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A Steps in proof for Eotvos' law

  1. Sep 29, 2016 #1

    georg gill

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    REVuMFZm.jpe

    I have purchased an article after recommendation on wikipedia that as far as I am aware proves eotvos law. Here is a quote from wikipedia from this site: https://en.wikipedia.org/wiki/Eötvös_rule:

    ''John Lennard-Jones and Corner published (1940) a derivation of the equation by means of statistical mechanics''


    I unfortuntaely didn't get the proof. In the attachment at the top of this post which is from the article I wondered if someone could show the arithmetics from (9) to the place that I have marked as eotvos law.

    My attempt: No use writing anything unfortunately.
     
    Last edited: Sep 29, 2016
  2. jcsd
  3. Sep 29, 2016 #2
    Rename
    $$N_s k \log() V^{2/3}\rightarrow -\kappa $$
    $$(\psi_0-\phi_0) V^{2/3}/\kappa\rightarrow T_0 $$

    note that the logarithm is negative and constant in temperature.
     
  4. Sep 30, 2016 #3

    georg gill

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    Thank you for the answer! I also have tried to find the partition function log(F) somewhere on the internet. But I can not find the same formula. Could someone give me a link to this formula fron the internet and show how it is rewritten to log(F) in the attachment in the beginning of the first post.
     
  5. Sep 30, 2016 #4

    vanhees71

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    Can you tell us the reference? I'm a bit puzzled by the notation of the two pages you provided in #1. Usually you have the partion sum ##Z##, which is related to the grand potential ##\Phi=-T \ln Z## (in units where ##k_B=1##) which is a function of ##T##, ##\mu##, and ##V## with the relations to entropy, conserved particle number, and pressure given by
    $$S=-\partial_{T} \Phi, \quad N=-\partial_{\mu} \Phi, \quad P=-\partial_V \Phi.$$
     
  6. Sep 30, 2016 #5

    georg gill

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    This is the page where I bought the article:

    http://pubs.rsc.org/EN/content/articlelanding/1940/tf/tf9403601156#!divAbstract
     
    Last edited: Sep 30, 2016
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