Generalized van der Waals theory. II. Quantum effects on the equation of state

1980 ◽  
Vol 33 (9) ◽  
pp. 2029 ◽  
Author(s):  
MA Hooper ◽  
S Nordholm
Keyword(s):  
Equation Of State ◽  
Vapour Pressure ◽  
Van Der Waals ◽  
Translational Motion ◽  
Quantum Effects ◽  
Corresponding States ◽  
Critical Parameters ◽  
Van Der Waals Model ◽  
Van Der Waals Theory ◽  
Law Of Corresponding States

The light gases deviate markedly from the Law of Corresponding States approximately obeyed by the heavier gases. This is due, at least in part, to the quantization of translational motion at higher densities. This effect has been studied within the framework of a generalized van der Waals model. Each particle is treated as moving within a cubic volume determined by the surrounding particles. Changes to the critical parameters and to the shapes of the coexistence and vapour pressure curves are calculated and compare well with experiment, considering the simplicity of our model.

Generalized van der Waals theory. IV. Variational determination of the hard-sphere diameter

1981 ◽  
Vol 34 (9) ◽  
pp. 1809 ◽  
Author(s):  
MA Hooper ◽  
S Nordholm
Keyword(s):  
Equation Of State ◽  
Hard Sphere ◽  
Pair Correlation ◽  
Van Der Waals ◽  
Critical Parameters ◽  
Variational Parameter ◽  
Sphere Diameter ◽  
Entropy Functional ◽  
Van Der Waals Theory

The generalized van der Waals theory is here extended by incorporating the hard-sphere diameter as a variational parameter. Moreover, the entropy functional has been chosen so as to accurately reflect the density dependence of the excluded volume revealed by the hard-sphere equation of state. The combined effect of these two improvements yields a theory capable of describing the equation of state of the Lennard- Jones model of classical fluids to an accuracy comparable to that of the pair correlation theories. The results presented here include critical parameters and coexistence and vapour pressure curves.

Generalized van der Waals theory. V. Equation of state of two-dimensional simple fluid

1981 ◽  
Vol 34 (9) ◽  
pp. 1819 ◽  
Author(s):  
MA Hooper ◽  
S Nordholm
Keyword(s):  
Van Der Waals ◽  
Translational Motion ◽  
Volume Effect ◽  
Critical Parameters ◽  
Excluded Volume ◽  
Two Dimensional ◽  
Disc Diameter ◽  
Monolayer Adsorption ◽  
Excluded Volume Effect ◽  
Van Der Waals Theory

We have investigated the two-dimensional gas-liquid condensation of a LJ(12-6) system with relevance to monolayer adsorption. A recently developed generalized van der Waals theory has been used to calculate critical parameters, coexistence curves, vapour pressure curves and other thermodynamic information partially as an investigation into the validity of the theory. Two aspects are of particular concern. Firstly, we are interested in the temperature and density dependence of the excluded volume effect. The effective hard-disc diameter is determined variationally so as to minimize the free energy. Secondly, we apply a simple means of quantizing the theory to estimate shifts in the thermodynamic properties of light fluids due to the quantum character of the translational motion. Apparently useful accuracy is obtained.

An equation of state for non-polar substances based on the generalized van der Waals model

1993 ◽  
Vol 91 (2) ◽  
pp. 215-237 ◽  
Author(s):  
Nguyen Van Nhu ◽  
Gustavo A. Iglesias-Silva ◽  
Friedrich Kohler
Keyword(s):  
Equation Of State ◽  
Van Der Waals ◽  
Van Der Waals Model

Generalized van der Waals theory. I. Basic formulation and application to uniform fluids

1980 ◽  
Vol 33 (9) ◽  
pp. 2013 ◽  
Author(s):  
S Nordholm ◽  
ADJ Haymet
Keyword(s):  
Free Energy ◽  
Equation Of State ◽  
Particle Density ◽  
Van Der Waals ◽  
Three Dimensional ◽  
Energy Functional ◽  
Coarse Grained ◽  
Uniform Structure ◽  
Free Energy Functional ◽  
Van Der Waals Theory

A generalized van der Waals theory is derived on the basis of simple physical and mathematical arguments. The derivation results in a free- energy functional wherein the independent variable is a coarse-grained particle density. It is assumed that a well defined particle density dominates the free energy and this density is to be obtained by minimizing the free energy functional. The variational theory so obtained can be applied to non-uniform fluids. In the present work the possibility of stable non-uniform structure is neglected and the theory is applied to uniform fluids. It then produces an equation of state identical in form to that proposed originally by van der Waals but the excluded volume is only about half as large in the three-dimensional case. Applications to several two- and three-dimensional systems indicate that the new equation of state is a distinct improvement over the traditional van der Waals theory when the full range of fluid densities is considered. The quantitative accuracy in the case of simple uniform fluids is sufficient to warrant further development and exploitation of the theory.

THE LAW OF CORRESPONDING STATES AND COLD NEUTRON SCATTERING BY LIQUIDS

1966 ◽  
Vol 44 (4) ◽  
pp. 867-875 ◽  
Author(s):  
V. F. Sears
Keyword(s):  
Neutron Scattering ◽  
Cold Neutron ◽  
Quantum Effects ◽  
Theoretical Models ◽  
Corresponding States ◽  
Scattering Data ◽  
Velocity Spectrum ◽  
Simple Liquid ◽  
Law Of Corresponding States ◽  
The Law

Although the law of corresponding states can be used in the practical analysis of cold neutron scattering data from liquids only if quantum effects are negligible, it is of interest, nevertheless, to have a quantum mechanical derivation of this law, because it is only then that one can discuss, in a completely consistent way, the conditions under which quantum effects are negligible. Such a derivation is given in the present paper. We also present an extension of the law of corresponding states to the velocity spectrum of an atom in a simple liquid and indicate how this can be used to check the consistency and extend the range of applicability of theoretical models of the velocity spectrum.

Sign in / Sign up

Export Citation Format

Share Document