Question

Which of the following statements about the Carnot cycle is (are) incorrect? a) The maximum efficiency of a Carnot engine is \(100 \%\) since the Carnot cycle is an ideal process. b) The Carnot cycle consists of two isothermal processes and two adiabatic processes. c) The Carnot cycle consists of two isothermal processes and two isentropic processes (constant entropy). d) The efficiency of the Carnot cycle depends solely on the temperatures of the two thermal reservoirs.

Short answer

Answer: The correct statements about the Carnot cycle are B, C, and D.

Step-by-step solution

Statement A: Maximum Efficiency

The statement claim is that the maximum efficiency of a Carnot engine is \(100 \%\) since the Carnot cycle is an ideal process. This is incorrect. Although the Carnot cycle is an ideal process, it still obeys the laws of thermodynamics. No engine, even the ideal Carnot engine, can achieve \(100 \%\) efficiency as it would violate the second law of thermodynamics.

Statement B: Composition of the Carnot Cycle

The statement claim is that the Carnot cycle consists of two isothermal processes and two adiabatic processes. This statement is correct. The Carnot cycle consists of two reversible isothermal processes (heat exchange at constant temperature) and two reversible adiabatic processes (no heat exchange).

Statement C: Composition of Carnot Cycle (Isentropic Processes)

The statement claim is that the Carnot cycle consists of two isothermal processes and two isentropic processes (constant entropy). This statement is also correct. Isentropic processes are equivalent to adiabatic processes in a reversible system. Thus, the Carnot cycle has two isothermal processes and two reversible adiabatic (isentropic) processes.

Statement D: Efficiency Depends on Reservoir Temperatures

The statement claim is that the efficiency of the Carnot cycle depends solely on the temperatures of the two thermal reservoirs. This statement is correct. The efficiency of a Carnot engine is given by: \(\eta_{carnot} = 1 - \frac{T_{cold}}{T_{hot}}\), where \(T_{cold}\) and \(T_{hot}\) are the temperatures of the cold and hot reservoirs, respectively, in Kelvin. In summary, statement A is incorrect, and statements B, C, and D are correct.