We
are solving series of problems on the property of a liquid called surface
tension. This is due to molecular force of attraction among the liquid
molecules. If the molecules belongs to same liquid the force is called cohesive
force of attraction and if they are due to different liquid molecules then it
is called adhesive force of attraction. Which force among this two is
dominating depends on the nature of that liquids and the body in contact. Water
sticks to our body as adhesive force is dominating and mercury won’t as
cohesive force is dominating. This can be even understood in terms of angle of
contact and capillary rise of the liquid when a thin tube is placed in it.
Surface tension depends on the nature of the liquid as well as temperature of
the liquid. If temperature is raised, molecular force of attraction decreases
and hence surface tension also decreases.
Problem
A
liquid of known density and surface tension is placed in a capillary tube and
it has raised to a certain height. We need to find the potential energy of the
system and the problem is as shown in the diagram below.
Solution
We
know the formula for the gravitational potential energy in terms of the height
of the liquid but it is spread over the entire length and not focused at the
top. Thus we shall consider the concept of center of mass ans we can assume
that the entire mass is consecrated at the center of mass of the liquid which
is at geometrically half of the total height. By subsisting the value of the
capillary rise in terms of the surface tension, we can solve the problem as
shown in the diagram below.
Problem
Several
liquid drops of known radius and density are combined to foam a big drop of
known radius. If all the energy released in this process is converted into
kinetic energy, we need to find the velocity acquired by the drop.
Solution
Energy
released can be expressed as the difference between work done for both the
radius basing on the definition that surface tension is work done per unit
change in the area of cross section of the liquid. We shall equate it to the
kinetic energy where mass can be expressed as the product of density and
volume. Problem can be further simplified as shown in the diagram below.
Problem
A
glass rod of known radius is immersed into a capillary tube of known radius as
shown in the problem below. If the arrangement is immersed in the water, we
need to find the rise in the liquid level.
Solution
Liquid
will rise in the system until the force in the upward direction due to surface
tension is balanced by the weight of the raised liquid in the capillary tube
system. By writing the mass as the product of volume and density and further
volume as the product of area and length, problem can be solved as shown in the
diagram below.
Problem
Under
isothermal conditions two bubbles of known radius are combined to foam a single
drop of know radius. If the external pressure is given to us, we need to
measure the surface tension of the system and the problem is as shown in the
diagram below.
Solution
We
can apply Boyle’s law as the temperature of the system is constant as shown in
the diagram below. By simplifying it further we can solve the problem as shown
here.
Problem
A
soap bubble is blown at the end of very narrow tube as shown in the problem
below. Air flows into the tube with a known velocity and it comes to rest
inside it. After some time the bubble get some radius and comes out of the
tube. We need to find the radius of the bubble so that the air strikes the
bubble surface normally.
Solution
We
need to equate the force due to pressure to the force due to surface tension
and the problem can be solved as shown in the diagram below.
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