Showing papers on "Gibbs–Helmholtz equation published in 2001"

Effect of Temperature on Standard Transformed Gibbs Energies of Formation of Reactants at Specified pH and Ionic Strength and Apparent Equilibrium Constants of Biochemical Reactions

Abstract: When standard Gibbs energies of formation and standard enthalpies of formation are known for the species of a biochemical reactant at 298.15 K, it is possible to calculate the standard transformed Gibbs energy of formation and standard transformed enthalpy of formation of the reactant at any desired pH and low ionic strengths at 298.15 K. This article is concerned with the estimation of standard transformed Gibbs energies of formation of reactants, standard transformed Gibbs energies of reaction, and apparent equilibrium constants K‘ of biochemical reactions at specified pH and ionic strength in the temperature range 283.15−313.15 K on the basis of the assumption that the standard enthalpies of formation of the species are independent of temperature in this range. The standard transformed Gibbs energies of formation and standard transformed enthalpies of formation are given for 14 reactants as a function of pH and ionic strength at temperatures of 283.15, 298.15, and 313.15 K, and standard transformed Gib...

On the Gibbs adsorption equation and diffuse interface models

Abstract: In this paper we discuss some applications of the classical Gibbs adsorption equation to specific diffuse interface models that are based on conserved and non–conserved order parameters. Such models are natural examples of the general methodology developed by J. W. Gibbs in his treatment of the thermodynamics of surfaces. We employ the methodology of J. W. Cahn, which avoids the use of conventional dividing surfaces to define surface excess quantities. We show that the Gibbs adsorption equation holds for systems with gradient energy coefficients, provided the appropriate definitions of surface excess quantities are used. We consider, in particular, the phase–field model of a binary alloy with gradient energy coefficients for solute and the phase field. We derive a solute surface excess quantity that is independent of a dividing surface convention, and find that the adsorption in this model is influenced by the surface free energies of the pure components of the binary alloy as well as the solute gradient energy coefficient. We present one–dimensional numerical solutions for this model corresponding to a stationary planar interface and show the consistency of the numerical results with the Gibbs adsorption equation. We also discuss the Gibbs adsorption equation in the context of other diffuse interface models that arise in spinodal decomposition and order–disorder transitions.

Extended Irreversible Thermodynamics Approach to Magnetorheological Fluids

Abstract: Magnetorheological (MR) fluids have the unique ability to change properties from those of a fluid to those of a solid in the presence of a magnetic field. In this paper, we present a phenomenological theory for MR fluids within the framework of extended irreversible thermodynamics (EIT), which relates the dynamics of the fluxes to the form of the nonequilibrium equation of state and introduces the elasticity of MR fluids in a natural way. The Gibbs equation and the entropy inequality are derived to present the energy transfer and dissipative mechanisms. In particular, the viscoelastic behavior of the pre-yield regime and the fluid behavior of the post-yield regime are discussed in depth. Finally, according to the entropy inequality, we propose a mechanical model of MR fluids that can characterize the duplicate phenomena of the fluid-solid transition. The results of a numerical analysis of this model correspond with those of the functional tests of an MR damper.

Multilayer Adsorption on Solid Surfaces: Calculation of Layer Thickness on the Basis of the Athermal Parallel Layer Model

Abstract: A method for calculating the dependence of equivalent layer thickness on bulk phase composition in athermal binary mixtures has been devised The prerequisite to the procedure is knowledge of the adsorption excess isotherm and of the cross-sectional area of one component After integration of the excess isotherm according to the Gibbs equation, the equations of the parallel layer model are used to calculate the composition of the monolayer in contact with the surface, which in turn is used to calculate the thickness of the adsorption layer The proposed method was tested on a hypothetical experimental system with calculated excess isotherms and a known function of equivalent layer thickness Reliable results were obtained, especially when adsorption was preferential, the surface was relatively homogeneous, and the ratio of the cross-sectional areas of the individual components was close to the ratio of molar fractions

A Surface Tension Model for Liquid Mixtures Based on NRTL Equation

Abstract: A new equation for predicting surface tension is proposed based on the thermodynamic definition of surface tension and the expression of the Gibbs free energy of the system. Using the NRTL equation to represent the excess Gibbs free energy, a two-parameter surface tension equation is derived. The feasibility of the new equation has been tested in terms of 124 binary and 16 multicomponent systems(13-ternary and 3-quaternary) with absolute relative deviations of 0.59% and 1.55% respectively. This model is also predictive for the temperature dependence of surface tension of liquid mixtures. It is shown that, with good accuracy, this equation is simple and reliable for practical use.

Thermodynamic pressure in nonlinear nonequilibrium thermodynamics of dilute nonviscous gases.

Abstract: In this paper, using extended thermodynamics, we build up a nonlinear theory for a dilute nonviscous gas under heat flux. The fundamental fields are the density, the velocity, the internal energy density, and the heat flux. The constitutive theory is builtup without approximations. We single out the nonlinear complete expressions of the Gibbs equation and of the nonequilibrium pressure. In particular, we determine the complete expressions furnished by the theory for the nonequilibrium pressure tensor and thermodynamic pressure, i.e., the derivative of the nonequilibrium internal specific entropy with respect to the specific volume, times the nonequilibrium temperature. In a second-order approximation these expressions are identical with those obtained in Phys. Rev. E 51, 158 (1995), using information theory.

Application of the Geometric Gibbs Equation: Toward an Exact Closure Condition†

Abstract: The geometric Gibbs equation describes how the available space and corresponding surface area of a single-component hard particle fluid varies with the system density. When a closure condition is introduced, i.e., an additional equation describing how the surface area depends on the available space, the geometric Gibbs equation reduces to a second-order differential equation indicating how the available space varies with the system density. Solution of this new equation provides another route to the determination of the chemical potential and pressure of the hard particle fluid. The simplest proposed closure condition yields the properties of fully penetrable spheres. A modified closure condition is suggested, and its connection to thermophysical properties is derived. An extension of the exact form of the closure condition for the one-dimensional hard rod fluid yields a reasonably good approximation of the properties of the hard sphere fluid at low density, and is found to be the required form for densit...

Equation of state for porous mixtures

Abstract: An equation of state for porous mixtures is described based on the mixing properties of the Gibbs potential. For a mixture, neglecting surface energy, the Gibbs potential is simply the sum of the Gibbs potentials of the components. Nitrogen is added to account for porosity, with the mole number proportional to the porosity. The Gibbs potential for fluid species is calculated by means of a perturbation theory originated by Weeks, Chandler, and Anderson. A semi-empirical Debye-Gruneisen equation of state with a Murnaghan form for the zero degree isotherm is used to describe solids. Due to the complexity of the Weeks-Chandler-Anderson fluid equation of state, the possibility of using an ideal gas representation for nitrogen was investigated. A very good match to the shock Hugoniot for porous copper results from this approach. The model is also used to calculate the Hugoniot for an Al-TEFLON mixture and compared to data obtained by Miller and Lindfors and by Holt and Mock.

A principle to correlate extreme values of excess thermodynamic functions with partial molar quantities

Abstract: Excess thermodynamic properties are widely used quantitatively for fluids. It was found that at constant temperature and pressure a molar excess quantity of a mutually miscible binary mixture at the extreme points equals the excess partial molar quantities of the two components, i.e. F E 1 =F 2 E =F E m , forming a triple cross point. The relationship is hold for properties such as enthalpy, entropy, Gibbs free energy, and volume, and is applicable for excess functions with multi extreme points. Solutions at extreme points can be referred to as special mixtures. Particularly for a special mixture of Gibbs free energy, activity coefficients of the two components are identical.