The amount of energy you would get out of your turbine would be the same (or realistically) the same than you have required to power the air conditioner. So overall you would not earn any energy.
A heat pump, can bring something from Temperature 1 to temperature 2. This requires some amount of work (energy) (e.g. electricity). However you still get more heat energy from it than you have put work in (as additional energy comes from the temperature 1 reservoir), so you get efficiency over 100%.
If you build a machine which draws power from cooling something down, the efficency is limited (by the carnot efficiency limit). You will always get efficency below 100% and it is exactly the inverse of your heat pump. This is because the second law of thermodynamics (or the fact that entropy can never decrease globally)
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