Thermodynamics filled in class notes_Part_107

Thermodynamics filled in class notes_Part_107 - 6.4....

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Unformatted text preview: 6.4. ADIABATIC, ISOCHORIC KINETICS 221 Note finally that it can be shown that D , of dimension N ( N L ), and , of dimension N J , share the same column space, which is of dimension ( N L ); consequently, both matrices map vectors into the same space. 6.3.2 Species dominant: J < ( N L ) Next consider the case in which J < ( N L ). This often arises in models of simple chemistry, for example one- or two-step kinetics. The fundamental reaction dynamics are most concisely governed by the J equations which form 1 V d dt = r . (6.153) However, r is a function of the concentrations; one must therefore recover as a function of reaction progress . In vector form, Eq. (6.143) is written as d dt = 1 V d dt . (6.154) Take as an initial condition that the reaction progress is zero at t = 0 and that there are an appropriate set of initial conditions on the species concentrations : = , t = 0 , (6.155) = o , t = 0 . (6.156) Then, since is a constant, Eq. (6.154) is easily integrated. After applying the initialis a constant, Eq....
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Thermodynamics filled in class notes_Part_107 - 6.4....

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