Physical Chemistry Third Edition

10.3 The Gas Kinetic Theory of Transport Processes in Hard-Sphere Gases 465

We will apply this expression only to a monatomic gas. For a diatomic or polyatomic

gas the thermal conductivity is more complicated, since it is not an adequate approxi-

mation to assume that rotational and vibrational motions are equilibrated at the upper

and lower planes.

EXAMPLE10.13

Calculate the thermal conductivity of argon gas at 20◦C from its hard-sphere diameter in

Table A.15 in the appendix. Compare your value with that in Table A.16 in the appendix.

Solution

κ

25

32

(

3

2

)

1. 3807 × 10 −^23 JK−^1

(3. 61 × 10 −^10 m)^2

(

(8.3145 J K−^1 mol−^1 )(293.15 K)

π(0.039948 kg mol−^1 )

) 1 / 2

 0 .0173 J s−^1 m−^1 K

The value in Table A.16 is 0.01625 J s−^1 m−^1 K.

Exercise 10.12

Calculate the effective hard-sphere diameter of helium at 20◦C and 1.00 atm from its thermal

conductivity in Table A.16 of the appendix. Compare your result with the value in Table A.15

in the appendix.

The Viscosity of the Hard-Sphere Gas

If a fluid has a velocity in theydirection that depends onz, theycomponent of the

momentum is transported in thezdirection as each layer of fluid puts a frictional force

on the next layer. An analysis similar to that of self-diffusion and thermal conductivity

can be carried out for a hard-sphere gas. The net flow of the momentum is computed

and the result is an expression for theviscosity coefficient:^7

η

5 π

32

mλ〈v〉N 

5

16

1

d^2

√

mkBT

π

(10.3-12)

This equation is at the level of accuracy of Eqs. (10.3-9) and (10.3-11).

All three transport coefficients are proportional to the mean speed of the molecules

and to the mean free path, which means that they are proportional to the square root of

the temperature at constant density. A gas becomes more viscous when the temperature

is raised (opposite to the behavior of a liquid). The coefficient of viscosity and the

coefficient of thermal conductivity are independent of the number density. This behavior

was predicted by kinetic theory before it was observed experimentally.

(^7) R. D. Present,Gas Kinetic Theory, McGraw-Hill, New York, 1958, Section 11-2.