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Homework Help: Determine error caused by average coefficient of expansion approximation.

  1. Jan 20, 2009 #1
    The relationship Lf = Li(1 + α ΔT ) is an approximation that works when the average coefficient of expansion is small. If α is large, one must integrate the relationship dL/dT = α L to determine the final length.

    a)Assuming that the average coefficient of linear expansion is constant as L varies, determine a general expression for the final length. Use L_i for Li, alpha for α, and DeltaT for ΔT as necessary.

    b)Given a rod of length 4.00 m and a temperature change of 100.0°C, determine the error caused by the approximation when α = 2.00 multiplied by 10-5 (°C)-1 (a typical value for a metal)

    Lf = Li(1 + α ΔT )


    ( 4( 1 + (2.00E-5(100)) ) / (4*100*2.00E-5)
    .002/1.002 = .001996008 * 100 = .1996008

    It says that:
    Your answer is off by a multiple of ten.% for part b
  2. jcsd
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