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Thermodynamics filled in class notes_Part_125

Thermodynamics filled in class notes_Part_125 - 7.1...

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Unformatted text preview: 7.1. ISOTHERMAL, ISOCHORIC KINETICS 257 We find three finite roots to this problem: 1 : ( ρ NO , ρ N ) = ( − 1 . 605 × 10 − 6 , − 3 . 060 × 10 − 8 ) mole cm 3 , non-physical , (7.211) 2 : ( ρ NO , ρ N ) = ( − 5 . 173 × 10 − 8 , − 2 . 048 × 10 − 6 ) mole cm 3 , non-physical , (7.212) 3 : ( ρ NO , ρ N ) = (7 . 336 × 10 − 7 , 3 . 708 × 10 − 8 ) mole cm 3 , physical . (7.213) Obviously, because of negative concentrations, roots 1 and 2 are non-physical. Root 3 however is physical; moreover, it agrees with the equilibrium we found by direct numerical integration of the full non-linear equations. We can use local linear analysis in the neighborhood of each equilibria to rigorously ascertain the stability of each root. Taylor series expansion of Eqs. (7.207-7.208) in the neighborhood of an equilibrium point yields d dt ( ρ NO − ρ e NO ) = f NO | e bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright =0 + ∂f NO ∂ ρ NO vextendsingle vextendsingle...
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Thermodynamics filled in class notes_Part_125 - 7.1...

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