A real gas within a closed chamber at \(27^{\circ} \mathrm{C}\) undergoes the cyclic process as shown in figure. The gas obeys \(P V^3=\mathrm{RT}\) equation for the path \(A\) to \(B\). The net work done in the complete cycle is _______.(assuming \(R=8 \mathrm{~J} / \mathrm{molK}\) )

\(=\int \frac{\mathrm{RTdV}}{\mathrm{V}^3}\)

\(=\mathrm{RT} \int_2^4 \mathrm{~V}^{-3} \mathrm{dV}\)

\(=8 \times 300 \times\left(-\frac{1}{2}\left[\frac{1}{4^2}-\frac{1}{2^2}\right]\right)\)

\(=225 \mathrm{~J}\)

\(\mathrm{~W}_{\mathrm{BC}} =\mathrm{P} \int_4^2 \mathrm{dV}=10(2-4)=-20 \mathrm{~J}\)

\(\mathrm{~W}_{\mathrm{CA}} =0\)

\(\therefore \mathrm{W}_{\text {cyck }} =205 \mathrm{~J}\)

Note: Data is inconsistent in process \(A B\).

So needs to be challenged.