Heat pump

A heat pump is a refrigerator whose useful output is the heat delivered to the hot reservoir rather than the heat removed from the cold one. It is physically the same device: the same compressor, the same working fluid, the same four components. Only the accounting changes. Its coefficient of performance is COP_pump = Q_h/W, bounded by T_h/(T_h − T_c), and it always exceeds the same machine's refrigerator COP by exactly 1 — because Q_h = Q_c + W, so the work paid also lands in the warm room as heat.

The consequence is that a heat pump is not a marginally better heater than a resistive element; it is a categorically better one. A resistive heater converts one joule of electricity into exactly one joule of heat and can never do better: its COP is pinned at 1. A heat pump delivering 20 °C indoors from 0 °C outdoors has a Carnot ceiling near 14.7 and, at real-world efficiencies, still delivers three to four joules of heat per joule of electricity. It achieves this not by making heat more cleverly but by importing heat that already exists outdoors and paying only for the transport.

The formula also names the technology's weakness: COP_pump = T_h/(T_h − T_c) falls as the outdoor temperature drops, so a heat pump performs worst exactly when it is needed most. Engineering answers this by finding a warmer cold reservoir — ground loops tap soil at a steady ~10 °C instead of frigid air — rather than by arguing with the thermodynamics, which is not negotiable. Because building heat is roughly a quarter of global energy demand, this factor of three is load-bearing in most decarbonisation plans.

The heat pump is as old as the refrigerator — William Thomson (Lord Kelvin) proposed using a reversed heat engine for heating in 1852, calling it a 'heat multiplier' — but it stayed a curiosity while fuel was cheap. Robert Webber built an experimental ground-source unit in the late 1940s, and Norway, Sweden, and Switzerland adopted heat pumps at scale after the 1970s oil shocks. Their current prominence is a policy story rather than a physics one: the thermodynamics has been unchanged since Carnot, but the exhaust is now counted.