Problems and Solutions on Thermodynamics and Statistical Mechanics

Statiatical Phymcs 343

velocity is v, and the mean collision time is 7. We have

1 kT

l=-=- % 4 x

nu pa m ,

1

r=--4~10-~s.

V

(b) The electron number density is

2154
A container is divided into two parts by a partition containing a small
hole of diameter D. Helium gas in the two parts is held at temperature
TI = 150 K and Tz = 300 K respectively through heating of the walls.

(a) How does the diameter D determine the physical process by which

the gases come into a steady state?

(b) What is the ratio of the mean free paths 11/12 between the two

(c) What is the ratio 11/12 when D >> 11, D >> 12?

parts when D << 11, D << 12, and the system has reached a steady state?

(Prince ton)
Solution:
(a) At the steady state the number of molecules in each part is fixed. If
D >> 11 and D >> 12, the molecules are exchanged by macroscopic gas flow.
If D << 11, D << 12, the molecules are exchanged by leakage gas flowing
through the pinhole.

(b) When 11 >> D and 12 >> D, the steady state occurs under the
condition