A cylinder with adiabatic walls is closed at both ends and is divided… | JEE Main 2026 (6 Apr, Shift 2)

Q50JEE Main 2026 · 6 APR · SHIFT 2Difficult

Thermodynamic Processes

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 $27P/8$ . If initial volume of each compartment was 9 litres then the final volume in right-hand side compartment is ______ litres. (for this ideal gas $C_P/C_V = 1.5$ )

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Answer: (b)

The right compartment is compressed adiabatically by the piston: $PV^{\gamma} =$ constant with $\gamma = 1.5$ .
Pressure on both sides is equal, so right side ends at $\frac{27P}{8}$ .
$V_2 = 9\left(\frac{P}{27P/8}\right)^{1/1.5} = 9\left(\frac{8}{27}\right)^{2/3} = 9 \times \frac{4}{9}$
$V_2 = 4$ litres, so the answer is (b).

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