# Thermal Expansion of Gas in a Tank

1. Oct 21, 2007

### slong89

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

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

3. 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

2. Oct 21, 2007

### Staff: Mentor

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?

3. Oct 21, 2007

### 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.