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 Times 10^8 N/m^2. (Take the bulk modulus of seawater to be 2.34 Times 10^9 N/m^2) Calculate the change in volume of 1.10 m^3 of seawater carried from the surface to this deepest point. The density of seawater at the surface is 1.03 Times 10^3 kg/m^3. Find its density at the bottom. Is it a good approximation to think of water as incompressible? Yes No

Explanation / Answer

P = 1.13*10^8 N/m^2 , V =1.1 m^3

B =2.34*10^9 N/m^2

(a) Bulk modulus B = P/(DV/V)

DV = PV/B = (1.13*10^8*1.1)/(2.34*10^9)

DV = 0.053 m^3

(b) = m/V

V = m/

V = -(m/²)

You can rewrite
K = (P/)
or
K = (P/)

Hence,
= (P/K)
=>
= + = *(1 + (P/K))

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

= 1.079×10^3 kg/m^3

(c) No

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