Question

What is the energy required to increase the radius of a soap bubble from \( R \) to \( 2R \) considering the surface tension \( T \)?

• A. \( 8 \pi T R^2 \)
• B. \( 4 \pi T R^2 \)
• C. \( 2 \pi T R^2 \)
• D. \( 16 \pi T R^2 \)

Hint:

The energy required to increase the size of a soap bubble is related to the work done to overcome the surface tension. Always consider the change in surface area when solving these types of problems.

Answer 1

The Correct Option is A

The energy required to increase the radius of a soap bubble is related to the work done against the surface tension. For a soap bubble, the total surface area is \( 4 \pi R^2 \) for a single surface, but there are two surfaces for a bubble (inside and outside), so the total surface area is \( 8 \pi R^2 \). The energy required to increase the radius is given by: \[ \Delta E = \text{Surface Tension} \times \Delta \text{Area} \] Initially, the surface area is \( 8 \pi R^2 \), and finally, it is \( 8 \pi (2R)^2 = 32 \pi R^2 \). The change in surface area is: \[ \Delta A = 32 \pi R^2 - 8 \pi R^2 = 24 \pi R^2 \] Thus, the energy required is: \[ \Delta E = T \times 24 \pi R^2 = 8 \pi T R^2 \] Therefore, the correct answer is option (A).