Why does the evaporation of water cool the air near the water`s surface?
The water is at some temperature T. Temperature is a measure of the average kinetic energy of the molecules. The kinetic energy is actually a distribution – a spread over a wide range of energies. Because of the thermal distribution – what’s called the Boltzmann distribution, after a physicist who discovered it – some of the molecules are at a higher energy than others. Those with sufficiently high energy can escape the water and evaporate into gas. However, when the highest energy molecules evaporate, the average energy of the water falls – so the temperature of the water falls. If the air and water were in equilibrium at the start of the situation, the water is now cooler than the air. The water then absorbs some of the energy of the air (by Newton’s Law of Cooling – check wikipedia, e.g.), cooling the air. This is the principle of evaporative coolers, used in many homes in the United States.