One mole of an ideal gas at (P₁,V₁) is allowed to expand reversibly and isothermally from A to B, so that its pressure is reduced to one-half of the original pressure, as shown in the figure. This is followed by a constant-volume cooling from B to C until the pressure is reduced to one-fourth of th…

Question

One mole of an ideal gas at (P₁,V₁) is allowed to expand reversibly and isothermally from A to B, so that its pressure is reduced to one-half of the original pressure, as shown in the figure. This is followed by a constant-volume cooling from B to C until the pressure is reduced to one-fourth of the initial value. It is then restored to its initial state by a reversible adiabatic compression from C to A. The net work done by the gas is equal to

Accepted Answer

(4) RT(ln 2-1/(2(γ-1))). A to B, isothermal, pressure halved so volume doubles: W_AB=RT ln 2. B to C, constant volume: W_BC=0, and the pressure falls to (P₁)/4. C to A, adiabatic compression from ((P₁)/4,2V₁) back to (P₁,V₁): W_CA=(P_CV_C-P_AV_A)/(γ-1)=((P₁V₁)/2-P₁V₁)/(γ-1)=-(RT)/(2(γ-1)). W=RT ln 2-(RT)/(2(γ-1)).

Step-by-step solution

Why the other options are wrong