The energy required to increase the radius of a soap bubble from 1 cm to 2 cm is: (The surface

step 1 In this problem, initial radius ri is equal to 1 cm, final radius rf is equal to 2 cm, surface t

The energy required to increase the radius of a soap bubble...

The energy required to increase the radius of a soap bubble from $1 \mathrm{~cm}$ to $2 \mathrm{~cm}$ is: (The surface tension is 30 dyne $/ \mathrm{cm}$ )
(a) $240 \pi \mathrm{erg}$
(b) $720 \pi$ erg
(c) $480 \pi$ erg
(d) none of these

Key Concepts

Surface Tension

Surface tension is a physical property of liquids that represents the force per unit length along the liquid's surface, or equivalently, the energy required per unit area to increase the surface area of the liquid. It arises from the imbalance of molecular forces at the interface between the liquid and another medium (such as air), and plays a crucial role in phenomena involving interfaces, such as bubble formation and capillary action.

Surface Energy

Surface energy is the energy associated with the surface of a liquid, defined as the work needed to create a new unit area of the interface. In problems involving the expansion of a bubble, the work done is directly related to the increase in surface energy, which is calculated as the product of the surface tension and the change in the surface area. This concept provides the basis for understanding the energy requirements when altering the geometry of a bubble or droplet.

Change in Surface Area for Spherical Objects

For spherical objects, the surface area is given by the formula 4?r², where r is the radius. When the radius of a sphere changes, the corresponding change in surface area is computed using this formula. Understanding how the surface area scales with the radius is essential for calculating the work done in processes like inflating a bubble, as the energy required is proportional to the additional surface area created.

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