:

Nitrogen, viscosity, Refs. 10-25

temperature range 75 - 1200 °K.

Oxygen, viscosity, Refs. 10, 12-17, 21, 23, 26-29

temperature range 75 - 1166°K.
Nitrogen, thermal conductivity, Refs. 30-48

temperature range 75 - 1173°K.

Oxygen, thermal conductivity, Refs. 21,30,38,43,45,49-56

temperature range 75 - 1173°K.

5. VISCOSITY

As in the method described for argon, the suitabilities of the

potential functions above were investigated by first observing the

variation of e /k with T at a fixed R, then observing any subsequent

changes caused by varying R. Accordingly, for a particular function,

experimental values of r\ and the corresponding temperatures 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 Q into a given set of Q (T*) for the function. From T* and the expression £ /k = T/T#, £ /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 four

potential functions.

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

had the least variation of e /k over the widest temperature range allowing for the approximate 1% experimental and interpolation error. We

thus estimated e /k to about 1% and R to about 0. 2%.

5.1 NITROGEN

For the Lennard- Jones potential the best value of CJ was selected

at C = 3. 68 A. Figure 1 shows the best value and also two other curves

which show the patterns caused by an approximately 5% change in CJ. Note the pattern is the same as found for argon. A best value of

e /k from Fig. 1 is seen to be about 90 °K, and this was adjusted to
e/k = 90. 9°K (Table I) to obtain agreement between the experimental

and calculated viscosity coefficients at 293 °K. The reason for choosing

293 °K is because the viscosity coefficient at that temperature has been

carefully measured by several workers [e.g., Refs. 13, 14, 17] with

close agreement. Figure 5 shows a percentage deviation curve for

the Lennard- Jones potential using the selected O and e/k. It was

verified that the choice of a given set of collision integrals did not

alter the conclusions or the best values of o or e/k by any significant

amount.

TABLE I Best values of the parameters obtained

from each potential function for nitrogen.

Function e /k, °K R, A

L - J 90.9 3.68

Kihara (y = 0.2) 116. 7 3. 55

Exp: 6 (a = 17. 0) 104. 3 3.99

Morse (c = 5.0) 74. 8 3.82

The best values of the Kihara potential function were found for

five values of the parameter Y. The best value graphs of e /k - vs - T

for each value of Y are shown in Fig. 2, and it was decided that the

o most suitable of these was Y = . 2 , (J = 3 . 55 A. Again, obtaining agreement between the experimental and calculated viscosity coefficient at

293°K, the value of e/k chosen was £ /k = 116. 7°K (Table I) and the

deviation curve (Fig. 6) was plotted.

The Exp: 6 was treated in the same manner and the best value

plot for the different values of a are shown in Fig. 3. Here a = 17 was

chosen with rm = 3 . 99 A ( Table I) and e /k = 104. 3 °K. The deviation

curve is shown in Fig. 5.
It is remarked that the behavior of the variation of R is verysimilar for these functions as was found for argon.

The Morse function, treated in the same fashion, has the best

value o curves shown for c = 4, 5, and 6 (Fig. 4). Here c = 5 was

chosen with a = 3. 82 A and e /k - 74. 8°K. Figure 4 also shows the

variation of at c = 5. It is evident, by comparing the Morse deviation

curve (Fig. 5) with those of the other functions for nitrogen, that

the Morse is the least satisfactory of the four.

5.2 OXYGEN

Oxygen was treated by exactly the same procedure as described

for nitrogen. The pattern of the curves as R was varied for a given

CC

, y, or c was the same, and we list in Table II the best values of R

and the corresponding best values of e /k for all functions. The percentage deviation curves (Fig. 7) compare the functions. The Kihara

function, Y = 0.1, again was chosen as the best function (Fig. 6),

while the Morse function was again the least satisfactory.

TABLE II Best values of the parameters obtained

from each potential function for oxygen.

Function e /k, °K R, A

L - J 110.

