Two soap bubbles of radii `a` and `b` coalesce to form a single bubble of radius `c`. If the external pressure is `P`, find the surface tension of the soap solution.

Answer

`(P_(0))(c^(3)-a^(3)-b^(3))/(4(a^(2)+b^(2)-c^(2)))`

Explanation

For mass conservation

`n_(1)+n_(2)=n'`
`(P_(1)V_(1))/(RT)+(P_(2)V_(2))/(RT)=(PV)/(RT)`
`P_(1)V_(1)+P_(2)V_(2)=PV` ………i
`P_(1)=(4T)/c+P_(0), P_(2)=(4T)/b+P_(0)`
and `P=(4T)/C+P_(0)` in eqn i to get the given answer.