What is the excess pressure inside a bubble of soap solution of radius 5.00mm, given that the surface tension of soap solution at the temperature `(20^(@)C)` is `2.50xx10^(-2)Nm^(-1)`? If an air bubble of the same dimension were formed at a depth of 40.0 cm inside a container containing the soap solution (of relative density 1.20), what would be the pressure inside the bubble? (1atm. is `1.01 xx 10^(5)Pa`).

Explanation

` r = 5.00 xx 10^(-3) m, T = 2.50 xx 10^(-2) N//m , h = 40 cm = 0 0.4 cm `
` rho = 1.20 xx10^(3) kg//m^(3) and P_(0) = 1.01 xx10^(5)` Pascal
Excess pressure inside a bubble in soap solution
` (2T)/(r ) = (2xx2.50 xx10^(-2))/(5.00 xx10^(-3)) = 10 Pa`
Total pressure inside the air bubble ` = P_(0) + h rho g + (2T)/r`
` = 1.01 xx10^(5) + 0.4 xx1.2 xx10^(3) xx 9.8 + 10 = 1.06 xx10^(5) ` Pa