A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston

Question

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 $\frac{C_{p}}{C_{v}} = 1.5$ ) [2026]

Smart Achievers · Accepted Answer

(2)

$P_{Left} = P_{Right} = \frac{27 P}{8}$

$For right side process in Adiabatic$

$P_{i} V_{i}^{γ} = P_{f} V_{f}^{γ}$

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

$27 = \frac{27}{8} V_{f}^{3 / 2} \Rightarrow V_{f} = 4 litres$

Solution

1 3

2 4

3 14

4 9

Ans.
(2)

$P_{Left} = P_{Right} = \frac{27 P}{8}$

$For right side process in Adiabatic$

$P_{i} V_{i}^{γ} = P_{f} V_{f}^{γ}$

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

$27 = \frac{27}{8} V_{f}^{3 / 2} \Rightarrow V_{f} = 4 litres$

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Solution

1 3

2 4

3 14

4 9

Ans. (2) PLeft=PRight=27P8 For right side process in Adiabatic PiViγ=PfVfγ P(9)3/2=27P8×Vf3/2 27=278Vf3/2⇒Vf=4 litres

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Ans.
(2)

$P_{Left} = P_{Right} = \frac{27 P}{8}$

$For right side process in Adiabatic$

$P_{i} V_{i}^{γ} = P_{f} V_{f}^{γ}$

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

$27 = \frac{27}{8} V_{f}^{3 / 2} \Rightarrow V_{f} = 4 litres$