The core idea
A vapour-compression machine never makes heat; it moves it. A compressor raises a refrigerant's pressure (and so its condensing temperature), the condenser rejects heat to the warm side, the expansion valve drops the pressure, and the evaporator absorbs heat from the cold side. Nothing in that physics says which side is "useful" — a fridge, an air conditioner and a heat pump are the same machine, differing only in which coil you stand next to. An air conditioner already is a heat pump: it pumps heat out of your bedroom and dumps it into the street.
What makes a dedicated heat pump is the four-way reversing valve, which swaps the roles of the two coils. In cooling mode the indoor coil is the evaporator; slide the valve and the indoor coil becomes the condenser, so the same unit now heats the room. Two consequences follow from the numbers. The heating COP is the cooling COP plus one, because the useful heat on the hot side equals the heat lifted plus the compressor's electrical input:
- COP_heating = COP_cooling + 1 (same machine, ideal valve)
- COP ≈ T_hot / (T_hot − T_cold) — Carnot ceiling, temperatures in kelvin
That second formula is the whole story of heat-pump design: efficiency depends not on the machine alone but on the temperature lift between source and sink. Shrink the lift and the COP soars; stretch it and the COP sags towards 1 — the value of a plain electric heater.
Real-world example
A supermarket runs refrigerated display cases all year, so its machine room condenses heat around the clock. Instead of throwing that heat to the sky through the roof condensers, the store recovers it: desuperheaters on the racks pre-heat domestic hot water, and warmed air heats the sales floor in winter — the "heating bill" is mostly a by-product of keeping milk cold. The same logic scales down to a home: an air-to-water unit pulling heat from −5 °C night air and feeding 35 °C water to underfloor heating can run at COP 3–4, delivering 3–4 kWh of heat per kWh bought, where a direct electric heater delivers exactly 1.
Common pitfall
Expecting COP to be a fixed number on the nameplate. It is not: COP falls as the lift grows. Fit a heat pump to old 70 °C radiators instead of 35 °C floor heating and the condensing temperature must climb, the lift widens, and the COP can nearly halve — the same box suddenly costs twice as much to run. Rule: heat pumps love low flow temperatures and big emitter surfaces; the radiator upgrade is part of the heat pump, not an optional extra.