JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Heat & Thermodynamics

For an adiabatic change no heat is exchanged, $Q=0$, so the first law gives $\Delta U+W=0$ and the work done equals the change in internal energy in magnitude, so the claim that the work done equals the change in internal energy is correct. This work is $W=-n{C}_v(T_2-T_1)$, so its magnitude is proportional to $(T_2-T_1)$, which makes the claim that the work is proportional to the temperature change correct. The internal energy does change with temperature, so the claim that the internal energy stays constant fails; and the adiabatic relations are $T{V}^{\gamma -1}=\text{constant}$ and $P{V}^{\gamma }=\text{constant}$, not $TV=\text{constant}$ or $PV=\text{constant}$, so those two claims fail as well. The correct statements are that the work equals the change in internal energy in magnitude and that the work is proportional to $(T_2-T_1)$.