Question

The radius of a soap bubble is $r$. The surface tension of soap solution is $'S'$. Keeping temperature constant, the radius of the soap bubble is doubled. The energy necessary for this will be

• A. $24 \,\pi r^{2} \,S$
• B. $8\, \pi r^{2} \,S$
• C. $16\, \pi r^{2} S$
• D. $12\, \pi r^{2} S$

Answer 1

Answer: (A)

Work done in making a soap bubble of radius
$r=4 \pi r^{2} S \times 2=8 \pi r^{2} S$
$\therefore $ Energy of bubble $=8 \pi r^{2} S=E_{r}$
$\{$ Multiply by 2 due to two free surface $\}$
Work done in making a $2 r$ radius soap bubble
$=4 \pi\left(2 r^{2}\right) S \times 2=32 \pi r^{2} S$
$\therefore $ Energy of bubble $=32 \pi r^{2} S=E_{2 r}$
So energy required to expand a bubble from $r$ to $2 r$ will be equal to $E_{2 r}-E_{r}$,
Substituting values
We get,
$32 \pi r^{2} S-8 \pi r^{2} S=24 \pi r^{2} S$