Critical Constants Correlation from van der Waals Equation

The cubic van der Waals equation of state at the critical condition is reduced to a linear function (Vc vs. Tc /Pc coordinates) with one adjustable parameter. It is shown that at the critical point the relation Vc = 3Vo must not hold as van der Waals suggested, but the attractive constant α = Pc Vc2 remains. Selected values of Tc, Pc, Vc compiled by Ihmels where focused on testing the quality of several empirical equations relating critical conditions. It is shown that the obtained critical constants correlation is a general form of the empirical expressions proposed by Young, Meissner, Bird, Grigoras and Ihmels. From the resulting correlation function, a function for the critical compressibility is proposed. The critical volume Vc and the ratio Tc /Pc have been expressed in group contributions.

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Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State

Nelineinaya Dinamika ◽

10.20537/nd210109 ◽

2021 ◽

Vol 17 (1) ◽

pp. 119-138

Author(s):

M. R. Koroleva ◽

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O. V. Mishchenkova ◽

V. A. Tenenev ◽

T. Raeder ◽

...

Keyword(s):

Equation Of State ◽

Critical State ◽

Stokes Equations ◽

Safety Valve ◽

Van Der Waals ◽

Local Approximation ◽

Critical Conditions ◽

Nonlinear Processes ◽

Real Gas ◽

Van Der Waals Equation

The paper presents a modification of the digital method by S. K. Godunov for calculating real gas flows under conditions close to a critical state. The method is generalized to the case of the Van der Waals equation of state using the local approximation algorithm. Test calculations of flows in a shock tube have shown the validity of this approach for the mathematical description of gas-dynamic processes in real gases with shock waves and contact discontinuity both in areas with classical and nonclassical behavior patterns. The modified digital scheme by Godunov with local approximation of the Van der Waals equation by a two-term equation of state was used for simulating a spatial flow of real gas based on Navier – Stokes equations in the area of a complex shape, which is characteristic of the internal space of a safety valve. We have demonstrated that, under near-critical conditions, areas of nonclassical gas behavior may appear, which affects the nature of flows. We have studied nonlinear processes in a safety valve arising from the movement of the shut-off element, which are also determined by the device design features and the gas flow conditions.

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Limiting temperature of pion gas with the van der Waals equation of state

Journal of Physics G Nuclear and Particle Physics ◽

10.1088/0954-3899/43/9/095105 ◽

2016 ◽

Vol 43 (9) ◽

pp. 095105 ◽

Cited By ~ 4

Author(s):

R V Poberezhnyuk ◽

V Vovchenko ◽

D V Anchishkin ◽

M I Gorenstein

Keyword(s):

Equation Of State ◽

Van Der Waals ◽

Van Der Waals Equation

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Swarm Intelligence Approach for Rational Global Approximation of Characteristic Curves for the Van der Waals Equation of State

Lecture Notes in Computer Science - Computational Science – ICCS 2020 ◽

10.1007/978-3-030-50426-7_45 ◽

2020 ◽

pp. 604-616

Author(s):

Almudena Campuzano ◽

Andrés Iglesias ◽

Akemi Gálvez

Keyword(s):

Equation Of State ◽

Swarm Intelligence ◽

Van Der Waals ◽

Global Approximation ◽

Characteristic Curves ◽

Van Der Waals Equation ◽

Intelligence Approach

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4. States of matter

Physical Chemistry: A Very Short Introduction ◽

10.1093/actrade/9780199689095.003.0004 ◽

2014 ◽

pp. 51-69

Author(s):

Peter Atkins

Keyword(s):

Nuclear Magnetic Resonance ◽

Liquid Crystals ◽

Magnetic Resonance ◽

Equation Of State ◽

Soft Matter ◽

Van Der Waals ◽

Two Dimensional ◽

X Ray Diffraction ◽

Van Der Waals Equation ◽

Intermediate States

‘States of matter’ describes the three traditional states — gas, liquid, and solid — and the models used to predict and understand their behaviour. The van der Waals equation of state captures many of the properties of real gases. The classical way of studying the motion of molecules in liquids is to measure its viscosity. Techniques include neutron scattering and nuclear magnetic resonance. X-ray diffraction is used to determine the structures of solids. Intermediate states of matter — where liquid meets gas and liquid meets solid — are also considered. Examples include supercritical fluids, soft matter such as liquid crystals, and graphene, a remarkable and essentially two-dimensional material.

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