An air bubble rises from the bottom of a lake to the top and increases its volume 15 times thereby….

Problem :    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 × 10kg/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

$ \displaystyle h = \frac{14 \times 0.75 \times 13.6 \times 10^3 \times 9.8}{1.02 \times 10^3 \times 9.8} $

h  = 140 m

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