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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Even when it’s cold outside, there is still lots of heat energy in the air. Although heat naturally wants to move from hot to cold, the job of the heat pump is to move the heat from cold to hot. You can either use your energy to create heat, or use it to move the heat. Moving heat is often much easier–for example, it takes very little energy to move around a pot of soup, but a lot of energy to heat it up in the first place.
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