7

3.44

Kihara (y = 0. 1) 124. 5 3. 38

Exp: 6 (a = 16.0) 121. 6 3. 78

Morse (c = 5.0) 98. 7 3. 53

SUMMARY: For nitrogen, the chosen best function with parameters was the Kihara, y =0.2, e/k = 1 16. 7°K, a = 3.55A. Similarly,

for oxygen, Kihara, y = 0. 1, 6 /k = 124. 5°K, a = 3. 38 A.
140

130

120

10

100

e/k,°K

90

80

70

60

50

40

<T = 3.85 A

J_ 200 400 600 800

TEMPERATURE, °K

1000 1200

Fig. 1. Variation of e /k versus T (both in degrees Kelvin)

for selected values of o using the Lennard-Jones

potential function for nitrogen.
e/K,°K

200 400 600 800 1000 1200 TEMPERATURE, °K

€/k,°K

130

120

I 10

100

- X= 02

- cr=3.55 A /

-

1 1 1 1 1 1

150

140

130

120

X

= 03

cr=349 A

I 200 400 600 800 1000 1200 200 400 600 800 1000 1200

TE M PER ATURE , °K •

e/k ,°K

200 400 600 800 1000 1200 200 400 600 800 1000 1200

TEMPERATURE , °K

Fig. 2. Best values of a for various values of Y for the

Kihara potential function for nitrogen.
90- a= 12 loo- a= 13

80-

€/k,°K

70-

90-

80

r m = 4.28 A

60 J L J L 70 J_ 200 400 600 800 1000 1200 200 400 600 800 1000 1200

TEMPER ATURE , °K

100 _ a = 14

€/k ,°K

80

70

90 ~ r m =4.20A 100

90

80

a = 15

r m =4.l2 A

J L 200 400 600 800 1000 1200 200 400 600 800 1000 1200

TEM PER ATURE , °K

€/k , °K

120

100

90

a = i7

On =3.99 A

200 400 600 800 1000 1200 200 400 600 800 1000 1200 TEM PERATURE , °

K

Fig. 3. Best values of rm for various values of OC for the

Exp: 6 potential function for nitrogen.

10
80 - c=4.0

€/k,°K

70

60

50

<T=4.05 A

J I I L 200 400 600 800 1000 1200 TEMPERATURE , °K

100

e/k,°K

200 400 600 800 1000 1200 TEMPERATURE, °K

€/k,°K

€/k,°K

120

1 10 —

100-

90

c=6.0

a =3.66 A

200 400 600 800 1000 1200

TEMPERATURE , °K

(a)

130

120

I 10

100

90

80

70 h

60

50

40

c = 5.0

200 400 600 800 1000 1200

TEMPERATURE, °K

(b)

Fig. 4. (a) Best values of a for three values of c for the

Morse potential function, (b) Variation of a for

a given value of c. Nitrogen.

11
-2

O

LiJ Q

H-O

CC

UJ0.

LENNARD-JONES

o

X

05" ^ x

EXP: 6 ," V V *sx

1

A h s

k

^^o^_^_ MORSE

<Px §

S

a

A«

A H X

A S_

200

[10]

[15]

[20] [25]

400 600 800 1000 TEMPERATURE , °K

• [II] e [12] a [13] a [14] o [16] a [17] s [18] [19]

x [21] e [22] a [23] v [24]

1200

Fig. 5. Nitrogen percent deviation curves ( Me x p -'leal

-") x 100 i T)c ale

of experimental and calculated viscosity coefficients for three

potential functions using the best values selected by the

method explained in the text.

12
<

>

Q

NITROGEN

— _°_<*a§^Sw

I-2 -I UJo

a:bj -2 o

v A *

X A

X X ^ X S X

* A

KIHARA

QCia- .^_s_

A®;

rS H

c

o

STo

00 400 600 800 1000

TEMPERATURE , °K

[10] • [II] • [12] * [13] a [14]

[15] o [16] d [17] H [18] [19]

[20] x [21] © [22] A [23] v [24]

[25]

:200

<

>

UJQ

UJO

UJ

a.

OXYGEN

KIHARA

-A-C

200 400 600 800

TEMPERATURE , °K

o [io] • [12] ^ [13] A [14] ° [16] [17] x [2 1] * [23]

[27] [28] © [29]

1000

[15]

[26]

1200

Fig. 6. Nitrogen and oxygen deviation curves calculated from the

Kihara functions (for nitrogen y - 0.2, for oxygen Y =0.1).

