Physics Q30 – JEE-MAIN 2026

Home Physics ThermodynamicsQuestion #514

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

. Heating is started from left side until pressure changes to

\frac{27}{8} P

. 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

)

Clue 1 of 3: Identify the process

The right compartment is separated by an adiabatic piston and the cylinder walls are adiabatic, implying an adiabatic process for the gas in the right compartment.

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Step 1: Identify the process for the right compartment✦ Active

The cylinder has adiabatic walls, and the piston dividing the compartments is also adiabatic and frictionless. This means that the gas in the right compartment undergoes an adiabatic process.

Step 2: Apply the adiabatic equation and pressure equilibrium○ Expand

For an adiabatic process, $P V^{γ} = constant$ . So, for the right compartment: $P_{R} V_{R}^{γ} = P_{R}^{'} V_{R}^{' γ}$ . We are given initial conditions $P_{R} = P$ , $V_{R} = 9$ L, and $γ = C_{P} / C_{V} = 1.5 = 3 / 2$ . Since the piston is frictionless, the pressure on both sides must be equal at equilibrium. Thus, the final pressure in the right compartment $P_{R}^{'}$ is equal to the final pressure in the left compartment $P_{L}^{'}$ , which is given as $P_{L}^{'} = \frac{27}{8} P$ . Therefore, $P_{R}^{'} = \frac{27}{8} P$ .

Step 3: Calculate the final volume of the right compartment○ Expand

Substitute the known values into the adiabatic equation:

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

Cancel $P$ from both sides and simplify:

(9)^{3 / 2} = \frac{27}{8} V_{R}^{' 3 / 2}

(\sqrt{9})^{3} = \frac{27}{8} V_{R}^{' 3 / 2}

3^{3} = \frac{27}{8} V_{R}^{' 3 / 2}

27 = \frac{27}{8} V_{R}^{' 3 / 2}

1 = \frac{1}{8} V_{R}^{' 3 / 2}

V_{R}^{' 3 / 2} = 8

To find $V_{R}^{'}$ , raise both sides to the power of $2 / 3$ :

V_{R}^{'} = (8)^{2 / 3} = (2^{3})^{2 / 3} = 2^{2} = 4 litres

💡 Teacher's Secret Hint

Ensure correct handling of fractional exponents.

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Physics Question 30 – JEE-MAIN 2026

Clue 1 of 3: Identify the process

🧠 Full Solution Path