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Lecture3-SeparThermo

# Lecture3-SeparThermo - Thermodynamics of Separations This...

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Lecture 3: Separations Basics 1 Thermodynamics of Separations This lecture primarily focuses on the thermodynamics of separations. We’ll cover: • Phase Stability and the Gibbs phase rule. • A simple separation based on a vapor-liquid phase diagram. • The lever rule. • Equilibrium ratios (K-values, distribution coefficients, etc.). • The activity, and activity coefficients. • Measures of separations.

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Lecture 3: Separations Basics 2 Conditions for Phase Stability Integrate dU From the definition of G Substituting U into our expression for G Gives the Gibbs Free Energy in terms of chemical potentials and concentrations.
Lecture 3: Separations Basics 3 The Gibbs-Duhem Equation Starting with our expressions for the Gibbs free energy We consider how it changes for an infinitesimal process We see that G changes because the amount of components changes or because the chemical potential of the components changes Since these two expressions for dG are equivalent we can equate them to find: The Gibbs-Duhem Equation which relates T, P and μ at equilibrium in a single phase system G changes because T changes or P changes or because the composition changes Consider a single phase in equilibrium:

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Lecture 3: Separations Basics 4 Gibbs Phase Rule Each phase of a system in internal equilibrium is governed by its own Gibbs-Duhem equation: Each phase is described by C+2 intensive variables: T, P and the C chemical potentials.
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Lecture3-SeparThermo - Thermodynamics of Separations This...

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