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It is clear that water gets cooled in an earthern pot thru evaporation etc. If we blow (fast) warm/hot air around such an enclosed pot (pot is further lying in say another bigger pot) so that the air is not in direct contact with atmosphere, will this blown air become cooler.

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If air temperature is higher than the pot temperature, it can be cooled. This is especially true in summer time when temperature is high and vapor pressure is low. When air flow over the top of the water surface, it carries away vapor (reducing partial pressure, in thermodynamics). The water evaporates. The phase change needs heat that cool down both air and water, which will be heated up by the surrounding. This makes the pot temperature a bit lower so to form a temperature gradient to get heat from the bottom side (the heat will be injected in from the top side as well). As the amount of evaporation is small, the temperature drop is not significant. If you can see air stream somehow, the air, after it flow over the pot, will fall down due to temperature decrease forming a beautiful picture that I hope I can find it in youtube.

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