Explain surface energy and surface tension.

Explanation

An extra energy is associated with surface of liquid , the creation of more surface keeping volume fixed requires additional energy.

As shown in figure (a) a U- shape frame is made from wire , the wire PQ slide without firction over the rides AP and BQ.
This frame dipped and taken out of the soap solution , thin film APQB is formed from the frame.
In figure (a) film is in equilibrium.
In figure (b) it is shown that the film is stretched at extra distance d.
Since the area of the surface increases ,the system now more energy , means that some work has been done against an internal force.
Let this internal force be F.The work done by the applied force is ,
`W=vecF*vecd=Fd` ...(1)
From the conservation of energy , this is stored as additional energy in the film.
If the surface energy of the film is S per unit area , the extra area is 2ld. (Because `DeltaA`=length `xx` breadth ld and film has two free surface,so 2ld is present.
The liquid in between , so there are two surfaces and the extra energy is `=(2ld)S`.
`thereforeW=(2ld)S=SDeltaA[because2ld`= increase in area]
`thereforeS=(W)/(DeltaA)`
`thereforeS=(fd)/(2ld)=(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 lenght exerted by the fluid on the movable bar.