Multiple-Concept Example 4 reviews the principles that play roles in this proble

Question

Multiple-Concept Example 4 reviews the principles that play roles in this problem. 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 17.5 m. Atmospheric pressure at the surface of the lake is 1.01 x 105Pa. Find the fraction of the tank's volume that is filled with air.

Explanation / Answer

Ideal gas law: pV = nRT

If n and T (and of course R) are constant, then

(pV)_a = (pV)_b

where pressure is absolute.

At the surface, p = 1.01e5 Pa

and at 17.5 m, p = 1.01e5Pa + (1000kg/m³*9.8m/s²*17.5m) = 2.73e5 Pa

so

1.01e5Pa * Va = 2.73e5Pa * Vb

Vb / Va = 1.01 / 2.73 = 0.37 (= 37%)

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