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Thermodynamics filled in class notes_Part_95

Thermodynamics filled in class notes_Part_95 - 5.6 SOME...

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Unformatted text preview: 5.6. SOME CONSERVATION AND EVOLUTION EQUATIONS 197 Solving, we get dρ dt = − 1 T dT dt ∑ N i =1 ρ i − r ∑ N i =1 ν i ∑ N i =1 ρ i ρ . (5.449) One takes dT dt from Eq. (5.442) to get dρ dt = 1 T r P N i =1 h i ν i ρc P ∑ N i =1 ρ i − r ∑ N i =1 ν i ∑ N i =1 ρ i ρ . (5.450) Now recall that ρ = ρ/M and c P = c P M , so ρ c P = ρc P . Then Equation (5.450) can be reduced slightly: dρ dt = rρ P N i =1 h i ν i c P T =1 bracehtipdownleft bracehtipuprightbracehtipupleft bracehtipdownright N summationdisplay i =1 ρ i ρ − ∑ N i =1 ν i ∑ N i =1 ρ i , (5.451) = rρ ∑ N i =1 h i ν i c P T − ∑ N i =1 ν i ∑ N i =1 ρ i , (5.452) = rρ ∑ N i =1 ν i parenleftBig h i c P T − 1 parenrightBig P RT , (5.453) = r ρ RT P N summationdisplay i =1 ν i parenleftbigg h i c P T − 1 parenrightbigg , (5.454) = rM N summationdisplay i =1 ν i parenleftbigg h i c P T − 1 parenrightbigg , (5.455) where M is the mean molecular mass. Note for exothermic reactionis the mean molecular mass....
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Thermodynamics filled in class notes_Part_95 - 5.6 SOME...

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