IdealGasMixtureLect21ME501F2011

IdealGasMixtureLect21ME501F2011 - Purdue University ME 501:...

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Patterned Border Template 1 Purdue University School of Mechanical Engineering ME 501: Statistical Thermodynamics Lecture 21: Statistical Thermodynamic Analysis of Ideal Gas Mixtures Prof. Robert P. Lucht Room 2204, Mechanical Engineering Building School of Mechanical Engineering Purdue University West Lafayette, Indiana Lucht@purdue.edu , 765-494-5623 (Phone) October 28, 2011
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Patterned Border Template 2 Purdue University School of Mechanical Engineering Lecture Topics • Mixtures of nonreacting ideal gases. • Definition of energy reference for mixtures of reacting ideal gases. • Statistical thermodynamic analysis for mixtures of reacting ideal gases.
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Patterned Border Template 3 Purdue University School of Mechanical Engineering Mixtures of Nonreacting Ideal Gases • From the assumption of weakly interacting particles, it can be seen that the mixture properties are the sum of the properties from each species i : • Further examples:  , 1 ,, 11 1 ln M tot tot i i M MM B tot B tot i B tot i i ii i WW Sk W k W k W S        2 = = i iB i Z EE k T N T       ln = = = i B i i i T Z kT P Pk T N N 
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Patterned Border Template 4 Purdue University School of Mechanical Engineering Mixtures of Reacting Ideal Gases: Definition of the Reference of Energy • How can the assumption of weakly interacting particles apply when chemical reactions are occurring? Time involved in the reactive particle collisions is very small compared to the time between collisions. • Consider an assembly composed of the molecule AB at room temperature. At an elevated temperature T , collisions will occur which raise the energy of AB above its dissociation threshold, and atomic species A and B will be formed: Knowing the pressure and temperature of the mixture, what are the values for N AB , N A , and N B ? AB A B  Incropera, Introduction to Molecular Structure and Thermodynamics
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Patterned Border Template 5 Purdue University School of Mechanical Engineering Mixtures of Reacting Ideal Gases: Definition of the Reference of Energy • Chemical Internal Energy needs to be treated properly. Energies for A , B , and AB must be referenced to the same zero of energy. • Initially, consider that all species are in the ground internal state with negligible translational energy. For the molecule, this implies J = v = 0. • Molecule AB must absorb a quantity of energy D 0 to dissociate to A and B . •A t om s A and B would release a quantity of energy D 0 upon combining.
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IdealGasMixtureLect21ME501F2011 - Purdue University ME 501:...

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