Logo
Jeeify
MCQMediumJEE 2025Isothermal & Adiabatic Processes

JEE Physics 2025 Question with Solution

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 an isothermal process, PV=constantPV = \text{constant}, while in an adiabatic process PVγ=constantPV^\gamma = \text{constant}. Here, γ\gamma is the ratio of specific heats, PP is the pressure and VV 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

Answer

Correct answer:D

Step-by-step solution

Standard Method

Given: Assertion (A) states that with increase in pressure, volume falls off more rapidly in an isothermal process than in an adiabatic process.

Find: Which option correctly evaluates Assertion (A) and Reason (R).

For an isothermal process,

PV=constantPV = \text{constant}

so,

V∝1PV \propto \frac{1}{P}

For an adiabatic process,

PVγ=constantPV^\gamma = \text{constant}

so,

V∝P−1γV \propto P^{-\frac{1}{\gamma}}

Since γ>1\gamma > 1, the variation of volume with pressure is steeper for the adiabatic process. Therefore, volume decreases more rapidly with increasing pressure in the adiabatic process, not in the isothermal process.

Hence, Assertion (A) is false.

Reason (R) correctly states that

PV=constantPV = \text{constant}

for an isothermal process and

PVγ=constantPV^\gamma = \text{constant}

for an adiabatic process.

Therefore, Reason (R) is true.

The correct option is D.

Stepwise Comparison of Processes

Given:

  • Assertion (A): With the increase in pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.
  • Reason (R): In an isothermal process, PV=constantPV = \text{constant}, while in an adiabatic process PVγ=constantPV^\gamma = \text{constant}.

Find: Whether Assertion (A) and Reason (R) are true or false.

Step 1: Understanding the relations

For an isothermal process,

PV=constant⇒V∝1PPV = \text{constant} \Rightarrow V \propto \frac{1}{P}

For an adiabatic process,

PVγ=constant⇒V∝P−1γPV^\gamma = \text{constant} \Rightarrow V \propto P^{-\frac{1}{\gamma}}

Step 2: Compare the dependence on pressure

Since γ>1\gamma > 1, we have

∣−1∣>∣−1γ∣\left|-1\right| > \left|-\frac{1}{\gamma}\right|

The solution text concludes that the volume decreases more rapidly in the adiabatic process as pressure increases.

Step 3: Evaluate Assertion (A)

Assertion (A) says that the volume decreases more rapidly in the isothermal process. This is opposite to the conclusion stated in the solution.

So, Assertion (A) is false.

Step 4: Evaluate Reason (R)

Reason (R) correctly gives the equations for isothermal and adiabatic processes.

So, Reason (R) is true.

Therefore, the correct answer is D, that is, (A) is false but (R) is true.

Common mistakes

  • A common mistake is to assume that because PV=constantPV = \text{constant} looks simpler than PVγ=constantPV^\gamma = \text{constant}, the isothermal volume must decrease faster. This is wrong because the comparison must be made from how VV depends on PP, not from the visual form of the equation. Rewrite both relations in terms of VV versus PP before comparing.

  • Students often judge the assertion only from the truth of the reason. This is incorrect because in Assertion–Reason questions, a true reason does not guarantee a true assertion. First test Assertion (A) independently, then verify whether Reason (R) is true.

  • Another mistake is to forget that γ>1\gamma > 1 for an ideal gas. Without using this fact, the comparison between isothermal and adiabatic processes remains incomplete. Always use the condition on γ\gamma before deciding which process shows a faster change in volume.

Practice more Isothermal & Adiabatic Processes questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step — free to start.

Start free trialMore on Isothermal & Adiabatic Processes

Related questions