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Explanation:
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.
Expert's answer
Bulk modulus by definition
B=\rho_0\frac{\Delta P}{\Delta \rho}.B=ρ
0
Δρ
ΔP
.
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})ρ=ρ
0
+Δρ=ρ
0
(1+
B
ΔP
)
=1100\times(1+\frac{(520-1)\times 10^5}{2.3\times 10^9})=1125\:\rm kg/m^3.=1100×(1+
2.3×10
9
(520−1)×10
5
)=1125kg/m
3
.