[pdonis]

> Entropy favors the vapor form.

Under the conditions of these experiments (and under most ordinary conditions on Earth), yes. However:

> It doesn't necessarily take energy to evaporate.

Yes, it does. The water molecules in liquid water are bound to each other; that binding energy has to be supplied to enable evaporation. It just doesn't have to be "thermal" energy.

It would be correct to say that it doesn't necessarily take externally applied energy for water to evaporate. Water can evaporate using just its own internal thermal energy. In this case the evaporation process will cause the water to cool.