# Surface Energy , Surface Tension

Relation between Surface Energy & Surface Tension

If the area of the liquid surface has to be increased, work has to be done against the force of surface tension. The work done to form a film is stored as potential energy in the surface and the amount of this energy per unit area of this surface under isothermal condition is the “intrinsic surface energy” or free surface energy density.

Work done in small displacement dx

dW = F × dx = 2TL dx

$\displaystyle W = \int_{0}^{x}2TL dx = 2TLx = T A$

As A = 2Lx (area of both sides)

$\displaystyle \frac{W}{A} = T$

Exercise : Several small drops of liquid are added together to make a big drop. How is the temperature of the drops affected?

Illustration : What is the surface energy of a soap bubble of radius r ?

Solution: E = TA = T × 4πr2 × 2 (as it has two surfaces)

= 8πr2T

Illustration : What is the surface energy of an air bubble inside a soap solution ?

Solution: E = T × A = 4πr2T , as it has only one surface