A thermally isolated container of length L is divided by a thermally conducting movable piston of area A. The left and right compartments contain 3/2 and 1 moles of ideal gas. A spring of constant k and natural length 2L/5 connects the left wall to the piston. At equilibrium the piston is at L/2. If the right-side pressure is P = (kL/A)α, find α. Image
Physics · Circular Motion
JEE Advanced 2025 Paper 2

Question

A thermally isolated container of length L is divided by a thermally conducting movable piston of area A. The left and right compartments contain 3/2 and 1 moles of ideal gas. A spring of constant k and natural length 2L/5 connects the left wall to the piston. At equilibrium the piston is at L/2. If the right-side pressure is P = (kL/A)α, find α. Image

Physics · Circular Motion

JEE Advanced 2025 Paper 2

G1 Physics · Accepted Answer

The piston is thermally conducting, so both gases have the same temperature. Their volumes are equal, AL/2. Since the left side contains 3/2 moles and the right side contains 1 mole, left pressure / right pressure = 3/2. Let the right-side pressure be P. Then the pressure difference is P/2. The spring length is L/2 and its natural length is 2L/5, so the extension is x = L/2 − 2L/5 = L/10. Mechanical equilibrium gives (P/2)A = kL/10. Hence P = kL/(5A). Comparing with P = (kL/A)α, we get α = 1/5…