These functions were selected as the best. Note: the high

temperature values of viscosity from Ref . 28 are known to

be in error (private communication - C. J. G. Raw).

13
>

UJQ

O

LlI o

Q.

LENNARD-JONES _

A g A A

EXP:6

o-~x~"x ^o^^P-°-.-^- £> A 8

- O » A

T A

MORSE

__x_(* i % °° 3bD3_

X_

X

200 400 600 800 1000 TEMPERATURE , °K

O [10] » [12] a [13] a [14] * [15] o [16] a [17] x [21] a [23] • [26]

[27] [28] e [29]

1200

Fig. 7. Oxygen percent deviation curves for three functions.

Note: in Figs. 5-7 some experimental points were omitted

in the temperature range 273-300 °K for clarity of presentation. The experimental values omitted were from

Refs. 11, 12, 14, 16, 20,21 for nitrogen and Refs. 14, 16

for oxygen.

14
6. THERMAL CONDUCTIVITY

The coefficient X ... was calculated from Eq (6) with the best

dilute

function and best values of the function for nitrogen and oxygen respectively. The Eucken correction to X ... (Eq (7)) was then added with

dilute

specific heats taken from Ref . 57. Percentage deviation curves

(Fig. 8) were plotted for both gases. It is seen that the experimental

data deviates systematically from the theoretical predictions of Eq (7),

although agreement is reasonable in the limited temperature range 200

300 °K. The Eucken correction has usually been tested in this limited

region. It is easily verified that any realistic errors in C v would not

produce this pattern and that, hence, despite the large scatter in the

data, the Eucken correction is not satisfactory. This correction will

be examined in more detail in a later publication.

Rather than further empirically modify the equation for X, it was

decided to represent the thermal conductivity coefficients by a polynomial in the temperature. Selected data [nitrogen, Refs. 30,36,37,

39,40, 44, 45; oxygen, Refs. 30 , 45, 52 , 53, 56] were fitted by the method

of least squares and the equations below were most suitable.

Nitrogen

U06 = - 16.20 + 1.28825 T - 1.65770 (10" 3

) T

3

(8) + 1.66105 (10" 6

) T

3

- 6. 1505 (10

_1 °) T

4

Oxygen

X 10s =- 14.24 + 1. 11127 T - 6. 7362 ( 10" 4

) T

2 + 2. 9405 ( 10" 7

) T

3

, (9)

where: X = the thermal conductivity of the gas.

T = the absolute temperature, °K.

15
>

WQ

UJ

<-> 8

(£

UJ

°- 6

NITROGEN

o ° " _ ° B —

O _

B P n

" _A _ B a

A * V

..* T * ° T

° ° -

B ~

a B

* 9 ° A

x*

x T X * ^

XX il o

X *

o

e

x

x o

X

xx * 1

1 1

1

1 OXYGEN

A

a

•

• * o o -°- ^x* * A ^ ° ° a — • A t, a

° V* ° ° ~~

i* A _ %

W*

• e

Vwx e v ' v8

XT 4'

•

200 400 600 800 1000 1200 TEMPERATURE

N ITR0GEN OXYGEN

[30] a [31] * [3 2] x [21] v [30] e [38]

[33] O [34] a [35] o [43] 4 [45] e [49]

[36] [37] • [38] t [50] 7 [51] • [52]

[39] a [40] D [41] a [53] t [54] e [55]

[42] o [43] T [44] a [56] [45] x [46] b [47]

[48]

Fig. 8. Percent deviation curves f

l eip o a 1 c

c a 1 c } x lOo]

for the thermal conductivity of nitrogen and oxygen. A c al c was calculated from Eq(7) which included the Eucken correction

using the Kihara function with parameters given in Tables I and II.

