Problems and Solutions on Thermodynamics and Statistical Mechanics

Statiatical Physic8 365

aT

(a) Suppose a temperature gradient - exists along the x-direction

and consider a unit area perpendicular to it. The net heat flow resulting
from exchanging a pair of molecules across the unit area is

ax

ax

• UP
  m

The number of such pairs exchanged per unit time is -, so the heat flux

is

and the thermal conductivity is

C

K - XVpc - -(mkT):.

R2

(b) The change of the component vy of the average velocity in the

exchange of a pair of molecules as mentioned in (a) is - X-vv,(z), so that

the tangential force on a unit area perpendicular to the x-%rection is

a

Fv - -mXA. av vp -.

dx m

Hence the coefficient of viscosity is

(mkT)

q - XUp - ~

R2 *

(c) Suppose the mass density p(z) is inhomogeneous in the z-direction.

The mass flux in this direction is

so the diffusion coefficient is

D = XU N (mkT)'I2/R2p.