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Linear and Volume expansion Problem

  1. Jun 12, 2013 #1
    [a]The problem statement, all variables and given/known data

    1.) A 2.00-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 58.0°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.

    2.)Assuming all have the same initial volume, compare the following substances by the amount of volume expansion due to an increase in temperature: glass, mercury, aluminum, ethyl alcohol. (See the table below. Select all that apply.)
    Ethyl alcohol would have the smallest expansion.
    Ethyl alcohol would have the largest expansion.
    Mercury would have the smallest expansion.
    Mercury would have the largest expansion.
    Glass would have the smallest expansion.
    Glass would have the largest expansion.
    Aluminum would have the largest expansion.
    Aluminum would have the smallest expansion.

    Relevant equations

    ΔV=V°βΔT

    Coefficient of Volume Expansion
    Ethyl 1.12e-4
    mercury 1.82e-4
    glass 2.7e-5
    aluminum 7.2e-5
    gasoline 2.88e-3


    [c] Attempt
    For the first question, I do not know how to factor in the expansion of the container. This is what I did.
    ΔV=(2L)(2.88e-3/°C)(53°C)= 0.30528 L= 305 cm3

    I thought for the second question that aluminum would have the largest expansion and ethyl alcohol would have the smallest, but this was not correct.
     
  2. jcsd
  3. Jun 12, 2013 #2

    Redbelly98

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    Staff Emeritus
    Science Advisor
    Homework Helper


    Apply the same equation to the aluminum container.
    The designation "e-4" after a number means ×10-4. Likewise for e-3 and e-5. So for example, 3e-2 is the same as 0.03. Does that help?
     
  4. Jun 12, 2013 #3
    nevermind I figured it out. thanks
     
    Last edited: Jun 12, 2013
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