An isolated system consists of two perfectly sealed cuboidal compartments A and B separated by a movable rigid wall of cross-sectional area 0.1 m², as shown in the figure. Initially, the movable wall is held in place by latches L1 and L2 such that the volume of compartment A is 0.1 m³. Compartment A contains a monoatomic ideal gas at 5 bar and 400 K. Compartment B is perfectly evacuated and contains a massless Hookean spring of force constant 0.3 N/m at its equilibrium length (stored elastic energy is zero). The latches L1 and L2 are released, the wall moves to the right by 0.2 m, where it is held at the new position by latches L3 and L4. Assume all walls and latches are massless. The final equilibrium temperature, in K, of the gas in compartment A, rounded off to 1 decimal place, is _________

Question

Accepted Answer

The correct answer is 396.6 to 397. GATE 2024 official key: 396.6 to 397.0 K. Applying an energy balance to the isolated system (accounting for the free/irreversible nature of the expansion against the near-negligible spring resistance and the vacuum in compartment B) gives a final gas temperature of ≈396.8 K, per the official solution.