The amount of work done in blowing a soap bubble such that...

The amount of work done in blowing a soap bubble such that its diameter increases from $d$ to $D$ is ( $S=$ surface tension of solution) (a) $\pi\left(b^{2}-d^{2}\right) 5$ (b) $2 \pi\left(D^{2}-d^{2}\right) \varsigma$ (c) $4 \pi\left(b^{2}-d^{2}\right) 5$ (d) $8 \pi\left(D^{2}-d^{2}\right) 5$

The amount of work done in blowing a soap bubble such that its diameter increases from $d$ to $D$ is ( $S=$ surface tension of solution)
(a) $\pi\left(b^{2}-d^{2}\right) 5$
(b) $2 \pi\left(D^{2}-d^{2}\right) \varsigma$
(c) $4 \pi\left(b^{2}-d^{2}\right) 5$
(d) $8 \pi\left(D^{2}-d^{2}\right) 5$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Dual Surface Nature of Bubbles

Soap bubbles are unique because they have two surfaces—an inner and an outer surface—each contributing to the overall energy required to form and expand the bubble. This dual nature means that the calculation of work must account for both surfaces when determining the energy needed to increase the bubble's size.

Geometric Analysis of Spherical Surfaces

The computation of changes in surface area for spherical objects involves using geometric formulas that relate the sphere’s radius or diameter to its surface area. Such calculations are central to determining how variations in the dimensions of a sphere affect its overall surface area and thus the work required to alter it.

Surface Tension

Surface tension is a measure of the cohesive forces at the surface of a liquid, which causes the liquid to minimize its surface area. It plays a crucial role in phenomena like the formation of bubbles, droplets, and interfaces, acting as an energy barrier that must be overcome to create new surfaces.

Work Associated with Surface Energy

When a new surface area is created in a liquid, work is done against the force of surface tension. The energy required to produce this increase in surface area is given by the product of the surface tension and the change in area, representing the work done during the process.

Transcript

Please give Ace some feedback