HELP please. Physics question.

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 half when the distance between the surface of the water in the tank and the surface of the lake is 18.2 m. Atmopspheric pressure at the surface of the lake is 1.01 X 10^5 Pa. Find the fraction of the tank's volume that is filled with air.

 

I know i use the Boyle's Law.. but I can't seem to set it up correctly. 

Answer 1

Assuming constant water density, pressure increases by 1 atm (  about 100.9 kPa ) with each 10 m of depth below the surface. So at 10 m, the pressure is 2 atm (1 atm of air + 1 atm of water) or 201.8 kPa. 

At 18 atm, the pressure is 282.3 kPa. Now for Boyle's law, you now have P2 (282.3 kPa) and P1 (100.9 kPa). V1 is unknown, but that's OK. You just want the fraction that the volume decreased, so V2 = V1(P1/P2),

the fraction filled with air is P1/P2.