Question

Derive the relation between the surface tension and surface energy of a

liquid.​

Answer 1

Answer:

The surface energy of free surface is the increament in potential energy of the surface per unit increment in area. ... Surface tension is a property of liquid surface due to which liquid surface behaves like a stretched membrane.

Explanation:

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Answer 2

Answer:

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Consider a rectangular wire frame ABCD in which the wire AB is movable. Dip the wireframe in soap solution. A film is formed which pulls the wire AB inward due to surface tension by a force ( σ × 2l ).

Here σ is the surface tension of the film and l is the length of the wire AB. The length is taken twice because the soap film touches the wire above as well as below.

If the film is stretched by a small distance x to the position A’ B’ keeping the temperature constant, then the work done is given by σ × 2l × x

Now, 2l × x is the total increase in the area of the soap film on both sides.

∴ Work done = σ × Increase in area

Work done per unit area = σ (or)Surface energy = σ

So, the force due to surface tensions numerically equal to the surface energy per unit area.