Discuss the below:
Apply the thermodynamic relation TdS =dE+pdV to a photon gas. Here one can write that E = Vu where u(T), the mean energy density of the radiation field, is independent of the volume V. The radiation pressure p =u/3
(a) Considering S as a function of T and V, express dS in terms of dT and dV. Find (∂S/∂T)v and (∂s/∂m)T
(b) Show that the mathematical identity (∂2s/∂V∂T)= (∂2s/∂T∂V)gives immediately a differential equation for u which can be integrated to yield the bolzman law u ∝ T4