Two spherical soap bubbles of radii a and b in vacuum coalesce under isothermal conditions. The resulting bubble has a radius given by:

Two bubbles coalesce to form a bigger bubble at isothermal conditions i.e T=constant
Excess pressure inside the soap bubble P=4T/r where T is the surface tension of soap bubble
From PV=nRT we get n=PV/RT
As no mole of soap bubble is lost, thus n=n1+n2
∴ PV/RT = P1V1/RT + P2V2/RT
⟹ PV = P1V1 + P2V2 (∵T=constant)
4Tr × (4/3)πr³ = 4Ta × (4/3)πa³ + 4Tb × (4/3)πb³
⟹ r² = a² + b²
OR r = √a² + b²