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(c^(3)+a^(3)+b^(3)))/(4(a^(2)+b^(2)-c^(2)))`
B. `(P(c^(3)-a^(3)-b^(3)))/(4(a^(2)+b^(2)-c^(2)))`
C. `Pc^(3)-4a^(2)-4b^(2)`
D. `Pc^(3)-2a^(2)-3b^(2)`

Answer

B

Explanation

Assuming is isothermal conditions
`(P+(4sigma)/a)(4/3pia^(3))+(P+(4sigma)/b)(4/3pib^(3))`
`=(P+(4sigma)/c)(4/3pic^(3))`
or `P[a^(3)+b^(3)-c^(3)]=4sigma[c^(2)-a^(2)-b^(2)]`
or `sigma=(P(c^(3)-a^(3)-b^(3)))/(4(a^(2)+b^(2)-c^(2)))`