Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process. Reason (R): In isothermal process, PV = constant, while in adiabatic process PVγ = constant. Here 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) (A) is true but (R) is false (b) Both (A) and (R) are true but (R) is NOT the correct explanation of (A) (c) (A) is false but (R) is true (d) Both (A) and (R) are true and (R) is the correct explanation of (A)

Answer: (d). Isothermal: PV = const ⇒ dV/dP = -V/P. Adiabatic: PVγ = const ⇒ dV/dP = -(V)/(γ P). Since γ > 1, volume falls faster with pressure in the isothermal process, so (A) is true. (R) gives exactly the relations used, so it explains (A). So the answer is (d).

Given below are two statements. One is labelled as Assertion (A) and… | JEE Main 2025 (29 Jan, Shift 2)

Q67JEE Main 2025 · 29 JAN · SHIFT 2Medium

Thermodynamic Processes

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

Assertion (A): With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.

Reason (R): In isothermal process, PV = constant, while in adiabatic process $PV^{\gamma}$ = constant. Here $\gamma$ 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:

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Answer: (d)

Isothermal: $PV =$ const $\Rightarrow \dfrac{dV}{dP} = -\dfrac{V}{P}$ .
Adiabatic: $PV^{\gamma} =$ const $\Rightarrow \dfrac{dV}{dP} = -\dfrac{V}{\gamma P}$ .
Since $\gamma > 1$ , volume falls faster with pressure in the isothermal process, so (A) is true.
(R) gives exactly the relations used, so it explains (A). So the answer is (d).

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