Blackbody radiation — UPSC Physics Optional IFoS 2014 Paper I

Suppose a cavity of volume V contains blackbody radiation in equilibrium with the walls of the cavity at a temperature T. For a reversible adiabatic change of volume show that : VT^3 = \text{constant}. If the initial temperature is 2000^\circ\text{K} and the volume is increased from 10\text{ cm}^3 to 1250\text{ cm}^3, reversibly and adiabatically, what would be the final temperature of the radiation ?