Review Note
Last Update: 08/18/2023 10:41 PM
Current Deck: Combustion Quals
PublishedCurrently Published Content
Front
How is the statistical mechanics approach for reacting PGs different than for single species?
Back
Still assume all components are TPG so molecules are weakly interacting
Still want to find the Boltzmann relation, but since reactions are possible,
where A, B, and C are gas components defined by and Wx(Nix ) = number of microstates in distribution of species X based on number of molecules Nix in each energy level
Assuming the system is isolated, the total E and total number of each nuclei type becomes constrained, and we want to find
To find the total energy of the mixture but previously we allowed the lowest energy level of each species to be 0, however for multiple species we need to define one common zero for all species
Still follow the general Lagrange' Method of Undetermined Multipliers method but you now have an alpha for each species (beta is the same b/c we still have perfect gasses) which results in a population distribution for each species that maximes W
Still want to find the Boltzmann relation, but since reactions are possible,
where A, B, and C are gas components defined by and Wx(Nix ) = number of microstates in distribution of species X based on number of molecules Nix in each energy levelAssuming the system is isolated, the total E and total number of each nuclei type becomes constrained, and we want to find
To find the total energy of the mixture
but previously we allowed the lowest energy level of each species to be 0, however for multiple species we need to define one common zero for all speciesStill follow the general Lagrange' Method of Undetermined Multipliers method but you now have an alpha for each species (beta is the same b/c we still have perfect gasses) which results in a population distribution for each species that maximes W
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