Janus van der waals equations for real molecules with two-sided phase transitions

Abstract

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We obtained families of generalized van der Waals equations characterized by an even number n = 2, 4, 6 and a continuous free parameter, which is tunable for a critical compressibility factor. Each equation features two adjacent critical points which have a common critical temperature Tc and arbitrarily two close critical densities. The critical phase transitions are naturally two-sided: the critical exponents are αP=γP=23 and βP=δ−1=13 for T > Tc and αP=γP=nn+1 and βP=δ−1=1n+1 for T < Tc. In contrast with the original van der Waals equation, our novel equations all reduce consistently to the classical ideal gas law in the low-density limit. We tested our formulas against the NIST data for 11 major molecules and showed agreements better than the original van der Waals equation, not only near to the critical points but also in low-density regions.

Keywords

• equations of state
• van der Waals equation
• critical point
• two-sided phase transition
• NIST reference data
• analyticity