## Tuesday, January 3, 2017

### Surface Tension Problems with Solutions One

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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