Question

A gas filled freely collapsible balloon is pushed fro the surface level of a lake to a depth of $50m$. Approximately what per cent of its original volume will be balloon finally have, assuming that the gas behaves ideally and temperature is same at the surface and at $50m$ depth?

Answer 1

$P_1=$ Pressure at the surface $=1atm$
$=760\times 13.6\times 981dyne/c{m}^2$
$P_2=$ Pressure at a depth of $50m$
$=76.0\times 13.6\times 981+(50\times 100)\times 1\times 981dyne/c{m}^2$
$981[76.0\times 13.6+5000]$
$=981\times \left(6033.6\right)dyne/c{m}^2$
Now apply Boyle's law, $P_1{V}_1=P_2{V}_2$
or $\frac{V_2}{V_1}=\frac{P_1}{P_2}=\frac{76.0\times 13.6\times 981}{981\times 6033.6}=0.1713$
% $=0.1713\times 100=17.13$.