JEE Advanced 2026 Paper 2, Physics Section 2 Q5: Thermodynamic Processes

JEE Advanced2026Paper 2Physics Section 2

Ten moles of an ideal monoatomic gas, initially in state $a$ at atmospheric pressure and temperature $T_{a} = 2 7^{\circ}$ C, is enclosed in a metal cylinder of volume $V_{0}$ fitted with a frictionless piston. The gas is suddenly compressed to state $b$ with volume $V_{0} /3$ . Now, keeping the piston stationary, the cylinder is submerged in a water bath of temperature $1 1^{\circ}$ C until the gas reaches the temperature of the water bath, which is denoted as state $c$ . Finally, while still in the water bath, the piston is brought slowly to its initial position, which is denoted as state $f$ . If $R$ is universal gas constant, then the correct option(s) is/are: [Given: $9^{1/3} = 2.08$ ]

A
The schematic P-V diagram of the processes described above is:
B
The change in internal energy in going from state $a$ to $b$ is $4860 R$ .
C
The net change in the internal energy in the whole process is $- 240 R$ .
D
The pressure and temperature of the state $b$ are $2.08$ times the atmospheric pressure and $624$ K, respectively.

Solution

Process identification. $a \to b$ is adiabatic compression, $b \to c$ is isochoric cooling, $c \to f$ is isothermal expansion. Option (A) matches.

State b temperature. For an adiabatic process with monoatomic gas, $γ = 5/3$ and $T V^{γ - 1} =$ const:

$T_{b} = T_{a} (\frac{V _{0}}{V _{0} /3})^{2/3} = 300 \cdot 3^{2/3} = 300 \cdot 9^{1/3} = 300 \times 2.08 = 624$ K.

State b pressure. $P V^{γ}$ const gives $P_{b} = P_{a} \cdot 3^{5/3} \approx 6.24 P_{a}$ , not $2.08 P_{a}$ . Option (D) is incorrect.

Internal energy change $a \to b$ . $Δ U_{ab} = n C_{V} Δ T = 10 \cdot \frac{3 R}{2} \cdot (624 - 300) = 4860 R$ . Option (B) correct.

Net internal energy change. Since $U$ depends only on $T$ , and $T_{f} = T_{c} = 284$ K (water bath at $1 1^{\circ}$ C $= 284$ K):

$Δ U_{net} = n C_{V} (T_{f} - T_{a}) = 10 \cdot \frac{3 R}{2} \cdot (284 - 300) = - 240 R$ . Option (C) correct.

$∴$ Correct options are (A), (B), (C).

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JEE Advanced 2026 Paper 2, Physics Section 2 Q5: Thermodynamic Processes

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