Two moles of helium gas undergo a reversible cyclic process as shown in figure. Assuming gas to be ideal, what is the net work involved in the cyclic process?

 

$\begin{array}{l}{\mathrm{W}}_{\text{net }}=\text{ area enclosed }\\ \mathrm{V}=\frac{nRT}{P}\\ {\mathrm{V}}_{\mathrm{A}}=\frac{2R\times 300}{1}=\frac{600R}{1}\\ {\mathrm{V}}_{\mathrm{B}}=\frac{2R\times 300}{2}=\frac{300R}{1}; {\mathrm{V}}_{\mathrm{c}}=\frac{2R\times 400}{2}=\frac{400R}{1}\\ \\ \\ {\mathrm{V}}_{\mathrm{D}}=\frac{800R}{1}\end{array}$

$\begin{array}{l}{\mathrm{W}}_{\mathrm{AB}}=-{\mathrm{nRTT}}_{\mathrm{A}}\ln \frac{V_B}{V_A}=-2\mathrm{R}\left(300\right)\ln \frac{1}{2}=600\mathrm{Rln}2\\ {\mathrm{W}}_{\mathrm{BC}}=-2(400-300)\mathrm{R}=-200\mathrm{R}\\ {\mathrm{W}}_{\mathrm{CD}}=-2\mathrm{R}\left(400\right)\ln \frac{V_D}{V_C}=-800\mathrm{Rln}2\\ {\mathrm{W}}_{\mathrm{AD}}=-1(600\mathrm{R}-800\mathrm{R})=200\mathrm{R}\\ {\mathrm{W}}_{\text{Total }}={\mathrm{W}}_{\mathrm{AB}}+{\mathrm{W}}_{\mathrm{BC}}+{\mathrm{W}}_{\mathrm{CD}}+{\mathrm{W}}_{\mathrm{AD}}=200\mathrm{Rln}2=-100\mathrm{RIn}4\end{array}$