Problems and Solutions on Thermodynamics and Statistical Mechanics

Statiatiod Physics 293

This implies that the interaction energy is much less than the kinetic energy,
which makes the approximation in (a) reasonable.

(d) The mean free time is t - l/nqv, where the average speed

kT

Hence t - (E)-3c7~1 (z) - 10-z3 S.

The assumption that the gas remains in equilibrium is reasonable for the
mean free time is much shorter than the expansion time which is of the
order of 10-4s.

4. ENSEMBLES (2116 - 2148)

2116

Heat Capacity.

The constant volume heat capacity of a system with average energy

(E) is given by C,, =

Use the canonical ensemble' to prove that: C is related to the mean-

square fluctuation in the energy as follows:

Solution:

The partition function is

Z = exp(-E,/kT).

1

z

Therefore, (E) = - C E,e-EnIkT. Then