Thermodynamics, Statistical Physics, and Quantum Mechanics

190 SOLUTIONS

But

Therefore,

We may then find the pressure P of the gas:

The isothermal work done by the gas

b) For a photon gas in a cuboid box

where is a constant.

So,

The same is true for a relativistic Fermi gas with dispersion law

c) For a nonrelativistic Fermi gas the energy is

where is a constant. So,

and

This result was already obtained directly in Problem 4.66 (see (S.4.66.8)).