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 : ( NO , N ) = ( 1 . 605 10 6 , 3 . 060 10 8 ) mole cm 3 , non-physical , (7.211) 2 : ( NO , N ) = ( 5 . 173 10 8 , 2 . 048 10 6 ) mole cm 3 , non-physical , (7.212) 3 : ( NO , 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 ( NO e NO ) = f NO | e bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright =0 + f NO NO vextendsingle vextendsingle...
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This note was uploaded on 11/26/2011 for the course EGN 3381 taught by Professor Park-sou during the Fall '11 term at FSU.

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Thermodynamics filled in class notes_Part_125 - 7.1....

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