Answer to Question #102213 in Physics for Nyx

Question

Find the density of seawater at a depth where
the pressure is 520 atm if the density at the
surface is 1100 kg/m3. Seawater has a bulk
modulus of 2.3 × 109 N/m2. Bulk modulus is
defined to be
B ≡ρ0 ∆P/∆ρ
Answer in units of kg/m3.

Answer 1

Bulk modulus by definition

$$B=\rho_0\frac{\Delta P}{\Delta \rho}.$$

Hence, the density of seawater at a depth where the pressure is 520 atm

$$\rho=\rho_0+\Delta\rho=\rho_0(1+\frac{\Delta P}{B})$$

$$=1100\times(1+\frac{(520-1)\times 10^5}{2.3\times 10^9})=1125\:\rm kg/m^3.$$