$n$ mole a perfect gas undergoes 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 $V _{2}=2 V _{1}$ 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 change of pressure from $P _{2}$ to $P _{1}$

Total workdone in the complete cycle $ABCA$ is

  • A$0$
  • B$nRT \left(\ln 2+\frac{1}{2}\right)$
  • C$nRTIn2$
  • D$nRT \left(\ln 2-\frac{1}{2}\right)$
JEE MAIN 2021, Diffcult
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