Essay about Minimization Of The Gibbs Free Energy

794 Words Dec 8th, 2015 4 Pages
Minimization of the Gibbs free energy represent one of the most acceptable methods in order to create phase diagrams [3, 12]. By using this method, the equilibrium state of a system at one specific temperature, pressure, and overall composition can be found as an optimization problem in which the total Gibbs free energy is defined in terms of the compositions and amounts of each phase by using different solution models. In addition, the total Gibbs free energy function is constrained to mass conservation and relation of molar fractions of the components on each phase.
Another common method to calculate phase diagrams is associated with the chemical equilibrium condition in which it is required that the chemical potentials for each component must be the same in the corresponding phases that are coexisting at equilibrium [12]. With this methodology, the total Gibbs free
2energy function become unconstrained by using Lagrange multipliers and after the properly differentiation, a nonlinear system of equations is obtained as a function of the compositions at equilibrium. This set of equations is usually solve by using numerical methods for finding roots such as the
Newton-Raphson method. A detailed description of both methods is provided in this section.
The total Gibbs free energy is given as the summation of the Gibbs free energies for the different phases that are coexisting at equilibrium. These Gibbs free energies depend on temperature, pressure and composition of the…

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