JEE Main 2025 Jan 24 Shift 1, Physics Q20: Thermodynamic Processes

JEE Main2025Jan 24, Shift 1Physics

An ideal gas goes from an initial state to final state. During the process, the pressure of gas increases linearly with temperature.

A. The work done by gas during the process is zero.

B. The heat added to gas is different from change in its internal energy.

C. The volume of the gas is increased.

D. The internal energy of the gas is increased.

E. The process is isochoric (constant volume process)

Choose the correct answer from the options given below :-

A
A, B, C, D Only
B
A, D, E Only
C
E Only
D
A, C Only

Solution

"Pressure increases linearly with temperature" means $P = k T$ for some constant $k$ , i.e. $P / T = const.$

For an ideal gas $P V = n R T$ , so $\frac{P}{T} = \frac{n R}{V}$ . Constant $P / T$ therefore implies constant volume $V$ $\Rightarrow$ the process is isochoric.

Evaluate each statement:

A. Isochoric $\Rightarrow W = \int P d V = 0$ . $✓$

B. First law: $Q = Δ U + W = Δ U + 0 = Δ U$ . So $Q = Δ U$ , not different from it. $\times$

C. Volume is constant, not increasing. $\times$

D. Pressure rises and so does temperature (linear in $T$ ); $Δ U = n C_{V} Δ T > 0$ . $✓$

E. Isochoric. $✓$

Correct: A, D and E. $∴$ Option (2).

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JEE Main 2025 Jan 24 Shift 1, Physics Q20: Thermodynamic Processes

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