when a laege bubble rises from the bottom of a lake to the surface , its radius doubles , ifbatmospheric pressure isbequal to that of the column of water height h , then the depth of the lake is ....?
Answers
Volume of the bubble is inversely proportional to the pressure of air inside bubble.
Pressure * volume = constant at same temperature.
As the bubble raises to the top, the pressure on the bubble by water at that level decreases and hence bubble expands.
Bubble's volume is 8 times at surface compared to volume at the bottom of lake. So pressure at the bottom will be 8 times that at the surface. Reason is the radius is twice and hence volume is 2^3 times.
Pressure at surface of water lake = 1 atm = water density * H * g (given)
Pressure at the bottom of lake = 8 * 1 atm = 8 atm = density * 8 * H * g
= density * depth * g + 1 atm at the surface
Hence the depth of lake = 8 * H - 1 * H = 7 * H