How a coefficient of performance greater than 1 is possible?

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How is it that a machine (like a heat pump) can consume 1kw of power and produce an amount greater than that of heat? What am I misunderstanding?

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The coefficient of performance is for heat pumps. As the name suggests, heat pumps “pump” heat from low temperature to high temperature (against the natural tendency of the heat to flow from high to low). The COP is calculated as the heat moved divided by energy added. The energy that is used to this is work and is a high grade energy. Further, it’s only being used to move heat, not to create heat. If all the high grade energy was “converted” to heat, then yes, it could not be greater than 1. Like electricity being used to turn a filament heater. But since we are only “moving” heat from one source to another, a heat pump can have COP greater than 1.

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