Physics Question from JEE Main 2026 · 24 January, Shift 2

10 mole of an ideal gas is undergoing the cyclic process described below, drawn on a $P$-$V$ diagram with $P$ in $\text{Pa}$ and $V$ in $\text{m}^3$ (the volume axis is marked at $1$, $2$, $3$, $4$ and $5$): the gas is first taken along the constant-volume line $V = 1 \, \text{m}^3$ from $P_1$ up to $P_2$, then expanded along a falling curve from $V = 1 \, \text{m}^3$ out to $V = 5 \, \text{m}^3$, then dropped vertically at $V = 5 \, \text{m}^3$, and finally compressed along a lower curve back to the starting state $(V = 1 \, \text{m}^3,\ P = P_1)$. The heat involved in the process from $P_1$ to $P_2$ is $\alpha$ Joule $(P_1 = 21.7 \, \text{Pa},\; P_2 = 30 \, \text{Pa},\; C_v = 21 \, \text{J/K}\cdot\text{mol},\; R = 8.3 \, \text{J/mol}\cdot\text{K})$. The value of $\alpha$ is _____.