Question

At what depth in an ocean will a bubble of air have one fifth the volume is will have on reaching the surface? (Atmospheric pressure $=$ 76 cm of Hg and density of Hg $=13.6gc{m}^{-3})$

Answer 1

Let volume of bubble on the surface of water of V
Volume of bubble inside $=\frac{V}{4}$
Pressure P at surface $=76cm$ of Hg
Let depth of bubble inside $=$ h cm
$\therefore$ Pressure of bubble inside water
$=(76+\frac{h}{13.6})cm$ of Hg
Given, $P_1=76cm$ of Hg, $V1=V$
$P_2=(76+\frac{h}{13.6})cm$ of Hg,
$V_{p2}=\frac{V}{4}$
According to Boyle's law,
$P_1{V}_1=P_2{V}_2$
$\left(76\right)V=(76+\frac{h}{13.6})\left(\frac{V}{4}\right)$
$76=\frac{76}{4}+\frac{h}{13.6\times 4}$
$\frac{h}{13.6\times 4}=57$
$h=3100.8cm.$