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

The correct option is D $24\pi T{r}^2$

Initially area of soap bubble $A_1=4\pi r^2$
Under isothermal condition radius becomes 2r,
Then, area $A_2=4n(2r{)}^2$
$=4n\cdot 4r^2$
$=16\pi r^2$
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 $W=24\pi T{r}^{2}J$