Thermodynamics, Statistical Physics, and Quantum Mechanics

192 SOLUTIONS

where we let Performing the integralgives

Substituting theenergy for this mode werecover theentropy

in the form

4.78 Photon Gas (Stony Brook)

The photon gas is aBose gas with zero chemicalpotential

leading to Planck’sdistribution:

Replacing the sumoverdifferentmodes by anintegral in spherical coordi-

nates, we maywrite, for thenumber ofquantumstates in a volume V,

Substituting into (S.4.78.2) andtaking intoaccount the two
possibletransversepolarizations ofphotons, we obtain