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Air coolers work by evaporating water into the air. Because air can only hold a certain amount of moisture, the more moisture in the air to begin with, the less you can add.

The technical answer is to use a psychrometric chart to analyze the problem.

A common thermometer measures dry bulb temperatures (the x-axis on the chart). From that temperature follow a vertical line up until you reach the current relative humidity value. This intersection gives the properties for the air you're trying to cool. From this point, a horizontal line all the way to the left side of the graph will give you the temperature for 100% relative humidity level. This value is the theoretical minimum temperature you can reach through evaporative cooling.

Seeing this with numbers shows that a common value for someplace humid, like Florida today is, 80 deg F and around 80% humidity. If you follow these values on the chart, the minimum temperature you can achieve is around 74 deg F @ 100% humidity.

The same problem with cooling someplace dry, like Arizona, where the temperature is warmer, 100 deg F, but the humidity is lower, 15%, can get a minimum temperature of 44 deg F @ 100% humidity.

This level of humidity is uncomfortable, and most people shoot for around 50%. If you live someplace dry use evaporative cooling (adding moisture to cool a space) and if you live someplace humid, use air conditioning (cooling & removing moisture to condition a space).

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Q: Why air coolers will not provide effective cooling in humid areas?
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