Evaluating the number of photons per unit volume in the frequency range dω, as
(Nω/V)dω=(Uω/V)dω/ℏω
where Uω is given in problem 16.8-2, calculate the total number of photons per unit volume. Show that the average energy per photon (U/N) is approximately 2.2kBT. Note that the integral encountered can be written in terms of the Riemann zeta function, as in the preceding footnote.