Showing papers on "Gibbs–Helmholtz equation published in 2011"

The cosmological constant and black-hole thermodynamic potentials

Abstract: The thermodynamics of black holes in various dimensions are described in the presence of a negative cosmological constant which is treated as a thermodynamic variable, interpreted as a pressure in the equation of state. The black hole mass is then identified with the enthalpy, rather than the internal energy, and heat capacities are calculated at constant pressure not at constant volume. The Euclidean action is associated with a bridge equation for the Gibbs free energy and not the Helmholtz free energy. Quantum corrections to the enthalpy and the equation of state of the BTZ black hole are studied.

Modeling Surface Tension of Concentrated and Mixed-Solvent Electrolyte Systems

Abstract: A comprehensive model has been developed for calculating the surface tension of aqueous, nonaqueous, and mixed-solvent electrolyte systems ranging from dilute solutions to fused salts. The model consists of a correlation for computing the surface tension of solvent mixtures and an expression for the effect of electrolyte concentration. The dependence of surface tension on electrolyte concentration has been derived from the Gibbs equation combined with a modified Langmuir adsorption isotherm for modeling the surface excess of species. The model extends the Langmuir adsorption formalism by introducing the effects of binary interactions between solute species (ions or molecules) on the surface. This extension is especially important for high electrolyte concentrations and in strongly speciated systems. The surface tension of mixed solvents is calculated by utilizing the surface tensions of the constituent pure components together with an effective surface concentration, which is defined for each component an...

A method for the calculation of the adsorbed phase volume and pseudo-saturation pressure from adsorption isotherm data on activated carbon

Abstract: We propose a new method for evaluating the adsorbed phase volume during physisorption of several gases on activated carbon specimens. We treat the adsorbed phase as another equilibrium phase which satisfies the Gibbs equation and hence assume that the law of rectilinear diameters is applicable. Since invariably the bulk gas phase densities are known along measured isotherms, the constants of the adsorbed phase volume can be regressed from the experimental data. We take the Dubinin-Astakhov isotherm as the model for verifying our hypothesis since it is one of the few equations that accounts for adsorbed phase volume changes. In addition, the pseudo-saturation pressure in the supercritical region is calculated by letting the index of the temperature term in Dubinin's equation to be temperature dependent. Based on over 50 combinations of activated carbons and adsorbates (nitrogen, oxygen, argon, carbon dioxide, hydrocarbons and halocarbon refrigerants) it is observed that the proposed changes fit experimental data quite well.

Analysis of Gibbs adsorption equation and thermodynamic relation between Gibbs standard energies of adsorption and micellization through a surface equation of state.

Abstract: The calculation of surface molecular areas through Gibbs adsorption equation has been questioned in some early works on the belief that these areas have been obtained from the apparently constant slope of the surface tension vs. logarithm of concentration curve along the entire region at which surface tension declines rapidly as the concentration increases. This premise leads to consider that Gibbs equation predicts that surface saturation is reached at the beginning of this region. However, through an analysis of the forementioned curve in accordance to Gibbs equation, it can be easily shown that surface saturation is attained at the end of the region. On the other hand, based on a thermodynamic model, it is also shown that the adsorption process, and thus, surface saturation, proceeds before micellization.

The reduced Redlich–Kister excess molar Gibbs energy of activation of viscous flow and derived properties in 1,4-dioxane + water binary mixtures from 293.15 to 309.15 K

Abstract: The excess molar volume, viscosity deviation and excess Gibbs free energy of activation of viscous flow have been investigated from the density and shear viscosity measurements of water–dioxane mixtures over the entire range of mole fractions from 293.15 to 309.15 K. The results were fitted by the Redlich–Kister equation. Partial molar volume and Gibbs energy at infinite dilution were deduced from four methods, activation parameters and partial molar Gibbs energy of activation of viscous flow against compositions were investigated. The water–dioxane interactions have principally an H-bound character and there are two principal types’ structures limited by 0.08 mole fraction in dioxane. The reduced Redlich–Kister excess properties provide an indication of the intermolecular interactions and for dioxane–water cluster formation as suggested in the literature.

