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Showing papers on "Gibbs–Duhem equation published in 2009"


Journal ArticleDOI
T. Noda1, Katsunari Oikawa1, Satoshi Itoh1, Mitsutaka Hino1, Tetsuya Nagasaka1 
TL;DR: In this article, the Gibbs energy of Cu 3 P formation was determined by means of triple Knudsen cell mass spectrometry and the calculated vapor pressure of phosphorus and phase diagram of the Cu-P system were excellently consistent with the literature data.
Abstract: Thermodynamic evaluation of Cu–Cu 3 P system has been conducted by applying subregular solution model with Gibbs energy of Cu 3 P formation that was newly determined by means of triple Knudsen cell mass spectrometry. Both the calculated vapor pressure of phosphorus and phase diagram of Cu–P system are excellently consistent with the literature data in the composition range of Cu–Cu 3 P, indicating that there is no significant thermodynamic inconsistency between the present work based on the Gibbs energy of Cu 3 P formation determined and the literature data.

9 citations


Journal Article
TL;DR: In this article, the application of substitutional model in oxide systems, in comparison with that of sublattice model, is discussed, and the results show that in the case of crystalline phases and liquid phases without molecular-like associates or the shortage of element in sub lattice, these two models get consistent in the description of the Gibbs freeenergies of phases and obtain the same result of phase diagram calculation when the valence of the cations keep the same.

3 citations


Journal ArticleDOI
TL;DR: The implementation and use of Transformed Gibbs Energies in the Gibbs energy minimization framework is demonstrated with educational examples and the combined method has the advantage of being able to calculate transient thermodynamic properties during dynamic simulation.
Abstract: Gibbs free energy is the thermodynamic potential representing the fundamental equation at constant temperature, pressure, and molar amounts. Transformed Gibbs energies are important for biochemical systems because the local concentrations within cell compartments cannot yet be determined accurately. The method of Constrained Gibbs Energies adds kinetic reaction extent limitations to the internal constraints of the system thus extending the range of applicability of equilibrium thermodynamics from predefined constraints to dynamic constraints, e.g., adding time-dependent constraints of irreversible chemical change. In this article, the implementation and use of Transformed Gibbs Energies in the Gibbs energy minimization framework is demonstrated with educational examples. The combined method has the advantage of being able to calculate transient thermodynamic properties during dynamic simulation.

3 citations


Journal ArticleDOI
TL;DR: It is shown that the Wassiljewa Gibbs free energy form turns out to have the same composition dependence as the nonrandom two-liquid (NRTL) equation.
Abstract: A continuous family of excess Gibbs free energy expressions is derived based on the double-weighted power mean mixture model and concepts from cubic equations of state. This family has two types of parameters: The model form is determined by two power indices, whereas the matrix of binary coefficients characterizes pure component behavior and binary interactions. It is shown that the Porter, Margules, and Wassiljewa composition dependence are but special forms of this more general expression. In particular, the Wassiljewa Gibbs free energy form turns out to have the same composition dependence as the nonrandom two-liquid (NRTL) equation.

2 citations


Journal ArticleDOI
TL;DR: In this article, the authors prove that for expansive dynamical systems and interaction potentials satisfying certain conditions of analyticity, the associated Gibbs states are unique, and draw an analogy between some quantities in classical thermodynamics and abstract dynamics in the spirit of the previous work.
Abstract: By applying Grothendieck theory and Ruelle thermodynamic formalism, we prove that, for expansive dynamical systems and interaction potentials satisfying certain conditions of analyticity, the associated Gibbs states are unique. This allows us to draw an analogy between some quantities in classical thermodynamics and abstract dynamics in the spirit of the previous work of the authors [13].

2 citations


Journal ArticleDOI
TL;DR: In this paper, an approximate distribution of the number of ways arranging molecules in a binary lattice solution of nonrandom mixing with a specific interaction was derived from the distribution of excess Gibbs energy.
Abstract: Performing random number simulations, we obtained an approximate distribution of the number of ways arranging molecules in a binary lattice solution of nonrandom mixing with a specific interaction. From the distribution an approximate equation of excess Gibbs energy for a binary lattice solution was derived. Using the equation, liquid-vapor equilibrium at constant pressure for 15 binary solutions were calculated and compared with the result from Wilson equation, Van Laar equation and Redlich-Kister equation.

