(a) Consider a collection of photons with a distribution function N that, in the mean rest frame of the photons, is isotropic. Show, using Eqs. (3.49b) and (3.49c), that this photon gas obeys the equation of state P = 1/3ρ.

(b) Suppose the photons are thermalized with zero chemical potential (i.e., they are isotropic with a blackbody spectrum). Show that ρ =aT⁴, where a is the radiation constant of Eq. (3.54c).

(c) Show that for this isotropic, blackbody photon gas the number density of photons is n = bT³, where b is given by Eq. (3.54b), and that the mean energy of a photon in the gas is

Transcribed Image Text:

00 = [ NEDV₁ = 4x * NEp²dp, P = 700 4π = = √ √ N₁2²¹²00 = 47 √²° N- P 3 p¹dp √m² + p² (3.49b) (3.49c)