Math 2.0

Classical thermodynamics, heat transfer Definition

Thermal efficiency

Builds on Heat engineHeatThermodynamic workKelvin–Planck statement of the second law

Definition

Let a heat engine absorb heat QH>0Q_H > 0 and reject heat QC≥0Q_C \ge 0 in each cycle, so that it does net work W=QH−QCW = Q_H - Q_C. The thermal efficiency of the engine is η=WQH=1−QCQH.\eta = \frac{W}{Q_H} = 1 - \frac{Q_C}{Q_H}.

Remarks

An engine that takes 1000 J1000\,\mathrm{J} and rejects 600 J600\,\mathrm{J} per cycle has η=400/1000=0.4\eta = 400/1000 = 0.4. A non-example: the ratio W/QC=400/600W/Q_C = 400/600 for the same engine is not its efficiency, because the work must be divided by the heat absorbed, not the heat rejected. For a heat engine 0<η≤10 < \eta \le 1, and the Kelvin–Planck statement of the second law gives η<1\eta < 1. Between reservoirs at thermodynamic temperatures TH>TCT_H > T_C, Carnot's theorem gives η≤1−TC/TH\eta \le 1 - T_C/T_H. Efficiency is often given as a percentage.

Reading path

To understand this page from the ground up, read these 8 pages in order. The foundations come first.

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Heat, concept, no evidence levelHeatconceptHeat engine, concept, no evidence levelHeat engineconceptTemperature, concept, no evidence levelTemperatureconceptThermodynamic cycle, concept, no evidence levelThermodynamic cycleconceptThermodynamic work, concept, no evidence levelThermodynamic workconceptClausius statement of the second law, statement, no evidence levelClausius statement of…statementKelvin–Planck statement of the second law, statement, no evidence levelKelvin–Planck stateme…statementThermal efficiency, definition, no evidence levelThermal efficiencydefinition
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. Heat engine concept
  3. Temperature concept
  4. Thermodynamic cycle concept
  5. Thermodynamic work concept
  6. Clausius statement of the second law statement
  7. Kelvin–Planck statement of the second law statement
  8. Thermal efficiency definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Thermal_efficiency
About this page
TagWPZ883JC06
URIm2://WPZ883JC06
Kinddefinition
WritingW0 stub
MSC80A10, 80A05
DefinesThermal efficiency
UsesHeat engine, Heat, Thermodynamic work, Kelvin–Planck statement of the second law
Changed3 November 2026

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