Showing papers on "Gibbs–Duhem equation published in 2000"

Explicit Gibbs free energy equation of state applied to the carbon phase diagram

Abstract: We provide a simple explicit form for the Gibbs free energy $G(P,T)$ of diamond, graphite, and liquid carbon. The Gibbs free energy function is shown to reproduce the known equation of state properties of carbon up to pressures of 600 GPa (6 MBar) and temperatures of 15 000 K. Recent experiments on graphite melting suggest the presence of a first-order liquid-liquid phase transition at roughly 6 GPa. We show that such a transition is consistent with shock compression data at higher pressures. We reanalyze experiments on the diamond-liquid melting line with our equation of state. Our analysis suggests that the diamond-liquid melting line may have a more positive slope as a function of pressure than previously estimated. A maximum in the diamond melting line is predicted by the model, in agreement with recent ab initio simulations.

Adjusting the melting point of a model system via Gibbs-Duhem integration: Application to a model of aluminum

Abstract: This is the publisher's version, also available electronically from http://journals.aps.org/prb/abstract/10.1103/PhysRevB.62.14720.

Thermodynamic fluctuations within the Gibbs and Einstein approaches

Abstract: A comparative analysis of the descriptions of fluctuations in statistical mechanics (the Gibbs approach) and in statistical thermodynamics (the Einstein approach) is given. On this basis solutions are obtained for the Gibbs and Einstein problems that arise in pressure fluctuation calculations for a spatially limited equilibrium (or slightly nonequilibrium) macroscopic system. A modern formulation of the Gibbs approach which allows one to calculate equilibrium pressure fluctuations without making any additional assumptions is presented; to this end the generalized Bogolyubov – Zubarev and Hellmann – Feynman theorems are proved for the classical and quantum descriptions of a macrosystem. A statistical version of the Einstein approach is developed which shows a fundamental difference in pressure fluctuation results obtained within the context of two approaches. Both the 'genetic' relation between the Gibbs and Einstein approaches and the conceptual distinction between their physical grounds are demonstrated. To illustrate the results, which are valid for any thermodynamic system, an ideal nondegenerate gas of microparticles is considered, both classically and quantum mechanically. Based on the results obtained, the correspondence between the micro- and macroscopic descriptions is considered and the prospects of statistical thermodynamics are discussed.

Gibbs energy minimization in gas + liquid + solid systems

Abstract: An algorithm is described for the calculation of equilibrium compositions of multiple highly nonideal liquid and solid solutions, as well as pure stoichiometric phases, coexisting with a mixture of ideal gas species at fixed temperature and pressure. The total Gibbs free energy of the system is approximated as a quadratic function of the compositions of the gas phase and stable condensed phases, in an orthogonal basis set of pure elements. Only changes in thermal energy and energy related to pressure-volume work are considered. The total Gibbs energy is minimized directly by use of both the slope and the curvature of the Gibbs energy surface with respect to the gas and condensed phase compositions in the basis elements. The algorithm described has been implemented in a computer code for the calculation of condensation sequences for cosmic nebular gases enriched in dust. Machine, compiler and library requirements for performing these calculations in the C programming language are compared. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 247–256, 2000

Equivalence of thermodynamical fundamental equations

Abstract: The Gibbs function, which depends on the intensive variables T and P, is easier to obtain experimentally than any other thermodynamical potential. However, textbooks usually first introduce the internal energy, as a function of the extensive variables V and S, and then proceed, by Legendre transformations, to obtain the Gibbs function. Here, taking liquid water as an example, we show how to obtain the internal energy from the Gibbs function. The two fundamental equations (Gibbs function and internal energy) are examined and their output compared. In both cases complete thermodynamical information is obtained and shown to be practically the same, emphasizing the equivalence of the two equations. The formalism of the Gibbs function is entirely analytical, while that based on the internal energy is, in this case, numerical. Although it is well known that all thermodynamic potentials contain the same information, usually only the ideal gas is given as an example. The study of real systems, such as liquid water, using numerical methods, may help students to obtain a deeper insight into thermodynamics.

Equivalence Between Canonical Gibbs Measures and Stationary Measures for Stochastic Lattice-Gas Model

Abstract: It is proved that, under appropriate conditions on the jump rate and potential, one- and two-dimensional stochastic lattice-gas models (exclusion process with speed change) have only canonical Gibbs measures as their stationary measures. This extends the previously known result, which treats only a special jump rate and potential.