Question

Two equal spherical bubbles of radius $a$ each coalesce to form a spherical bubble of radius $b$. If $P$ is the atmospheric pressure, show that the surface tension of the bubble is $\frac{P(2a^3-b^3)}{4(b^2-2a^2)}$.

Answer 1

$p_1{V}_1+p_2{V}_2=pV$
$(p+\frac{4T}{a})\frac{4}{3}\pi a^3+(p+\frac{4T}{a})\frac{4}{3}\pi a^3=(p+\frac{4T}{b})\frac{4}{3}\pi b^3$
$(2p+\frac{8T}{a})a^3=(p+\frac{4T}{b})b^3$
$T=\frac{p(2a^3-b^3)}{4(b^2-2a^2)}$