Definition

Coefficient of performance

(T4.2.1) T4.2 · Refrigerators and Heat Pumps →

COP = \frac{Q _{c}}{W} (refrigerator), COP = \frac{Q _{h}}{W} (heat pump)

Statement

Heat moved per unit of work input, for a refrigerator (heat removed from the cold side) or a heat pump (heat delivered to the hot side).

Symbols and units

$COP$	coefficient of performance	—
$Q_{c}, Q_{h}$	heat moved from cold, to hot side	J
$W$	work input	J

When it applies

Any refrigerator or heat pump operating in a cycle between two reservoirs.

Derivation

Defined analogously to engine efficiency, but for a reversed heat engine — work goes in, heat is moved against its natural direction:

COP = \frac{Q _{c}}{W} or \frac{Q _{h}}{W}

Worked examples

What COP = 3 means

Q_{h} = 3 W

Three units of heat delivered per unit of work — not energy created from nothing, but existing heat moved from outside using that work.

Watch out for

COP can exceed 1 — a heat pump can deliver more heat energy than the electrical work it consumes, because it moves existing heat rather than creating it.