Isobaric Critical Exponents: Test of Analyticity against NIST Reference Data

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 $n=2$.