A primitive diving bell consists of a cylindrical tank with one end open and one

Question

A primitive diving bell consists of a cylindrical tank with one end open and one end closed. The tank is lowered into a freshwater lake, open end downward. Water rises into the tank, compressing the trapped air, whose temperature remains constant during the descent. The tank is brought to a halt when the distance between the surface of the water in the tank and the surface of the lake is 42.0 m. Atmospheric pressure at the surface of the lake is 1.01 105 Pa. Find the fraction of the tank's volume that is filled with air.

Explanation / Answer

Pressure at the surface of the water in the tank = atmospheric pressure + water pressure = 101105 + þgh = 101105 + (1000 x 10 x 28.4) = 385 105 Pa Pressure at the water level in the tank is equal to the pressure of the air inside the tank. P1V1 = P2V2 101 105 x V1 = 385 105 x V2 V2 = 101 105/385 105 x V1 V2 = 0.262 V1

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