Question

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:

• 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

Hint:

In thermodynamic processes, adiabatic processes involve no heat transfer, and the temperature change is due to the work done by or on the system. Free expansion is different from compression and does not affect the temperature in the same way.

Answer 1

The Correct Option is C

- Assertion (A) is true: When a gas is adiabatically compressed to half its initial volume, the temperature decreases. This is a result of the first law of thermodynamics and the fact that no heat is exchanged in an adiabatic process.

- Reason (R) is also true: Free expansion of an ideal gas is an irreversible and adiabatic process. However, it is not the correct explanation of Assertion (A) because free expansion does not involve compression or a change in volume as described in Assertion (A). Free expansion involves no work and no change in internal energy.

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

Answer 2

Step 1: Analyze the assertion (A).
The assertion states: "In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases." This is consistent with the principles of an adiabatic process. In an adiabatic process, there is no heat exchange with the surroundings. For an ideal gas undergoing adiabatic compression, its internal energy increases due to the work done on the gas, which results in an increase in temperature. However, in the case of adiabatic expansion (not compression), the temperature would decrease. Thus, the assertion that the temperature decreases in the case of adiabatic compression contradicts the expected behavior in an adiabatic process.

Step 2: Analyze the reason (R).
The reason states: "Free expansion of an ideal gas is an irreversible and an adiabatic process." Free expansion is indeed an adiabatic process, as there is no heat exchange with the surroundings. However, it is an irreversible process because the gas expands without performing any work, and the process is not controlled. The reason is true but does not explain the assertion about the temperature behavior during adiabatic compression.

Step 3: Conclusion.
- The assertion (A) is partially incorrect because adiabatic compression typically results in an increase in temperature, not a decrease. - The reason (R) is true but does not explain why the temperature decreases in the given situation.

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