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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): 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:\text{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 false

  • B

    Both (A) and (R) are true and (R) is the correct explanation of (A)

  • C

    Both (A) and (R) are true but (R) is NOT the correct explanation of (A)

  • D

    (A) is false but (R) is true

Answer

Correct answer:C

Step-by-step solution

Standard Method

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

Find: Which option correctly describes the truth of Assertion (A) and Reason (R).

From the solution, the conclusion given is that Assertion (A) is true and Reason (R) is also true, but Reason (R) is not the correct explanation of Assertion (A).

Reason (R) states that free expansion of an ideal gas is an irreversible and adiabatic process. This statement is true.

However, free expansion is a different thermodynamic process from adiabatic shrinking or compression. Therefore, even if Reason (R) is true, it does not explain Assertion (A).

Hence, the correct choice according to the extracted solution is: Both (A) and (R) are true but (R) is NOT the correct explanation of (A).

The correct option is C.

Note: The second approach in the solution contains an internal inconsistency in its explanation of adiabatic compression, but its final marked answer still identifies option C. Since the solution explicitly declares The Correct Option is C, that is taken as the final answer.

Using the Provided Explanation

Given:

  • Assertion (A) discusses a gas in an insulated container being adiabatically shrunk to half of its initial volume.
  • Reason (R) states that free expansion of an ideal gas is an irreversible and adiabatic process.

Find: The correct relation between Assertion (A) and Reason (R).

The hint says that in adiabatic processes there is no heat transfer, and temperature change depends on the work done by or on the system. It also states that free expansion is different from compression and does not affect temperature in the same way.

So, the solution evaluates the statements as follows:

  1. Assertion (A) is taken as true in the provided solution.
  2. Reason (R) is also taken as true.
  3. But Reason (R) is not the correct explanation of Assertion (A), because free expansion is not the same process as adiabatic shrinking.

Thus, the answer extracted from the solution is:

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

Therefore, the correct option is C.

Common mistakes

  • Confusing adiabatic compression with free expansion. These are different processes, so a true statement about free expansion does not automatically explain what happens during shrinking or compression.

  • Assuming that if both Assertion and Reason are true, then the Reason must explain the Assertion. In assertion-reason questions, truth and explanation are checked separately.

  • Relying only on the raw wording of the assertion without comparing it to the process named in the reason. The correct method is to test each statement independently and then check the explanatory link.

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