Question

What should be the pressure inside a small air bubble of 0.1 mm radius situated just below the water surface? Surface tension of water is $7.2\times {10}^2$ N/m and atmospheric pressure is $1.013\times {10}^5$ Pa.

Answer 1

Given,

$R=0.1mm$

$T=7.2\times {10}^{2}N/m$ surface tension

$P_1=1.013\times {10}^{5}Pa$ atmospheric pressure.

$P_2=$ pressure inside the bubbles.

The excess pressure inside a small air bubbles.

$P_2-P_1=\frac{2T}{R}$

$P_2-P_1=\frac{2\times 7.2\times {10}^2}{0.1\times {10}^{-3}}=144\times {10}^{5}Pa$

$P_2=P_1+144\times {10}^5$

$P_2=1.013\times {10}^5+144\times {19}^5$

$P_2=145.013\times {10}^{5}Pa$