n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes. A→B : Isothermal expansion at temperature T, so that the volume is doubled from V1 to V2=2V1 and pressure changes from p1 to p2. B→C: Isobaric compression at pressure p2 to initial volume V1. C→A : Isochoric change leading to change of pressure from p2 to p1. Total work done in the complete cycle ABCA is
As, AB is isothermal process, so work done by isothermal process is given by ‌WAB=nRT‌ln(‌
V2
V1
) ‌WAB=nRT‌ln(‌
2V1
V1
)=nRT‌ln‌2 As, BC is isobaric process, so work done by isobaric process is given by WBC‌‌=p∆V=p2(V1−V2) ‌‌=p2(‌
V2
2
−V2)=−‌
p2V2
2
‌‌=‌
−nRT
2
As, CA is isochoric process, so work done by isochoric process is given by, WCA=0‌‌[∵∆V=0] Total work done in the cycle ABCA, WABCA‌‌=WAB+WBC+WCA ‌‌=nRT‌ln‌2+(‌