Problems and Solutions on Thermodynamics and Statistical Mechanics

380 Problems d Solutionn on Thermcdpam'cs d Statistical Mechanics

Solution:

The mean free path of the gas is

With T = 400 K, d = 3.6 x 10-l' m and p = atm M 10 N/m2, we
get X M m. Thus we can consider the gas in the bottle as being in
thermal equilibrium at any instant. From the Maxwell distribution, we find
the rate of decrease of molecules in the bottle to be

subject to the initial condition

N(t = 0) = No.

Hence

N(t) = Noexp --

( 43) *

That is, the number of particles in the bottle attenuates exponentially with

time.

The number of particles in the bottle is N at time 7 given by

4V No

~=-ln-

A5 N

For N = N0/10, with

?i = EM 514 m/s ,

V = 0.25 x low5 m3, A = r(10-G)2m2, we find

T M 1.43 x 10Gs.