How Does Pressure Affect Water Density in the Mariana Trench?

[mandy9008]

Homework Statement

The deepest point in the ocean is in the Mariana Trench, about 11 km deep. The pressure at that point is huge, about 1.13 x10⁸ N/m².
(a) The deepest point in the ocean is in the Mariana Trench, about 11 km deep. The pressure at that point is huge, about 1.13 x10⁸ N/m².
(b) The density of water at the surface is 1.03 x10³ kg/m³. Find its density at the bottom.

Homework Equations

P=B(ΔV/V)

The Attempt at a Solution

a. 1.13 x10⁸ N/m² = -(2.15 x10⁹ Pa)(ΔV/(1.00 m³))
ΔV = -0.053 m³
b. Since water is not compressible, shouldn't the density be the same at the bottom of the ocean as the top?

 

[Tusike]

Well, everything is compressible, only the force required to compress it is different for each material. I don't know what your a. question was, since it seems you copied it wrong, but I see you calculated some sort of deltaV. If the volume changed, shouldn't the density have also changed?

http://hyperphysics.phy-astr.gsu.edu/hbase/permot3.html

 

[mandy9008]

yes, i did copy part a wrong. the question for part a was: (a) Calculate the change in volume of 1.00 m3 of water carried from the surface to the bottom of the Pacific.
so, if the density is different, how do i determine the change?

 

[Tusike]

Well I'm not sure, but you should be able to calculate the weight of 1m3 water (don't know the density of sea-water...), and after you carried it down, the mass is still the same, so because m = qV, where q is density, you could say q1*V1 = q2*V2, and only q2 is unknown.