A vessel filled with air under pressure `p_0` contains a soap bubble of diameter `d`. The air pressure having been reduced isothermally `n-fold`, the bubble diameter increased `eta-fold`. Find the surface tension of the soap water solution.

Explanation

By Boyle's law
`(p_0 +(8 alpha)/(d))(4 pi)/(3) ((d)/(2))^3= ((p_0)/(n) + (8 alpha)/(eta d)) (4 pi)/(3) ((eta d)/(2))^3`
or `p_0(1 - (eta^3)/(n)) = (8 alpha)/(d) (eta^2 - 1)`
Thus `alpha = (1)/(8) p_0 d(1 - (eta^3)/(n))(eta^3 - 1)`.