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Early in the morning, when the temperature is 5.5 °C, gasoline is pumped into a car’s 53-L steel gas tank until it is filled to the top. Later in the day the temperature rises to 27 °C. Since the volume of gasoline increases more for a given temperature increase than the volume of the steel tank, gasoline will spill out of the tank. How much gasoline spills out in this case?

Respuesta :

Answer:

Volume of gasoline spills out is 0.943 L.

Explanation:

Volumetric expansion of both gasoline and steel tank is :

[tex]\beta_{gas}=9.5 \times10^{-4}/K\\\beta_{steel \ gas}=3.6 \times 10^{-5}/K.[/tex]  { source Internet}

We know expansion due to temperature change is :

[tex]\Delta V=\beta\times\Delta T\times V[/tex]

For gasoline:

[tex]\Delta V_g=0.98 \ L.\\[/tex]

Similarly for Steel tank:

[tex]\Delta V_{steel \ gas}=0.037\ L[/tex].

Now, volume of gasoline spills out is equal to difference between expansion in volume.

[tex]\Delta V_{gas}-\Delta V_{Steel \ gas}=0.98-0.037\ L=0.943\ L.[/tex]

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