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# Determine the decrease in volume of $2000 \mathrm{~ft}^3$ of alcohol in a railroad tank car if the temperature drops from $75{\degree} \mathrm{F}$ to $54{\degree} \mathrm{F}$.

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$\textbf{Given:}$

$V=2000 \text{ ft}^3$

$T_1=75 ^\circ \text{F}$

$T_2=54 ^\circ \text{F}$

$\beta= 6.62 \times 10^{-4} \dfrac{\text{ }}{^\circ\text{F}}$

The change in the volume of the material under the influence of the change in temperature is given by the formula:

$\Delta V=\beta \cdot V \cdot \Delta T$

By including the given data in the formula we get:

\begin{align*} \Delta V&=\beta \cdot V \cdot (T_2-T_1) \\ &=6.62 \times 10^{-4} \cdot 2000 \cdot (54-75)\\ &\boxed{\Delta V=-28 \text{ ft}^3 } \end{align*}

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