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Homework Help: Energy Fluctuations in Canonical Ensemble

  1. Mar 30, 2010 #1
    1. The problem statement, all variables and given/known data

    In deriving <E2>-<E>2

    starting from <E>=U=sum(Eiexp(-beta Ei))/sum(exp(-beta Ei). the taking derivative of U with respect to beta, the book always notes E (thus Volume) is held constant. what i am trying to do is taking the derivative of U with respect to beta or T (temp) and V (volume). but i get stuck

    2. Relevant equations

    <E>=U= sum(Ei*exp(-beta*Ei)/sum(exp(-beta*Ei)
    dU=dU/dT+dU/dV

    3. The attempt at a solution

    I applied the above equation dU to U as listed above. i performed the quotient and product rule obtaining terms partial derivative with respect to V and T. I tried to look for a way to combine terms and cancel terms. but I cannot. anyone help thank you.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 30, 2010 #2
    Why are you taking the derivative of U with respect to V? It only asked you to take the derivative with respect to beta.
     
  4. Mar 30, 2010 #3
    in the notes in the book its hold Ei constant, i want to perform the derivative more generally allowing Ei to vary
     
  5. Mar 31, 2010 #4
    But I am pretty sure, they take a partial derivative with respect to beta. So you don't worry about N or V.
     
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