Which process of the water cycle occurs when water absorbs 2260 joules of heat energy per gram?

Evaporation occurs when water absorbs 2260 Joules of heat energy per gram.  It is process by which water changes from a liquid to a gas or vapor. It takes energy for the molecules to break those bonds (to overcome the bonding forces). This energy is the latent heat of vaporization. 

Water requires the  addition of 2260 Joules of heat energy for every gram of water that evaporates (vaporizes). The heat energy that is required to change water into vapor is called the latent heat of vaporization.