Question

The graph that represents the temperature (T) – entropy (S) variation of a Carnot cycle is 

 

• A. (A)
• B. (B)
• C. (C)
• D. (D)

Hint:

In T-S diagrams for the Carnot cycle, the isothermal processes are represented by horizontal lines, while the adiabatic processes are vertical lines.

Answer 1

The Correct Option is B

The Carnot cycle is an idealized thermodynamic cycle that provides the maximum possible efficiency for a heat engine. It consists of four reversible processes: two isothermal processes and two adiabatic processes. The temperature (T) versus entropy (S) diagram for the Carnot cycle is crucial in understanding the cycle's operation:

1. Isothermal Expansion: During this process, the system absorbs heat from a high-temperature reservoir at a constant temperature, and entropy increases.
2. Adiabatic Expansion: In this stage, the system expands without exchanging heat (adiabatically), causing a temperature drop and entropy remains constant.
3. Isothermal Compression: The system releases heat to a low-temperature reservoir at constant temperature, and entropy decreases.
4. Adiabatic Compression: Finally, the system compresses adiabatically, causing a rise in temperature with constant entropy.

The temperature-entropy (T-S) graph for the Carnot cycle is a rectangle, where the horizontal lines represent isothermal processes, and the vertical lines represent adiabatic processes.

Based on this understanding, Option (B) correctly represents the T-S diagram of a Carnot cycle:

• The horizontal lines show entropy change during the isothermal processes.
• The vertical lines indicate the temperature change during adiabatic processes.

Conclusion: The correct graph for the T-S diagram of a Carnot cycle is Option (B).