'n' moles of an ideal gas undergoes a process A → B as shown in the… | JEE Main 2016

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P-V Diagrams & Cyclic Processes

$\text{'}n\text{'}$ moles of an ideal gas undergoes a process $A \rightarrow B$ as shown in the figure. The maximum temperature of the gas during the process will be:

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Answer: (c)

Line AB through $(V_0, 2P_0)$ and $(2V_0, P_0)$ : $P = 3P_0 - \frac{P_0}{V_0}V$ .
$T = \frac{PV}{nR}$ is maximum when $PV$ is maximum: $\frac{d}{dV}\left(3P_0V - \frac{P_0}{V_0}V^2\right) = 0 \Rightarrow V = \frac{3}{2}V_0$ .
Then $P = \frac{3}{2}P_0$ , so $T_{max} = \frac{9P_0V_0}{4nR}$ .
So the answer is (c).

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