AIIMS 2006 Physics Entropy Assertion Reason Question

To analyze the given question regarding entropy in an isolated system, we will evaluate both the assertion and the reason provided.

Assertion: In an isolated system the entropy increases.

This statement is true. In thermodynamics, the second law states that the total entropy of an isolated system can never decrease over time. Entropy, a measure of disorder or randomness, tends to increase as energy is dispersed throughout the system. For an isolated system, where no matter or energy is exchanged with the surroundings, processes that occur tend to lead to a state of greater disorder, hence an increase in entropy.

Reason: The processes in an isolated system are adiabatic.

This statement is also true, but it is not the correct explanation for why entropy increases in an isolated system. An adiabatic process is one where no heat is exchanged with the surroundings. While it is true that processes in an isolated system can be adiabatic, the increase in entropy is not solely due to the adiabatic nature of these processes. Instead, the increase in entropy is a result of the natural tendency of systems to evolve towards thermodynamic equilibrium, which generally corresponds to a state of maximum entropy.

Conclusion

Given the above analysis:

• The assertion (A) is true.
• The reason (R) is true, but R does not correctly explain A.

Therefore, the correct answer is Option B: "A is true, R is true but R is not the correct explanation of A."

Why Other Options Are Incorrect:

• Option A: This option states that both A and R are true and that R is the correct explanation of A. This is incorrect because, while both statements are true, R does not provide a valid explanation for A.

• Option C: This option claims that A is true and R is false. Since both A and R are true, this option is incorrect.

• Option D: This option asserts that both A and R are false. Since we have established that both are true, this option is also incorrect.

Relevant Concepts:

1. Second Law of Thermodynamics: It states that the total entropy of an isolated system can never decrease; it can only increase or remain constant in reversible processes.

2. Adiabatic Process: A process where no heat is transferred to or from the system.

3. Entropy Change: For an isolated system, the change in entropy can be expressed as: $\Delta S \geq 0$ where $\Delta S$ is the change in entropy, indicating that it is always greater than or equal to zero.

In summary, the assertion about the increase in entropy in isolated systems is true, while the reasoning provided does not correctly explain this phenomenon, leading us to the conclusion that Option B is the correct choice.