A military vehicle is fueled with gasoline in the United...

A military vehicle is fueled with gasoline in the United States, preparatory to being shipped overseas. Its fuel tank has a capacity of $213 \mathrm{~L}$. When it is fueled, the temperature is $57^{\circ} \mathrm{F}$. At its destination, it may be required to operate in temperatures as high as $120^{\circ} \mathrm{F}$. What is the maximum volume of gasoline that should be put in its tank?

Key Concepts

Thermal Expansion of Liquids

Thermal expansion is the phenomenon where liquids increase in volume as their temperature rises. In the context of fuel in a tank, understanding thermal expansion is crucial because the fuel’s volume will change as it is subjected to different temperatures during transport and operation. This concept helps ensure that the tank is not overfilled at lower temperatures, so it does not overflow when the fuel expands at higher temperatures.

Coefficient of Volumetric Expansion

The coefficient of volumetric expansion quantifies how much a liquid's volume changes per degree change in temperature. It is a key parameter in calculating the effect of temperature variations on the volume of fluids such as gasoline. Engineers use this coefficient to determine the appropriate fill level of a tank at one temperature to prevent overflow at another.

Temperature Conversion

Temperature conversion, particularly from Fahrenheit to Celsius, is essential when applying formulas that involve thermal expansion. Many thermal expansion coefficients are given in terms of Celsius, so converting temperatures from Fahrenheit to Celsius ensures accurate calculations regarding the change in fuel volume under different temperature conditions.

Maximum Capacity Calculation

Calculating the maximum capacity involves determining the initial volume of fuel that can be safely filled in a tank at a lower temperature, such that when the temperature increases, the expanded volume remains within the tank’s fixed capacity. This concept applies principles of thermal expansion and requires careful adjustment to avoid operational issues or safety hazards during transport or use.

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