[QUE/TH-13004] TH-PROBLEM

The fundamental equation for a system is given by
\begin{equation*}
u = \Lambda \frac{s^{3/2}}{v^{1/2}}
\end{equation*}
where \(\Lambda\) is a constant.
Prove the following equations
\begin{eqnarray}
T &=& \frac{5}{2} \frac{\Lambda S^{3/2}}{NV^{1/2}}\\
P V^{2/3} &=& N \frac{N \Lambda 2^{1/2}}{5*{3/2}} T^{5/3}\\
\mu &=& - \Big(\frac{2}{5}\Big)^{5/2} \frac{2}{\Lambda ^{2/3}} \Big(\frac{V}{N}\Big)^{1/3} T^{5/3}.
\end{eqnarray}