Evaporation of water in an open vessel is a process which takes place by itself, by absorption of heat from the surroundings, because the gaseous water molecules are more random than the liquid water molecules.
$
\mathrm{H}_2 \mathrm{O}(l) \longrightarrow \mathrm{H}_2 \mathrm{O}(g) ; \quad \Delta H=+40.8 \mathrm{~kJ} \mathrm{~mol}^{-1}
$
In other words, the process is spontaneous because it is accompanied by increase of entropy, which is further a measure of randomness or disorder of the system