Cooling effect of evaporation when temperature difference is zero

Question

Evaporation is a cooling process as molecules with greater KE could escape from the liquid surface.

I know that evaporation can happen even when the liquid has the same temperature as the environment. However, without a difference in temperature between the liquid and the environment, there should be no heat transfer and thus, no change in temperature for the liquid.

When the molecules with greater KE has escaped, the average KE of the liquid should be reduced. How can there be no change in temperature for the liquid when evaporation is happening?

My guess: The environment has an increase in temperature as it gains energy from the molecules escaped from the liquid. As there is a temperature difference, there is a heat transfer back to the liquid from the environment so the temperature of the liquid remains constant.

I know that other factors such as humidity and surface area matters too. However, my focus is on the effect of temperature difference.

Answer 1

Whenever evaporation happens, liquid will cool down irrespective of temperature difference between liquid and environment. This happens because of the latent heat of evaporation.

Answer 2

The environment takes the "warm" molecules until it is saturated. Eg air takes water molecules until it reaches 100% humidity. From that point on, water will not evaporate anymore, and both air and water remain at the same temperature.

If the air is not at 100% humidity, water will evaporate until it is, then the air is warmer than before. Heat exchange will eventually equalize the temperatures of both air and water.