Question

A bubble of gas released at the bottom of a lake increases to eight times its original volume when it reaches the surface. Assuming that atmospheric pressure is equivalent to the pressure exerted by a column of water 10 m height, the depth of the lake is :

A
80 m
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B
90 m
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C
40 m
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D
10 m
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E
70 m
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Solution

The correct option is D 70 mhroughout the entire process, the number of moles of the gas bubble remains same. So, we can apply the ideal gas equation PV = constant.Let us assume that the bubble is h meters below the surface of the water, and P0 is the atmospheric pressure.Pressure only due to water at a depth of h meters would be equal to ρgh. Also, atmospheric pressure would be acting on the bubble. So, the total pressure on the gas bubble at that depth =P0+ρgh=ρg×10+ρgh=ρg(h+10).At the surface of water, only atmospheric pressure would be acting on the bubble i.e. P=P0=ρg×10As PV = constant, ρg(h+10)×V=ρg10×8Vh+10=80 h=70 meters.

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