Black-body radiation as a photon gas consider a radiation cavity of volume v at temperature t. bose treats the cavity radiation as an ideal gas of photons in thermal equilibrium. a photon gas is an ideal boson gas with zero chemical potential because their number is not conserved. the energy of a photon is proportional to the frequency of the radiation: e = hw and the density of states in w space is: d(w) = w2 t (a) write down the energy density spectrum u(w, t) as a function of w and t (or b). (b) show that the total energy density w(t) scales as u (t) = ato and find b. (c) let wmax be the angular frequency at which the energy density u(w, t) reaches its maximum, shows that wmat t.