Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 189

where wehave used theintegral given in the problem.Finally,

4.75 D-Dimensional Blackbody Cavity (MIT)

For a photon gas the average number of photons per mode is given by

The energy

whereV is the volume of the hypercube:

Substituting into(S.4.75.2), weobtain

The energy density is simply

ForD= 3 we recover the Stefan–Boltzmann law:

4.76 Fermi and Bose Gas Pressure (Boston)

a) Using and substituting the entropy from the problem, we
obtain