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Why (particularly with ground source heat pumps) can the same principle not be used to run it rather than having to pump in electricity?
I'm guessing it's because electricity on tap is cheap, while making a generator to drive the compressor and fan in a heat pump is expensive. It's not easy to get motive power out of a system with such a low temperature differential, since the maximum theoretical efficiency of a heat engine is governed by the difference in temperature between the hot and cold sides.
My wood burning stove has a fan that works by the temperature difference between the base and the head to provide the motive power for the fan.
Why (particularly with ground source heat pumps) can the same principle not be used to run it rather than having to pump in electricity?