Total work done by gas, WTotal=WAB+WBC+WCA
WAB=nRTln4VV=2nRTln2=2PVln2.
Also PAVA=PBVB (As AB is an isothermal process)
or, PB=PAVAVB=PV4V=P4.
In the step BC, the pressure remains constant. Hence the work done is,
WBC=P4(V−4V)=−3PV4.
In the step CA, the volume remains constant and so the work done is zero. The net work done by the gas in the cyclic process is
W=WAB+WBC+WCA
=2PVln2−3PV4+0
Hence, the work done by the gas is 0.636PV.