JEE Main · 2025 · 24 Jan 2025 · Shift 1 · Heat & Thermodynamics

The pressure increases linearly with temperature, so $P=kT$ for some constant $k$, i.e. $\frac{P}{T}$ is constant.

From the ideal gas law $PV=nRT$, $\frac{P}{T}=\frac{nR}{V}$. Since the left side is constant, $V$ must also be constant — the process is isochoric.

Checking the statements:

A. Work done $W=\int PdV=0$ since $V$ is constant — true.

B. For a constant-volume process, the first law gives $Q=\Delta U+W=\Delta U$, so the heat added equals the change in internal energy — the statement that they differ is false.

C. Volume is constant, not increasing — false.

D. Since pressure and hence temperature rises, and $\Delta U=n{C}_v\Delta T$ for an ideal gas, internal energy increases — true.

E. The process is isochoric, as shown above — true.

Statements A, D and E are correct.