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Q27P

Expert-verifiedFound in: Page 383

Book edition
9th Edition

Author(s)
Raymond A. Serway, John W. Jewett

Pages
1624 pages

ISBN
9781133947271

**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 3 108 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 3 103 kg/m3. Find its density at the bottom. **

**(c) Explain whether or when it is a good approximation to think of water as incompressible.**

a) the change in volume $=1,128.987\times {10}^{5}\text{N}/{\text{m}}^{2}$

** **

b) B is the bulk modules of sea water is as follows:

$B=2.34\times {10}^{9}\text{N}/\text{m}2$

c) Bulk modules are familiar to us. $=\frac{-(1,128.987\times {10}^{5}\text{N}/{\text{m}}^{2})\times (0.9{\text{m}}^{3})}{2.34\times {10}^{9}\text{N}/{\text{m}}^{2}}$

In the surface pressure is ${P}_{s}=1.013\times {10}^{5}\text{N}/{\text{m}}^{2}$

In the depth pressure is ${P}_{d}=1.13\times {10}^{8}\text{N}/{\text{m}}^{2}$

pressure variation

$\begin{array}{l}{\Delta}_{p}={P}_{S}-{P}_{d}\\ =1.13\times {10}^{8}-1.013\times {10}^{5}\\ =1,128.987\times {10}^{5}\text{N}/{\text{m}}^{2}\end{array}$

B is the bulk modules of sea water is as follows:

$B=2.34\times {10}^{9}\text{N}/\text{m}2$

Bulk modules are familiar to us.

$\begin{array}{l}B=\frac{(-\Delta p){v}_{0}}{\Delta v}\\ \Delta v=\frac{-\left(\Delta P\right){v}_{0}}{B}\\ =\frac{-(1,128.987\times {10}^{5}\text{N}/{\text{m}}^{2})\times (0.9{\text{m}}^{3})}{2.34\times {10}^{9}\text{N}/{\text{m}}^{2}}\end{array}$

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