1 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that given a Holder continuous potential φ satisfying a summability condition, there exists a non-lacunary Gibbs measure with positive Lyapunov exponents and infinitely many hyperbolic times almost everywhere.
Abstract: In this paper, we study non-uniformly expanding repellers constructed as the limit sets for a non-uniformly expanding dynamical systems. We prove that given a Holder continuous potential φ satisfying a summability condition, there exists non-lacunary Gibbs measure for φ, with positive Lyapunov exponents and infinitely many hyperbolic times almost everywhere. Moreover, this non-lacunary Gibbs measure is an equilibrium measure for φ.

1 citations


01 Jan 2009
TL;DR: In this paper, the Gibbs energy of an ideal gas mixture and the chemical potentials of its components are derived, and the molar entropy of the mixture is evaluated a posteriori, as the temperature gradient of Gibbs energy.
Abstract: A b s t r a c t There are three, assentialy independent, derivations of the Gibbs energy of an ideal gas mixture and the chemical potentials of its components. One approach is to flrst derive the expressions for the chemical potentials („i), which are then used in the expression for the molar Gibbs energy G m = P Xi„i, where Xi is the molar concentration of the i-th component in the mixture. In this approach, the molar entropy of the mixture is evaluated a posteriori, as the temperature gradient of the Gibbs energy. The second derivation is the simplest, and is based on the assumed additive decomposition of the Gibbs energy in terms of the partial Gibbs energies of individual components. The third derivation is based on the additive decomposition of the entropy of mixture in terms of partial entropies of its components. The three derivations are here critically examined and discussed.

1 citations


Posted Content
TL;DR: The standard theory of ideal gases ignores the interaction of the gas particles with the thermal radiation (photon gas) that fills the otherwise vacuum space between them as mentioned in this paper, which is an unphysical feature of the theory since every material in this universe, and hence also the particles of a gas, absorbs and radiates thermal energy.
Abstract: The standard theory of ideal gases ignores the interaction of the gas particles with the thermal radiation (photon gas) that fills the otherwise vacuum space between them. This is an unphysical feature of the theory since every material in this universe, and hence also the particles of a gas, absorbs and radiates thermal energy. The interaction with the thermal radiation that is contained within the volume of the body may be important in gases since the latter, unlike solids and liquids, are capable of undergoing conspicuous volume changes. Taking this interaction into account makes the behaviour of the ideal gases more realistic and removes Gibbs' paradox.

1 citations


Journal ArticleDOI
I. I. Gul’tyai1
TL;DR: In this article, the reliability of the thermodynamic data obtained by the Gibbs-Duhem equation for binary systems is analyzed, and the testing of this reliability is shown to be highly efficient.
Abstract: The reliability of the thermodynamic data obtained by the Gibbs-Duhem equation for binary systems is analyzed, and the testing of this reliability is shown to be highly efficient A similar testing technique is developed for a ternary system, and the application of this technique to a model system supports its validity and efficiency The use of the developed technique for testing the data for the ternary Cd-Bi-Pb system of metallic melts confirms its validity and efficiency

Journal ArticleDOI
TL;DR: In this paper, a derivation of the Gibbs fundamental equation for multi-component systems can be derived directly from the first and second law of thermodynamics, and it is shown that the expression for the entropy generation arises automatically without any further assumptions.
Abstract: The Gibbs fundamental equation for multi-component systems can be derived directly from the first and second law of thermodynamics. This approach has been outlined already by Haase [1], but the approach adopted in that work required the assumption that, besides dissipation of mechanical work, chemical reactions contribute to a generation of entropy within the system. In this paper, a derivation is presented, which shows that the expression for the entropy generation arises automatically without any further assumptions. It is shown that the correct driving forces for chemical reactions can be obtained over the whole composition range only if the adequate caloric equation of state for the molar entropy is used for the components in the mixture. Two chemical reactions of industrial importance are presented to show this impact over the entire range of educt and product compositions. Furthermore, it is shown that the different approaches based on molar free enthalpy of reaction as the driving force of chemical reactions, minimum Gibbs free enthalpy and functional equations based on equilibrium constants, are inherently similar since all of them reflect more or less the second law of thermodynamics.