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Work done by rod when heated

  1. Aug 30, 2015 #1
    1. The problem statement, all variables and given/known data
    a metal rod of length "L",cross sectional area "A",young modulus "Y" and coefficient of linear expansion "α " is heated to "t" degree celsius .The work that can be performed by the rod when heated is
    2. Relevant equations
    work done by rod when heated=1/2 force exerted by rod(when heated) multiplied by extension
    I know force exerted by rod(when heated)=Y α ∆t multiplied by A
    (here ∆t is increase in temperature by due to heating)and extension would be final length -initial length let L' be final length.So extension would be L' - L
    As L'=L(1 +α ∆t )
    So L' - L=Lα ∆t

    3. The attempt at a solution
    with the help of equations above we can see
    work done by rod when heated=1/2 Y α ∆t A multiplied by Lα ∆t
    =1/2 YAL(α ∆t )^2
    right?but in my book answer is given 1/2 YAL(αt)^2
    which one is right?
     
  2. jcsd
  3. Aug 30, 2015 #2

    BvU

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    It looks like the reference for the exercise writer is zero degrees celsius. You take a more general approach where the environment temperature can be 0 or 20 or whatever.
    Apart from that I see no difference between your answer and the book answer ..

    --
     
    Last edited: Aug 30, 2015
  4. Aug 30, 2015 #3
    if that's the case then
    but as we can see nothing such is mentioned in the question
     
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