The deepest point in any ocean is in the Mariana Trench, which is about 11 km de

Question

The deepest point in any ocean is in the Mariana Trench, which is about 11 km deep, in the Pacific. The pressure at this depth is huge, about 1.13 x 108 N/m2. (Take the bulk modulus of seawater to be 2.34 x 1o9 N/m2) (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 103 kg/m3. Find its density at the bottom. kg/m3 (c) Is it a good approximation to think of water as incompressible? O Yes O No

Explanation / Answer

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from the Definition of Bulk modulus

K = chnage in pressure /(frational change of Volume)

K = -dP/(dV/v)

K = - V dP/dV

Change of Volume dV = VdP/k

dV = 1 * 1.13*10^8/(2.34 *10^9)

dV = 0.0482 m^3
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part D:

Density rho = rho 0 + delta rho

density = rho 0 * (1 + delta P/K)

rho = density = (1.03*10^3)* (1 + (1.13*10^8/2.34*10^9)

rho at the Bottom = 1.079×10³ kg/m³

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part C:

as variation of density is too less, it is a good apporximation to think water as incompressible.

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