The amount of work done in blowing a soap bubble such that its diameter increases from d 1 to d 2 is ( T = surface tension of soap solution)

Question

The amount of work done in blowing a soap bubble such that its diameter increases from d 1 ​ to d 2 ​ is ( T = surface tension of soap solution)

TestHub · Accepted Answer

A soap bubble has two free surfaces (inner and outer).

Initial surface area of the soap bubble, $A_{1} = 2 \times 4 π r_{1}^{2} = 2 \times 4 π (\frac{d _{1}}{2})^{2} = 2 π d_{1}^{2}$

Final surface area of the soap bubble, $A_{2} = 2 \times 4 π r_{2}^{2} = 2 \times 4 π (\frac{d _{2}}{2})^{2} = 2 π d_{2}^{2}$

Increase in surface area, $Δ A = A_{2} - A_{1} = 2 π (d_{2}^{2} - d_{1}^{2})$

Work done in blowing the bubble is given by the product of surface tension and the increase in surface area:

$W = T \times Δ A = 2 π (d_{2}^{2} - d_{1}^{2}) T$

Answer: $2 π (d_{2}^{2} - d_{1}^{2}) T$

Physics - Fluid Question with Solution | TestHub

Options:

Doubts & Discussion