JEE Main 2026 Apr 6 Shift 2, Physics Q5: Thermodynamic Processes

JEE Main2026Apr 6, Shift 2Physics

A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same $P, V, T$ . Heating is started from left side until pressure changes to $\frac{27 P}{8}$ . If initial volume of each compartment was 9 litres then the final volume in right-hand side compartment is ____ litres. (for this ideal gas $C_{P} / C_{V} = 1.5$ )

A
3
B
4
C
14
D
9

Solution

The piston is frictionless, so at equilibrium the right chamber pressure equals the left chamber pressure: $P_{R, f} = \frac{27 P}{8}$ .

The right side is compressed adiabatically (it is bounded by an adiabatic piston and adiabatic walls), so $P V^{γ} =$ constant with $γ = 1.5$ :

$P (9)^{3/2} = \frac{27 P}{8} V_{f}^{3/2}$

$(9)^{3/2} = 27$ , hence $27 = \frac{27}{8} V_{f}^{3/2}$ $\Rightarrow$ $V_{f}^{3/2} = 8$ $\Rightarrow$ $V_{f} = 4$ litres.

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JEE Main 2026 Apr 6 Shift 2, Physics Q5: Thermodynamic Processes

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