Question

An air bubble released by a deep-water diver, 105 m below the surface of a lake, has a volume of 1.65 cm3. The surface of the lake is at sea level, and the density of the lake water can be approximated as that of pure water. As the bubble rises to the surface, the temperature of the water and the number of air molecules in the bubble can each be approximated as constant. Find the volume (in cm3) of the bubble just before it pops at the surface of the lake. cm3

Answer 1

Take,

At the depth 105m below the surface of the lake

Depth, h = 105m

Density of water,

Therefore, pressure at this depth is given by,

Given,

At the surface of the lake

The pressure will be equal to atmospheric pressure, ie,

According to Boyles law,  at a constant temperature, the volume of a given mass of a dry gas is inversely proportional to its pressure. Mathematically,

(Ans.)