About the Carnot Efficiency Calculator
What is the Carnot Efficiency Calculator?
No heat engine can be more efficient than a Carnot engine working between the same two temperatures. The Carnot efficiency sets that upper limit from the hot and cold temperatures alone.
The same temperatures give the best possible coefficient of performance (COP) for refrigerators and heat pumps.
How to use the Carnot Efficiency Calculator
- Hot Reservoir Temperature (°C) (sample: 500)
- Cold Reservoir Temperature (°C) (sample: 30)
- Heat Supplied (kJ, optional) (sample: 1,000)
- Press Calculate Carnot Efficiency (results also refresh as you type). The result card shows the Carnot Efficiency, along with Maximum work from the heat supplied, Heat rejected, Refrigerator COP (Carnot) and Heat pump COP (Carnot).
Formula used
η = 1 − T_cold ÷ T_hot
- T = absolute temperatures in kelvin
- Refrigerator COP = T_cold ÷ (T_hot − T_cold)
- Heat pump COP = T_hot ÷ (T_hot − T_cold)
Real engines reach roughly 50–70% of the Carnot limit.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| Hot Reservoir Temperature (°C) | 500 |
| Cold Reservoir Temperature (°C) | 30 |
| Heat Supplied (kJ, optional) | 1,000 |
| Result | Value |
|---|---|
| Carnot Efficiency | 60.79% |
| Maximum work from the heat supplied | 607.9 kJ |
| Heat rejected | 392.1 kJ |
| Refrigerator COP (Carnot) | 0.645 |
| Heat pump COP (Carnot) | 1.645 |
Tips for using the Carnot Efficiency Calculator
- Raising the hot temperature is why modern power plants use supercritical steam.
- An AC works harder – with lower COP – on very hot days when the outdoor temperature rises.