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Question

Determine the decrease in volume of 2000 ft32000 \mathrm{~ft}^3 of alcohol in a railroad tank car if the temperature drops from 75°F75{\degree} \mathrm{F} to 54°F54{\degree} \mathrm{F}.

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Given:\textbf{Given:}

V=2000 ft3V=2000 \text{ ft}^3

T1=75FT_1=75 ^\circ \text{F}

T2=54FT_2=54 ^\circ \text{F}

β=6.62×104 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:

ΔV=βVΔT\Delta V=\beta \cdot V \cdot \Delta T

By including the given data in the formula we get:

ΔV=βV(T2T1)=6.62×1042000(5475)ΔV=28 ft3\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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