Concept 1 / 3
Heat Pumps — COP Calculations
Heat pumps move heat — they don't generate it. COP > 1 always.
COP_heat_pump = Q̇_output / P_el
Theoretical maximum (Carnot): COP_Carnot = T_out / (T_out − T_in)
⚠️ TEMPERATURES MUST BE IN KELVIN
Real heat pump: COP_real = g · T_out / (T_out − T_in)
- Quality grade g = 0.50–0.60
Example: Source = 10°C (283 K), sink = 45°C (318 K), g = 0.55:
COP_real = 0.55 · 318 / (318 − 283) = 0.55 · 9.09 ≈ 5.0
→ 1 kWh electricity → 5 kWh heat!
Ground-source beats air-source in winter:
- Ground: T_in ≈ 10°C year-round → high COP
- Air-source: T_in = −10°C in winter → much lower COP
Carnot efficiency (heat engines):
η_Carnot = 1 − T_cold / T_hot (T in Kelvin)