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Allday
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Hi forums. I have what I think is a simple question but I'm making myself confused. I'm trying to work out the relationship between energy density ( [itex] u [/itex] = energy per unit volume ) and temperature in a multi-species ideal gas (no molecules just different mass ions). The simplest example of something like this would be a hydrogen gas and the species would be neutral hydrogen, ionized hydrogen, and free electrons. I assume all species are at the same temperature. I know the monatomic answer is,
[tex] u = \frac{3}{2} n k T [/tex]
where [itex] n [/itex] is the number density of all particles and [itex] k [/itex] is Boltzmann constant. I'm trying to decide if I need to add a factor of the mean molecular mass ( [itex] \mu [/itex] = the mean mass of an ion divided by the proton mass) in this relation for the multi-species case. [itex] \mu [/itex] is dimensionless so I can't decide on the basis of dimensional analysis.
I suppose the question is equivalent to asking if the energy density of a box of hydrogen at a fixed temperature is equal to that of a box of helium at the same temperature ... the more I think about this, the more I'm thinking the factor of [itex] \mu [/itex] is not needed. Can anyone confirm this?
Any help appreciated.
[tex] u = \frac{3}{2} n k T [/tex]
where [itex] n [/itex] is the number density of all particles and [itex] k [/itex] is Boltzmann constant. I'm trying to decide if I need to add a factor of the mean molecular mass ( [itex] \mu [/itex] = the mean mass of an ion divided by the proton mass) in this relation for the multi-species case. [itex] \mu [/itex] is dimensionless so I can't decide on the basis of dimensional analysis.
I suppose the question is equivalent to asking if the energy density of a box of hydrogen at a fixed temperature is equal to that of a box of helium at the same temperature ... the more I think about this, the more I'm thinking the factor of [itex] \mu [/itex] is not needed. Can anyone confirm this?
Any help appreciated.
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