Thermal equilibrium — UPSC Physics Optional IFoS 2012 Paper I

Find out the number of photons in a cavity of volume 1\cdot 00\text{ cm}^3 under thermal equilibrium at temperature T = 1000\ {}^\circ\text{K}. Assume that \int_0^\infty \frac{x^2 dx}{e^x - 1} = 2\cdot 405.