Carnot efficiency calculator
No heat engine between two temperatures can beat the Carnot limit. Run it backwards and the same ratio gives the best possible heat pump.
Maximum efficiency
61.4370%
- Maximum work from the heat supplied
- 614.369 79
- Heat that must be rejected
- 385.630 21
- Best heat pump COP
- 1.6277
- Best refrigerator COP
- 0.6277
Show the working
- Hot reservoir = 500
- Cold reservoir = 25
- Heat supplied = 1000
- th = 500 + 273.15 = 773.15
- tc = 25 + 273.15 = 298.15
- Maximum efficiency = 773.15 > 0 ? (1 - 298.15/773.15) * 100 : 0 = 61.437
- Maximum work from the heat supplied = 1000 * 61.437 / 100 = 614.37
- Heat that must be rejected = 1000 - 614.37 = 385.63
- Best heat pump COP = (773.15 - 298.15) != 0 ? 773.15/(773.15 - 298.15) : 0 = 1.627 68
- Best refrigerator COP = (773.15 - 298.15) != 0 ? 298.15/(773.15 - 298.15) : 0 = 0.627 684
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- Carnot efficiency = 1 - Tc/Th, with both in kelvin
- heating COP = Th / (Th - Tc), cooling COP = Tc / (Th - Tc)
Real engines reach perhaps half to two thirds of the Carnot figure. A combined-cycle gas turbine at 60% is close to the practical ceiling.
The COP result is why a heat pump can deliver more heat energy than the electricity it consumes: it is moving heat, not making it.