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Thermodynamics, composite bar linear expansion

  1. Jul 21, 2012 #1
    1. The problem statement, all variables and given/known data

    "A composit bar is made of two metals joined in series, with coefficients of linear thermal expansion 2.2E-5 and 0.9E-5 K^-1 respectively. The bar expands by 0.5% in length with a temperature rise of 500 K. Calculate the ratio of the initial lengths of the two metal sections."

    2. Relevant equations
    The main equation I think to be useful is ΔL=α L ΔT


    3. The attempt at a solution

    I am thinking that I cannot assume that the two bars will expand the same amount, meaning that the sum of ΔL1+ΔL2+L=1.005L...

    500(ΔL1α1+ΔL2α2)+L=1.005L
    500(ΔL1α1+ΔL2α2)/L=0.005

    Whatever way I look at this I just see myself going round in circles :/
     
  2. jcsd
  3. Jul 21, 2012 #2

    TSny

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    Are you sure you want the Δ's in this equation?

    Also, can you express L in terms of the initial lengths of each section?
     
  4. Jul 21, 2012 #3

    tiny-tim

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    Hi RJWills! :smile:

    What does the question ask for?

    The ratio L1/L2 …

    so call that ratio "r", and put it into the equation! :wink:
     
  5. Jul 21, 2012 #4
    Okay so tried it the way you suggested, here's what I did:

    500(L1α1+L2α2) +L1+L2 = 1.005(L1+L2)
    1.011L1 + 1.0045L2 = 1.005(L1+L2)
    Therefore L1/L2 = 1/12 (0.0833...)
    right?
     
  6. Jul 21, 2012 #5

    TSny

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    Looks good. :smile:
     
  7. Jul 21, 2012 #6
    Awesome thanks for the help guys :)
     
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