Define surface tension and provide its formula in the context of $(i)$ intermolecular forces,$(ii)$ potential energy,and $(iii)$ work done.

(N/A) Surface tension is a property of the liquid surface that allows it to resist an external force,due to the cohesive nature of its molecules.
$(i)$ In terms of intermolecular forces: Surface tension is defined as the force per unit length acting on an imaginary line drawn on the free surface of a liquid,perpendicular to the line and parallel to the surface. If $F$ is the force acting on a line of length $l$,then surface tension $S$ is given by:
$S = \frac{F}{l} \left( \frac{\text{N}}{\text{m}} \right)$
$(ii)$ In terms of potential energy: Surface tension is defined as the potential energy stored per unit area of the free surface of a liquid. If $E$ is the potential energy and $A$ is the area,then:
$S = \frac{E}{A} \left( \frac{\text{J}}{\text{m}^2} = \frac{\text{N} \cdot \text{m}}{\text{m}^2} = \frac{\text{N}}{\text{m}} \right)$
$(iii)$ In terms of work done: Surface tension is defined as the work done per unit increase in the surface area of a liquid. If $W$ is the work done to increase the area by $\Delta A$,then:
$S = \frac{W}{\Delta A} \left( \frac{\text{J}}{\text{m}^2} = \frac{\text{N}}{\text{m}} \right)$