Reversible vs. irreversible heat engines In classical thermodynamics, what is the correct statement about the efficiencies of reversible engines compared with irreversible engines operating between the same two heat reservoirs?

Introduction / Context:
Heat-engine efficiency is a cornerstone concept in thermodynamics. The Carnot framework compares any engine against an ideal reversible benchmark operating between two fixed temperature reservoirs. This question checks whether you recognize the unique property of reversible engines and how their efficiency compares with that of irreversible (real) engines.

Given Data / Assumptions:

• Two thermal reservoirs at fixed temperatures Th (hot) and Tc (cold).
• Engines may be reversible (idealized, no dissipation) or irreversible (real, with friction, gradients, losses).
• All engines considered operate in cycles between the same Th and Tc.

Concept / Approach:

The Carnot theorem states two key results: (1) No engine operating between given reservoirs can be more efficient than a reversible engine operating between the same reservoirs; and (2) All reversible engines operating between the same two reservoirs have the same efficiency, which depends only on Th and Tc. Therefore, reversibility defines an upper bound that real engines can only approach but never exceed.

Step-by-Step Solution:

Verification / Alternative check:

Consider connecting a reversible engine to drive a reversible refrigerator between the same reservoirs. If two reversible engines had different efficiencies, one could form a perpetual motion of the second kind by cycling heat and work contradictorily—impossible by the Second law—thus they must have identical efficiencies.

Why Other Options Are Wrong:

Same efficiency for reversible and irreversible: violates Carnot’s inequality.Irreversible engines have maximum efficiency: false; irreversibility reduces efficiency.All engines are designed reversible: real designs can only approximate reversibility.Reversible less efficient than irreversible: contradicts the Second law.

Common Pitfalls:

Confusing “highly efficient” with “reversible.” Reversible is an idealization with zero entropy production; practical engines always incur losses, so their efficiencies depend on design, but all lie below the reversible limit.

Final Answer:

All the reversible engines have the same efficiency.