IIT JEE and NEET Physics @ Venkats Academy IIT-JEE and NEET Physics

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 4^th 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 4^th 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.

Problems and Solutions on Young's Modulus of a wire

Rigidity Modulus and Bulk Modulus

Behavior of a Wire under Increasing Load

Breaking Stress and Its Applications

Experimental determination of Youngs modulus of the wire

Energy stored in the wire

Problems and Solutions on Elasticity

Surface Tension and Concept Related Problems

Surface Tension Explanation basing on Molecular Theory

To explain the surface tension of a liquid we can depend on molecular theory. As per the molecular theory each molecule is having a certain molecular range up to where it can influence the surrounding molecules. Taking that molecule at the center and the molecular Range as radius we can draw a sphere and that sphere is called as sphere of influence.

Let us consider a liquid in a vessel and three different molecules at three different locations. One molecule is at the middle of the liquid surface, one molecule is on the surface of the liquid, another molecule is near to the surface of the liquid. For each of them we can draw the sphere of influence as shown.

The molecule who is there completely inside the water it is completely filled with the water molecules.The molecule at the centre is equally pulled by the surrounding molecules in all directions and it is in a kind of equilibrium state. In this case there is no resultant force acting on the molecule and there is no force due to the surface tension on that.

Let us consider the molecule that is close to the surface of the liquid. Its lower sphere of influence is full of liquid molecules whereas the upper sphere of influence only partially filled. The molecule is equally pulled by both the left and the right side molecules. But the force on the molecule in the downward direction is more than that of the upward direction because of the more number of the molecules in the lower sphere of influence. Thus this molecules experience a little bit of the downward force due to the surface tension.

Let us consider the molecule on the surface of the liquid itself. Its lower sphere of influence is full of liquid molecules where as the upper spirit of influence completely empty. Thus the molecules on the surface of the liquid experience maximum download force. It is the same for all the molecules on the surface and this generates a certain force on the surface of the liquid called a surface tension.

For the molecules who are close to the surface of the container ,there is a adhesive force which is dominating the cohersive force in general.Therefore the molecules there stick to the surface of the container itself whereas the remaining molecules comes in the downward direction because of the force of attraction in the downward direction. Hence the surface of the liquid will change from a plain shape to a curved shape. This is what do you mean by stretching elastic membrane.

Because of the surface tension the liquid surface molecules always tries to acquire a minimum surface area. This is simply to reduce their potential energy and to get the better stability. This can be easily observed in the following example.

Let us take a thin wire and metal frame and immerse it in a soap solution. We can arrange a lightweight thread which is connected between both the ends gently on this soap solution and by default it acquires jig jag shape. If you punch it a little bit at the Centre there will be the soap only between the thread that the frame but no soap solution within the thread. The soap solution that is there between the thread and frame tires to acquire minimum surface area by pulling the thread from all the direction so that the thread will finally acquire a circular shape as shown.

The shape is simply circular because among all the shapes,area of circle is having a largest possible area. As the thread is occupying the maximum area the soap solution is obviously going to occupy the minimum area. This is due to the surface tension.

Even the water drops thrown into the air always acquires a spherical shape due to the surface tension only. Among all the shapes the sphere is having the least possible area and hence water drops are acquire spherical shape. If the size of the drop is big,because of dominating gravitational force it is not going to acquire the exact spherical area and it will be something like a dumbbell and other different shapes.