Define surface energy and show that surface energy is equal to surface tension.
Surface energy is defined as the mechanical work required to increase the unit area of free surface under isothermal condition.
Take a wired rectangular frame ABCD whose three sides are rigid and one side AB is free to slide.
Dip the frame in soap solution to form the film. The surface tension acts on all the sides of the frame. Three sides of the frame being fixed cannot be displaced, but side AB is free to slide and due to surface tension it slides towards the left direction and free surface tries to contract.
Let surface tension of the soap solution be T and length of movable side AB be l.
Since there are two free surfaces of liquid which touch the movable wire AB, due to surface tension total inward force on the wire is 2Tl. If frame AB is displaced by distance x in the right direction, then work done against surface tension to increase the surface area is
W = 2Tlx
Increase in surface area of film is
lx + lx = 2lx
Surface energy =
Hence, surface energy is equal to surface tension.