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 40.3 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

given, one end open, one enmd closed
distance between surface of water and surface of lake = d = 40.3 m
atmospheric pressure Po = 1.01*10^5 Pa
let the pressure inside the tank pe P
and let h height of tank be filled with water
then P + rho*gh = Po + rho*g*(h + d)
P - Po = rho*g( h + d - h) = rho*gd [ rho is density of water]
P = Po + rho*gd

now when the cylinder was just entering the water, number of moles of gas be n
then, Po*V = nRT [ V is total volume of the cylinder]
and PV' = nRT [ V' is the final volume of air in cylinder]
PV'/PoV = 1
V'/V = Po/P = Po/(Po + rho*gd) = 1.01*10^5/(1.01*10^5 + 9.81*1000*40.3) = 0.203

this is the fractio of volume of air occupied by the air in the cylinder

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