Isobaric Critical Exponents: Test of Analyticity against NIST Reference Data

Abstract

Finite systems may undergo first or second order phase transitions under not isovolumetric but isobaric condition. The `analyticity' of a finite-system partition function has been argued to imply universal values for isobaric critical exponents, ${\alpha }_P$, ${\beta }_P$ and ${\gamma }_P$. Here we test this prediction by analyzing NIST REFPROP data for twenty major molecules, including ${\mathrm{H}}_2\mathrm{O},\mathrm{C}{\mathrm{O}}_2,{\mathrm{O}}_2$, etc. We report they are consistent with the prediction for temperature range, $10^{-5}<|T/T_c-1|<10^{-3}$. For each molecule, there appears to exist a characteristic natural number, $n=2,3,4,5,6$, which determines all the critical exponents for $T<T_c$ as ${\alpha }_P={\gamma }_P=\frac{n}{n+1}$ and ${\beta }_P={\delta }^{-1}=\frac{1}{n+1}$. For the opposite $T>T_c$, all the fluids seem to indicate the universal value of $n=2$.

V2) 1+21 pages, 4 figures, with concluding remark: `In the sense of Thomas Kuhn, our result might be viewed as "anomaly" within the standard paradigm of taking the thermodynamic limit for critical phenomena. Nevertheless, our analysis represents truthfully the NIST experimental data.... We call for further theoretical as well as experimental investigations.'