Physics: 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?

Early in the morning, when the temperature is 5.5

aubriebv2020

12.01.2022

Volume of gasoline spills out is 0.943 L.

Explanation:

Volumetric expansion of both gasoline and steel tank is :

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

We know expansion due to temperature change is :

$\Delta V=\beta\times\Delta T\times V$

For gasoline:

$\Delta V_g=0.98 \ L.\\$

Similarly for Steel tank:

$\Delta V_{steel \ gas}=0.037\ L$ .

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

$\Delta V_{gas}-\Delta V_{Steel \ gas}=0.98-0.037\ L=0.943\ L.$

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