Showing papers on "Gibbs–Duhem equation published in 2004"
TL;DR: In this paper, a new method to test the thermodynamic consistency of phase equilibrium data in binary mixtures containing a liquid solute and a supercritical fluid is presented, specially designed for treating incomplete P-T-x-y data, that is, data that do not cover the whole range of concentration of the components in the mixture.
68 citations
01 Sep 2004
TL;DR: In this paper, the Gibbs free energy (GFE) formulation of the P-T partition function in statistical thermodynamics is used to derive semi-empirical formulations of the GFE for minerals and fluids.
Abstract: The P–T partition function in statistical thermodynamics can be used to derive semi-empirical formulations of the Gibbs free energy G for minerals and fluids Parameterization of these equations includes simultaneous regression of experimental heat capacity and molar volume data, allowing fitting, appraisal and optimization of various data sources, as required in the construction of internally consistent petrological data bases This approach can also be extended to minerals with λ-transitions and to fluids by considering the Gibbs free energy as a function of pressure P, temperature T and an ordering parameter Xα, so that accurate modelled representation and extrapolation of the thermodynamic properties of large numbers of petrologically significant minerals and coexisting fluids can be attained The ordering parameter is chosen to denote the equilibrium mole fraction (thermodynamic probability) of ordered clusters (structural units) in a substance when G(T,P, Xα)=min The procedure is tested on existing experimental data for the system MgO–SiO2–H2O The proposed Gibbs free energy formulation permits thermodynamic properties of minerals, fluids and phase equilibria to be described and extrapolated over a wide range of pressure (0–800 kbar) and temperature (20–3000 K), thus allowing effective use in thermodynamic data bases of petrological interest
39 citations
01 Oct 2004
TL;DR: In this article, a variational principle for Gibbs and generalized Gibbs states is established, and a new class of intuitively Gibbs measures is introduced and a typical example of a non-Gibbsian measure arising from an industrial application is presented.
Abstract: We present a novel approach to establishing the variational principle for Gibbs and generalized (weak and almost) Gibbs states. Limitations of a thermodynamic formalism for generalized Gibbs states will be discussed. A new class of intuitively Gibbs measures is introduced, and a typical example is studied. Finally, we present a new example of a non-Gibbsian measure arising from an industrial application.
21 citations
TL;DR: A derivation based on a previously unrecognized recursive relationship is presented, which will provide explicit criteria for testing various approximations built into alternative analytic strategies for quantifying derivatives that specify the dependences of mukappa for selected components.
13 citations
TL;DR: In this article, a continuous infinite system of point particles interacting via finite-range many-body potentials of superstable type is considered in the framework of classical statistical mechanics and it is shown that for any temperature and chemical activity there exists at least one Gibbs state.
Abstract: A continuous infinite system of point particles interacting via finite-range many-body potentials of superstable type is considered in the framework of classical statistical mechanics. We prove that for any temperature and chemical activity there exists at least one Gibbs state.
13 citations
TL;DR: In this paper, a complete mechanical-thermodynamical formulation for multicomponent nematic polymer-isotropic fluid interfaces is derived, validated, and used to derive the structure and shape equations for these soft anisotropic polymer interfaces.
Abstract: A complete mechanical-thermodynamical formulation for multicomponent nematic polymer-isotropic fluid interfaces is derived, validated, and used to derive the structure and shape equations for these soft anisotropic polymer interfaces. The fundamental role of liquid crystalline order and long range effects in coupling bulk and interfacial effects, and in coupling thermodynamical/liquid crystalline order/geometrical variables is demonstrated, discussed, and validated. The Gibbs-Duhem nemato-thermodynamics equation emerges from an interfacial tension γ = γ=(Θ, μ s i , Q, ⊇ s Q, k) that depends on temperature (Θ), chemical potential (μ s i ), nematic tensor order parameter Q, surface gradients of Q, and geometry k, and leads to new couplings in these enhanced phase spaces. The role of entropy and adsorption, and long range effects on interfacial shape and structure selection is revealed. For flat interfaces the preferred structure emerges from a competition between energy, entropy, and adsorption.
9 citations
TL;DR: In this article, the Gibbs free energy of formation from the respective oxides of solid LaGaO 3 and La 4 Ga 2 O 9 has been obtained and the excess Gibbs-free energy of the liquid has been calculated.
4 citations
TL;DR: In this article, the role of the Gibbs entropy in the discussion of the emergence of irreversibility in the macroscopic world from the microscopic level is elucidated, by using an extension of the Onsager theory to the phase space.
2 citations
TL;DR: The Gibbs free energy of a periodic, d-dimensional crystalline assembly can be estimated using thermodynamic integration at constant pressure from a nonlocal Einstein crystal using a two-dimensional, harmonic crystal with hexagonal symmetry.
Abstract: The Gibbs free energy of a periodic, d-dimensional crystalline assembly can be estimated using thermodynamic integration at constant pressure from a nonlocal Einstein crystal. The method is demonstrated using a two-dimensional, harmonic crystal with hexagonal symmetry for which the isobaric Gibbs function can be derived analytically.
2 citations
TL;DR: For elastic deformation of arbitrary magnitude in an isotropic solid, Legendre conjugate strain variables are found and used to define the Gibbs free energy of a deformable solid.
Abstract: For elastic deformation of arbitrary magnitude in an isotropic solid, Legendre conjugate strain variables are found and used to define the Gibbs free energy of a deformable solid. An additional thermodynamic equilibrium condition is found in the case when transition in a nonuniform strain field is incomplete and there exists an equilibrium boundary between phases.