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Boltzmann's version of 2nd Law -log relationship

  1. Sep 5, 2004 #1
    Hello List,

    I understand Boltzmann defined entropy as log W where W is the number of microstates in the system time a constant "k" ; hence S= k Log W.

    Can someone explain to me where the logarithmic relationship comes from please ?

    Many thanks in advance,

    Celal Berker
    London, England
  2. jcsd
  3. Sep 5, 2004 #2
    You want the Entropy to be a quantum that adds up when you're looking at more than one system: E. g. if you have two containers filled with gas, you want the relationship S(container A & container B) = S(container A) + S(container B).

    But if the system A has [itex]W_a[/itex] states and the system B has [itex]W_b[/itex] states, the combined system has [itex]W_a W_b[/itex] states: a product, not a sum. So youo have to take the logarithm of this number to get the relation above.
  4. Sep 6, 2004 #3
    Many Thanks Bruno (is that your name?)

    So how did Planck, by what thought or reasoning processes did he go from the relation S= k log W to E=Hf ?

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