Question

Given the bulk modulus of sea water is 2.2*10^9Pa

and the density of

surface sea water is 1.025*10^3 kg/m^3

Calculate the volume of

1.025*10^3 kg of sea water at a depth near

5 km where the pressure is

5.0*10^7 Pa.

Answer 1

$$\dfrac{ΔV}V=\dfrac{ΔP}B,\\\space\\ \dfrac{V-V'}V=\dfrac{ΔP}{B},\\\space\\ V'=V\bigg(1-\dfrac{ΔP}B\bigg)=\dfrac mρ ·\bigg(1-\dfrac{ΔP}B\bigg),\\\space\\ V'=(1.025·10^3)/(1.025·10^3 ) ·(1-(5.0·10^7)/(2.2·10^9 ))=0.98\text{ m}^3$$