JEE MAIN - Physics (2025 - 24th January Evening Shift - No. 11)

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases.

Reason (R) : Free expansion of an ideal gas is an irreversible and an adiabatic process.

In the light of the above statements, choose the correct answer from the options given below :

Both $(\mathbf{A})$ and $(\mathbf{R})$ are true and $(\mathbf{R})$ is the correct explanation of $(\mathbf{A})$
Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
(A) is false but (R) is true
(A) is true but $(\mathbf{R})$ is false

Explanation

(A) $\mathrm{T}_1 \mathrm{~V}_1^{\gamma-1}=\mathrm{T}_2 \mathrm{~V}_2^{\gamma-1}$

Temp increases

R) Free expansion is assumed fast, so Adiabatic

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