[UPSC CSE 2026] Black Body Radiation (Q431, 15M)

Blackbody radiation in a cavity at 2000\text{ K} is subject to isothermal reversible expansion through 10^3\text{ cm}^3. Calculate (i) the heat transferred and (ii) the work done. If the initial volume was 10\text{ cm}^3 and expansion had been adiabatic, calculate the change in temperature of the radiation. (Given, Stefan--Boltzmann constant, \sigma = 5\cdot 672 \times 10^{-8}\text{ J}\cdot\text{m}^{-2}\cdot\text{K}^{-4}\cdot\text{s}^{-1})