Carnot Efficiency Calculator
The upper limit set by the second law of thermodynamics.
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Carnot efficiency
Carnot efficiency
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Maximum work output (kJ)
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Minimum heat rejected (kJ)
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Carnot Efficiency Calculator by TheCalcTools
How the Carnot Efficiency Calculator works
Enter the hot and cold reservoir temperatures in °C.
They are converted to kelvin, because the law needs absolute temperature.
Efficiency is 1 minus the ratio of cold to hot temperature.
The formula
η = 1 − T_cold ÷ T_hot (kelvin)W = η × Q_in
Worked example
Using the default values shown in the calculator:
| Hot reservoir temperature (°C) | 500 |
|---|---|
| Cold reservoir temperature (°C) | 25 |
| Heat input (kJ) | 1000 |
- T_hot = 773.15 K, T_cold = 298.15 K. η = 1 − 298.15 ÷ 773.15 = 61.44%.
- From 1,000 kJ of heat, at most 614.4 kJ becomes work, and at least 385.6 kJ is rejected.
Result:
| Carnot efficiency | 61.44% |
|---|---|
| Maximum work output (kJ) | 614.4 |
| Minimum heat rejected (kJ) | 385.6 |
Frequently asked questions
Can a real engine reach Carnot efficiency?
No. Friction, heat loss and finite-speed operation always keep real engines below the Carnot limit.
How can efficiency be raised?
Increase the hot temperature or lower the cold temperature. Practical limits include materials and ambient conditions.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.