Two soap bubbles coalesce to form a single bubble. If V is the subsequent change in volume of contained air and S change in total surface area, T is the surface tension and P atmospheric pressure, then which of the following relation is correct?

Let moles of air in firs t bubble of radius R1 be n1 and that in second bubble of radius R2 be n2. Since, number of moles of gas is conserved. n1+n2=n' where n' is the number of moles of gas in the final single bubble of radius R' . ⇒P1V1RT+P2V2RT=P'V'RT⇒P1V1+P2V2=P'V'Now,P'=P+4TR'andV'=4π3R'3∴(P+4 TR1)(4π3R13)+(P+4 TR2)(4π3R23)=(P+4TR')(4π3R'3)⇒P(4π3R13+4π3R23−4π3R'3)+4T3(4πR12+4πR22−4πR2)=0⇒PV+4T3S=0⇒3PV+4ST=0