Relation between surface tension and surface energy
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Consider a liquid film to be formed on a rectangular surface ABCD. On forming a film, the surface film contracts (see arrows) due to surface tension i.e., AB is pulled inwards. To keep AB in its original position, a force F is applied in the outward direction, all along its length. If T is force due to surface tension (i.e. T=F/l).
Then F = T x 2l. Since the film has two free surfaces, the RHS of the equation is multiplied by 2.
If the wire AB is to be pulled by an additional distance dx, then the additional work done W in this case is,
i.e. Work done in increasing the surface area by unity, is equal to the surface tension T at constant temperature. Therefore, this work done, is the surface energy of the film.
SI. unit of surface energy is N/m and Dimension of Surface energy [MT - 2]
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Excess pressure inside a liquid drop and a bubble
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We know that in small drops and bubbles, the effect of gravity is negligible on account of surface tension. Small drops do not collapse due to surface tension. This means that the pressure inside the drop is greater than the pressure outside. Let this excess pressure i.e., p
i - p
o = p. Due to this pressure difference, let the radius increase from R to R +
dR.
Outside force = pressure difference x surface area
Hence, to increase the surface area
Work done by the excess pressure is stored in the form of potential energy.
Increase in P.E. = surface tension x increase in surface area.
dW = increase in P.E.
