Two soap bubbles in vacuum having radii 3 cm and 4 cm respectively coalesce under isothermal conditions to form a single bubble. What is the radius of the new bubble (in cm)?

Let r₁ and r₂ be the radii of two given soap bubbles and r be that of the coalesced bubble.

Here, r₁ = 3 cm and r₂ =4 cm.
Number of moies in bubble 1 , $n_1 = P_1{V}_1/RT$

Similarly $n_2=P_2{V}_2/RT$

In the resulting bubble formed , n = PV/RT

 NOW n = $n_1+n_2 \Rightarrow \left(\frac{4S}{r_1}\right)\left(\frac{4\mathrm{\pi }{\left({\mathrm{r}}_1\right)}^3}{3}\right)+\left(\frac{4S}{r_2}\right)\left(\frac{4\mathrm{\pi }{\left({\mathrm{r}}_2\right)}^3}{3}\right) = \left(\frac{4S}{r}\right)\left(\frac{4{\mathrm{\pi r}}^3}{3}\right)$  

$\begin{array}{l} \\ {\mathrm{r}}^2={\mathrm{r}}_1^2+{\mathrm{r}}_2^2=(3{)}^2+(4{)}^2=25\\ \mathrm{r}=5\mathrm{cm}\end{array}$