Carnot Efficiency
The maximum possible efficiency of any heat engine working between two temperatures — and the best possible performance (COP) of a refrigerator or heat pump. Enter temperatures in kelvin, Celsius or Fahrenheit.
What is the Carnot Limit?
A heat engine turns part of the heat flowing from a hot place to a cold place into work. In 1824 Sadi Carnot showed that no engine can beat an ideal, perfectly reversible engine running between the same two temperatures — whatever its design or working fluid.
The limit depends only on the temperatures, measured in kelvin. Some heat must always be dumped into the cold reservoir; that is the second law of thermodynamics. Real engines lose more through friction and finite-speed heat transfer, typically reaching 40–70% of the Carnot limit.
Energy Flow
η = 50%Real Engines vs the Limit
| Machine | Th / Tc | Carnot | Actual |
|---|---|---|---|
| Combined-cycle gas plant | 1700 / 300 K | 82% | ~60% |
| Coal power station | 840 / 300 K | 64% | ~38% |
| Nuclear (PWR) | 590 / 300 K | 49% | ~33% |
| Car petrol engine | 2300 / 300 K | 87% | 25–30% |
| Ocean thermal (OTEC) | 298 / 278 K | 6.7% | ~3% |
Key Ideas
The formula only works on the absolute scale. Plugging in Celsius gives nonsense — this calculator converts for you.
Energy is conserved: whatever heat is not turned into work must flow into the cold reservoir.
Run the engine backwards and work pumps heat uphill. The COP can exceed 1: a heat pump delivers several joules of heat per joule of electricity.
Sources & Verification
- Y. A. Çengel & M. A. Boles, Thermodynamics: An Engineering Approach, 8th ed., McGraw-Hill, 2015 — Ch. 6 (The Second Law of Thermodynamics).
- D. Halliday, R. Resnick & J. Walker, Fundamentals of Physics, 10th ed., Wiley, 2014 — Ch. 20 (Entropy and the Second Law of Thermodynamics).