Q2. Consider a photon gas enclosed in a volume V and in equilibrium at temperature T. The photon is a massless particle, so that the single photon energy is € = pc. (a) What is the chemical potential of the gas? Explain. (b) Determine how the number of photons in the volume V depends upon the temperature T. (c) Find the energy spectral density u(w) such that the energy density is 00 == Lou (w) dw V where U is the total energy of the photon gas and w is the angular frequency of photons. x3 (d) Find the temperature dependence of U/V. Given: 500 x dx = 14 (e) Show that the pressure of photon gas is given by P = ex-1 1 U 3 V' Hints: P can be found from the volume dependence of F. (f) Find the entropy of a photon gas S. 15 (g) Our universe is currently pervaded by a cosmic microwave background radiation (CMR) at a temperature of 2.73K. Find the temperature of the CMR when the universe is expanded to a volume twice of the current value.