Q.15 Define surface tension. Obtain the relation between surface tension and surface energy.
Best answer
Answer: Surface tension is the tangential force per unit length acting perpendicular to an imaginary line drawn on the free surface of a liquid. Surface energy per unit area = surface tension.
Definition: \(T = \dfrac{F}{l}\); SI unit N/m.
Relation: [Figure: a rectangular wire frame ABCD with a movable wire PQ of length l sliding on its arms; a soap film is formed in the frame on one side of PQ. The film pulls PQ inwards; PQ is pulled out through a small distance dx to the position P′Q′.]
The soap film has two free surfaces, so the inward force on the wire is \(F = 2Tl\).
To pull the wire out isothermally through \(dx\), work must be done against this force:
\[dW = F\,dx = 2Tl\,dx\]Increase in surface area of the film (two surfaces):
\[dA = 2l\,dx\]This work is stored as the surface energy of the extra surface. Surface energy per unit area:
\[\frac{dW}{dA} = \frac{2Tl\,dx}{2l\,dx} = T\]Hence, surface energy per unit area of a liquid surface is numerically equal to its surface tension (\(\Delta E = T\,\Delta A\)).
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