Question

A soap bubble of radius $r$ is blown up to form a bubble of radius $2r$ under isothermal conditions. If $T$ is the surface tension of soap solution, the energy spent in the blowing

• A. $3\pi T{r}^2$
• B. $6\pi T{r}^2$
• C. $12\pi T{r}^2$
• D. $24\pi T{r}^2$

Answer 1

Answer: (B)

Initially area of soap bubble
$A_1=4\pi r^2$
Under isothermal condition radius becomes $2r$,
Then, area $A_2=4\pi (2r{)}^2$
$=4\pi \cdot 4r^2$
$=16\pi r^2$
Increase in surface area
$\Delta A=2\left(A_2-A_1\right)$
$=2\left(16\pi r^2-4\pi r^2\right)=24\pi r^2$
Energy spent
$W=T\times \Delta A$
$=T\cdot 24\pi r^2$
or $W=24\pi T{r}^{2}J$