Historically, the theory of Surface Tension was postulated the first time in the XVIII century and uses the concepts of hydrostatics to explain capillary rise. The concept of Surface Energy (E) is part of Thermodynamic Theory and was developed by W. Gibbs, in the second part of the 19th century. The initial theory of Surface Tension (hydrostatic) did not include the influence of temperature.
By definition, surface energy (γ) is the work needed to create a new unit of area. The measurement unit used for surface area is Joule(J)/m2, which is equivalent to N/m, used for surface tension. The fact that the force per unit length is equal to energy per unit area can be verified by the behavior of soap film in a wire frame, that can be pulled (Figure 2.3.5 below). With γ being the surface tension of the soap-air, a force of F = 2.γ.l will be necessary to maintain the movable wire piece at rest (there are two surfaces of soap-air that resist F). The surface energy is the needed energy to increase the surface area. If the wire is moved to the right a distance of dx, an area of 2.l.dx will be created at a work cost of F.dx. However the surface tension will be:
\[\frac{work}{Area}= \frac{Fdx}{2ld x}=\frac{2\gamma ldx}{2ldx} = \gamma \tag{3.1} \]
