Marianas Trench Homework: Volume & Density Calcs

[javacola]

Homework Statement

In the Challenger Deep of the Marianas Trench, the depth of seawater is 10.9 km and the pressure is 1.16x10^8 Pa (about 1.15x10^3 atm.

A) If a cubic meter of water is taken from the surface to this depth, what is the change in its volume? (Normal atmospheric pressure is about 1.0x10^5 Pa. Assume that k for seawater is 45.8x10^-11 Pa^-1

B)What is the density of seawater at this depth? (At the surface, seawater has a density of 1.03x10^3 kg/m^3

Homework Equations

DeltaP/K

The Attempt at a Solution

Well for part A I multiplied the K of seawater by the pressure, and got the right answer which is -5.3 x 10^-2 m.
Now I'm kind of stumped on part B. I feel like it's incredibly easy but don't really know where to begin. Obviously m/v=d, but I'm not sure if that's relevant here. Don't know how to relate pressure or depth with density.

 

[Sethric]

You are given density at the surface, and you calculated how much the volume would change if you moved a certain mass of water down. Keep in mind, that volume of water had a mass, and it did not change. Therefore you have the quantities needed to calculate density.

 

[javacola]

Alright well let's see.

mass divided by initial volume is 1030.
mass divided by initial volume + delta volume = the density I'm looking for.

Is this the right track?

 

[javacola]

My first instant was that since mass is negligent, the change in volume should equal the change in density. But that doesn't seem to be working.

 

[ideasrule]

Alright well let's see.

mass divided by initial volume is 1030.
mass divided by initial volume + delta volume = the density I'm looking for.

Is this the right track?

Yes. You also know that the initial volume is 1m^3, because that's what the problem says. You can easily find the mass, and from there, the final density.

 

[Sethric]

Mass divided by initial volume is 1030. Use this, since you know initial volume, to find mass. Take this mass and divide it by initial volume - delta volume to find the density you are looking for.

 

[javacola]

Thanks a lot guys. Got it with 3 minutes to spare. Have no clue how you knew initial volume was 1, that's what threw me off.

 

[ideasrule]

Thanks a lot guys. Got it with 3 minutes to spare. Have no clue how you knew initial volume was 1, that's what threw me off.

We know that because the question states:

"If a cubic meter of water is taken..."