Question

The work done in blowing a soap bubble of radius r of the solution of surface tension T will be
(A) $8\pi {r^2}T$
(B) $2\pi {r^2}T$
(C) $4\pi {r^2}T$
(D) $\dfrac{4}{3}\pi {r^2}T$

Answer 1

Hint: The work against surface tension is done by increasing the soap bubble's surface area. A liquid surface's propensity to constrict to take up the least amount of space is known as surface tension. Surface tension and the change in volume are the cause of this work against the surface tension. Prior to applying a formula to compute the work required to increase the surface area, convert the radius to a SI unit.

Formula used:
$W=T\times \Delta A$
W is the work done, T is the surface tension and $\Delta A$is the change in area

Complete answer:
Start with the formula of the amount of work done in blowing a soup bubble. We know that, Work done is equal to tension in surface energy and surface energy is tension multiply to change in area as follows:
$W = T \times \Delta A$
Where,
W is work done
T is surface tension and
$\Delta A$is change in area.

Now, in given case of soap bubble, work done will be;
$W = 4\pi {r^2} \times 2 \times T = 8\pi {r^2}T$

Hence the correct answer is Option A.

Additional information:
By virtue of surface tension, a liquid's free surface at rest behaves like an elastic, stretched membrane that is prone to constrict and occupy the smallest possible surface area.
When a line is drawn on a liquid surface, surface tension is calculated as the force acting along its length, with the force acting perpendicular to the line and tangential to the liquid surface.

Note: We should be aware that the force that the molecules under the surface of the liquid exert on the molecules on the liquid's surface is what causes the property of surface tension to form. The liquid's molecules constantly have a propensity to pull the liquid's surface molecules into the bulk of the liquid. As a result, the molecules have a tendency to contract and occupy the smallest surface area. This surface tension force, which functions as a sort of cohesive force, is only felt while facing inward.