One may wonder when does evaporative cooling occur? To describe the liquid gas interface for say a substance X, we must use the concept of vapour pressure. Every Liquid at a given pressure and temperature has a definite value for its vapour pressure. If the partial pressure,(pressured exerted by the gas molecules only of X) is less than the vapour pressure of the liquid at that temperature then the liquid has a tendency to evaporate.
Why is some particular molecules chosen to escape the Liquid? The molecules of the substance X have a tendency to attract each other, To separate them one needs to provide energy to fuel their separation. Evaporation happens at the surface, Molecules tend to experience an average attractive force at the surface pulling not allowing them to escape.
Since the liquid is at a certain temperature, some molecules move faster than the others. If a particular molecule at the surface has a large enough Kinetic energy that it can overcome the attractive barrier allowing it to escape. Since only the fastest of the molecules escape the, liquid will consequently find itself with molecules of lower average energy, thus an overall decrease in its temperature. This will continue until the vapour pressure of the liquid is equal to the partial pressure of vapour outside.