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

`T=2.50 xx 10^(-2) Nm^(-1)`
`R=5 mm =5 xx 10^(-3)m`
Excess pressure inside the air bubble is `P=(2T)/(R)`
`P=(2 xx 2.50 xx 10^(-2) Nm^(-1))/(5 xx 10^(-3) m)=10Pa`
Excess pressure inside the soap bubble `P.=(4T)/(R)`
`=(4 xx 2.50 xx 10^(-2) Nm^(-1))/(5 xx 10^(-3) m)`
=20Pa
Total Pressure inside air bubble at a depth of 40 cm in soap `=P_("atm") +hpg +P`
`=1.01 xx 10^(5) +0.4 xx 10^(3) xx 1.2 xx 9.8 +10 `
`=1.01 xx 10^(5) +0.047 xx 10^(5) +10`
`=1.057 xx 10^(5) +10`
=105710 Pa
`=1.06 xx 10^(5)Pa`