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205.


Problem 23.11 (RHK)


An air bubble of volume is at the bottom of a lake 41.5 m deep where the temperature is . The bubble rises to the surface, which is at a temperature of . We can take the temperature of the bubble to be the same as that of the surrounding water. We have to find its volume just before it reaches the surface.


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We shall first calculate the amount of air in the bubble. Let it be n mol. Pressure of air at a depth of 41.5 m will be


It is given that the volume of the air bubble at the bottom of the lake that is at a depth of 41.5 m is



Temperature of the lake at that depth is . Therefore the initial temperature of the bubble is



Assuming the ideal gas equation for the air in the bubble, we can find the amount of gas in the bubble,



Therefore, the volume of this air bubble, , just before it reaches the surface of the lake, where the temperature is (), will be