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Just from a physics standpoint.

If you discharge water into a river, there are environmental limits to the outlet temperature (this is a good thing btw). The water can't be very hot. That means you need to pump a large volume of water through because you can only put a small amount of energy into each kg of water.

If you evaporate the water on the other hand, not only is there no temperature limit but it also absorbs the latent heat of vaporisation. The downside is it's a lot more complex and also the water is truly consumed rather than just warming it up.





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