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Math Help - expanding steel problem

  1. #1
    Newbie
    Joined
    Jul 2005
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    2

    help please

    i'm finding this question difficult to work out,any help would be great thanks!
    here is the question:

    A piece of steel is 11.5 meters long at 22 degrees Celsius. It is heated to 1221 degrees Celsius, close to its melting temperature. How long is it?
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    1,631
    It should not be that difficult. It is only a substitution, or plugging in, problem. Nothing to analyze really. That is if you know the formula and constants to use.

    The question is about linear thermal expansion of a length of steel.
    In Physics we learned for this case that
    "the change in length is proportinal to the change in temperature"
    delta L ----> L*(delta T)
    delta L = k*[L*(delta T)] -------(i)

    where
    >>>delta L is (change in length) = (final length minus initial length)
    Or, (final length) = (initial length) +(delta L)

    >>>k = constant of proportionality = average coefficient of linear expansion.
    For steel, k = 11*[10^(-6)] per degree Centigrade

    >>>L = initial length

    >>>delta T = change in temperature = (final temp. minus initial temp.)

    Given:
    L = 11.5 m
    delta T = (1221 -22) = 1099 deg Celsius

    So, substituting all those into (i),
    delta L = [11*10^(-6)]*[11.5 * 1099] = 0.139 m

    Therefore, that piece of steel is
    11.5 + 0.139 = 11.639 m long
    when its temperature is 1221 degrees Celsius.
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  3. #3
    Newbie
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    Jul 2005
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    thanks that really helped
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