91影视

Volume expansion is the expansion of the dimensions of an object with respect to temperature changes and can be expressed as,

$\mathbf{鈭�}\mathbf{V}\mathbf{=}{\mathbf{V}}_{\mathbf{0}}\mathbf{尾}\mathbf{鈭�}\mathbf{T}$ ...(i)

Here, V is the expansion in volume, V₀ is the unexpanded volume, 尾 is the coefficient of volume expansion and T is the absolute temperature.

Volume lost,

$鈭�\mathrm{V}=\left(106.0鈥�103.4\right)\mathrm{L}=2.6\mathrm{L}$

This lost volume gives the measure of the difference between volume expansion of the fuel and the tank.

Rearranging equation (i).

$鈭�\mathrm{T}=\frac{鈭�\mathrm{V}}{{\mathrm{V}}_0\mathrm{尾}}=\frac{鈭�\mathrm{V}}{{\mathrm{V}}_0\left({\mathrm{尾}}_{\mathrm{fuel}}鈥�{\mathrm{尾}}_{\mathrm{Aluminium}}\right)}$

Substitute all the values in the above equation,

$$\begin{gathered} 鈭�\mathrm{T}=\frac{2.6\mathrm{L}}{\left(106.0脳{10}^{-3}{\mathrm{m}}^3\right)\left(9.5脳{10}^{-4}{\left(掳\mathrm{C}\right)}^{-1}-7.2脳{10}^{-5}{\left(掳\mathrm{C}\right)}^{-1}\right)} \\ =28掳\mathrm{C} \end{gathered}$$

The maximum temperature was,

$28掳\mathrm{C}+4掳\mathrm{C}=32掳\mathrm{C}$

The tank should be filled just before the takeoff to ensure there is no loss in fuel. This is because there is a measure of volume expansion in both the gasoline and the aluminum tank when the temperature increases. But, the expansion itself depends on the coefficient of volume expansion characteristic to the material, i.e. it is different for gasoline and aluminum. So, when the temperature comes down 4潞C the next morning, there is an air gap left for the apparently lost fuel.