Equations · equation

Coefficient of Performance

Thermodynamics · 1834

Equation
COP_heating = Q_h/W ≤ T_h/(T_h − T_c)
Field
Thermodynamics
Symbols
COP heat delivered per unit of work · Q_h heat moved to the warm side · W work in · T_h, T_c the two temperatures in kelvin
Year
1834

Significance

A heat pump is a heat engine run backwards, and its figure of merit can exceed 1 without breaking anything: a COP of 4 means four joules of heat moved for one joule of electricity. The Carnot limit shows why it works best when the two temperatures are close — and why heat pumps struggle in the deep cold.

Machines

Requires

Referenced by

equation
machine

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From the Equations database in Notion, last edited 2026-08-18. This page is the row, rendered by the build; nothing on it is written by hand.