JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Heat & Thermodynamics

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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✓ Correct
(C)14
(D)9

Answer: (B)

Solution

The piston is free, so at the end the pressures on the two sides are equal,

P_{f} = \frac{27 P}{8}

. The right-hand gas, untouched by the heater, is compressed adiabatically and obeys

P V^{γ} = const

with

γ = 1.5

P (9)^{1.5} = \frac{27 P}{8} V_{f}^{1.5}

. Since

9^{1.5} = 27

, this gives

V_{f}^{1.5} = 8

, so

V_{f} = 8^{2/3} = 4 litres

JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Single correct option

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JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Heat & Thermodynamics

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