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Thermal Expansion of Gas in a Tank

by slong89
Tags: expansion, tank, thermal
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slong89
#1
Oct21-07, 01:27 PM
P: 2
1. The problem statement, all variables and given/known data

An underground gasoline tank at 54F can hold 1100 gallons of gasoline. If the driver of a tanker truck fills the underground tank on a day when the temperature is 82F, how many gallons, according to his measure on the truck, can he pour in? Assume that the temperature of the gasoline cools to 54F 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
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Doc Al
#2
Oct21-07, 01:48 PM
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The equation for volume expansion will look like this:
[tex]\Delta V = \beta V_0 \Delta T[/tex]

where [itex]\beta[/itex] 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
#3
Oct21-07, 02:53 PM
P: 2
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.


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