tailieunhanh - Modeling of Combustion Systems A Practical Approach 8

Tham khảo tài liệu 'modeling of combustion systems a practical approach 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Appendix H Equilibrium Primer Consider a general reaction r1R1 r2R2 - o p1P1 p2P2 - or equivalently m n z r R z PrPr j 1 k 1 Here j is an index from 1 to m reactants r refers to the number of moles of the jth reactant Rj is the jth reactant the double-headed arrow means that both the forward and reverse reactions occur typically at different rates k is an index from 1 to n products pk is the number of moles of the kth product and Pk is the kth product. For Reaction we may define an equilibrium constant with the following relation n Pp P2p. n PkT K 1 1 L1 1 k 2 nr m R1 1 IR - n Rjr j 1 The brackets denote the volume concentrations of the enclosed species. If we wish to express Keq in terms of mole fraction rather than concentration for gases then using the ideal gas law we obtain n D1 1 r I -sip- 2. in -rnysrk K I-L ys yh I 1 J L__ IRT B. 1 B r - 1 RTl n V yR y n y j 1 617 2006 by Taylor Francis Group LLC 618 Modeling of Combustion Systems A Practical Approach Please note that P and R italicized are the pressure and universal gas constant while P and R nonitalicized refer to products and reactants respectively. For constant-pressure systems such as combustion we may also incorporate the pressure dependence as part of the equilibrium constant as í RT Azpk-r K Ky í p J n n ypkPk Ky - .--------- n yRkrr In either case the equilibrium constant is defined as products over reactants. K or Ky is a function of temperature according to an Arrhenius relation _b_ K Ae T Thus K or Ky is only constant if the reaction temperature is constant. Since temperature is in the exponential it usually overwhelms the temperature effects shown in Equation . In particular note that Ky is neither necessarily dimensionless nor independent of pressure except in the case that the number of moles remains invariant. 2006 by Taylor Francis Group .