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.

Options

A. `(p_0(2r^2-R^3))/(4(r^2-2r^2))`
B. `(p_0(2r^3-R^3))/(4(R^2-2r^2))`
C. `(p_0(2r^3-R^3))/(2(R^2+2r^2))`
D. `(p_0(2r^3+R^3))/(4(R^2+2r^2))`

Answer

A

Explanation

Total number of moles of air in the two soap bubbles`=`number of moles of air in the resulting bubble.
`(2pv)/(RT)=(\p'v')/(RT)`
`2pv=p'v'`
`2(p_(0)+(4T)/(r))(4)/(3)pir^(3)=(p_(0)+(4T)/(R))(4)/(3)piR^(3)`
`2(p_(0)+(4T)/(r))r^(3)=(p_(0)+(4T)/(R))R^(3)`
`thereforeT=(p_(0)(R^(3)-2r^(3)))/(8r^(2)-4R^(2))=(p_(0)(R^(3)-2r^(3)))/(4(2r^(2)-R^(2)))`