Question

Prove that surface energy is numerically equal to the surface tension

Answer 1

Let PQR be the liquid film.  

Let the wire free to slide on the plane be AB.

Now the surface tension (T) pulls the wire towards Q.  

The force applied on the wire to keep the system in equilibrium is F.  

So,

F = 2Tl

l is the length of the wire.  

Work done by the force.  

W = Fx = 2Tlx = TA

A is the total increase is the surface area of the film.

So surface energy,

E = W/A = T

Therefore the surface energy and the surface tension are numerically equal.

         

Answer 2

hence surface energy is numerically equivalent to its surface tension

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