   Chapter 9, Problem 74P

Chapter
Section
Textbook Problem

The deepest point in the ocean is in the Mariana Trench, about. 11 km deep. The pressure at the ocean floor is huge, about 1.13 × 108 N/m2. (a) Calculate the change in volume of 1.00 m3 of water carried from the surface to the bottom of the Pacific. (b) The density of water at the surface is 1.03 × 103 kg/m3. Find its density at the bottom.

(a)

To determine
The change in volume of 1.00m3 water carried from the surface to the bottom of the Pacific.

Explanation
The bulk modulus is defined as ΔP=B(ΔV/V0) and it is rearranged of the change in volume.

Given info: The pressure at the depth 11km of the Mariana Trench is 1.13×108N/m2 , the pressure at the surface of the Pacific ocean is 1.01×108Pa , the bulk modulus of the water is 0.21×1010Pa , and the volume of water is 1.00m3 .

The formula for the change in volume of the cube of water is,

ΔV=(ΔP)V0B

• ΔP is change in pressure.
• V0 is initial volume of the cube of water.
• B is bulk modulus of water.

Substitute (1.13×108N/m21.01×108Pa) for ΔP , 0.21×1010Pa for B , and 1

(b)

To determine
The density at the bottom.

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