Math 2.0

Classical thermodynamics, heat transfer Definition

Coefficient of performance

Builds on Thermodynamic cycleHeatThermodynamic workFirst law of thermodynamicsClausius statement of the second law

Definition

Consider a system that repeatedly performs a thermodynamic cycle. In each cycle it absorbs heat QC>0Q_C > 0 from a cold reservoir and receives work W>0W > 0 from its surroundings. It gives heat QHQ_H to a hot reservoir. When the purpose is cooling, the system is a refrigerator and its coefficient of performance is COPR=QCW.\mathrm{COP}_R = \frac{Q_C}{W}. When the purpose is heating, the system is a heat pump and its coefficient of performance is COPHP=QHW.\mathrm{COP}_{HP} = \frac{Q_H}{W}.

Remarks

By the first law of thermodynamics, QH=QC+WQ_H = Q_C + W, so COPHP=COPR+1\mathrm{COP}_{HP} = \mathrm{COP}_R + 1. By the Clausius statement of the second law, heat cannot pass from cold to hot with no other effect, so the cycle needs work W>0W > 0. For a reversible cycle between thermodynamic temperatures TC<THT_C < T_H, the values are TC/(TH−TC)T_C/(T_H - T_C) and TH/(TH−TC)T_H/(T_H - T_C), and no cycle between these reservoirs does better. Example: a reversible heat pump between TC=270 KT_C = 270\,\mathrm{K} and TH=300 KT_H = 300\,\mathrm{K} has COPHP=300/30=10\mathrm{COP}_{HP} = 300/30 = 10. A non-example: an electric resistance heater turns work into heat but takes no heat from a cold reservoir, so the condition QC>0Q_C > 0 fails; its ratio QH/WQ_H/W is only 11.

Reading path

To understand this page from the ground up, read these 10 pages in order. The foundations come first.

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Heat, concept, no evidence levelHeatconceptInternal energy, concept, no evidence levelInternal energyconceptState function, concept, no evidence levelState functionconceptTemperature, concept, no evidence levelTemperatureconceptThermodynamic cycle, concept, no evidence levelThermodynamic cycleconceptThermodynamic system, concept, no evidence levelThermodynamic systemconceptThermodynamic work, concept, no evidence levelThermodynamic workconceptFirst law of thermodynamics, statement, no evidence levelFirst law of thermody…statementClausius statement of the second law, statement, no evidence levelClausius statement of…statementCoefficient of performance, definition, no evidence levelCoefficient of perfor…definition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Heat concept
  2. Internal energy concept
  3. State function concept
  4. Temperature concept
  5. Thermodynamic cycle concept
  6. Thermodynamic system concept
  7. Thermodynamic work concept
  8. First law of thermodynamics statement
  9. Clausius statement of the second law statement
  10. Coefficient of performance definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Coefficient_of_performance
About this page
TagT65EB2RBR8
URIm2://T65EB2RBR8
Kinddefinition
WritingW0 stub
MSC80A10, 80A05
DefinesCoefficient of performance
UsesThermodynamic cycle, Heat, Thermodynamic work, First law of thermodynamics, Clausius statement of the second law
Changed3 November 2026

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