In some household air conditioners used in dry climates, air is cooled by blowing it through a water-soaked filter, evaporating some of the water. How does this cool the air? Would such a system work well in a high-humidity climate? Why or why not?

Air conditioners are being used to cool down the air.

When the warm air, which is at a higher temperature and has thermal energy, goes into the filter, they come in contact with the water. The contact then will lead to the transfer of thermal energy from higher temperature air molecules to lower temperature water molecules. The water molecules will be at a higher temperature now, and water will change form become vapor and evaporate.

Thus the air after it loses the thermal energy will be at a lower temperature, which means it cools down.

In the area where there is high humidity,

We know the rate of evaporation depends on the level of humidity in the area.

Thus, in high humidity areas, the air already has enough molecules of water in it, and there is not much space left for new water molecules that it can receive from evaporation. Thus, cooling will only happen if air transfers the thermal energy to water and evaporates it, but it is not possible here, and cooling will not happen up to the desired level.

Thus, the air cools down due to the evaporative cooling process. This system would not work well in a high-humidity climate because high humidity levels prevent water from evaporating.