Answer to Question #90500 in Mechanics | Relativity for Avisek Gurung

Question

why chemical potential of a photon gas is zero

Answer 1

Chemical potential defines the change of thermodynamic potentials (such as Gibbs energy, enthalpy, internal energy and so on) due to change of number of particles in a system. Roughly speaking, chemical potential is the work one has to do to put an additional particle in a system.

Photons are interesting particles which do not subject to the rule of conservation of number of particles. Photons may emerge and destroy in vacuum without changing gas equilibrium, otherwise the entropy would go up. That is why chemical potential of a photon gas is zero.