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I live in the Middle East where the temperatures often are north of 50C in the summer.

As long as the humidity is low, the AC units perform very well and cool the apartment easily.

If relative humidity is high (usually we can tell this by the haze in the morning or when condensation start forming on glass windows), then the AC struggles to keep the house cool - but what's more interesting, it starts forming ice (on the cooling pipes) and this ice soon starts melting which leads to further issues that water starts leaking from the AC compressor unit.

My question therefore is, how can the ice formation be explained, and what is its relation to humidity and cooling?

In light of the comment below, I would like to clarify that I am not looking for a solution to the problem, I'm trying to understand the physics or the reasons behind it. I know that blasting some air through some of the drainage holes usually solves it; but I'm curious what is it specifically about humidity that makes this happen.

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What is it specifically about humidity that makes this happen?

In the atmosphere, Warm Air carries more water vapor than an equal volume of cold air, so this phenomenon connects heat with humidity.

enter image description here

From the above chart, you can see how the warmer the air, the more saturated it may become.

The freeezing process starts with the intake of warm, water vapor saturated air. The coolent liquid in the system acts to lower the temperature of the water vapor below it's freezing point. This change of liquid to solid is called a Phase Transition, and it results in ice forming on the coolest surfaces of the air conditioner. The heat extracted from the outside air turns (by means of another phase transition), the liquid coolent into a gas, which a compressor then turns back to liquid, and the whole cycle restarts.

If you left out the air blower, it's the same system by which your refrigerator eventually converts the water vapor in the air within the fridge to ice, and deposits it on the icebox surfaces.

enter image description here

Image Source: www.azairconditioning.com

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A phase transition diagram.

If the air was perfectly dry then, in a fridge, the food would cool down, without any ice build up, but perfectly dry air is rarely found.

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