We can express a surface tension in terms of surface energy
also. When the shape of the liquid is change and it acquire some energy that energy could be called as a surface
energy. We can define surface tension even in terms of surface energy per unit
area. We can derive the mathematical equation for surface energy as shown
below.
Let us consider a
metal frame who is in a rectangular shape with 3 sides fixed and the 4th
side is having a movable piston. You can immerse it in a soap solution and get
it out therefore there will be a thin soap film formed in the frame as shown.
The soap film because of the surface tension tries to require a minimum surface
area. It tried to pull all the sides but being the 3 sides are fixed they are
not going to move to the 4th side is going to move.
We can apply an
external force on the piston therefore we can get it back to its original shape
and during this process we have to do some work. This work is done due to the
surface tension and the same work can be stored in the format of the surface
energy inside the liquid.
Basing on the definition of the work done as the surface
tension multiplied by the change in the area with can solve different problems
and we can deal with a different applications. If a liquid drop is rising from
the zero radius to a particular radius we can calculate the work done as shown.
If a big drop of known radius splits into an number of
identical drops of unknown radius we can calculate the equation for the work
done basing on the concept of surface tension as shown below.
We can also calculate the work done when multiple drops of
known radius and identical in size are combined together to form a big drop of
unknown radius. In solving both this problem is we have to understand that area
of the small drops together will have a
larger area than the area of the big drop.
Problem and solution
A water drop of radius 1 cm is broken up into small water
drops each of radius 1 mm assuming that at constant temperature what is the
work done in this process?
We can solve this problem basing on the concept of work done
as shown below. Using the same concept that is explained above to more problems
are solved in the given diagram below.
Expression for potential energy
In a capillary tube rain water raises to a certain height due to
the capillarity, some work has to be done. This work is stored in the format
of potential energy. Here we can derive the equation for the potential energy
as shown below. The mass of the water in the capillary tube distributed over
its entire height. Its Centre of mass has to be considered at exactly the
middle because the mass is uniformly distributed.
In the place of the height we can use the equations that we
had derived in the in the capillary
action derivation.
When two plates are attached with each other with the water
layer between them we can calculate the force of attraction acting between them
as shown below.
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