n moles of an ideal gas is taken through a four step cyclic process as shown in the diagram. Calculate work done by the gas in a cycle in terms of temperatures T₁, T₂, T₃ and T₄.

Process 1 – 2 and 3 – 4 are isochoric process.
$\therefore$ W₁₂ = W₃₄ = 0
2 – 3 and 4 – 1 are isobaric processes.
$\begin{array}{l}\therefore {\mathrm{W}}_{23}={\mathrm{P}}_2\mathrm{\Delta V}={\mathrm{P}}_2{\mathrm{V}}_3-{\mathrm{P}}_2{\mathrm{V}}_2\\ ={\mathrm{nRT}}_3-{\mathrm{nRT}}_2=\mathrm{nR}\left({\mathrm{T}}_3-{\mathrm{T}}_2\right)\\ {\mathrm{W}}_{41}={\mathrm{P}}_1\mathrm{\Delta V}={\mathrm{P}}_1{\mathrm{V}}_1-{\mathrm{P}}_1{\mathrm{V}}_4\\ =\mathrm{nR}\left({\mathrm{T}}_1-{\mathrm{T}}_4\right)=-\mathrm{nR}\left({\mathrm{T}}_4-{\mathrm{T}}_1\right)\\ \therefore \mathrm{W}=\mathrm{nR}\left[{\mathrm{T}}_3-{\mathrm{T}}_2-{\mathrm{T}}_4+{\mathrm{T}}_1\right]\end{array}$