We
are going to solve series of problems with detailed solutions about a topic
called surface tension. Surface tension is the property of liquid due to which
the liquid surface experiences a tension and they tend to acquire minimum
surface area. It is because of this surface tension, small insects are able to
float on the surface of water. It is defined as the force acting on the
tangential surface of the liquid normal to the surface of contact per unit
length. Surface tension can be explained basing on molecular theory. Every
molecule can influence the surrounding and attract the neighboring molecules
up to some extend and that distance is called molecular range. Taking the
molecule as the center, molecular range as the radius, if we draw a sphere, it
is called sphere of influence and within the sphere of influence, core molecule
can attract the other molecules.
Problem
The
length and thickness of a glass plate is given to us as shown in the diagram
below. If this edge is in contact with a liquid of known surface tension, we
need to know the force acting on the glass plate due to the surface tension of
the liquid.
Solution
We
know that surface tension is mathematically force acting on it per unit length.
Here length means the length of free surface of the body that is in contact
with the liquid. The glass plates both inner and outer surface are in contact
with the liquid and hence two lengths has to be taken into count. The problem
is solved as shown in the diagram below.
Problem
A
drop of water of known volume is pressed between two glass plates so as to
spread across a known area. If surface tension of the liquid is known to us, we
need to know the force required separating the glass plate and the problem is
as shown in the diagram below.
Solution
We
can write the volume as the product area of cross section with the length of
the liquid. We also know that the surface tension can also be expressed in
terms of work done per unit area. Intern work done can be expressed as the product
of force and displacement. Taking this into consideration, we can solve the
problem as shown in the diagram below.
Problem
A
big liquid drop of known radius splits into identical drops of same size in
large number and we don’t know the radius of the small drop. We need to measure
the work done in this process and the problem is as shown in the diagram below.
Solution
We
know that the volume of the liquid is conserved. It means the volume of the big
drop is the sum of the volumes of all small drops together and basing on that
we can find the relation between smaller and bigger radius as shown in the
diagram below. We can write the equation for the work done as the product of
surface tension and the change in the area.
Problem
Work
done in blowing a soap bubble of radius R is given to us as W. We need to
measure the work done in blowing the same bubble to a different radius and the
problem is as shown in the diagram below.
Solution
As
discussed in the previous problem, we can define the work done as the product
of surface tension and the change in the area of cross section. By applying
that data, we can solve problem as shown in the diagram below.
Problem
We
need to find the capillary rise of a liquid in a capillary tube when it is
dipped in that liquid where surface tension and density of the liquid is given
to us. We can treat angle of contact as zero and the problem is as shown in the
diagram below.
Solution
We
know that when angle of contact is less than ninety degree, the liquid raises
above the normal level of the beaker and that property is called capillarity.
The capillary rise depends on the radius of the tube, density and surface
tension of the liquid. We can apply the formula and solve the problem as shown
in the diagram below.
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