Calculation
COPCarnot = Thigh/(Thigh−Tlow); quality grade = COPreal/COPCarnot
The Carnot COP is the thermodynamically best possible value between two temperature levels; real heat pumps typically reach 40 to 60% of it.
Dubbel Thermodynamik D 8.3.1 Carnot-Prozess, Gl. (19) η = 1 − T0/T, Wärmepumpe εWP,Carnot = T/(T−T0); reale Leistungszahl εWP nach D 8.4.2, Gl. (41)
Heat pump quality grade against the Carnot limit
The Carnot COP is the thermodynamically best possible value between two temperature levels; real heat pumps typically reach 40 to 60% of it.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Quality grade (0 to 1) — Ratio of the real COP to the thermodynamically maximum possible Carnot COP at the same temperatures.
- Upper temperature (heating flow) Thigh — Temperature the heat pump delivers to the heating system (condenser temperature).
- Lower temperature (heat source) Tlow — Temperature of the heat source used, e.g. outdoor air, ground or groundwater (evaporator temperature).
- Real heat pump COP COPreal — Actual COP value at the same temperatures, e.g. from a test bench or datasheet.
Example
Thigh=35 °C, Tlow=0 °C and COPreal=3.5 give COPCarnot=308.15/35≈8.80 and a quality grade of about 0.40 (40%).
Assumptions and limits
Ideal Carnot reference cycle between two constant temperature levels in Kelvin; real compressor losses, quality-grade dependence on temperature lift and part-load operation are captured only in aggregate through the quality grade itself.
Understand Heat pump quality grade against the Carnot limit
This calculator places a heat pump's real coefficient of performance (COP) against the thermodynamically best-possible Carnot value, separate from the existing annual-cost calculator for heat pump systems.
What does this quantity describe?
Between two temperature levels Thigh and Tlow (in Kelvin), COPCarnot=Thigh/(Thigh−Tlow) is the thermodynamically maximum possible value. Quality grade compares the real COP against it: quality grade=COPreal/COPCarnot.
Formula and variables
COPCarnot = Thigh/(Thigh−Tlow); quality grade = COPreal/COPCarnot
COPCarnot = Thigh/(Thigh−Tlow)quality grade = COPreal/COPCarnot
| Symbol / input | Meaning |
|---|---|
| Quality grade (0 to 1) | Ratio of the real COP to the thermodynamically maximum possible Carnot COP at the same temperatures. |
| Upper temperature (heating flow) Thigh | Temperature the heat pump delivers to the heating system (condenser temperature). |
| Lower temperature (heat source) Tlow | Temperature of the heat source used, e.g. outdoor air, ground or groundwater (evaporator temperature). |
| Real heat pump COP COPreal | Actual COP value at the same temperatures, e.g. from a test bench or datasheet. |
Choose the inputs correctly
Thigh is the temperature delivered by the heat pump's condenser (heating flow), Tlow the temperature of the heat source used, COPreal the real COP at these temperatures.
How to use the calculator
Set Thigh and Tlow for the considered operating point, take COPreal from a datasheet, test bench or measurement.
Worked example
Thigh=35 °C, Tlow=0 °C and COPreal=3.5 give COPCarnot≈8.80 and a quality grade of about 0.40 (40%).
Understand the result and units
Real heat pumps typically reach 40 to 60% of the Carnot value; a notably lower quality grade points to unfavourable operating conditions or an inefficient machine.
Thigh and Tlow are temperatures, COPreal dimensionless. Quality grade is output as a ratio between 0 and 1.
Typical applications
Placing measured or datasheet COP values in context, comparing different heat pumps or operating points, and sensitivity analysis of temperature lift.
Assumptions, limits and common mistakes
Ideal Carnot reference cycle between two constant temperature levels; real compressor losses, part-load behaviour, defrost cycles and the quality grade's own temperature dependence are not broken out individually.
Common mistake: Do not substitute Celsius temperatures unconverted into a pure-Kelvin formula; the calculator handles conversion automatically, so a manual comparison with other sources should account for this.
Frequently asked questions
What is “Heat pump quality grade against the Carnot limit” used for?
Placing measured or datasheet COP values in context, comparing different heat pumps or operating points, and sensitivity analysis of temperature lift.
Where do the input values come from?
Thigh is the temperature delivered by the heat pump's condenser (heating flow), Tlow the temperature of the heat source used, COPreal the real COP at these temperatures.
What does the result not cover?
Ideal Carnot reference cycle between two constant temperature levels; real compressor losses, part-load behaviour, defrost cycles and the quality grade's own temperature dependence are not broken out individually.