Question

What is capillarity? Give any two applications of capillarity. Calculate the work done in blowing a soap bubble of radius $0.1m$ . (Surface tension of soap solution $ = 30\,dyne\,c{m^{ - 1}}$ )

Answer 1

Hint: The tendency of a liquid to rise or fall in a capillary tube as a result of surface tension is called capillarity. The surface tension of the soap solution is given. The work done in blowing a soap surface is the surface tension multiplied by surface area. A soap bubble has two surfaces; inside and outside.

Complete step by step solution:
When a liquid is filled in a capillary tube the liquid elevates and contracts based on the relative attraction of the molecules of the liquid. This property is known as capillarity.
Applications of capillarity:
Sponge absorbs the liquid due to capillary action.
When ink drops on blotting paper it gets absorbed due to capillary action.
We are given a soap bubble having radius $r = 0.1m$ . The work done $W$ in blowing the soap bubble is given as:
$W = surface\,tension\, \times \,surface\,area$
We are given that the surface tension of the soap solution is $ = 30\,dyne\,c{m^{ - 1}}$ . In SI units the surface tension will be $0.03\,N{m^{ - 1}}$. As $1\,dyne\,c{m^{ - 1}} = 0.001\,N{m^{ - 1}}$
The surface area of the soap bubble is taken as the sum of inner surface area and the outer surface area. As the difference in radius is negligible, we consider the inner and outer surface radius to be the same.
The total surface area $ = 2 \times 4\pi {r^2}$ = $2 \times 4 \times \pi \times {\left( {0.1} \right)^2}$
The total surface area $ = 0.2513\,{m^2}$
$W = surface\,tension\, \times \,surface\,area$
$ \Rightarrow W = \left( {0.03} \right) \times \left( {0.2513} \right)$
$ \Rightarrow W = 0.00754\,J$
$ \Rightarrow W = 7.54 \times {10^{ - 3}}\,J$
This will be the work done in blowing a soap bubble of radius $0.1m$ .

Note: A soap bubble has two surfaces, one inside and one outside. For calculating the work done, both the surfaces are to be considered. Convert the units of surface tension in SI units. The final units of work done will be in Joules. The rise or fall in the level of fluid inside a tube depends on the relative attraction of the molecules of the liquid.