Problems and Solutions on Thermodynamics and Statistical Mechanics

358 Problems 8 Solution, on Thermodynamics €9' Statistical Mechanics

n

3

Solution:
(a) The coefficient of viscosity is q = -m.isX, where n is the particle

number density. The pressure of the gas is

p = nkT.

Hence

. Neglecting the dif-

• 3kT
  The mean-square speed of the molecues is u2 = -

ference between the average speed and the rms speed, we have

m

which is the average number of collisions per unit time for a molecule.

(b) At STP, the pressure is p = 1.013 x 10' dyn/cm2. Hence the

number of collisions per unit time is

1.013 x 10'

• p- - = 5.63 x 109.
  1.8 x 10-4

2169

(a) Assuming moderately dilute helium gas so that binary collisions of

helium atoms determine the transport coefficients] derive an expression for

the thermal conductivity of the gas.

(b) Estimate the ratio of the thermal conductivity of gaseous 3He to

(c) Will this ratio become different at a temperature near 2 K? Why?

that of gaseous 4He at room temperature.

( wis co nsin)

Solution:
(a) Consider an area element dS of an imaginary plane at z = zo.which
divides the gas into two parts A and B (see Fig. 2.35). We assume that the
temperatures of A and B are TA and TB respectively. In the case of a small
temperature difference] we can take approximately nAGA = nBcB = nG,