You don't need to supply the energy for evaporation. It can be extracted from the environment. If you have a glas of water then without adding any energy, you can extract a lot of work by letting it evaporate reversibly into the atmosphere
Similarly, if you have salt and fresh water, you can extract work by letting the salt dissolve in the water in a reversible way (which involves using filters that let's through only the water or the salt so that osmotic pressure builds up). Note that when salt disolves into water that process actually costs energy.
Suppose you have some stuff in a system that is kept at constant pressure and temperature. It can be coal, or just plain water, water and salt, or whatever. Assume that the system is in (metastable) thermodynamical equilibrium. If the system then changes into some other form and the system is again in thermodynamical equilibrium, then the total amount of work that you can extract from that change is the drop in the Gibbs energy.
So, suppose we start with water and air and no water vapor at 1 bar pressure. This system has a certain Gibbs energy. If the water evaporates a bit until the partial pressure of the water vapor equals the thermal equilibrium value at the temperature the system is kept at, then the Gibbs energy will have reached its minimal value.
So, we can clearly extract work from such a system as long as the relative humidity is not 100%. To do this in practice will involve using filters that only let through air molecules or only let through water molecules.