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§ 16

Carnot COP and facility's coefficient of performance

What is best possible compression ratio and how good is my system?

Answer: The highest COP a cooling system can possibly have between two temperatures is the Carnot COP. It depends only on evaporation and condensing temperature in kelvin. When you compare the facility's measured COP with that, you get the coefficient of performance. The calculator also shows how much it theoretically gains to raise evaporation or lower condensing, and is used to explain to the customer why a dirty condenser costs power.

Formula

COP_Carnot = T0 ÷ (Tk − T0), med T0 i kelvin (°C + 273,15)

Temperature difference Tk − T0 is the same in kelvin and in °C

Godhedsgrad = COP_målt ÷ COP_Carnot

Symbols and units in the formula
SymbolMeaningUnit
t0Evaporation temperature°C
tkCondensation temperature°C
cop_maaltFacility's measured or calculated COP
=Carnot COP
=Goodness factor (measured COP ÷ Carnot)%
=Carnot COP if condensing is lowered 5 K

Validity and source

Source
Thermodynamics second law (Carnot process)

Does not apply when

  • The Carnot COP is a theoretical limit. Real facilities are well below due to losses in compressor, valve and heat exchangers. Use it to compare operating conditions, not as a measure for a particular facility.

Worked example

The calculator's own default values inserted. The figures are calculated with exactly the formula the tool uses.

Substituted

  • Evaporation temperature-10 °C
  • Condensation temperature40 °C
  • Facility's measured or calculated COP3

Giver

  • Carnot COP5.26
  • Goodness factor (measured COP ÷ Carnot)57 %
  • Carnot COP if condensing is lowered 5 K5.85

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Sådan bruger du den

Carnot-kuldetallet viser, hvor godt et anlæg teoretisk kan blive. Med det kan du forklare kunden, hvorfor en lavere kondensering eller en højere fordampning sparer strøm.

Step by step

  1. Indtast fordampningstemperaturen.
  2. Indtast kondenseringstemperaturen.
  3. Indtast anlæggets COP.
  4. Aflæs Carnot-tallet og godhedsgraden.

Typical errors

  • At regne i °C uden kelvin i tælleren.
  • At sammenligne med en anden temperaturforskel.
  • At tro, at et anlæg kan nå Carnot-tallet.

Examples from everyday life

Kølerum

Et kølerum kører med −10 °C fordampning og 40 °C kondensering, og COP er 3,0.

Evaporation temperature
-10 °C
Condensation temperature
40 °C
Facility's measured or calculated COP
3

It means: Carnot-tallet er 5.26, så godhedsgraden er 57 %. Sænkes kondenseringen 5 K, stiger Carnot-tallet til 5.85.

Snavset kondensator

Kondensatoren er snavset, så kondenseringen stiger til 50 °C, og COP falder til 2,4.

Evaporation temperature
-10 °C
Condensation temperature
50 °C
Facility's measured or calculated COP
2.4

It means: Carnot-tallet falder til 4.39, og godhedsgraden er 55 %. Rengøring betaler sig.

Rule of thumb

Hver grad lavere kondensering giver ca. 2-3 % bedre COP.

How to check the answer

Godhedsgraden er altid under 100 %.