Question

What should be the pressure inside a small air bubble of 0.1 mm radius situated just below the surface of water? Surface tension of water = $72\times {10}^{-3}$ N/m and atmospheric pressure = $1.013\times {10}^{5}N/m^2.$

Answer 1

Given that,

Radius of air bubble $r=0.1mm={10}^{-3}m$

Surface tension of water $T=72\times {10}^{-3}N/m$

Atmospheric pressure $P_{atm}=1.013\times {10}^{5}N/m^2$

We know that,

The pressure is

$\Delta P=P_i-P_o=\frac{2T}{r}$

$P_i=P_0+\frac{2T}{r}$

$P_i=1.013\times {10}^5+\frac{2\times 72\times {10}^{-3}}{{10}^{-3}}$

$P_i=(1.013+0.00144)\times {10}^5$

$P_i=1.014\times {10}^{5}N/m^2$

Hence, the required pressure inside a small air bubble is $1.014\times {10}^{5}N/m^2$