If one mole of an ideal gas at  P1,  V1 is allowed to expand reversibly and isothermally (A to B) its pressure is reduced to one-half of the original pressure (see fig.) This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value B→C. Then is restored to its initial state by a reversible adiabatic compression (C to A). The net work done by the gas is equal to:

At A, let say, temperature is T∴P1V1=(1)RT ⇒TA=T=P1V1R−−−−−(1)Work done in isothermal process (AB)WAB=(1)RTln2V1V1=RTln(2)----(2)Work done in isochoric process (BC)WBC=0----(3)Work done in adiabatic process (CA)WCA=−△U=−nCvΔT=−(1)Rγ−1TA−TC−−−−(4) here, TC=P142V1nR=P1V12R=T2−−−−(5) from equation (1) From equations (1),(4) and (5) we get ⇒WCA=−Rγ−1T−T2=−RT2(γ−1) Thus, net work ⇒Wnet =WAB+WBC+WCA=RTln⁡(2)+−RT2(γ−1)=RTln⁡2−12(γ−1)