AIIMS 2007 Physics Entropy Assertion Reason Question

To analyze the given question, we need to understand the concepts of entropy, free expansion, and the nature of natural processes.

Assertion:

In free expansion of an ideal gas, the entropy increases.

In a free expansion, an ideal gas expands into a vacuum without doing any work on the surroundings and without heat exchange (adiabatic process). Since the gas is expanding freely, it occupies a larger volume, leading to an increase in the number of accessible microstates (configurations of particles) available to the gas molecules.

The change in entropy ($\Delta S$) for a system can be defined using the formula:

$$\Delta S = k \ln \Omega$$

Where $k$ is the Boltzmann constant and $\Omega$ is the number of accessible microstates. As the volume increases, $\Omega$ increases, leading to an increase in entropy. Thus, the assertion is true.

Reason:

Entropy increases in all natural processes.

This statement is indeed a generalization of the second law of thermodynamics, which states that the total entropy of an isolated system can never decrease over time. In natural processes, spontaneous changes lead to an increase in entropy, making this reason true.

Conclusion on Options:

Given that both the assertion and the reason are true, we need to determine if the reason provides the correct explanation for the assertion.

1. Correct Answer: A) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

   • Since both the assertion and the reason are true and the reason explains why the entropy increases in free expansion (as it is a natural process), option A is correct.

Why Other Options Are Incorrect:

• B) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

  • This option is incorrect because the reason does explain the assertion well. Both are true and the reason logically supports the assertion.

• C) Assertion is true but Reason is false.

  • This option is incorrect as both the assertion and reason are true.

• D) Both Assertion and Reason are false.

  • This option is incorrect since we have established that both statements are true.

Summary:

In summary, the correct answer is A, because both the assertion about the increase in entropy during the free expansion of an ideal gas and the general principle that entropy increases in natural processes are true, with the reason providing a valid explanation for the assertion. Understanding the principles of thermodynamics and entropy is crucial for tackling such questions effectively.