If you use a bicycle pump to inflate a tire, you’ll feel it get hot. That’s the result of the air being squeezed so much it heats up.
No additional energy has been put into the air, it’s just now all in a smaller space so feels hotter (because Physics!). If you can find a way to take that heat energy out and put it somewhere else, like into water, then that’s how an Air Source Heat Pump works.
The coldest anything can ever get is minus 273C, so even 0C air still has a LOT of heat energy in it. If it takes 1kW of electrical energy to squeeze air enough to get 4kW of that heat energy out, then that’s a COP of 4.
When you let the air expand again, it will get very cold because you’ve removed that heat, which is why there’s cold air being blown out of the ASHP fan.
So you’re not using electricity to heat anything. You’re using it so squeeze existing heat out some air.
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