## Tuesday, January 3, 2017

### Surface Tension Problems with Solutions Three

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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