The radii of two soap bubbles are r 1 and r 2. In isothermal conditions, two meet together in vaccum. Then the radius of the resultant bubble is given by
r2 =r12+r22
In isothermal Condition.
Δ P1 V1+ΔP2V2=ΔPVΔP143πr31+ΔP243πr32=ΔP43πr3ΔP1r31+ΔP2r32=ΔPr3[where ′r′ is the radius of new bubble]4Tr1(r31)+4Tr2(r32)=4Tr(r3)⇒r21+r22=r2⇒r=√r21+r22