scholarly journals Fluids confined in wedges and by edges: Virial series for the line-thermodynamic properties of hard spheres

2014 ◽  
Vol 141 (24) ◽  
pp. 244906 ◽  
Author(s):  
Ignacio Urrutia
Keyword(s):  
Thermodynamic Properties ◽  
Hard Spheres ◽  
Virial Series

Critical consolute point in hard-sphere binary mixtures: Effect of the value of the eighth and higher virial coefficients on its location

2010 ◽  
Vol 75 (3) ◽  
pp. 359-369 ◽  
Author(s):  
Mariano López De Haro ◽  
Anatol Malijevský ◽  
Stanislav Labík
Keyword(s):  
Equation Of State ◽  
Binary Mixtures ◽  
Hard Sphere ◽  
Hard Spheres ◽  
Virial Coefficients ◽  
Fluid Mixture ◽  
Binary Fluid ◽  
Virial Series ◽  
Consolute Point ◽  
Critical Constants

Various truncations for the virial series of a binary fluid mixture of additive hard spheres are used to analyze the location of the critical consolute point of this system for different size asymmetries. The effect of uncertainties in the values of the eighth virial coefficients on the resulting critical constants is assessed. It is also shown that a replacement of the exact virial coefficients in lieu of the corresponding coefficients in the virial expansion of the analytical Boublík–Mansoori–Carnahan–Starling–Leland equation of state, which still leads to an analytical equation of state, may lead to a critical consolute point in the system.

Thermodynamic Properties of Mixtures of Hard Spheres

1964 ◽  
Vol 41 (1) ◽  
pp. 133-138 ◽  
Author(s):  
J. L. Lebowitz ◽  
J. S. Rowlinson
Keyword(s):  
Thermodynamic Properties ◽  
Hard Spheres

Introduction

1984 ◽  
Author(s):  
C. G. Gray ◽  
K. E. Gubbins
Keyword(s):  
Thermodynamic Properties ◽  
Thermodynamic Functions ◽  
Energy Levels ◽  
Virial Coefficients ◽  
Intermolecular Forces ◽  
Great Accuracy ◽  
Perfect Gas ◽  
Mathematical Basis ◽  
Virial Series ◽  
Simple Molecules

The application of statistical mechanics to the study of fluids over the past fifty years † or so has progressed through a series of problems of gradually increasing difficulty. The first and most elementary calculations were for the thermodynamic functions (heat capacities, entropies, free energies, etc.) of perfect gases. These properties are related to the molecular energy levels, which for perfect gases can be determined theoretically (by quantum calculations) or experimentally (by spectroscopic methods, for example). For simple molecules (CO2 , CH4 , etc.) the energy levels, and hence the thermodynamic properties, can be determined with great accuracy, and even for quite complex organic molecules it is now possible to obtain thermodynamic properties with satisfactory accuracy. With the advent of digital computers it became possible to calculate thermodynamic properties for a wide variety of substances and temperatures, and several useful tabulations of perfect gas properties now exist. Having successfully treated the perfect gas, it was natural to consider gases of moderate density, where intermolecular forces begin to have an effect, by expanding the thermodynamic functions in a power series (or virial series) in density. Although the mathematical basis for a theoretical treatment of this series was laid by Ursell in 1927, it was not exploited until ten years later, when Mayer re-examined the problem. Since that time a great deal of effort has been put into evaluating the virial coefficients that appear in the series for a variety of intermolecular force models. As the expressions for the virial coefficients are exact, they provide a very useful means of checking such force models by comparison of calculated and experimental coefficients. While the theory of dilute gases at equilibrium is essentially complete, this is far from being the case for all dense gases and liquids. The virial series cannot be applied directly to liquids. As an alternative to the ‘dense gas’ approach to liquids, there were early attempts to treat liquids as disordered solids by using cell or lattice theories; these were popular from the mid-1930s until the early 1960s.

Thermodynamic properties of a fluid of hard spheres with water-like dipole and quadrupole moments

1981 ◽  
Vol 79 (3) ◽  
pp. 588-590 ◽  
Author(s):  
Steven L. Carnie ◽  
Derek Y.C. Chan ◽  
Glen R. Walker
Keyword(s):  
Thermodynamic Properties ◽  
Hard Spheres ◽  
Quadrupole Moments

Statistical Geometry and Cavity Correlations in the Hard Sphere Fluid

2008 ◽  
Vol 73 (3) ◽  
pp. 344-357 ◽  
Author(s):  
Robin J. Speedy ◽  
Richard K. Bowles
Keyword(s):  
Computer Simulation ◽  
Thermodynamic Properties ◽  
Hard Sphere ◽  
Hard Spheres ◽  
Sphere Diameter ◽  
Statistical Geometry ◽  
Empirical Expression ◽  
Hard Sphere Fluid ◽  
A Site ◽  
Exact Relations

The statistical geometry of a system of hard spheres is discussed in terms of the volumes Vj that lie with a sphere diameter, σ, of exactly j sphere centres. A site that has no sphere centre within σ is called a cavity site. We focus on the probability n00(r) that two sites separated by r are both cavity sites. n00(0), n00(σ), and the limiting slope (d ln n00(r)/dr)r=0, are all known in terms of the thermodynamic properties. The Vj and n00(r) are measured by computer simulation and an empirical expression, which satisfies the known exact relations, is shown to represent n00(r) precisely in the range 0 ≤ r ≤ σ.

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