Discussion
The temperature of the working fluid in a real heat engine cycle changes during heat addition and heat rejection processes. The maximum and minimum temperatures of the cycle are \(T_{\max}\) and \(T_{\min}\), respectively. If \(\eta_{C}\) is the thermal efficiency of a Carnot engine operating between these temperature limits, then the thermal efficiency, \(\eta\) of the real heat engine satisfies the relation
Answer: B
The real engine satisfies \(\eta \lt \eta_{C}\).
The Carnot efficiency \(\eta_{C} = 1 - T_{min}/T_{max}\) is the highest possible for any engine working between these temperature limits. A real engine falls short for two reasons: it is irreversible, and its heat is added and rejected over a range of temperatures, so the mean temperature of heat addition is below \(T_{max}\) and the mean temperature of rejection is above \(T_{min}\).
\(\eta \gt \eta_{C}\) would violate the second law, \(\eta = \eta_{C}\) needs a fully reversible engine with heat exchange only at the extremes, and \(1 + \eta_{C}\) exceeds 100%.
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