Tomaschitz,
R. (2022). Multiparameter equation of state for classical and quantum fluids, *Journal
of Supercritical Fluids ***181**, 105491, DOI:
10.1016/j.supflu.2021.105491

**Abstract **ScienceDirect

A closed-form multi-parameter fluid equation of state (EoS) is proposed and tested with empirical pressure isotherms of water and hydrogen. The EoS is non-algebraic but elementary, applicable in the full temperature range above the melting point, and remains accurate at high pressure. The critical-point conditions (vanishing density-derivatives of pressure) are exactly implemented in the exponential attractive term of the EoS. The singular repulsive term is structured similar to the Carnahan-Starling EoS and depends on five substance-specific parameters, which can be regressed from the critical isotherm. The temperature evolution of the EoS above the critical temperature is regressed from supercritical isotherms. In the subcritical regime above the melting point, the temperature-dependent scale factors of the EoS are inferred from the empirical coexistence curve, which is fully implemented in the EoS. The pressure singularity occurs at a limit density that is noticeably higher than predicted by universal cubic EoSs such as the Peng-Robinson EoS. The parameters of the analytic and non-perturbative EoSs of water and hydrogen are derived from high-pressure data sets.

description:
Roman Tomaschitz (2022) Multiparameter equation of state for classical and
quantum fluids, *J. Supercrit. Fluids ***181**, 105491.

**Keywords:**
Non-cubic fluid equation of state (EoS); Critical, sub- and supercritical
isotherms; Vapor-liquid equilibrium and saturation
densities; Saturation pressure and coexistence curve; Pressure singularity and
limit density; High-pressure EoSs of water and hydrogen

**Highlights**

An analytic multi-parameter fluid equation of state (EoS) is proposed.

The critical point conditions and the empirical saturation curve are implemented in the EoS.

The EoS is non-perturbative and suitable for the high-density regime close to the pressure

singularity.

The EoS is of closed form and applicable in the full temperature range above the melting point.

The EoS is tested with critical, sub- and supercritical pressure isotherms of water and hydrogen.

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