Radius of a soap bubble is increased from R to 2 R work done...

Radius of a soap bubble is increased from $R$ to $2 R$ work done in this process in terms of surface tension is
[CPMT 1991; RPET 2001; BHU 2003]
(a) $24 \pi R^{2} S$
(b) $48 \pi R^{2} S$
(c) $12 \pi R^{2} S$
(d) $36 \pi R^{2} S$

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

Surface Tension

Surface tension is a physical property of liquids manifesting as a force per unit length along the interface, which also represents the energy cost per unit area to create a new surface. This concept is essential when determining the work required to increase the surface area of a liquid, such as in the formation or expansion of a soap bubble.

Work Done in Changing Surface Area

The work done in changing a system's surface area is directly associated with the surface energy, and it is calculated by multiplying the change in the area by the surface tension. This principle is critical in understanding how energy is expended when a bubble is enlarged, as the expansion increases the surface area that must be sustained by the soap solution.

Double Surface of a Soap Bubble

A soap bubble consists of two surfaces – an inner and an outer surface – due to the thin film structure of the soap solution. When computing the total work done in changing the bubble's radius, it is necessary to account for the increase in surface area on both sides of the liquid film, thereby doubling the contribution from the change in area.

Transcript

Please give Ace some feedback