Thermodynamics filled in class notes_Part_97

# Thermodynamics filled in class notes_Part_97 - 5.7 SIMPLE...

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Unformatted text preview: 5.7. SIMPLE ONE-STEP KINETICS 201 Define forward and reverse reaction coefficients, R ′ , and R ′′ , respectively, as R ′ ≡ k ( T ) N productdisplay i =1 ρ ν i ′ i , (5.483) R ′′ ≡ k ( T ) K c N productdisplay i =1 ρ ν i ′′ i . (5.484) Both R ′ and R ′′ have units of kmole/m 3 /s . It is easy to see that r = R ′ −R ′′ . (5.485) Note that since k ( T ) > 0, K c > 0, and ρ i ≥ 0, that both R ′ ≥ 0 and R ′′ ≥ 0. Since ν i = ν ′′ i − ν ′ i , one finds that 1 K c N productdisplay i =1 ρ ν i i = 1 K c k ( T ) k ( T ) N productdisplay i =1 ρ ν ′′ i − ν ′ i i = R ′′ R ′ . (5.486) Then Eq. (5.482) reduces to dS dt vextendsingle vextendsingle vextendsingle vextendsingle U,V = − RV R ′ parenleftbigg 1 − R ′′ R ′ parenrightbigg ln parenleftbigg R ′′ R ′ parenrightbigg ≥ . (5.487) Finally, we get dS dt vextendsingle vextendsingle vextendsingle vextendsingle U,V = RV ( R ′ −R ′′ ) ln parenleftbigg...
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Thermodynamics filled in class notes_Part_97 - 5.7 SIMPLE...

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