Question

Establish relation between the surface tension of a liquid and the work done in increasing its surface area. Write the unit of surface tension on this basis.

Accepted Answer

When the surface area of a liquid is increased, the molecules from the interior rise to the surface. This requires work against force of attraction of the molecules just below the surface. This work is stored in the form of potential energy. Thus, the molecules in the surface have some additional energy due to their position. This additional energy per unit area of the surface is called 'surface energy". The surface energy is related to the surface tension as discussed below:

Let a liquid flim be formed on a wire frame and a straight wire of length I can slide on this wire frame as shown in figure. The film has two surface and both the surface are in contact with the sliding wire and hence, exert forces of surface tension on it. If $T$ be the surface tension of the solution, each surface will pull the wire parallel to itself with a force Tl. Thus, net force on the wire due to both the surface is $2 T I$ . One has to apply an external force $F$ equal and opposite to it to keep the wire in equilibrium. Thus,

$F = 2 T I$

Now, suppose the wire is moved through a small distance $d x$ , the work done by the force is,

$d W = F d x = (2 T I) d x$

But $(2 I) (d x)$ is the total increase in area of both the surface of the film. Let is be $d A$ . Then,

$d w = T d A$

or

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

Thus, the surface tension $T$ can also be defined as the work done in increasing the surface area by unity.

unit of surface tension $(T) = W / A$ . Joule per metre $(S I)$

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