Between two isotherm we have a cycle as shown.  Find the work done by the gas during the cycle.  (in J) [Take  $T_1={127}^{0}C,T_2={16}^{0}C,n=1$ mole]

$$\begin{gathered} \frac{P_2}{P_1}=\frac{V_2}{V_1} \\ \Rightarrow P_2{V}_1=P_1{V}_2 \\ W=P_2(V_2-V_1)-P_1(V_2-V_1) \\ =nR{T}_2+nR{T}_1-P_2{V}_1-P_1{V}_2 \\ {P}_2=\frac{nR{T}_2}{V_2},P_1=\frac{nR{T}_1}{V_1} \\ \frac{P_2}{P_1}=\frac{T_2}{T_1}\times \frac{V_1}{V_2}=\frac{V_1}{V_2} \\ \Rightarrow \frac{V_1}{V_2}=\sqrt{\frac{T_2}{T_1}} \\ \Rightarrow P_2{V}_1=P_1{V}_2=nR\sqrt{T_1{T}_2} \\ \Rightarrow W=nR{(\sqrt{T_1}-\sqrt{T_2})}^2 \\ =1\times \frac{25}{3}{(20-17)}^2 \\ =75J \end{gathered}$$