Question

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?

Answer 1

Volume of gasoline spills out is 0.943 L.

Step-by-step explanation:

Volumetric expansion of both gasoline and steel tank is :

`\beta_(gas)=9.5 *10^(-4)/K\\\beta_(steel \ gas)=3.6 * 10^(-5)/K.` { source Internet}

We know expansion due to temperature change is :

`\Delta V=\beta*\Delta T* 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.`