Ideal heat engine benchmark – identifying the four processes of the Carnot cycle Which set of processes correctly describes a complete Carnot cycle?

Introduction / Context:The Carnot cycle is the theoretical standard of heat-engine efficiency. It defines the maximum possible efficiency between two thermal reservoirs and serves as a benchmark for real cycles.

Given Data / Assumptions:

• Two heat reservoirs at temperatures Th (hot) and Tc (cold).
• System (often an ideal gas) undergoing reversible processes.
• No irreversibilities (quasi-equilibrium, no friction, infinitesimal temperature differences for heat transfer).

Concept / Approach:The Carnot cycle comprises four reversible processes: (1) isothermal expansion at Th while absorbing heat, (2) isentropic (adiabatic, reversible) expansion from Th to Tc, (3) isothermal compression at Tc while rejecting heat, and (4) isentropic compression back to the initial state. This combination ensures the highest efficiency possible between Th and Tc.

Step-by-Step Solution:Identify heat addition at constant temperature → isothermal at Th.Follow with adiabatic reversible expansion → entropy constant.Compress isothermally at Tc to reject heat.Finish with adiabatic reversible compression to close the cycle.

Verification / Alternative check:Efficiency expression η = 1 − Tc/Th derives directly from these steps, relying on the isothermal heat transfers and isentropic links that preserve reversibility and define temperature limits.

Why Other Options Are Wrong:

• Constant-volume or constant-pressure pairs do not produce the Carnot efficiency relation.
• Mixed CP/CV sequences are characteristic of other idealized cycles (e.g., Otto, Diesel), not Carnot.

Common Pitfalls:Equating “adiabatic” with “isentropic” without the reversibility qualifier; Carnot specifically requires reversible adiabats (isentropes).

Final Answer:two isothermal and two isentropic processes