Journal ArticleDOI
Statistical Mechanics of Imperfect Gases
Reads0
Chats0
TLDR
In this article, a technique is developed which expresses these integrals in terms of the characteristic values of the integral equation, which is applied to the calculation of third virial coefficients and the molecular distribution function for imperfect gases with potential energy functions.Abstract:
The application of statistical mechanical equations to the calculation of thermodynamic properties of imperfect gases has been hindered by the occurrence of highly multiple integrals in these equations. By observing that some of these multiple integrals are related to the iterated kernels of an integral equation involving the potential energy function of a pair of molecules, a technique is developed which expresses these integrals in terms of the characteristic values of the integral equation. This technique is applied to the calculation of third virial coefficients and the molecular distribution function (which is essentially the probability of finding two specified molecules in two small volume elements a distance r from each other) at various temperatures for imperfect gases with Lennard‐Jones potential energy functions.read more
Citations
More filters
Journal ArticleDOI
New method for the calculation of the pair correlation function. I
TL;DR: In this article, a new method is described to approximate the pair correlation function, which takes into account in the successive steps of the approximation, diagrams of increasing complexity as regards "the basic structure".
Journal ArticleDOI
The Theory of Ionic Solutions
TL;DR: In this paper, the authors used the virial development for the osmotic pressure of a solution to compute the deviations from perfect solution behavior, and obtained the expression for the logarithm of the activity coefficient as a sum of coefficients multiplied by powers of concentration.
Journal ArticleDOI
Quantum Statistics of Interacting Particles; General Theory and Some Remarks on Properties of an Electron Gas
TL;DR: In this paper, a generalization of the Mayer cluster integral theory for quantum statistics of interacting particles has been developed, where the cluster integrals are integrals over propagators which are derived from the Green's function solution of the Bloch equation (which follows from the Schroedinger equation by replacing it/ℏ by β = 1/kT).
Journal ArticleDOI
Nodal Expansions. III. Exact Integral Equations for Particle Correlation Functions
TL;DR: In this paper, the density expansions of the pair distribution function and the potential of average force are analyzed topologically in terms of cutting points and bifocal points, leading to conversion of the expansions into series with cluster integrals involving products of the total correlation functions, at finite density, rather than the usual zero-density Ursell f • functions.
References
More filters
Journal ArticleDOI
On the determination of molecular fields. —II. From the equation of state of a gas
TL;DR: In this paper, it was shown that a molecular model of the same type will also explain available experimental data concerning the equation of state of a gas, and if so, whether the results so obtained, when taken in conjunction with those obtained from viscosity, will definitely fix the molecular field.
Book
Methoden der mathematischen Physik
Richard Courant,David Hilbert +1 more
TL;DR: In this paper, Courant et al. describe an approach for the klassical Ideal einer gewermassen atomistischen Auffassung der Mathematik verlangt, den Stoff in Form of Voraussetzungen, Satzen and Beweisen zu kondensieren.
Journal ArticleDOI
Die Beugung von Röntgenstrahlen in Flüssigkeiten als Effekt der Molekülanordnung
F. Zernike,J. A. Prins +1 more
TL;DR: The Einfuhrung einer Verteilungsfunktion fur die gegenseitige Entfernung der Molekule ermoglicht die Ableitung ein Formel fur die Zerstreuung von Rontgenstrahlen in Flussigkeiten, welche alle Eigentumlich keiten der Beobachtungen gut wiedergibt as mentioned in this paper.
Journal ArticleDOI
Statistical Mechanics of Condensing Systems. III
Joseph E. Mayer,S. F. Harrison +1 more
TL;DR: In this article, it was shown that for a system composed of N identical molecules with mutual potential energy, the assumption that the total potential energy can be expressed as the sum of that between pairs of molecules allows the derivation of simple, accurate formal equations for the thermodynamic properties of the system.