Problem 1: An air bubble rises from the bottom of a lake to the top and increases its volume 15 times thereby. If the atmospheric pressure is 75 cm and density of lake water is 1.02 × 103 kg/m3, then find the depth of lake.
Solution: From given information, it is clear that mass and temp. of air inside bubble is constant. Hence applying Boyle’s law,
P1V1 = P2V2 where 1 represents top & 2 represents bottom.
⇒ P1 (15V2) = (P1 + ρgh)V2
∴ ρgh = 14 P1
h = 140 m