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. \text{In the light of the above statements, choose the correct answer from the options given below:}
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. \text{In the light of the above statements, choose the correct answer from the options given below:}
Show Hint
- Both (A) and (R) are true but (R) is false
- Both (A) and (R) are true and (R) is the correct explanation of (A)
- Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
- (A) is false but (R) is true
The Correct Option is C
Solution and Explanation
- 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).
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