Study the statistical mechanics of an extreme relativisitic gas characterized by the single-particle energy states

\[
\varepsilon\left(n_{x}, n_{y}, n_{z}ight)=\frac{h c}{2 L}\left(n_{x}^{2}+n_{y}^{2}+n_{z}^{2}ight)^{1 / 2}
\]

instead of (1.4.5), along the lines followed in Section 1.4. Show that the ratio \(C_{P} / C_{V}\) in this case is \(4 / 3\), instead of \(5 / 3\).