Physics - Fluid Question with Solution | TestHub

In Iso-thermal process: $pV=\mathrm{C}$. The pressure inside bubble is: $p\propto 1/r$ and volume is: $V\propto r^3$. $\therefore pV\propto r^2$ And $n=\frac{pV}{RT}$, therefore number of moles of gas inside the bubble is proportional to the square of its radius $\therefore n\propto r^2$ On combining bubbles, the total number of moles is conserved: Therefore, $n_1+n_1=N$ $\therefore r_1^2+r_2^2=R^2$ The above result can also be obtained by total surface energy conservation: $2\times \left(4\pi R^2\right)\sigma =2\times \left(4\pi r_1^2\right)\sigma +2\times \left(4\pi r_2^2\right)\sigma$ or $R=\sqrt{r_1^2+r_2^2}$