Physics - Heat & Thermo Question with Solution | TestHub

For given graph, equation of $P$ - $V$ line is $$P-2P_0=\frac{2P_0-P_0}{V_0-2V_0}\left(V-V_0\right)$$ So, $P=3P_0-\frac{P_0}{V_0}V$ as $PV=nRT$ $$\Rightarrow \left(3P_0-\frac{P_0}{V_0}V\right)V=nRT;$$ For maximum temperature $\frac{dT}{dV}=0$ $$\Rightarrow \frac{dT}{dV}=3P_0-\frac{2P_0}{V_0}V=0\Rightarrow V=\frac{3}{2}{V}_0$$ Also $P=\frac{3}{2}{P}_0$ So, $T=\frac{PV}{nR}=\frac{1}{nR}\times \frac{3}{2}{P}_0\times \frac{3}{2}{V}_0=\frac{9P_0{V}_0}{4nR}$