a
Workdone during the complete cycle is equal to the area enclosed by the P-V graph

\(W=\frac{1}{2} \text { base } \times \text { height }+ \text { Area of rectangular }\)

\(=\frac{1}{2}\left(V_2-V_1\right) \times\left(P_1-P_2\right)+\left(V_2-V_1\right) P_2\)

\(=\left(V_2-V_1\right)\left[\frac{P_1}{2}-\frac{P_2}{2}+P_2\right]\)

\(=\left(V_2-V_1\right)\left[\frac{P_1}{2}+\frac{P_2}{2}\right]\)

\(=\frac{1}{2}\left(P_1+P_2\right)\left(V_2-V_1\right)\)