Explain surface energy and surface tension.

(N/A) Surface energy is the extra energy associated with the surface of a liquid. Creating more surface area while keeping the volume fixed requires additional energy.
As shown in figure $(a)$, a $U$-shaped frame is made from wire, and the wire $PQ$ slides without friction over the rods $AP$ and $BQ$.
When this frame is dipped into a soap solution and taken out, a thin film $APQB$ is formed. In figure $(a)$, the film is in equilibrium.
In figure $(b)$, it is shown that the film is stretched by an extra distance $d$.
Since the area of the surface increases, the system now has more energy, which means some work has been done against an internal force.
Let this internal force be $F$. The work done by the applied force is:
$W = \vec{F} \cdot \vec{d} = F d$
From the principle of conservation of energy, this work is stored as additional energy in the film.
If the surface energy per unit area of the film is $S$, the extra area created is $2ld$. (Because $\Delta A = \text{length} \times \text{breadth} = ld$, and the film has two free surfaces, so the total area increase is $2ld$).
The liquid film has two surfaces, so the extra energy is $E = (2ld)S$.
Therefore, $W = (2ld)S = S \Delta A$ (where $\Delta A = 2ld$ is the increase in area).
Thus, $S = \frac{W}{\Delta A}$.
Substituting the values, $S = \frac{Fd}{2ld} = \frac{F}{2l}$.
This quantity $S$ is the magnitude of surface tension. It is equal to the surface energy per unit area of the liquid interface and is also equal to the force per unit length exerted by the fluid on the movable bar.