AIIMS 2006 Physics Carnot Cycle Assertion Reason Question

To understand the question and the correct answer, we need to delve into the concepts of the Carnot cycle, heat engines, and the efficiency of thermodynamic processes.

Analysis of the Assertion and Reason

Assertion: The Carnot cycle is useful in understanding the performance of heat engines.

Reason: The Carnot cycle provides a way of determining the maximum possible efficiency achievable with reservoirs of given temperatures.

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

Explanation of the Correct Answer

1. Understanding the Carnot Cycle: The Carnot cycle is an idealized thermodynamic cycle that provides a benchmark for the efficiency of all heat engines. It consists of four reversible processes:

   • Two isothermal processes (one at a high temperature $T_H$ and one at a low temperature $T_C$).
   • Two adiabatic processes.

2. Efficiency of a Carnot Engine: The efficiency $\eta$ of a Carnot engine can be expressed as:

   $$\eta = 1 - \frac{T_C}{T_H}$$

   where:

   • $T_C$ is the absolute temperature of the cold reservoir,
   • $T_H$ is the absolute temperature of the hot reservoir.

   This formula shows that the efficiency depends solely on the temperatures of the two reservoirs. The Carnot cycle establishes that no engine operating between these two temperatures can be more efficient than a Carnot engine.

3. Link Between Assertion and Reason: The assertion states that the Carnot cycle is useful for understanding heat engine performance, which is true, as it sets the maximum efficiency limit. The reason further clarifies that this cycle can determine the maximum possible efficiency based on the temperatures of the reservoirs, thus providing a clear explanation for the assertion. Hence, both are true, and the reason correctly explains why the assertion holds.

Clarification of Incorrect Options

• B) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion: This option is incorrect because the reason indeed explains how the Carnot cycle helps understand the performance of heat engines by determining maximum efficiency.

• C) Assertion is true but Reason is false: This option is incorrect as both the assertion and the reason are true. The reason is not false; it accurately describes the efficiency aspect of the Carnot cycle.

• D) Both Assertion and Reason are false: This option is incorrect because both the assertion and reason are true regarding the Carnot cycle's relevance in thermodynamics.

Summary

In conclusion, both the assertion and the reason are valid statements regarding the Carnot cycle's role in thermodynamics. The Carnot cycle not only aids in understanding the performance of heat engines but also provides a means to calculate the maximum efficiency achievable based on the temperatures of the heat reservoirs. Therefore, the correct answer is A.