## Tuesday, January 3, 2017

### Surface Tension Problems with Solutions Two

We are solving series of problems based on the concept surface tension. It is the property of the liquid because of which the liquid surface behaves like a stretched elastic membrane. Because of surface tension, liquids always try to acquire minimum surface area. This is the reason why water drops are spherical in shape as the sphere has minimum surface area among all possible three dimensional shapes. Angle of contact is a parameter that measures weather cohesive or adhesive forces are dominating in a given system. If adhesive forces are dominating, angle of contact is less than ninety  degree and vice versa.Angle of contact is the angle drawn between two tangents drawn at the point of contact where one tangent is drawn to the liquid surface and the other tangent is drawn to the wall of the capillary tube into the liquid. Basing on that there will be capillarity rise or fall.

Problem

When a capillary tube is immersed in water the mass of water that raised in the tube is of 5 gram. If the radius of the tube is doubled we need to find the raise of the water in the new tube and the problem is as shown in the diagram below.

Solution

We know that when a capillary tube is placed in a liquid, a component of surface tension generates a force that pulls the liquid upward. Simentaniouly we have liquids weight acting in the downward direction. When this downward force compensate the upward force due to surface tension, liquid stops rising further. By equating this two forces, we can solve the problem as shown in the diagram below.

Problem

We need to find the excess pressure inside an air bubble when the bubble radius is known to us and surface tension of the liquid is also given to us. Problem is as shown in the diagram below.

Solution

When the drop is acquiring spherical shape, there is pressure acting towards its center and it generate excess pressure inside the spherical bubble. Basing on the formula that we have derived, we can solve the problem as shown in the diagram below.

Problem

Surface area and surface tension of the liquid is given to us in the problem as shown in the diagram below. We need to find the excess pressure inside the drop.

Solution

We know the surface area of the sphere and hence we can express the radius of the drop in terms of area of cross section as shown in the diagram below. Substituting that data in the excess pressure formula, we can solve the problem as shown in the diagram below.

Problem

Two soap bubbles are combined to form a single bubble. In this process change in volume and area is given to us in the problem. Pressure and surface tension are given to us and we need to find the relation between them.

Solution

We know that under isothermal conditions, Boyle's law is valid and we can equate product of pressure and volume is conserved as shown in the diagram below. By applying the formula for the pressure and the volume of the sphere we can solve the problem as shown in the diagram below.

Problem

A thread of length L is placed on a soap film of known surface tension. If the film is pierced with a needle we need to measure the tension in that thread and the problem is as shown in the diagram below.

Solution

We can equate the force due to surface tension to the force and centripetal force and solve the problem as shown in the diagram below.

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