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 35.0 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.

Answer 1

Given that
The distance between the surface of the water in the tank andthe surface of the lake is (h) =38.0m.
The Atmospheric pressure at the surface of the lake is(P_surface)=1.01*10⁵Pa
The density of the warwe is(?)=1000kg/m3
The acceleration due to gravity is(g)=9.8m/s2
Now finding the absolute pressure at a depth h is
p_h =Psurface +?gh
=1.01*10⁵Pa+(1.00*10³kg/m3)(9.8m/s2)(35.0m)
=4.44*10⁵pa
From the Boyle' law we can write as
V_h/V_tank =Psurface/P_h
=1.01*10⁵ Pa/(4.44*10⁵pa)
=0.22