Thermal Expansion of Gas in a Tank

[slong89]

Homework Statement

An underground gasoline tank at 54°F can hold 1100 gallons of gasoline. If the driver of a tanker truck fills the underground tank on a day when the temperature is 82°F, how many gallons, according to his measure on the truck, can he pour in? Assume that the temperature of the gasoline cools to 54°F on entering the tank.

Homework Equations

(delta)Length = 3(alpha) * Volume(initial) * (delta)Temp
i found the value alpha for gasoline to be 9.6e-4

The Attempt at a Solution

3(9.6e-4)(28)(1100)=delta(L)=88.7
thus the amount he could pour in is 1188.7
for some reason this isn't the answer though... I'm not really sure what I'm doing wrong

 

[Doc Al]

The equation for volume expansion will look like this:
$$\Delta V = \beta V_0 \Delta T$$

where $\beta$ is the volume coefficient of expansion, which would be about 3 times the linear coefficient. Are you sure you found the linear coefficient of expansion for gasoline?

 

[slong89]

You're right.. thank you so much. The 9.6e-4 already accounted for the times 3, and thus was the volume coefficient of expansion. I guess you couldn't really make one for gasoline anyway. Thanks again.