What is the excess pressure inside a bubble of soap solution of radius 500 mm, 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 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? (1 atmospheric pressure is `1.01xx10^(5)Pa`).

Explanation

Here, `T = 2.5 xx10^(-2) Nm^(-1)`
`r = 5.00 mm = 5 xx 10^(-3) m `
Density of soap solution ,
` rho = 1.2 xx10^(3) kgm^(-3)`
Excess pressure inside the soap bubble ,
`rho = (4T)/r = (4xx2.5 xx10^(-2))/(5xx10^(-3)) = 20 ` Pa
Excess pressure inside the air bubble,
`rho. = (2T)/r = (2xx 2.5 xx10^(2))/(5xx10^(-3)) = 10 Pa`
Total pressure inside the air bubble at depth h in soap solution
= p. + atmospheric pressure + `h rho g `
` = 10 + 1.01 xx 10^(5) + 0.4 xx1.2 xx10^(3) xx 9.8 `
` = 1.06 xx10^(5) Pa`