Question

The Carnot cycle consists of an alternate series of

• A. Two reversible isothermal processes and two reversible adiabatic processes
• B. Two reversible isobaric processes and two reversible adiabatic processes
• C. Two reversible isothermal processes and two reversible isobaric processes
• D. Two reversible isothermal processes and two polytropic processes

Hint:

The Carnot cycle achieves maximum efficiency and consists of two reversible isothermal processes (heat exchange) and two reversible adiabatic processes (no heat exchange).

Answer 1

The Correct Option is A

Step 1: Understand the Carnot cycle.
The Carnot cycle is a theoretical thermodynamic cycle that provides the maximum possible efficiency for a heat engine operating between two heat reservoirs. It is an idealized cycle consisting of four reversible processes, designed to achieve the highest efficiency as per the second law of thermodynamics.
Step 2: Identify the processes in the Carnot cycle.
The Carnot cycle consists of the following four processes, performed in a cyclic manner:
Process 1-2: Reversible isothermal expansion at a high temperature \( T_H \). The gas absorbs heat \( Q_H \) from the hot reservoir and expands, doing work while maintaining constant temperature.
Process 2-3: Reversible adiabatic expansion. The gas continues to expand and do work, but no heat is exchanged (\( Q = 0 \)), so the temperature decreases to the cold reservoir temperature \( T_C \).
Process 3-4: Reversible isothermal compression at the low temperature \( T_C \). The gas is compressed, rejecting heat \( Q_C \) to the cold reservoir while maintaining constant temperature.
Process 4-1: Reversible adiabatic compression. The gas is further compressed with no heat exchange (\( Q = 0 \)), increasing the temperature back to \( T_H \).
Thus, the cycle consists of:
Two reversible isothermal processes (one expansion, one compression),
Two reversible adiabatic processes (one expansion, one compression).
Step 3: Evaluate the options.
(1) Two reversible isothermal processes and two reversible adiabatic processes: Correct, as described above. Correct.
(2) Two reversible isobaric processes and two reversible adiabatic processes: Incorrect, as the Carnot cycle involves isothermal processes, not isobaric (constant pressure) processes. Incorrect.
(3) Two reversible isothermal processes and two reversible isobaric processes: Incorrect, as the Carnot cycle involves adiabatic processes, not isobaric processes. Incorrect.
(4) Two reversible isothermal processes and two polytropic processes: Incorrect, as the Carnot cycle specifically uses adiabatic processes, not polytropic processes (which follow \( PV^n = \text{constant} \)). Incorrect.
Step 4: Select the correct answer.
The Carnot cycle consists of two reversible isothermal processes and two reversible adiabatic processes, matching option (1).