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Would it be possible (at some point) cool aur by pulling heatenergy from it?
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It is about temperature differential. If you had a cold well then yes you could heat up the cold well and extract energy in the process. But if you had a cold well why are you not already using that as part of the AC.
By the way, that is why AC using geothermal heat pump is way more energy efficient then air. Another cold sink is the sky specially a cloudless one. Another one is a heat pump hot water heater. You pump the heat into hot water that your going to use anyway cooling the room at the same time.
So physics, yes energy/entropy stuff but then it is a question what can you do. My only point, look for the loopholes too... that is what can you do.