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Thermal Radiation. Quantum Nature of Light.

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
 5.253. (a) Cv=(∂U/∂T)V=16σT3V/c=3 nJ/K, where U==4σT4V/c; (b) S=16σT3V/3c=1.0 nJ/K\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}
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