Question

A collapsible balloon is inflated to a volume of 10 L at a pressure of 1 atm. When the balloon is submerged all the way to the bottom of a lake, its volume reduces to 1.25 L. Assume the atmospheric pressure to be equivalent to a 10 m column of water and that there is no change in the temperature. If the depth of the lake is $x\times {10}^3\text{cm}$, what is the value of $x$?

Answer 1

$n$ and $T$ are constants, So $PV=\text{const.}$
$\therefore 1\text{atm}\times 10\text{L}=P_{\text{bottom}}\times 1.25\text{L}$
$P_{\text{bottom}}=P_{\text{atm}}+P_{\text{water}}=\frac{10}{1.25}=8\text{atm}$
$P_{\text{water/Lake}}=8-1=7\text{atm}$
$\Rightarrow 7\times 10\text{m}=70\text{m}=7\times {10}^3\text{cm}$
$\Rightarrow x=7$