Under isothermal condition two soap bubbles of radii `r_(1)` and `r_(2)` coalesce to form a single bubble of radius r. The external pressure is `p_(0)`. Find the surface tension of the soap in terms of the given parameters.

Answer

A, B, C, D

Explanation

As mass of the air is conserved,
`:. n_(1)+n_(2)=n (as pV=nRT)`
`:. (p_(1)V_(1))/(RT_(1))+(p_(2)V_(2))/(RT_(2)) =(pV)/(RT)`
As temperature is constant,

`T_(1)=T_(2)=(T)`
`:. p_(1)V_(1)+p_(2)V_(2)=pV`
`:. (p_(0)+(4S)/(r_1))(4/3 pi r_(1)^(3))+ (p_(0)+(4S)/(r_(2)))(4/3 pi r_(2)^(3))= (p_(0)+(4S)/(r))((4)/(3) pi r^(3))`
Solving, this we get
`S = (p_(0)(r^(3)-r_(1)^(3)-r_(2)^(3)))/(4(r_(1)^(2)+r_(2)^(2)-r^(2)))`