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Thermodynamics filled in class notes_Part_93

# Thermodynamics filled in class notes_Part_93 - 5.6 SOME...

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5.6. SOME CONSERVATION AND EVOLUTION EQUATIONS 193 The term N i =1 φ li ρ i represents the number of moles of element l per unit volume, by the following analysis N summationdisplay i =1 φ li ρ i = N summationdisplay i =1 moleselementl molesspeciesi molesspeciesi volume = moleselementl volume ρ e l . (5.405) Here the elemental mole density , ρ e l , for element l has been defined. So the element concen- tration for each element remains constant in a constant volume reaction process: d ρ e l dt = 0 , l = 1 ,...,L. (5.406) One can also multiply by the elemental mass, M l to get the elemental mass density , ρ e l : ρ e l ≡ M l ρ e l , l = 1 ,...,L. (5.407) Since M l is a constant, one can incorporate this definition into Eq. (5.406) to get e l dt = 0 , l = 1 ,...,L. (5.408) The element mass density remains constant in the constant volume reaction. One could also simply say since the elements’ density is constant, and the mixture is simply a sum of the elements, that the mixture density is conserved as well.

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Thermodynamics filled in class notes_Part_93 - 5.6 SOME...

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