Calculate Volume of Diving Bell Air Space at 50m Depth

[winterwind]

Homework Statement

A diving bell has an air space of 3.0 m² when on the deck of a boat. What is the volume of the air space when the bell has been lowered to a depth of 50 m? Take the mean density of sea water to be 1.025 g cm^-3 and assume that the temperature is the same as on the surface.

Homework Equations

PV = nRT

The Attempt at a Solution

I'm thinking I should use the ideal gas law to solve this problem.

V₁P₁ = nRT

V₂P₂ = nRT

V₁P₁ = V₂P₂

P₁ = 1 atm (at surface of water)

P₂ = ? (would I use the density of sea water and surface area of diving bell somehow?)

Thanks!

 

[PhaseShifter]

$$P_{2}=P_{1}+\rho g \Delta z$$
where
g=gravitational acceleration
$$\Delta z$$= difference in depth