Steps in proof for Eotvos' law

[georg gill]

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.

 

[thephystudent]

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.

 

[georg gill]

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.

 

[vanhees71]

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
$$S=-\partial_{T} \Phi, \quad N=-\partial_{\mu} \Phi, \quad P=-\partial_V \Phi.$$

 

[georg gill]

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
$$S=-\partial_{T} \Phi, \quad N=-\partial_{\mu} \Phi, \quad P=-\partial_V \Phi.$$

This is the page where I bought the article:

http://pubs.rsc.org/EN/content/articlelanding/1940/tf/tf9403601156#!divAbstract