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, $α_{\scriptscriptstyle{P}}$, $β_{\scriptscriptstyle{P}}$ and $γ_{\scriptscriptstyle{P}}$. Here we test this prediction by analyzing NIST REFPROP data for twenty major molecules, including $\mathrm{H_{2}O, CO_{2}, O_{2}}$, 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 $T T_{c}$, all the fluids seem to indicate the universal value of ${n=2}$.