Problems and Solutions on Thermodynamics and Statistical Mechanics

(Ann) #1
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,

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