Question

When an air bubble, from the bottom of a lake ascends to the top level, its diameter becomes $n$ times, while temperature remains constant. If $P_o$ is the pressure at the top level and is equivalent to $h$ metre of column of water, then the depth of the lake is :

• A. $7h$
• B. $\frac{7}{2}nh$
• C. $7(n-1)h$
• D. $(n^3-1)h$

Answer 1

The correct option is D $(n^3-1)h$

Since the process is isothermal, $PV=constant$

$P_0\left(\frac{4}{3}\pi {\left(nr\right)}^3\right)=(P_0+P_1)\left(\frac{4}{3}\pi r^3\right)$ where $P_1$ is pressure at the bottom of lake and $x$ is its height.

$h{n}^3=h+x$

$x=(n^3-1)h$