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.l

Answer 1

Part(a)

d=11km=11000m

$\rho=1.03\times10^3kg/m^3$

$p_1=1.13\times10^8 Pa\\p_2=1.01\times10^5Pa$

$$∆P=1.13\times10^{8}-1.01\times10^{5}=1.12899\times10^8Pa$$

$\beta=-V\frac{∆p}{∆V}$

$2.1\times10^{9}=-1\times\frac{1.12899\times10^8}{∆V}$

$∆V=-0.05377m^3$

Part(b)

$$∆\rho=\frac{m∆\rho}{V}=\frac{0.053\times10^3}{1}=0.053\times10^3kg/m^3$$

$∆\rho=\rho_2-\rho_1$

$\rho_2=∆\rho+\rho_1$

$$\rho_2=(0.053+1.03)\times10^3kg/m^3=1.08\times10^3kg/m^3$$

Part(c)

Yes it is a good approximation because in the 11km the density of water changed by only (5-6)%.