Thermodynamics
As stated above, the mechanical work needed to increase a surface is . Hence at constant temperature and pressure, surface tension equals Gibbs free energy per surface area:
where is Gibbs free energy and is the area.
Thermodynamics requires that all spontaneous changes of state are accompanied by a decrease in Gibbs free energy.
From this it is easy to understand why decreasing the surface area of a mass of liquid is always spontaneous, provided it is not coupled to any other energy changes. It follows that in order to increase surface area, a certain amount of energy must be added.
Gibbs free energy is defined by the equation, where is enthalpy and is entropy. Based upon this and the fact that surface tension is Gibbs free energy per unit area, it is possible to obtain the following expression for entropy per unit area:
Kelvin's Equation for surfaces arises by rearranging the previous equations. It states that surface enthalpy or surface energy (different from surface free energy) depends both on surface tension and its derivative with temperature at constant pressure by the relationship.
Read more about this topic: Surface Tension