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Extensivity of an Ideal Solid

  1. Nov 1, 2012 #1
    [itex]\frac{}{}[/itex]1. The problem statement, all variables and given/known data
    Starting from S(E,N)=c(N)+3Nk[1+LN([itex]\frac{E}{3Nh\nu}[/itex])], derive a version of the Entropy, S(E,N) of an ideal solid that is extensive, that is, for which S([itex]\lambda[/itex]E,[itex]\lambda[/itex]N)=[itex]\lambda[/itex]S(E,N)


    2. Relevant equations



    3. The attempt at a solution
    Basically have to prove that S([itex]\lambda[/itex]E,[itex]\lambda[/itex]N)=[itex]\lambda[/itex]S(E,N).

    I can set it up, but I don't know how to eliminate terms to get to a form I can work with.
     
  2. jcsd
  3. Nov 1, 2012 #2
    I have it setup like this:

    S(λ E,λ N)=λ S(E,N)

    c(λN)+3(λN)k[1+ln[itex]\frac{λE}{3(λN)h\nu}[/itex]]=λ{c(N)+3Nk[1+ln[itex]\frac{E}{3Nh\nu}[/itex]]


    But 1. I dont know how to reduce the left side, and
    2. when I distribute λ through the right side, is it on everything ending up looking like this: c(λN)+λ(3Nk)[λ+ln[itex]\frac{λE}{λ(3Nh\nu)}[/itex]]? Or something else...
     
  4. Nov 1, 2012 #3

    haruspex

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    There's one too many lambdas in there:
    [itex]c(λN)+λ(3Nk)[1+ln\frac{λE}{λ(3Nh\nu)}][/itex]
     
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