Consider an \(n\)-dimensional Bose gas whose single-particle energy spectrum is given by \(\varepsilon \propto p^{s}\), where \(s\) is some positive number. Discuss the onset of Bose-Einstein condensation in this system, especially its dependence on the numbers \(n\) and \(s\). Study the thermodynamic behavior of this system and show that,

\[
P=\frac{s}{n} \frac{U}{V}, \quad C_{V}(T ightarrow \infty)=\frac{n}{s} N k, \quad \text { and } \quad C_{P}(T ightarrow \infty)=\left(\frac{n}{s}+1ight) N k
\]