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🔥 Carnot Efficiency Calculator
Enter hot and cold temperatures
What these results mean
η
Carnot efficiency = maximum work extractable per unit of heat absorbed from hot reservoir
W
Work output = η × Q_h (where Q_h is heat absorbed from hot reservoir)
Q_c
Heat rejected to cold reservoir = Q_h × (1 − η) = Q_h × T_c/T_h
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The Carnot Cycle
The Carnot cycle defines the upper limit of efficiency for any heat engine. No real engine can exceed Carnot efficiency while operating between the same two temperatures — this is a consequence of the Second Law of Thermodynamics.
- Real steam power plant: T_h ≈ 565°C (838 K), T_c ≈ 35°C (308 K) → η_Carnot ≈ 63%
- Actual thermal efficiency of a real power plant: 30–45% (due to irreversibilities)
- Car engine: η_Carnot ≈ 55%, real ≈ 20–30%
Refrigerators and Heat Pumps
For a Carnot refrigerator (running backwards): COP = T_c / (T_h − T_c). This gives the cooling effect per unit work input.
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