Physics Question from JEE Main 2024 · 6 April, Shift 1

A real gas within a closed chamber at $27^\circ \text{C}$ undergoes the cyclic process as shown in the figure. The gas obeys the $PV^3 = RT$ equation for the path $A$ to $B$. The net work done in the complete cycle is (assuming $R = 8 \, \text{J/mol}\cdot\text{K}$):

The figure shows: a pressure-volume diagram with pressure $P$ in $\text{N/m}^2$ on the vertical axis (the values $10$ and $20$ are marked) and volume $V$ in $\text{m}^3$ on the horizontal axis (the values $2$ and $4$ are marked). The three states are $A$ at $V = 2 \, \text{m}^3$, $P = 20 \, \text{N/m}^2$; $B$ at $V = 4 \, \text{m}^3$, $P = 10 \, \text{N/m}^2$; and $C$ at $V = 2 \, \text{m}^3$, $P = 10 \, \text{N/m}^2$. The cycle is traced $A \to B$ along the curve, then $B \to C$ along the horizontal line $P = 10 \, \text{N/m}^2$, then $C \to A$ along the vertical line $V = 2 \, \text{m}^3$.