Answer:
Option A
Explanation:
p-V equation for path AB
$p= -(\frac{p_{0}}{V_{0}})V+3p_{0}$
$\Rightarrow pV=3p_{0}V -\frac{p_{0}}{V_{0}}V^{2}$
OR $T=\frac{pV}{nR}=\frac{1}{nR}(3p_{0}V-\frac{p_{0}}{V_{0}}V^{2})$
For maximum temperature
$\frac{dT}{dV}=0$
$\Rightarrow 3p_{0}-\frac{2p_{0}V}{V_{0}}=0\Rightarrow V=\frac{3}{2}V_{0}$
and $p= 3p_{0}-\frac{p_{0}}{V_{0}}=\frac{3p_{0}}{2}$
Therefore, at these values,
$T_{max}=\frac{(\frac{3p_{0}}{2})(\frac{3V_{0}}{2})}{nR}=\frac{9p_{0}V_{0}}{4nR}$
