Problem 5.253

A cavity of volume $V=1.0$ $l$ is filled with thermal radiation at a temperature $T=1000 \mathrm{~K}$ . Find: (a) the heat capacity $C_{V}$ ; (b) the entropy $S$ of that radiation.

Reveal Answer

\begin{aligned} &\text { 5.253. (a) } C_{v}=(\partial U / \partial T)_{V}=16 \sigma T^{3} V / c=3 \text { nJ/K, where } U=\\ &=4 \sigma T^{4} V / c ; \text { (b) } S=16 \sigma T^{3} V / 3 c=1.0 \mathrm{~nJ} / \mathrm{K} \end{aligned}

Thermal Radiation. Quantum Nature of Light.