Approach to the Coulomb Contribution of Thermodynamic Properties from the Mean Electrostatic Potential of the Ions in (ZrO2)1–x(Y2O3)x

2017 ◽  
Vol 122 (1) ◽  
pp. 62-70 ◽  
Author(s):  
Gerardo Valadez Huerta ◽  
Malte Siemen ◽  
Stephan Kabelac
Keyword(s):  
Thermodynamic Properties ◽  
Electrostatic Potential ◽  
The Mean ◽  
Coulomb Contribution

DISQUAC predictions on thermodynamic properties of ternary and higher multicomponent mixtures. II. Results for HE of ternary mixtures containing nonpolar components, or one polar compound, two polar compounds, or one alcohol and hydrocarbons, or CCl4

2001 ◽  
Vol 79 (10) ◽  
pp. 1447-1459 ◽  
Author(s):  
Juan Antonio Gonzalez ◽  
Javier Carmona ◽  
Nicolas Riesco ◽  
Isaias Garcia de la Fuente ◽  
Jose Carlos Cobos
Keyword(s):  
Thermodynamic Properties ◽  
Binary Systems ◽  
Ternary Systems ◽  
Polar Compounds ◽  
Ternary Mixtures ◽  
Mean Deviation ◽  
Group Contributions ◽  
Polar Compound ◽  
The Mean ◽  
Vapor Liquid Equilibria

The ability of the DISQUAC model for predicting excess enthalpies (HE) of ternary systems on the basis of binary parameters only, i.e., neglecting ternary interactions is analyzed. At this end, DISQUAC results for a set of 95 ternary systems are examined. The solutions studied are formed by only hydrocarbons (or CCl4); or by one polar compound (not alcohols) and two hydrocarbons (or CCl4); or by two polar compounds (not alcohols) and one hydrocarbon (or CCl4); or by one alcohol and two hydrocarbons (or CCl4). Most of the HEs analyzed are endothermic, and valid at 298.15 K and atmospheric pressure. The mean deviation between experimental values and DISQUAC results is 5.5% for the ternary systems and 6.5% for the constituent binaries (181 mixtures). The interaction parameters used are valid for the description of thermodynamic properties of binary systems: vapor–liquid equilibria (VLE), liquid–liquid (LLE), and solid–liquid equilibria (SLE), HE and excess heat capacities at constant pressure (CEP), as well as HE and VLE of ternary solutions. Predictions are, in most of the cases, independent of the mixture compounds, or the number of groups present in the system. Larger deviations underline typical shortcomings of the group contributions methods (e.g., Patterson's effect; branching). Note that results for the ternaries and for the constituent binaries are of the same order. This is not the case for the Dortmund version of UNIFAC. The mean deviations obtained using this model are 10.5% and 14% for the ternary and binary mixtures, respectively. Results from other models (original UNIFAC, Flory's theory, Nitta–Chao, UNIQUAC association model) for a number of systems are also compared to those obtained using DISQUAC.Key words: predictions, HE, ternary systems, binary parameters, geometrical methods, Flory, group contributions.

scholarly journals Masses and Thermodynamic Properties of a Quarkonium System

2021 ◽  
Author(s):  
E.P. Inyang ◽  
E.P. Inyang ◽  
I.O. Akpan ◽  
J.E. Ntibi ◽  
E.S. William
Keyword(s):  
Thermodynamic Properties ◽  
Yukawa Potential ◽  
Laguerre Polynomials ◽  
Heavy Mesons ◽  
Special Cases ◽  
Radial Schrödinger Equation ◽  
Hellmann Potential ◽  
The Mean ◽  
Uvarov Method ◽  
Potential Parameters

Hulthen plus Hellmann potentials are adopted as the quark-antiquark interaction potential for studying the thermodynamic properties and the mass spectra of heavy mesons. We solved the radial Schrödinger equation analytically using the Nikiforov-Uvarov method. The energy eigenvalues and corresponding wave function in terms of Laguerre polynomials were obtained. The present results are applied for calculating the mass of heavy mesons such as charmoniumand cc and bottomonium bb, and thermodynamic properties such as the mean energy, the specific heat, the free energy, and the entropy. Four special cases were considered when some of the potential parameters were set to zero, resulting in Hellmann potential, Yukawa potential, Coulomb potential, and Hulthen potential, respectively. The present potential provides satisfying results in comparison with experimental data and the work of other researchers.

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