Question

The surface tension of soap solution is 0.03$\dfrac{N}{m}$. The amount of work done in forming a bubble of radius 5cm is:
A) $3.77$J
B) $1.885$J
C) .95×${10^{ - 3}}$J
D) 1.9×${10^{ - 3}}$J

Answer 1

Hint:The work done by a body is defined as the product of force and displacement. Here because of surface tension there will be a slight change in the formula. It will read as the work done in forming a bubble of radius r will be equal to 5cm is Surface tension × total surface area of bubble and bubble is a sphere.

Step by step solution:
Step 1:
Surface tension of soap solution is less, it can spread over large areas and wash clothes more effectively, since the dirt particles stick to the soap molecules. Antiseptics have low surface tension, so that they spread faster
Step 2:
The bubble is a sphere and the surface area of the sphere is $4\pi {r^2}$and a bubble has two surface areas.
So the surface area of bubble will be 2×$4\pi {r^2}$=$8\pi {r^2}$
Radius of soap bubble = 5cm (Given)
Surface tension of soap bubble = 0.03$\dfrac{N}{m}$ (Given)
Work = Force × Displacement OR
Work = Surface tension × Change in the surface area……(1)
Putting the values in (1)
Hence work done is, W= 0.03×$8\pi {r^2}$
This is equal to 1.9×${10^{ - 3}}$J

So, The amount of work done in forming a bubble of radius 5cm is: 1.9×${10^{ - 3}}$J

Note:Point of mistake:
This type of question is formula based and can be solved easily. Still if any value has been entered wrong then there will be an error occur. This can also happen when we enter different units for different values.
Work, energy etc. all have units as joules and need not to get confused in these.
Surface tension depends mainly upon the forces of attraction between the particles within the given liquid and also upon the gas, solid, or liquid in contact with it. ... An increase in temperature lowers the net force of attraction among molecules and hence decreases surface tension.