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cameron, you can use only one of them and have the other side passively cooled or heated. it'll still work, just not as well.

 

In fact, using ice is probably a bad idea. You need to cool the water to make ice, and generally speaking in process engineering: cooling is more expensive (and less favorable energetically) than heating.

 

In addition, I severely doubt that the Carnot efficiency will go up when you use ice, and when you include the production of ice as well. But I'm too lazy to calculate it (apologies). :D

 

Anyone really interested in this kind of stuff: make sure you know Mr. Carnot and his theoretical maximum efficiency. (It's the 2nd law of thermodynamics).

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