Question
Define surface tension and surface energy. Write units and dimensions of surface tension. Also prove that surface energy numerically equal to the surface tension.
✓
Answer
Surface Tension : Force on unit length of an imaginary line drawn on the surface of the liquid is called surface tension. Its S.I. unit is Nm-1 and its dimension is [ML0T2). Surface Energy: Energy possessed by the surface of the liquid is called surface energy. Change in surface energy is the product of surface tension and change in surface area under constant temperature. Let S = Surface tension of soap solution d = Length of the wire PQ l = length of wire PQ 
Surface tension acts on both the free surfaces of film. Hence, total inward force on wire PQ F = S × 2I Increase in area of the film PQ Q1P1
Surface tension acts on both the free surfaces of film. Hence, total inward force on wire PQ F = S × 2I Increase in area of the film PQ Q1P1 $=\Delta\text{A}=2=(\text{l}\times\text{x})$
Work done in stretching film is, W = Force applied × Distance moved$=(\text{S}\times2\text{l})\times\text{x}=\text{S}\times(\text{2l}\text{ x})$
$=\text{S}\times\Delta\text{A}(\because2\text{l x}=\Delta\text{A})$
This work done is stored in the film as this surface energy.$\text{E}=\text{W}=\text{S}\times\Delta\text{A}$
$\Rightarrow\text{S}=\frac{\text{W}}{\Delta\text{A}}$
If increase in area is unity then, $\Delta\text{A}=1$$\text{S}=\text{W}$
$\therefore$ Surface tension of a liquid is numerically equal to surface energy of the liquid surface.
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