JEE Advanced 2025 · Paper 2 · Physics Q13

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PhysicsNumerical+4Question 29 of 48

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 $\dfrac32$ 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 $\dfrac{2L}{5}$ . In thermodynamic equilibrium, the piston is at a distance $\dfrac{L}{2}$ 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 $P = \dfrac{kL}{A}\alpha$ , then the value of $\alpha$ is _____.

A closed horizontal container of length L divided at its middle (L/2 from each end) by a vertical piston. In the left compartment a horizontal spring joins the left wall to the piston.

Your answer

Answer and worked solution

Official answer: 0.2

Pressures. The piston conducts heat, so both gases are at the same temperature. Both compartments have length $\frac L2$ , so the same volume. Then
$P_{left}=\frac{3/2}{1}P=1.5P.$

Spring. It is stretched by $\frac L2-\frac{2L}5=\frac L{10}$ , so it pulls the piston to the left with force $\frac{kL}{10}$ .

Force balance on the piston.
$1.5PA=PA+\frac{kL}{10}\implies P=\frac{kL}{A}\cdot0.2,\qquad\alpha=0.2.$

Topics:Ideal gas equation Newton's laws

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JEE Advanced 2025 · Paper 2, Physics question 13