16
1-2

3-3

>

UJ°-4

o

cr£

3

NITRO GEN

~s st

• •

* A

a * *

XX XX* o

T ^ B o

B

V*

XX ? l ? ? OXYGEN

f\^#

e

e

e

200 400 600 800 1000 1200 TEMPERATURE

NITROGEN

V [30] a [31] V [32]

8 [33] O [3 4] a [35]

e [36] [37] c [38] • [39] a [40] a [41] A [42] o [43] [44] [45]

[48]

x [46] B [47]

OXYGEN

[21] v [30] e [38]

[43] a [45] 9 [49]

[50] * [51] • [52]

[53] r [54] b [55]

[56]

Fig. 9 Percent deviation curves of selected experimental thermal

conductivity data calculated from Eqs (8) and (9).

17
The data were not suitable to justify a rigorous approach to the

least squares fit, although this would have been the best procedure.

As the experimental inaccuracy precluded sensible weighting of the

data, the data were unweighted. The deviation curves (Fig. 9) were

plotted.

7. CONCLUSION

It has been shown that the kinetic theory expression for viscosity

is suitable to correlate data using the functions and parameters given

in Section 5. It does not, however, appear possible to apply kinetic

theory to the thermal conductivity coefficient at present. The usual

thermal conductivity expression for a polyatomic gas, i.e. , the kinetic

theory equation plus the Eucken correction, was found unsuitable for

nitrogen and oxygen. It is noted that more involved formulization

of the Eucken corrections are known; for example, Chapman and

Cowling [58] write

X '{ 1T

(Y - 1)+ !^ (5 - 3Y>Kuute C

v

< 10 ' where Y is the ratio of the specific heats and u a factor which has

a value of about 1.2. A comparison of Eq (10) with experiment

would reduce the high temperature deviations (Fig. 8) but would

increase the deviations at low temperature. As u also would have

to be found from experiment, it was felt that fitting the data by a polynomial equation is as suitable as applying Eq (10) or another

similar correction. As stated above, the Eucken correction will be

studied further.

There is another problem with the correlation of thermal conductivity: not only are the data widely scattered, but it is not always

known if the scatter is about "true" mean values. It is highly probable

18
that the experimental results also exhibit systematic error. (Systematic error can, of course, affect viscosity measurements but not to

such an extent.) The polynomial fits cannot take such errors into

account

.

Tables in the temperature range 100 - 1000 °K have been computed

and are given in Tables III and IV for nitrogen and oxygen respectively.

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

conductivity tables accurate to 5%.

8. ACKNOWLEDGMENT

This work was supported by a grant from NASA, Contract Number R-06-006-046.

19
TABLE III. VISCOSITY AND THERMAL CONDUCTIVITY

OF GASEOUS NITROGEN*

TEMPERATURE VISCOSITY

6/CM-SEC

-,6 ^10°

THERM4L CONDUCTIVITY J/CM-SEC-OEG XlO6

TEMPER4TURF VISCOSITY

G/CM-SEC

-,6

500 510

520

530

5*0

7710°

256.A 259.8

261.3 266.6

270.0

THERMAL CONDUCTIVITY J/CM-SEC-DEG

XlO6

382.7

388.*

394.0 399.7 405.3

55:) 560

570

580 590

273.3

276.6 279.9

283.

