The efficiency calculation here measures only electrical power in vs heat energy out. Heat pumps are always listed with greater than 100% efficiency. There is no problem with the laws of thermodynamics of doing this and it’s even listed in text books with the explanation of how it is possible.
The work of the heat pump is to move heat from one location to another, it does so with the byproduct of producing more heat, therefore it produces more heat energy than the electrical energy put in.
You’re right that conservation of energy says that the heat in being moved did come from somewhere but that’s outside the system, and you will always find heat anywhere but absolute zero. Calculations for turbines or engines don’t make any efficiency allotments for heat already in the air, which is also necessary for them to run.
Heat pump is not just the pump mechanism, but the entire system which includes mass of rock that is heat reservoir.
What typically happens is you drill deep in the ground or rock and circulate air, water or some other refrigerant underground. During summer you pump hot refrigerant to heat up the mass of rock. This can be for example water that has been made hot by the sun. During winter you push water through that warm rock to recover the heat to warm your home.
No, it is not thermodynamically possible to recover more than 100% of stored energy.
The work of the heat pump is to move heat from one location to another, it does so with the byproduct of producing more heat, therefore it produces more heat energy than the electrical energy put in.
You’re right that conservation of energy says that the heat in being moved did come from somewhere but that’s outside the system, and you will always find heat anywhere but absolute zero. Calculations for turbines or engines don’t make any efficiency allotments for heat already in the air, which is also necessary for them to run.