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Found in: Page 382

### Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271

# When water freezes, it expands by about ${\mathbf{9}}{\mathbf{.}}{\mathbf{00}}{\mathbit{%}}{\mathbf{.}}$ What pressure increase would occur inside your automobile engine block if the water in it froze? (The bulk modulus of ice is ${\mathbf{2}}{\mathbf{.}}{\mathbf{00}}{\mathbf{×}}{{\mathbf{10}}}^{{\mathbf{9}}}{\mathbf{}}{\mathbit{N}}{\mathbf{/}}{{\mathbit{m}}}^{{\mathbf{2}}}{\mathbf{.}}{\mathbf{\right)}}$

$\Delta P=-1.65×{10}^{8}N/{m}^{2}$

See the step by step solution

## Step 1: To find the pressure increase would occur inside your automobile engine block.

Given:

The initial volume is Vi

The change in volume is $\Delta V=9%{V}_{i}=0.09{V}_{i}\text{}$

The final volume is ${V}_{f}={V}_{i}+\Delta V={V}_{i}+0.09{V}_{i}=1.09{V}_{i}$

The bulk modulus is defined as:

$B=\frac{-\Delta P}{\Delta V/{V}_{i}}$

Solve for $\left(\Delta P\right)$:

$\Delta P=-\frac{B\Delta V}{{V}_{i}}=-\frac{B\left({V}_{f}-{V}_{i}\right)}{{V}_{i}}\text{}$

Substitute numerical values:

$\begin{array}{l}\Delta P=-\frac{\left(2×{10}^{9}\right)\left(0.09{K}_{i}\right)}{1.09{K}_{i}}=-1.65×{10}^{8}N/{m}^{2}\\ \Delta P=-1.65×{10}^{8}N/{m}^{2}\end{array}$