How is surface tension related to surface energy?

Explanation

Consider a rectangular frame of wire ABCD in a soap solution. Let AB be the movable wire. Suppose the frame is dipped in soap solution, soap film is formed which pulls the wire AB inward due to durface tension. Let F be the force due to surface tension, then
`F = (2T)l`
Here, 2 is introduced because it has two free surfaces. Suppose AB is moved by a small distance `Delta x` to a new position A'B'. Since the area increases, some work has to be done against the inward force due to surface tension.
Work done `= "Force" xx "distance" = (2T l) (Delta x)`
Increase in area of the film `Delta A = (2l) (Delta x) = 2l Delta x`
Therefore,
Surface energy `= ("work done")/("increase in surface area")`
`= (2T Delta x)/(2l Delta x) = T`
Hence, the surface energy per unit area of a surface is numercially equal to the surface tension.