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

Here surface tension of soap solution at room temperature
`T=2.50xx10^(-2)Nm^(-1)`, radius of soap bubble `r=5.00mm=5.00xx10^(-3)m`
`therefore` Excess pressure inside soap bubble, `P=P_(i)-P_(0)=(4T)/(r)`
`=(4xx2.50xx10^(-2))/(5.00xx10^(-3))=20.0Pa`
When an air bubble of radius `r=5.00xx10^(-3)` m is formed at a depth `h=40.0cm=0.4m` inside a container containing a soap solution of relative density 1.20 or density `rho=1.20xx10^(3)kgm^(-3)`, then excess pressure
`P=P_(i)-P_(0)=(2T)/(r)`
`thereforeP_(i)=P_(0)+(2T)/(r)=(P_(a)+h rhog)+(2T)/(r)`
`=[1.01xx10^(5)xx0.4xx1.2xx10^(3)xx9.8+(2xx50xx10^(-2))/(5.00xx10^(-3))]Pa`
`=(1.01xx10^(5)+4.7xx10^(3)+10.0)Pa`
`cong1.06xx10^(5)Pa`.