Question

Explain the surface energy of a liquid. What is the relation between surface tension and surface energy?

Accepted Answer

The extra energy possessed by the molecules of the surface film of unit area compared to the molecules in the interior is called surface energy. It is equal to the work done in increasing the area of the surface film by a unit amount.

$surface energy = \frac{work done}{increase in surface area}$

The molecules on the liquid surface experience net downward force. So to bring a molecule from the interior of the liquid to the free surface, some work is required to be done against the intermolecular force of attraction, which will be stored as the potential energy of the molecule on the surface. The potential energy of surface molecules per unit area of the surface is called surface energy.

If a rectangular wire frame $A B C D$ , equipped with a sliding wire $L M$ dipped in soap solution, a film is formed over the frame. Due to the surface tension, the film will have a tendency to shrink and thereby, the sliding wire $L M$ will be pulled in inward direction. However, the sliding wire can be held in this position under a force $F$ , which is equal and opposite to the force acting on the sliding wire $L M$ all along its length due to surface tension in the soap film.

If $T$ is the force due to surface tension per unit length, then $F = T \times 2 l$

Here, $l$ is length of the sliding wire $L M$ . The length of the sliding wire has been taken as $2 l$ for the reason that the film has got two free surfaces.

Suppose that the sliding wire $L M$ is moved through a small distance $x$ , to take the position $L M$ . In this process, the area of the film increases by $2 l \times x$ (on the two sides) and to do so, the work done is given by

$W = F \times x = (T \times 2 l) \times x = T \times (2 l x) = T \times △ A$

$∴ W = T \times △ A$ [ $△ A =$ Total increase in the area of the film from both sides.]

If the temperature of the film remains constant in this process, this work done is stored in the film as its surface energy.

From the above expression $T = \frac{W}{△ A}$ or $T = W$ [If $△ A = 1$ ]

G L Mittal and TARUN MITTAL Solutions for Chapter: Surface Tension, Exercise 1: QUESTIONS

G L Mittal Physics Solutions for Exercise - G L Mittal and TARUN MITTAL Solutions for Chapter: Surface Tension, Exercise 1: QUESTIONS

Questions from G L Mittal and TARUN MITTAL Solutions for Chapter: Surface Tension, Exercise 1: QUESTIONS with Hints & Solutions

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