1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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)


    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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    There's one too many lambdas in there:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook