526
A. del Val et al.
I
N I I = E
(16.8)
Statistical derivation of thermodynamic properties can be found in standard
textbooks [34]. The models for the different energy modes are depicted for a mixture
as a generalization of this particular case.
Mixture of Inert Perfect Gases
In a mixture of different species, the same principles apply. The equations for the
thermodynamic properties of the different energy modes are depicted hereafter for
the species i of the mixture:
e
T
i =
3
2
k B T
m i
(16.9)
h
T
i = e
T
i +
k B T
m i
(16.10)
s
T
i =
h T
i
T
+
k B
m i
ln
⎡
⎢
⎣
k B T
p
2πm i k B T
h 2
3
2
⎤
⎥
⎦
(16.11)
Electronic energies, enthalpies, and entropies of atoms and molecules read
e E i = h E i =
k B
m i
n g in θ E i,n exp
−θ E i,n
T
n g in exp
−θ E i,n
T
(16.12)
s E i =
h E i
T
+ ln
n
g in exp
−θ E i,n
T
(16.13)
Quantity g in stands for the degeneracy of the electronic level n of the species
i ∈ H and θ Ein for its energy (in K unit). The number of electronic levels retained
is limited for mathematical and physical standpoints [35].
For linear molecules, rotational energies, enthalpies, and entropies are expressed
as:
e R i = h R i =
k B T
m i
(16.14)