Physical Chemistry Third Edition

464 10 Transport Processes

Exercise 10.10

Evaluate the self-diffusion coefficient of argon at 1.00 atm and 0◦C from the value of the hard-

sphere diameter in Table A.15 in the appendix for this temperature. Compare your result with

the experimental value of the self-diffusion coefficient in Table A.19 in the appendix.

Exercise 10.11

Find the effective hard-sphere diameter of argon atoms from each of the self-diffusion coeffi-

cient values in Table A.19. Comment on your results. Compare your results with the values in

Table A.15 in the appendix.

Thermal Conduction in the Hard-Sphere Gas

An analysis of heat conduction that is very similar to that for self-diffusion can be

carried out for a system of hard spheres having a uniform pressure but a temperature

that depends onz.^6 We again consider the same three imaginary planes in the system

as before and assume that the molecules reaching the central plane were equilibrated

at the temperature of the upper plane or the temperature of the lower plane. We assume

that the heat capacity per molecule is constant and write for the mean molecular kinetic

energy

〈ε〉cVT

CV,m

NAv

T

wherecVis the heat capacity per molecule. The net (upward) energy flux is given by

qzνε(z′−λ)−νε(z′+λ)

1

4

N〈v〉

[

ε(z′−λ)−ε(z′+λ)

]

whereνis the rate per unit area of molecules reaching the center plane, as discussed

in Chapter 9.

ε(z′−λ)−ε(z′+λ)≈

∂ε

∂z

(2λ)

∂ε

∂T

∂T

∂z

(2λ)

CV,m

NAv

∂T

∂z

(2λ)

qz≈

1

4

N〈v〉(2λ)

CV,m

NAv

∂T

∂z

κ

∂T

∂z

κ

1

2

N〈v〉λ

CV,m

NAv

(10.3-10)

If the same corrections are applied that were used to derive Eq. (10.3-9), a more accurate

expression is obtained:

κ

25 π

64

cVλ〈v〉N (10.3-11a)

κ

25

32

cV

d^2

(

kBT

πm

) 1 / 2



25

32

cV

d^2

(

RT

πM

) 1 / 2

(more accurate

expression)

(10.3-11b)

(^6) J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird,Molecular Theory of Gases and Liquids, Wiley,
New York, 1954, p. 9ff.