Q. 7

Prove that surface tension is numerically equal to surface energy

Answer :

Surface Tension (σ): It is measured as force acting per unit length of an imaginary line drawn on liquid surface.


Where,


F = Force that liquid exerts


l = length of imaginary line drawn on the liquid surface


Surface Energy: It is the work done in increasing the area of the surface film by a unit amount.



Consider a rectangular frame ABCD in which wire AB is movable. Dip the frame in soap solution. A film is formed which pulls the wire AB inwards due to surface tension with a force,



We have included a factor of 2 because the soap film has two free surfaces.


Suppose AB is moved out through a distance x to the position A’B’. Then,




Increase in surface area of the film is =





Hence surface energy is numerically equivalent to its surface tension.


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