JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Chapter_pending

For an isothermal reversible expansion $\Delta U=0$, so $q=-w=nRT\ln \frac{V_2}{V_1}$, matching (II). In a free expansion the gas works against zero external pressure and exchanges no heat, so $q=0$, matching (I). For an irreversible compression the work against the constant external pressure is $w=-p_{ext}(V_1-V_2)$, matching (III). Over a complete reversible cycle the entropy returns to its initial value, so $\oint \frac{q_{rev}}{T}=0$, matching (IV). The pairing is reversible expansion with (II), free expansion with (I), irreversible compression with (III) and cyclic reversible with (IV).