A thermally insulated chamber of volume 2 V 0 is divided by a frictionless piston of area S into two equal parts A and B . Part A has an ideal gas at pressure P 0 and temperature T 0 and in part

Question

A thermally insulated chamber of volume $2 V_{0}$ is divided by a frictionless piston of area $S$ into two equal parts $A$ and $B$ . Part $A$ has an ideal gas at pressure $P_{0}$ and temperature $T_{0}$ and in part $B$ is vacuum. A massless spring of force constant $k$ is connected with piston and the wall of the container as shown. Initially spring is unstretched. Gas in chamber $A$ is allowed to expand. Let in equilibrium spring is compressed by $x_{0}$ . Then

TestHub · Accepted Answer

Equilibrium of piston gives PS = k x 0 ​ or P = S k x 0 ​ ​ Since, the chamber is thermally insulated Δ Q = 0 ∴ Elastic potential energy of spring = work done by gas or work done by gas = 2 1 ​ k x 0 2 ​ This work is done in the expense of internal energy of the gas. Therefore, internal energy of the gas is decreased by 2 1 ​ k x 0 2 ​ . Internal energy of an ideal gas depends on its temperature only. Internal energy of the gas is decreasing. Therefore, temperature of the gas will decrease.

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JEE Advanced 2026