Calculator Inputs
Responsive layout: three columns on large screens, two on medium, one on mobile.
Formula Used
Heat engine
Reversible (Carnot) efficiency: ηrev = 1 − Tc/Th. Second law efficiency: ηII = ηactual/ηrev.
Refrigerator
Reversible (Carnot) COP: COPrev = Tc/(Th − Tc). Second law efficiency: ηII = COPactual/COPrev.
Heat pump
Reversible (Carnot) COP: COPrev = Th/(Th − Tc). Second law efficiency: ηII = COPactual/COPrev.
Temperatures must be absolute for these relations; this tool converts °C to K. If you provide a reversible value, the calculator uses it directly.
How to Use This Calculator
- Select the system type: heat engine, refrigerator, or heat pump.
- Choose temperature units, then enter hot and cold temperatures.
- Enter actual efficiency (engine) or actual COP (refrigeration/heating).
- Use the Carnot limit, or enter a custom reversible reference.
- Optionally enter a load rate (kW) to estimate work and losses.
- Click Calculate to view results above the form.
- Use Download CSV or Download PDF to export your results.
Example Data Table
These are representative values for quick verification.
| System | Th (K) | Tc (K) | Actual performance | Reversible reference | Second law efficiency |
|---|---|---|---|---|---|
| Heat engine | 800 | 300 | ηactual = 0.38 | ηrev = 1 − 300/800 = 0.625 | ηII = 0.38/0.625 = 0.608 |
| Refrigerator | 300 | 260 | COPactual = 3.2 | COPrev = 260/(300−260) = 6.50 | ηII = 3.2/6.50 = 0.492 |
| Heat pump | 320 | 280 | COPactual = 3.8 | COPrev = 320/(320−280) = 8.00 | ηII = 3.8/8.00 = 0.475 |
For heat engines, second law efficiency is also called exergy efficiency.
Values above 100% indicate inconsistent inputs or reference choice.