Question

The deepest point in the ocean is in the Mariana Trench, about 11 km deep, in the Pacific. The pressure at this depth is huge, about 1.13 x 10^8 Pa. (a) Calculate the change in volume of 1.00 m3 of seawater carried from the surface to this deepest point. (b) The density of seawater at the surface is 1.03 x 10^3 kg/m3. Find its density at the bottom. (c) Explain whether or when it is a good approximation to think of water as incompressible.

Answer 1

a) $\beta=-\frac{1}{V}\cdot(\frac{\Delta V}{\Delta p})\to \Delta V=-\beta V\cdot\Delta p=$

$=-0.51\cdot10^{-9}\cdot1\cdot1.13\cdot10^8=-0.05763\ (m^3)$

b) $\rho_h=m/V_h=1030/(1-0.05763)=1093\ (kg/m^3)$

c) Since the coefficient of volumetric compression of water is $\beta=0.51\cdot10^{-9}\ (Pa^{-1})$ , it is a good approximation to think of water as incompressible.