Problems and Solutions on Thermodynamics and Statistical Mechanics

384 Problems €4 Solutionn on Thermodynamics €4 Statistical Mechanic8

is its mean free path. As A = &, where n is the number density of argon
molecules, u is the cross section for scattering:

We have

P

RT

n = - x NA = 1.01 x lo5 x 10 x 6.02 x 1023/(760 x 8.3 x 473)

= 2.04 x 1023m-3 ,

A M 1.7 x 10-14m ,

w 413 m/s.

23 x 10-3

r FJ 4 x 10-~~ ,

and hence

ax = -av x = - x2 w 3 x ~o-~A

Y cr

2192

A gas consists of a mixture of two types of molecules, having molecular

masses MI and Mz grams, and number densities N1 and N2 molecules per

cubic centimeter, respectively.

The cross-section for collisions between the two different kinds of

molecules is given by AlVl,l, where A is a constant, and V12 is the rel-

ative velocity of the pair.

(a) Derive the average, over all pairs of dissimilar molecules, of the

(b) How many collisions take place per cubic centimeter per second

(UC, Berkeley)

center-of-mass kinetic energy per pair.

between dissimilar molecules?

Solution:

According to the Maxwell distribution,