The core idea
An engine's efficiency is useful output divided by energy input, and it can never reach 1 — you always lose something. Refrigeration machines are measured differently. Their figure of merit is the Coefficient of Performance (COP): useful heat moved divided by electric work paid for.
- Cooling mode: COP_cool = Q_cold / W — heat pulled out of the cold side (kW) divided by compressor electrical power (kW).
- Heating mode: COP_heat = Q_hot / W — heat delivered to the warm side divided by the same W.
Because energy is conserved around the cycle, Q_hot = Q_cold + W, which gives the handy identity:
COP_heat = COP_cool + 1
A unit extracting 4 kW from outdoor air while consuming 2 kW delivers 6 kW indoors — a heating COP of 3. The extra kilowatt is simply the compressor's own electrical work arriving as heat.
COP is not a fixed number on a nameplate: it depends mainly on the temperature lift — the gap between evaporator and condenser temperatures. A small gap is easy pumping and yields high COP; a large gap makes the compressor work hard and COP falls. As a rule of thumb, each 1 K reduction in lift gains roughly 2–3 % COP.
Real-world example
A house heated by an air-to-water heat pump. With underfloor heating the water only needs ~35 °C; with classic radiators it needs ~55 °C. On a −5 °C day the lift differs by 20 K, so the radiator setup might run at COP 2.5 while the underfloor setup reaches 4.0 — roughly 40 % less electricity for exactly the same heat delivered. This is why heat-pump retrofits so often include oversized radiators or underfloor loops: the emitters are chosen to protect the COP.
Common pitfall
Treating a COP above 1 as "over 100 % efficiency" and therefore impossible. It is not a violation of thermodynamics: in a resistance heater the electricity is the heat (COP capped at 1), but a heat pump uses electricity to pump heat that already exists in the outdoor air, not to create it. A second trap: EER (BTU/h of cooling per watt) is not COP — divide EER by 3.412 to convert.