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Q32P

Expert-verifiedFound in: Page 382

Book edition
9th Edition

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

Pages
1624 pages

ISBN
9781133947271

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

$\Delta P=-1.65\times {10}^{8}N/{m}^{2}$

Given:

The initial volume is V_{i}

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

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

Substitute numerical values:

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

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