What is the volume of this system when brought below ocean at particular when given original volume?

Question

A diving bell has an air space of 3.0m^3 when on the deck of a boat. What is th evolume of the air space when the bell has been lowered to a depth of 50m? Take the mean density of sea water to be 1.025g / cm^3 and assume that the temperature is the same as on the surface.


First I took 1.025g/cm^3 and converted it to kg/m^3. Then I multiplied it by acceleration of gravity so that I could turn it into a pressure. After this I multiplied by 50m to get 50,225 N/m^2, which is 50,225 Pa (P2). Given that STP is 1 bar (10^5 Pa) I designated that P1. V1 is given as 3m^3 so I calculated V2 using P1*V1=P2*V2 but I got an answer that was higher than my original volume which can't be correct.

Okay I saw an error in units that I made that put my answer off by 10^-4. I got an answer of 0.597

Answer 1

Probably a math mistake somewhere. You're better off playing with atmospheres. 10 meters of water is 1 atm, so for seawater, it height would be 10/1.025. Now you can convert 50 meters "head" to atmospheres, which would be almost 5. So the air space would be cut to about 1/5 th its original volume.