About this time of year in my region people often look at the air conditioning compressor pumping heat to the outside air on one side of their house while their swimming pool heater tries to pump heat into the water on the other side, and wonder why they're paying twice to move heat. Inevitably someone thinks of submerging their compressor coils, but then they run the numbers and realize that it won't be too many days before their swimming pool is uncomfortably hot.
But this leads to an interesting engineering question: What is the practical breakeven point between air-source and water-source heat pumps (for cooling indoor air)? I.e.: Is it possible, due to its higher thermal conductivity, for a water sink at a higher temperature to be more efficient for cooling than an air sink at a lower temperature?
More specifically: Suppose we have an outdoor compressor with surface area x pumping y BTUs of heat. I am assuming that because water has something like 20 times the thermal conductivity of air that it would be a more efficient heat sink even when it's somewhat hotter than the air sink. (Is that correct?) But how much more efficient? I.e., at what temperature differential is air as efficient as water?
(Or is this not a practical question? For example, we run fans to force more air through air-cooled compressors. That takes energy, but maybe it raises the effective thermal conductivity to the point that it is breakeven with a convective water sink ... even including the energy to drive the fan?)