Coefficient of performance must be greater than 1.
The formula is Th/(Th-Tc) where Th is the temperature of the hot side and Tc is the temperature of the cold side both measured in Kelvin. The only time it can be 1 is if the cold side is at absolute 0, which can’t happen in the real world.
Take a heat pump for example. If it is operating with a CoP of 5, then for every 5kWh it uses of electrical energy, 25kWh of heat are added to your home. That’s because it’s taking energy from the air outside and moving it inside, even if the outside air is cold, it still has heat. Any losses that the heatpump experiences will still be turned into heat, and will therefore still heat you home. That’s 20kWh from outside and 5kWh from the electricity.
If we compare that to and electrical space heater (100% efficient by definition) it will consume 5kWh of energy and heat your home with 5kWh of heat.
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