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.

 

[rwisz]

The pressure at the bottom of the Mariana Trench is indeed huge, but the bulk modulus and density of water remain constant regardless of pressure. This is because water molecules are already tightly packed and cannot be compressed further. Therefore, the density of water at the bottom of the ocean would still be 1.03 x103 kg/m3, the same as at the surface. The pressure at the bottom of the ocean may be immense, but it does not affect the density of water.