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The Volume Expansion Formula is a key concept in understanding how fluids like gasoline respond to temperature changes. When the temperature of a substance increases, its volume generally increases as well. This relationship is captured by the equation:

• \( \Delta V = \beta \cdot V_0 \cdot \Delta T \)

Here, \( \Delta V \) represents the change in volume, \( V_0 \) is the initial volume of the substance, \( \beta \) is the coefficient of volume expansion, and \( \Delta T \) signifies the change in temperature. This formula allows us to calculate how much a substance will expand, based on these parameters.
In the context of the exercise, the initial volume \( V_0 \) is 106.0 L, and due to thermal expansion, the volume decreases to 103.4 L after some gasoline overflowed. By applying the volume expansion formula, we calculate the temperature change that resulted from a hot afternoon, helping us to understand the event's cause.

The Coefficient of Volume Expansion, \( \beta \), is a crucial factor that determines how much a given volume of a substance will expand when heated. It is specific to the material in question. For gasoline, the coefficient of volume expansion is provided as \( 9.5 \times 10^{-4} \, K^{-1} \).
This means that for each degree Kelvin (K) temperature increase, the volume of gasoline expands by \( 9.5 \times 10^{-4} \) times its original volume. This coefficient allows us to calculate the temperature change that led to the volume shrinkage observed on Sunday morning. By using the coefficient in the volume expansion formula, students can rearrange the equation to solve for the temperature change \( \Delta T \), illustrating how material and temperature interact.

Managing fuel in an aerobatic airplane involves understanding thermal expansion to prevent fuel loss during temperature changes. In aviation, the efficiency and safety of a flight can depend greatly on proper fuel management.
On a hot day, gasoline expands due to temperature increase. If the tanks were completely filled, as in the Pitts S-2C scenario, expanding gasoline can lead to overflow through vents, leading to needless fuel loss.
Pilots can manage this by timing the refueling process. Filling the fuel tanks during cooler parts of the day, like in the morning or late evening, ensures maximum fuel stays in the tanks as temperatures rise. This practice not only optimizes fuel capacity but also maintains the balance and performance of the plane during flight. Hence, understanding and applying thermal expansion principles can critically enhance an aircraft's operational efficiency.