JEE Main · 2025 · 24 Jan 2025 · Shift 2 · Heat & Thermodynamics

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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 statement, choose the correct answer from the options given below :

(A)Both (A) and (R) are true and (R) is the correct explanation of (A)
(B)(A) is true but (R) is false
(C)(A) is false but (R) is true✓ Correct
(D)Both (A) and (R) are true but (R) is NOT the correct explanation of (A)

Answer: (C)

Solution

For an adiabatic process on an ideal gas,

T V^{γ - 1} = constant

. If the volume is shrunk to half,

V_{2} = V_{1} /2

, then

T_{1} V_{1}^{γ - 1} = T_{2} (\frac{V _{1}}{2})^{γ - 1} ⟹ T_{2} = T_{1} \cdot 2^{γ - 1} .

Since

γ > 1

for every gas,

2^{γ - 1} > 1

, so

T_{2} > T_{1}

: adiabatic compression to half the volume raises the temperature, it does not lower it. Assertion (A) is therefore false.

Free expansion of an ideal gas happens into a vacuum with no heat exchanged (

Q = 0

, adiabatic) and no external work done, but it is not a sequence of equilibrium states, so it cannot be reversed by a small change in conditions — it is inherently irreversible. Reason (R) is a true, independent statement about free expansion, and correctly describes it.

Since (A) is false and (R) is true, the correct choice is: (A) is false but (R) is true.

JEE Main · 2025 · 24 Jan 2025 · Shift 2 · Single correct option

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JEE Main · 2025 · 24 Jan 2025 · Shift 2 · Heat & Thermodynamics

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