JEE Main 2025 Jan 29 Shift 2, Physics Q2: Thermodynamic Processes

JEE Main2025Jan 29, Shift 2Physics

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

Assertion (A) : During compression of an ideal gas, the pressure increases more rapidly in an adiabatic process than in an isothermal process.

Reason (R) : In an isothermal process, $P V = constant$ , while in an adiabatic process, $P V^{γ} = constant$ , where $γ$ is the ratio of specific heats, $P$ is the pressure and $V$ is the volume of the ideal gas.

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

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

Solution

For an isothermal process,

$P V = constant$

$\Rightarrow \frac{d P}{d V} = - \frac{P}{V}$

For an adiabatic process,

$P V^{γ} = constant$

$\Rightarrow \frac{d P}{d V} = - γ \frac{P}{V}$

Since $γ > 1$ ,

$\frac{d P}{d V}_{adiabatic} > \frac{d P}{d V}_{isothermal}$

Hence, during compression, the pressure increases more rapidly in an adiabatic process than in an isothermal process.

$∴$ Assertion is True and Reason is True. Also, Reason is the correct explanation of the Assertion.

$Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.$

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JEE Main 2025 Jan 29 Shift 2, Physics Q2: Thermodynamic Processes

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