JEE Advanced · 2025 · 18 May 2025 · Paper 2 · Heat & Thermodynamics

The left and right compartments of a thermally isolated container of length

L

are separated by a thermally conducting, movable piston of area

A

. The left and right compartments are filled with

\frac{3}{2}

and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant k and natural length

\frac{2 L}{5}

. In thermodynamic equilibrium, the piston is at a distance

\frac{L}{2}

from the left and right edges of the container as shown in the figure. Under the above conditions, if the pressure in the right compartment is

P = \frac{k L}{A} α

, then the value of

α

is ____

Answer: 0.2

Solution

Extension of spring:

x = 0.5 L - 0.4 L = 0.1 L

.

Force balance on piston:

k x + P_{2} A = P_{1} A

Since temperatures are equal (thermal equilibrium) and volumes are equal (both

L /2

\frac{n _{1} R T}{V _{1}} = P_{1}, \frac{n _{2} R T}{V _{2}} = P_{2}

\frac{P _{1}}{P _{2}} = \frac{n _{1}}{n _{2}} = \frac{3/2}{1} = \frac{3}{2}

From force balance:

P_{2} = P_{1} - \frac{k x}{A} = \frac{3}{2} P_{2} - \frac{k ( 0.1 L )}{A}

\frac{P _{2}}{2} = \frac{k L}{10 A} ⟹ P_{2} = \frac{k L}{5 A}

Therefore

α = \frac{1}{5} = 0.20

JEE Advanced · 2025 · 18 May 2025 · Paper 2 · Numerical answer