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An 8.3 EER 1200 W air conditioner will move 10000 BTU of heat per hour. 1 BTU is 1055 J of heat. Per second this is moving 2930 W of heat energy. It is possible to get them even more efficient e.g. 12 EER.

This means 4130 W of heating on hot side, and 2930 W of cooling on cold side.

The heating side of the air conditioner is used to boil water to power a steam turbine. The cooling side is used to produce coolant.

A condensing steam turbine is approx 40% efficient, so the 4130 W of heat will produce 1652 W of electricity, and 2478 W of heat.

The 2478 W of heat is cancelled by the coolant, with 452 W of cooling left over.

The 1200 W of power needed by the air conditioner is cancelled by the turbine, with 452 W of electricity left over.

The excess cold can be released into the environment or used some other way, and the excess power put into the power grid.

I was thinking about this while playing the computer game Oxygen not Included, and wondered if such a machine could exist in reality?

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No, such a machine cannot exist in reality. One critical thing that you neglected in your analysis is the temperature. Every heat engine or heat pump has a hot side and a cold side. The efficiency depends strongly on the temperature difference. The heat pump operates with a much lower heat difference than the steam engine. If you run it at the larger difference as you described then it will be nowhere near as efficient as you quoted.

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