Problems and Solutions on Thermodynamics and Statistical Mechanics

Statistical Physics 225

The classical partition function is

(2 cos 61 cos 82 - sin 81 sin 62 cos(pl - p2))] dnldQ2.

As X = pMlM2/R3 << 1, expanding the integsand with respect to A,
retaining only the first non-zero terms, and noting that the integral of a
linear term of cos6 is zero, we have

1

A2

z = [ 1 + ~(2 cos O1 cos e2 - sin 61 sin O2 cos(pl - p2))2 dnldn2

= 162 + 32r2 -A2 + - 47P = 4a2 -(37 + 8X^2 ) ,

9 9 9

1 aZ 16X .- Mi M2

u= =

zap 37+8X2 R3

2059

The molecule of a perfect gas consists of two atoms, of mass rn, rigidly

separated by a distance d. The atoms of each molecule carry charges q and

-q respectively, and the gas is placed in an electric field E. Find the mean

polarization, and the specific heat per molecule, if quantum effects can be

neglected.

State the condition for this last assumption to be true.

(UC, Berkeley)

Solution:

field is 0. The energy of a dipole in the field is

Assume that the angle between a molecular dipole and the external