The volume of an air bubble becomes 8 times the original volume in rising from the bottom of a lake to its surface. If the barometice height is 0.76 m of mercury (density of mercury is `13.6 g cm^(-3) and g = 9.8 ms^(-2))` what is the depth of the lake ?

Answer

72.35 m

Explanation

As the volume of the bubble while reaching the surface of lake becomes 8 times, the pressure on the surface of lake must be 1//8 times the pressure at the bottom of the lake. If P is the pressure at the surface of lake, then pressure at the bottom of lake = 8 P ac cording to Boyle's law. Thus the pressure due to coluum of liquid =8 P - P = 7P
` = 7 xx 0.76 xx 13.6 xx 10^3 xx 9.8 N//m^2`
`:.` Depth of lake
` =(7xx0.76 xx 13.6xx10^3 x 9.8)/(10^3xx9.8) = 72.35 m`