[0]Rough #. Carnot efficiency would define your max theoretical for a heat-engine process.
For example, I can use 10 watts of electricity to remove 10 watts of heat from a cold place and add 20 watts of heat to a hot place.
Later, I can apply the same in reverse. I can move 20 watts of heat from the same hot place, heating the cold place by 10 watts, while generating 10 watts of electricity.
The use of the phrase "efficiency" while discussing ideal heat pumps is misleading - no energy is ever wasted or lost, the law merely limits the ratio of electrical Vs heat energy you get in/out.
The process is not thermodynamically reversible in the sense that there's a net energy expenditure either way. No free lunches.
What a heat pump can do is to move a greater amount of energy than it uses to move it. Measurements of this include COP (coefficient of performance), EER (energy efficiency ratio), and SEER or ESEER ((European) seasonal energy ratio).
The COP is a direct measure of energy moved divided by energy input, and ranges from about 2--4, with typical ground-loop heat pumps achieving scores around 3--3.5. That is they move three times the heat energy that they run under. It's as if a furnace output three times more heat energy than fuel input.
In your example, we'd first want to correct power (watts) to energy (watt-hours or joules). But 10 watt-hours of electricity would move about 30 watt-hours worth of heat, for a typical heat pump. If you're heating, you'd dump the additional 10 watt-hours into the heated space, if you were cooling, you'd want the heat pump's own heat to be directed to the external environment.
Discussion of heat gained/wasted with heat pumps is ... complicated. Note that effectiveness in moving heat decreases as the differential being moved against increases. That is, if you're trying to cool a space in an environment that's already warm, you're pumping heat "uphill". Similarly, if you're trying to warm a space from a cold environment, there's not much external heat to extract.
Ground-loop heat pumps benefit by the fact that ground temperatures tend to be more moderate than outdoor ambient air temperatures, so the temperature gradients are more favourable and predictable.
Efficiencies above 50% are claimed by some dual-cycle plants (gas turbines with steam generation), and with cogeneration utilising waste heat, higher yet, but the electrical generation component remains in the 40--50% range.
https://www.powermag.com/another-world-record-for-combined-c...
I'll note it's a manufacturer claim (e.g., "value never to be exceeded" --- most optimal possibly conditions likely).
What's the significance of LHV in this context?
Otherwise, what's a typical percentage difference between LHV and HHV efficiencies?
https://en.wikipedia.org/wiki/Heat_of_combustion
The difference for natural gas is about 10%.