An air bubble starts rising from the bottom of a lake. Its diameter is at the bottom and at the surf — States of Matter and Gaseous State Chemistry Question
Question
An air bubble starts rising from the bottom of a lake. Its diameter is $3.6\text{ mm}$ at the bottom and $14.4\text{ mm}$ at the surface. Assuming the temperature of the lake is uniformly constant and the atmospheric pressure at the surface is equivalent to $10\text{ m}$ of water column, what is the exact depth of the lake (in $\text{m}$)?
Answer: 630
💡 Solution & Explanation
Since $V \propto d^3$, the volume ratio $V_{surface}/V_{bottom} = (14.4/3.6)^3 = 4^3 = 64$. By Boyle's Law, $P_{bottom}V_{bottom} = P_{surface}V_{surface} \implies P_{bottom} = P_{surface} \times 64 = 10\text{ m} \times 64 = 640\text{ m}$. Depth $h = P_{bottom} - P_{surface} = 640 - 10 = 630\text{ m}$.
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