Structure and thermodynamics of the key precipitated phases in the Al–Mg–Si alloys from first-principles calculations

Abstract: First-principles calculations have been carried out to investigate the structure, stability, and finite-temperature thermodynamic properties of the key precipitates in the Al–Mg–Si alloys including β″-Mg5Si6, U1-Al2MgSi2, U2-Al4Mg4Si4, β′-Mg9Si5, and β-Mg2Si. The calculated phonon densities of states indicate that these precipitated phases are vibrationally stable. Within the framework of the quasiharmonic approach, the finite-temperature thermodynamic properties of these precipitated phases including entropy, enthalpy, and Gibbs free energy have been calculated. The heat capacities at constant pressure for these precipitates are predicted. The finite-temperature entropies of formation, enthalpies of formation, and Gibbs free energy of formation for these precipitates are also computed. The acquired thermodynamic properties are expected to be utilized for the prediction of the metastable equilibria in the Al–Mg–Si alloys.

Thermodynamic modeling of the Fe-Zn system using exponential temperature dependence for the excess Gibbs energy

Abstract: The Fe-Zn binary system was re-modeled using exponential equation Li=hi·exp(-T/τi) (i=0,1,2…) to describe the excess Gibbs energy of the solution phases and intermetallic compounds with large homogeneities. A self-consistent set of thermodynamic parameters is obtained and the calculated phase diagrams and thermodynamic properties using the exponential equation agree well with the experimental data. Compared with previous assessments using the linear equation to describe the interaction parameters, the artificial miscibility gap at high temperatures was removed. In addition, the calculated thermodynamic properties of the liquid phase were more reasonable than those resulting from all the previous calculations. The present calculations yield noticeable improvements to the previous calculations.

A Model of Microemulsion Formation and Percolation: Experimental Validation

Abstract: Experimental results afford strong support for a previously proposed mathematical model of the formation of a microemulsion system. Water-in-oil microemulsions with various straight chain hydrocarbons as the continuous phase, and nonylphenol ethylene oxide (NP(EO)n) condensates as surfactants were prepared using the titration method. The free energies of the system were determined using the Gibbs equation. Next, the free energy of formation of a single microemulsion droplet was calculated. Free energy value obtained from the titration method showed a high degree of agreement with the free energy predicted by the mathematical model when experimental value for the interfacial tensions at the water/oil interface and bare interface, free energy of formation of the interfacial sheath, natural radius of the microemulsion, flexibility constant of the interfacial sheath, and maximum and minimum radii of the microemulsion were inserted in the appropriate equation. This finding validates our mathematical model, and...

Estimating the Gibbs energy of hydration from molecular dynamics trajectories obtained by integral equations of the theory of liquids in the RISM approximation

Abstract: A method of integral equations of the theory of liquids in the reference interaction site model (RISM) approximation is used to estimate the Gibbs energy averaged over equilibrium trajectories computed by molecular mechanics. Peptide oxytocin is selected as the object of interest. The Gibbs energy is calculated using all chemical potential formulas introduced in the RISM approach for the excess chemical potential of solvation and is compared with estimates by the generalized Born model. Some formulas are shown to give the wrong sign of Gibbs energy changes when peptide passes from the gas phase into water environment; the other formulas give overestimated Gibbs energy changes with the right sign. Note that allowance for the repulsive correction in the approximate analytical expressions for the Gibbs energy derived by thermodynamic perturbation theory is not a remedy.

Gibbs free energy and Helmholtz free energy for a three-dimensional Ising-like model

Abstract: The critical behavior of a 3D Ising-like system is studied at the microscopic level of consideration. The free energy of ordering is calculated analytically as an explicit function of temperature, an external field and the initial parameters of the model. Within a unified approach, both Gibbs and Helmholtz free energies are obtained and the dependencies of them on the external field and the order parameter, respectively, are presented graphically. The regions of stability, metastability, and unstability are established on the order parameter‐temperature plane. The way of implementation of the well-known Maxwell construction is proposed at microscopic level.

First and second laws of the thermodynamics

Abstract: Local volume and time averaging is used to derive rigorous energy equations for multiphase flows in heterogeneous porous media. The flow is conditionally divided into three velocity fields. Each of the fields consists of several chemical components. Using the conservation equations for mass and momentum and the Gibbs equation, entropy equations are rigorously derived. It is shown that the use of the specific entropy as one of the dependent variables results in the simplest method for describing and modeling such a complicated thermodynamic system. A working form of the final entropy equation is recommended for general use in multi-phase flow dynamics.