\(P-2 P_{0}=\frac{2 P_{0}-P_{0}}{V_{0}-2 V_{0}}\left(V-V_{0}\right)\)

So, \(P=3 P_{0}-\frac{P_{0}}{V_{0}} V\) as \(P V=n R T\)

\(\Rightarrow\left(3 P_{0}-\frac{P_{0}}{V_{0}} \cdot V\right) V=n R T\)

For maximum temperature \(\frac{d T}{d V}=0\) \(\Rightarrow \frac{d T}{d V}=3 P_{0}-\frac{2 P_{0}}{V_{0}} V=0 \Rightarrow V=\frac{3}{2} V_{0}\)

Also \(P=\frac{3}{2} P_{0}\)

So, \(T=\frac{P V}{n R}=\frac{1}{n R} \times \frac{3}{2} P_{0} \times \frac{3}{2} V_{0}=\frac{9 P_{0} V_{0}}{4 n R}\)