Heat Engine Efficiency

Carnot bound, Curzon-Ahlborn endoreversible efficiency & power output

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Carnot η_C = 1−T_C/T_H
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Curzon-Ahlborn η_CA = 1−√(T_C/T_H)
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Current efficiency η
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Power output (rel.)
800 K
300 K
0.20
0.50
The Carnot efficiency η_C = 1 − T_C/T_H is the maximum for any reversible engine. But reversible processes are infinitely slow → zero power. The Curzon-Ahlborn (endoreversible) engine maximizes power output, achieving η_CA = 1 − √(T_C/T_H). Real engines operate between these bounds. The power-efficiency curve shows the fundamental tradeoff: maximum efficiency occurs at zero power, maximum power at η_CA. Increasing heat leak α (irreversibility) shifts the operating point inward.