A question about fluid pressure

[rkrk]

Homework Statement

The deepest point in the ocean is in the Mariana Trench about 11 km deep. The pressure at the ocean floor is huge, about 1.13*10^8 Pa.
a) calculate the change in volume of 1.00 m^3 of water carried from the surface to the bottom of the Pacific.
b) The density of water at the surface is 1.03*10^3 km/m^3. Find its density at the bottom.

Homework Equations

I am not really sure how you could approach this problem, as the answers are supposed to be:
a) -5.4*10^-2 m^3
b)1.09*10^3 kg/m^3

The Attempt at a Solution

I first tried to use the equation: P= P(atmospheric) + (density)(g)(h) to find the density at the bottom of the ocean. then I figured I could set a proportion between the volumes and densities at the surface and at the bottom to find the volume at the bottom. But the density I get for the bottom is not 1.09*10^3, the actual right answer.

 

[berkeman]

It seems that you must have some relevant relation for the compressibility of the water. That is the only thing that will make the water denser at depth. We normally think of water as incompressible, but it sounds like at high enough pressures, a small amount of compression does occur. So where would you look to find the compressibility of water?

BTW, there are some typos in what you typed above in the units. Like in your statement for (b) where you say a density has units of km/m^3.

 

[rkrk]

Thanks

Oh yeah, I forgot about that. I found out the compressibility of water (the bulk modulus) which was 0.21 *10 ^10 Pa. Using the equation delta(P)=-B*[delta(V)/V], where B was the bulk modulus and rearranging for delta(V) I got the right answer.