# Number of Thermal photons

1. Mar 16, 2009

### Ignea_unda

1. The problem statement, all variables and given/known data
Show that the number of photons $$\sum_n <s_n>$$ in equilibrium at temperature $$\tau$$ in a cavity of volume V is
$$N = 2.404\pi^{-2}V(\tau / \hbar c)^3$$

2. Relevant equations
$$<s> = \sum_s s P(s) = Z^{-1} \sum s~ exp[-s \hbar \omega/ \tau] ~~~ (1)$$

$$<s> = 1/exp[\hbar \omega / \tau] - 1] ~~~ (2)$$

$$\omega_n = n \pi c/ L ~~~ (3)$$

3. The attempt at a solution
I have tried to convert omega and take the sum using (3), but haven't had any luck with that. Also I have tried taking the double summation over <s> but have run into a stumbling block with Z being of a similar form of the exact form (2) of <s>.