Performance
Carnot (ideal) COP from evaporating and condensing temperatures
- where
- ideal (Carnot) cooling COP
- evaporating temperature (°C)
- condensing temperature (°C)
- ideal (Carnot) heating COP
Explain this equation
Gives the theoretical best COP any machine could reach between an evaporating and a condensing temperature. Use it to see how much the temperature lift costs, and as a ceiling for real figures.
Adding 273.15 converts Celsius to kelvin, which the thermodynamics needs. The bottom line, T_c − T_e, is the lift: how far the heat is pumped uphill. Cooling COP uses the cold temperature on top; heating COP uses the hot one, and is always exactly one more.
From the Carnot cycle: the ideal ratio of heat moved to work in depends only on the absolute temperatures.
Sense check: −10 °C evaporating and 40 °C condensing gives about 5.3 cooling and 6.3 heating. Real machines achieve roughly half of that. Halve the lift and the ideal COP roughly doubles.
Watch out: use refrigerant temperatures, not air or water temperatures, which are a few degrees milder.
Gives the theoretical maximum COP for a refrigerator or heat pump working between two temperatures. Real systems reach roughly half of this.
Enter your values to see the result.
Good to know
Temperatures must be absolute (kelvin), which is why 273.15 is added. The temperature lift (Tc − Te) dominates: every kelvin less lift raises efficiency. Divide a measured COP by the Carnot COP to get a rough “Carnot efficiency”, typically 0.4–0.6 for good vapour-compression plant.
Common mistake
Using °C directly (gives nonsense), or using air or water temperatures instead of the refrigerant evaporating and condensing temperatures.
Limits
Ideal reversible cycle; no real system can reach it.
Sources
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the equipment manufacturer’s data, CIBSE guidance, BS EN 378, the F-gas Regulations and your company procedures. Refrigerant work needs the correct F-gas certification.