A 14 -gal container is filled with gasoline. Neglect the...

A 14 -gal container is filled with gasoline. Neglect the change in volume of the container, and find how many gallons are lost if the temperature increases by $27^{\circ} \mathrm{F}$. The volume expansion coefficient of gasoline is $9.6 \cdot 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$.

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Key Concepts

Volume Change Calculation

Calculating the change in volume involves multiplying the original volume by the volumetric expansion coefficient and the temperature change (in Celsius). This concept is used to determine the exact amount of volume lost or gained as a result of thermal expansion, assuming that the container itself does not change in volume.

Thermal Expansion

Thermal expansion is the phenomenon where a substance increases in volume as its temperature rises. This concept is crucial for understanding how substances like gasoline behave when subjected to temperature changes, as the increased kinetic energy of the molecules causes them to occupy more space.

Coefficient of Volumetric Expansion

The coefficient of volumetric expansion is a material-specific constant that quantifies the proportional change in volume per unit change in temperature. It is typically given in per degree Celsius (°C?¹) and is used to calculate how much a substance will expand or contract due to temperature variations.

Temperature Unit Conversion

In many thermal expansion problems, the temperature change must be accurately converted into the appropriate units. Since the coefficient of volumetric expansion is usually provided in °C?¹, converting temperature changes from Fahrenheit to Celsius is essential to maintain consistency in the calculations.

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