Question

If T is surface tension of soap solution, the amount of work done in blowing a soap bubble from diameter D to a diameter 2D is

• A. $2\pi D^{2}T$
• B. $4\pi D^{2}T$
• C. $6\pi D^{2}T$
• D. $8\pi D^{2}T$

Answer 1

The correct option is C $6\pi D^{2}T$

The amount of work done to blow a bubble is the change in surface energy of the bubble.

Hence W = change in surface energy

= $T△A=\int TdA$

= T $\times$ 16$\pi {\int }_{D/2}^{D}rdr$

= $\frac{16}{2}\pi T[D^2-\frac{D^2}{4}]$

= 8$\pi T\frac{{3D}^2}{4}$

$W=6\pi D^{2}T$