The relation between surface tension and surface energy is

Explanation

Suppose a soap film is isothermally stretched over the area enclosed by a U-shaped frame ABCD and a movable cros-piece PQ. as shown in the figure. Let T be the surface tension of the soap solution and l, the length of wire PQ in contact with the soap film.
The film has two sufaces. Hence, the net force on the wire PQ is 2T l.Suppose that wire PQ is pulled outward very slowly through a distance dx to the position P'Q' by an extrenal force F=2T l.

The work done by the extrenal force against the force due to the film is
W=applied force `xx`displacement
`:. W=Fdx=2Tl dx`
Due to the displacement dx, the surface area of the film increases by
A=2ldx
Thus, the work done per unit surface area is
`(W)/(A)=(2Tl dx)/(2l dx)=T`
This work is stored in the unit surface area of the liquid in the form of potential energy and is called the surface. Thus, the surface energy per unit area of a liquid is equal to its surface tension.