Question

Can you please show all your work so that I can understand how the problem is solved?

In the Challenger Deep of the Marianas Trench, the depth of water is 10.9 km and the pressure is 1.16 x 10^8 Pa.

a) if a cubic meter of sea water is taken from the surface to this depth, what is the chane in its volume?

b) what is the density of seawater at this depth?

Take the bulk modulus of seawater as 2.22 x 10^9 Pa.

Answer 1

The bulk modulus is E = 2.2*10^9 Pa

The fractional change in volume is:
dV/V = P/E = 1.16*10^8/2.22*10^9 = 0.0523.. which is a 5.2% decrease in volume (and increase in density)

(a) A cubic meter (at the surface) becomes 0.948 m^3.

(b) Look up the density of ocean water and divide it by 0.948 for the density at the 10.9 km depth.