Question

When an air bubble rises from bottom of the lake to the surface its radius double the atmospheric pressure is equal to that of columns of water of height H what is the depth of the lake

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Answer 1

The radius doubling implies that the volume has become eight times it's original volume(at the bottom) when it is at the top of the lake.

Now assuming the air to follow ideal gas behaviour we can write PV=K or pressure is inversely proportional to volume.

So since the volume increases eight times from bottom to top of the lake, pressure at the bottom has to be eight times more than what it is at the top of the lake.

Since the atmospheric pressure corresponds to a water level H,the depth of the lake would be 7 times H.

Note:Some maybe thinking that the depth of the lake has to be 8H,but it is wrong as 1H equivalent of pressure is already being exerted by the atmosphere. So,the lake has to exert only the remaining pressure i.e,7 times the atmospheric pressure which is 7H.

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