I

286.*

*11.0

416.6

22.2 *27.8

*33.*

100 69.3 97.6

110 75. 8 107.6

120 82.? 117.3

130 88.5 126.7

1*0 94.7 136.0

150 100.7 145.0

160 106.7 153.9

170 112.4 162.5

180 118.1 171.0

190 123.7 179.3

200 129.2 187.4

210 134.5 195.4

220 139.8 203.2

230 144.9 210.9

2*0 149.9 218.4

250 154. 8 225.8

260 159.7 233.1

270 164.4 240.2

28G 169.1 247.2

290 173.7 254.1

300 178.? 260.9

310 182.7 267.7

320 187.1 274.3

330 191.4 280.8

340 195.6 287.2

350 199.8 293.6

360 203.9 299.9

370 207.9 306.1

380 211.9 312.3

390 215. 8 318.*

400 219.7 324. 4 410 223.6 330.4

420 227.4 336.4

430 231.2 342.3

440 234.9 348.1

450 238.6 354.0

460 242.2 359.8

470 245.8 365.5

480 249.4 371.3

490 252.9 377.0

600

610

620

630

64U

650 660

670

680

690

700

710 720

730

740

750 760

770

780

790

800

810

820

830

840

850 860

870

880

890

900

910

920

930

940

Q5n

960 970

980

990

289.5

292.7 295.8

299.0

302.1

305.0

308.1

311.1

314.1

317.1

320.0 323.0 325.9

328.8

331.7

334.6

337.5

340.3 343.2

346.0

34P.8

351.6

354.4

357.1 359.8

362.6

365.3 367.9

370.6

373.3

375.9 378.5

381.2

383.8

386.4

389.0

391 .6 394.2 396.7

399.3

439.1 444.7

450.3 455.9

461.5

467.2

472.8

478.4

484.1 489.7

495.4

501.0 506.7 512.3

518.0

523.7

529.3

535.0 540.7

546.3

552.0

557.7 563.3

568.9

574.6

580.2

585.7

591.3

596.9

602.4

607.9

613.3

618.7

624.1 629.5

634.7

640.0 645.?

650.3

655.4

1000 401.7 660.4

*Viscosities calculated for the dilute gas by Kihara potential, with y

o =3.55 A, e/k=116.7°K. Thermal conductivities from Eq (8).

0.2,

20
TABLE IV. VISCOSITY AND THERMAL CONDUCTIVITY

OF GASEOUS OXYGEN*

TEMPERATURE VISCOSITY

K 6/CM-SEC

T) 106

THERMAL CONDUCTIVITY J/CM-SEC-DEG

XlO6

100 76.7 90.4

110 84.2 100.2

120 91.7 109.9

130 99.1 119.5

1*0 106.4 128.9

150 113.5 138.3

160 120.6 147.5

170 127.6 156.7

1B0 134.4 165.7

190 141.0 174.6

200 147.5 183.4

210 154.0 192.1 220 160.3 200.8

230 166.5 209.3

240 172.6 217.7

250 178.5 226.1

260 184.1 234.3

270 190.1 242.5

280 195.% 250.6

290 201.3 258.5

300 206.7 266.5

310 212.1 274.3

320 217.4 282.0

330 222.6 289.7

3*0 227.7 297.3

350 232.9 304.8

360 237.9 312.2

370 242. 8 319.6

380 247.7 326.9

390 252.5 334.1

*00 257.2 341.3

*10 261.9 348.4

*20 266.5 355.5

*30 271.1 362.4

**0 275.6 369.4

450 280.0 376.2

*60 284.4 383.0

470 288.8 389.8

480 293.1 396.5

490 297.3 403.1

TEMPERATURE VISCOSITY THERMAL CONDUCTIVITY

K fi/CM-SEC J/CM-SEC-DES

77 106 X106

500 301.6 409.7

510 305.8 416.3

520 310.0 422.8

530 314.1 429.3

540 318.2 435.7

550 322.2 442.1 560 326.2' 448.5

570 330.2 454.8

580 334.2 461.1

590 338.0 467.3

600 341.9 473.5

610 345.8 479.7

620 349.6 485.9

630 353.4 492.0

640 357.2 498.)

650 360.9 504.2

660 364.7 510.3

670 368.3 516,4

680 372.0 522.4

690 375.6 528.*

700 379.2 534.4

710 382.8 540.*

720 386.3 5*6.*

730 3«9.8 552.*

740 393.3 558.*

750 39ft.

8

564.4

760 400.3 570.3

770 403.8 576.3

780 407.2 582.3

790 410.7 588.2

800 414.1 594.2 em 417.5 600.2

820 420.9 606.2

830 424.3 612.2

840 *27.6 618.2

850 431.0 624.2

860 434.3 630.3

870 437.7 636.3

8811 441.0 642.*

890 444.2 6*8.5

900 447.3 65*.

6

911 450.6 660.8

920 453.8 666.9

930 457.0 673.1 940 460.2 679.4

95c 463.4 685.6

O60 466.5 691.9

970 469.6 698.3

980 472.8 70*.

6

990 475.9 711.0

717.5

* Viscosities calculated for the dilute gas by the Kihara potential, with

Y=0.1, a =3.38 A, e/k=124.5°K. Thermal conductivities from Eq (9)

21
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