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Unformatted text preview: 5.4. CHEMICAL EQUILIBRIUM 173 Written another way, one has n 1 − n 1 o ν 1 = n 2 − n 2 o ν 2 = n 3 − n 3 o ν 3 = n 4 − n 4 o ν 4 = ζ. (5.238) For an N-species reaction, ∑ N i =1 ν i χ i = 0, one can generalize to say dn i = = ν i dζ, (5.239) n i = ν i ζ + n io , (5.240) n i − n io ν i = ζ. (5.241) Note that dn i dζ = ν i . (5.242) Now, from the previous chapter, one manifestation of the second law is Eq. (4.399): dG | T,P = N summationdisplay i =1 μ i dn i ≤ . (5.243) Now, one can eliminate dn i in Eq. (5.243) by use of Eq. (5.239) to get dG | T,P = N summationdisplay i =1 μ i ν i dζ ≤ , (5.244) ∂G ∂ζ vextendsingle vextendsingle vextendsingle vextendsingle T,P = N summationdisplay i =1 μ i ν i ≤ , (5.245) = − α ≤ . (5.246) Then for the reaction to go forward, one must require that the affinity be positive: α ≥ . (5.247) One also knows from the previous chapter that the irreversible entropy production takes the form of Eq. (4.387): −...
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- Fall '11
- Dynamics, i=1, J. M. Powers, Irreversible entropy production, DNI, µi νi