Help with a volume expansion problem

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Homework Help Overview

The problem involves a volume expansion scenario where an aluminum cylinder filled with gasoline is heated, and the resulting expansion of both the container and the liquid is examined to determine how much gasoline spills out.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply the volume expansion formula for both aluminum and gasoline, calculating the respective expansions and then finding the difference. Some participants question the accuracy of the calculations and the assumptions made regarding the coefficients of expansion.

Discussion Status

There is an indication that the original poster has resolved the issue independently, but further inquiries about the solution process remain. Other participants are encouraged to provide assistance or clarification.

Contextual Notes

The problem specifies to ignore evaporation and assumes the volume coefficients are accurate to three digits, which may influence the calculations and assumptions discussed.

KTANNE
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Homework Statement



A 3.00-liter aluminum cylinder at 5.00°C is filled to the brim with gasoline at the same temperature. If the aluminum and gasoline are warmed to 53.0°C, how much gasoline spills out? [Hint: Be sure to account for the expansion of the container. Also, ignore the possibility of evaporation, and assume the volume coefficients are good to three digits.

Homework Equations



Coeff of Linear Expansion for Al : 24 X 10^-6
Coeff of Volume Expansion for gasoline: 9.6 X 10 ^-4
Volume Expansion Formula: ΔV = βVoΔT

The Attempt at a Solution



I calculated the volume expansion formula for each variable and came up this:
aluminum = (24 X 10^-6)(3.00L)(53.0 - 5.00)°C = .003456
gasoline = (9.6 X 10^-4)(3.00L)(53.0 - 5.00)°C = .13824

I then subtracted (.13824) - (.003456) = .134784 = .135
And this is the incorrect answer... The correct answer is 128 cm^3 so I don't know what I am doing incorrectly...
 
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I figured it out - NM
 
how did you solve this problem?
 
jk27, please stand by, I or somebody will post some help in your thread.

p.s. Welcome to PF to both of you.
 

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