Question:
Two spherical soap bubbles of radii $r_{1}$ and $r_{2}$ in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to:
Correct Option: , 3
Solution:
no. of moles is conserved
$\mathrm{n}_{1}+\mathrm{n}_{2}=\mathrm{n}_{3}$
$\mathrm{P}_{1} \mathrm{~V}_{1}+\mathrm{P}_{2} \mathrm{~V}_{2}=\mathrm{P}_{3} \mathrm{~V}$
$\frac{4 \mathrm{~S}}{\mathrm{r}_{1}}\left(\frac{4}{3} \pi \mathrm{r}_{1}^{3}\right)+\frac{4 \mathrm{~S}}{\mathrm{r}_{2}}\left(\frac{4}{3} \pi \mathrm{r}_{2}^{3}\right)=\frac{4 \mathrm{~S}}{\mathrm{r}_{3}}\left(\frac{4}{3} \pi \mathrm{r}_{3}^{3}\right)$
$\mathrm{r}_{1}^{2}+\mathrm{r}_{2}^{2}=\mathrm{r}_{3}^{2}$
$\mathrm{r}_{3}=\sqrt{\mathrm{r}_{1}^{2}+\mathrm{r}_{2}^{2}}$