AIIMS 2006 Physics Entropy Assertion Reason Question

To address the question comprehensively, we need to analyze both the Assertion and the Reason in the context of thermodynamics, particularly focusing on the concepts of entropy and the second law of thermodynamics.

Assertion:

"When a glass of hot milk is placed in a room and allowed to cool, its entropy decreases."

This assertion is false. When the hot milk cools down, it is losing heat to the surroundings (the room). According to the second law of thermodynamics, the total entropy of an isolated system must increase over time.

When the hot milk cools, its temperature decreases, which may suggest a decrease in its entropy; however, the entropy of the surroundings (the room) increases significantly more due to the heat transfer from the milk to the environment. Hence, while the entropy of the milk may decrease, the overall entropy of the system (milk + surroundings) increases. Therefore, the assertion that the entropy of the milk decreases is incorrect.

Reason:

"Allowing a hot object to cool does not violate the second law of thermodynamics."

This reason is true. The second law of thermodynamics states that the total entropy of an isolated system will not decrease over time; it can either increase or remain constant. When a hot object such as a glass of milk cools down, it releases heat into its surroundings, leading to an increase in the entropy of the surrounding environment. This process does not violate the second law. Instead, it illustrates the principle that while local decreases in entropy can occur, the total entropy (milk + surroundings) must increase.

Conclusion:

Given the analysis above, we find that:

• The Assertion is false (the entropy of the milk does not decrease).
• The Reason is true (cooling does not violate the second law).

Thus, the correct answer is B): Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

Why Other Options Are Incorrect:

• Option A: Both Assertion and Reason are true and Reason is the correct explanation of Assertion. (Incorrect because the Assertion is false.)
• Option C: Assertion is true but Reason is false. (Incorrect because the Reason is true.)
• Option D: Both Assertion and Reason are false. (Incorrect because the Reason is true.)

Relevant Concepts:

1. Entropy ($S$): A measure of the disorder or randomness in a system. When heat energy is transferred from a hot object to a cooler one, the system's entropy can be calculated using the formula:

   $\Delta S = \frac{Q}{T}$

   where $Q$ is the heat transferred and $T$ is the temperature in Kelvin. The total change in entropy must account for both the milk and the surroundings.

2. Second Law of Thermodynamics: In any natural thermodynamic process, the total entropy of a system and its surroundings will either increase or remain constant.

By understanding these concepts, students can better grasp the relationship between heat transfer, entropy, and the laws of thermodynamics, allowing for a clearer understanding of this question and similar scenarios in thermodynamic systems.