Question

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$\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{\times }{\mathbf{10}}^{\mathbf{9}}\mathbf{}\mathit{N}\mathbf{/}{\mathit{m}}^{\mathbf{2}}\mathbf{.}\mathbf{)}$

Short answer

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

Step-by-step solution

To find the pressure increase would occur inside your automobile engine block.

Given:

The initial volume is V_i

The change in volume is$\Delta V=9\%V_i=0.09V_i$

The final volume is$V_f=V_i+\Delta V=V_i+0.09V_i=1.09V_i$

The bulk modulus is defined as:

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

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

$\Delta P=-\frac{B\Delta V}{V_i}=-\frac{B(V_f-V_i)}{V_i}$

Substitute numerical values:

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