Endothermic Design

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Homework Statement


I need to design a cooling tower, where the air undergoes some endothermic process to get cooled (i.e. it can go into contact with a substance that changes state by extracting the heat from the passing air).


Homework Equations


To do this I am aware that an endothermic process will involve either evaporation (liquid to gas) or melting (solid to liquid). I chose to design this inexpensive and passive device such that hot air passes over a bucket of ice, melts it and in the process loses its' heat thus cooling the room.

The Attempt at a Solution


I was just curious if at one point the air around the melting ice would get so saturated because of the condensation of surrounding air with a cold surface that in effect, it turns into an exothermic design, or is this not possible because the ice will actually melt, sooner than condense and keep on gaining heat from the air so that it will actually start evaporating instead (which is an endothermic reaction anyway).
 

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