Question

The radius of a soap bubble is $r$. The surface tension of soap solution is ${}^{\prime }{S}^{\prime }$. 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 $2r$ radius soap bubble
$=4\pi \left(2r^2\right)S\times 2=32\pi r^{2}S$
$\therefore$ Energy of bubble $=32\pi r^{2}S=E_{2r}$
So energy required to expand a bubble from $r$ to $2r$ will be equal to $E_{2r}-E_r$,
Substituting values
We get,
$32\pi r^{2}S-8\pi r^{2}S=24\pi r^{2}S$