A New Model Approach for the Near-Critical Point Region: 1. Construction of the Generalized van der Waals Equation of State

2008 ◽  
Vol 112 (49) ◽  
pp. 15725-15741 ◽  
Author(s):  
Sukbae Lee ◽  
Joonhyeon Jeon ◽  
Wonsoo Kim ◽  
Tong-Seek Chair
Keyword(s):  
Equation Of State ◽  
Critical Point ◽  
Van Der Waals ◽  
Van Der Waals Equation ◽  
New Model ◽  
Model Approach

Simple Pressure and Energy State Equations for Lennard-Jones (12,6) Fluid

1990 ◽  
Vol 112 (1) ◽  
pp. 240-244 ◽  
Author(s):  
H. M. Paynter ◽  
E. P. Fahrenthold ◽  
G. Y. Masada
Keyword(s):  
Equation Of State ◽  
Critical Point ◽  
Energy State ◽  
Van Der Waals ◽  
Saturation Curve ◽  
State Equations ◽  
Configurational Energy ◽  
Van Der Waals Equation ◽  
Lennard Jones ◽  
Direct Extension

A recently published (Paynter, 1985, 1988) simple veridical equation of state represents a direct extension and generalization of the classical van der Waals equation, yet at the same time remains consistent with modern nonanalytical expansions about the critical point. With the use of this particular equation of state, compact expressions are here obtained for the pressure and configurational energy of the Lennard-Jones (12, 6) fluid, together with a saturation curve and other coexistence properties.

scholarly journals Local Shape of the Vapor–Liquid Critical Point on the Thermodynamic Surface and the van der Waals Equation of State

2021 ◽  
Vol 9 ◽  
Author(s):  
J. S. Yu ◽  
X. Zhou ◽  
J. F. Chen ◽  
W. K. Du ◽  
X. Wang ◽  
...  
Keyword(s):  
Equation Of State ◽  
Critical Point ◽  
Van Der Waals ◽  
Usual Condition ◽  
Local Shape ◽  
Van Der Waals Equation ◽  
Usual Form ◽  
Zero Gaussian Curvature ◽  
Two Parameters ◽  
Vapor Liquid

Differential geometry is a powerful tool to analyze the vapor–liquid critical point on the surface of the thermodynamic equation of state. The existence of usual condition of the critical point (∂p/∂V)T=0 requires the isothermal process, but the universality of the critical point is its independence of whatever process is taken, and so we can assume (∂p/∂T)V=0. The distinction between the critical point and other points on the surface leads us to further assume that the critical point is geometrically represented by zero Gaussian curvature. A slight extension of the van der Waals equation of state is to letting the two parameters a and b in it vary with temperature, which then satisfies both assumptions and reproduces its usual form when the temperature is approximately the critical one.

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

2016 ◽  
Vol 43 (9) ◽  
pp. 095105 ◽  
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

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

2021 ◽  
Vol 17 (1) ◽  
pp. 119-138
Author(s):  
M. R. Koroleva ◽  
◽  
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.

4. States of matter

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.

Application of the van der Waals equation of state to polymers III. Correlation and prediction of upper critical solution temperatures for polymer solutions

1994 ◽  
Vol 100 ◽  
pp. 63-102 ◽  
Author(s):  
Vassilis I. Harismiadis ◽  
Georgios M. Kontogeorgis ◽  
Ana Saraiva ◽  
Aage Fredenslund ◽  
Dimitrios P. Tassios
Keyword(s):  
Equation Of State ◽  
Polymer Solutions ◽  
Van Der Waals ◽  
Van Der Waals Equation ◽  
Critical Solution Temperatures
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