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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You’re thinking of _efficiency_. How much energy goes in, versus how much work (energy) gets done. Usually you lose energy to heat, noise, light, etc., hence why efficiency is always less than one.
I promise you that a heat pump isn’t defying this rule, and it’s not magic. The work that a heat pump does is to move around a fluid in a closed loop. That fluid is losing energy to friction in the piping. If you tried to measure the energy going in versus the mass flow flow and velocity of the fluid in that system, you would definitely measure an efficiency of less than 100%.
But that’s not what interests us about heat pumps, so it’s thermal efficiency is sort of meaningless. A heat pump allows that fluid to evaporate from liquid to gas and condense from gas to liquid exactly where we want. In doing so, we are able to remove heat from one place (where the evaporation /boiling occurs) and transport it to another (where the condensing occurs).
If you consider the amount of heat that you’re able to transport, that can be quite a bit more than the energy you put in to the system to operate the pump, compressor, fans and other equipment. We call that ratio a “performance factor”.
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