$n$ moles of a perfect gas undergo a cyclic process $ABCA$ (see figure) consisting of the following processes:
$A \rightarrow B :$ Isothermal expansion at temperature $T$ so that the volume is doubled from $V_{1}$ to $V_{2}=2V_{1}$ and pressure changes from $P_{1}$ to $P_{2}$.
$B \rightarrow C :$ Isobaric compression at pressure $P_{2}$ to initial volume $V_{1}$.
$C \rightarrow A :$ Isochoric change leading to a change of pressure from $P_{2}$ to $P_{1}$.
Total work done in the complete cycle $ABCA$ is

  • A
    $0$
  • B
    $nRT \left(\ln 2+\frac{1}{2}\right)$
  • C
    $nRT \ln 2$
  • D
    $nRT \left(\ln 2-\frac{1}{2}\right)$

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