Page 188 - Chemical equilibria Volume 4

164 Chemical Equilibria
A2.1. The three branches of statistics
Each element in the collection has an energy ε i and the number of
elements which has that energy is n i. The total number of elements will be N,
such that:
N = ∑ n [A2.2]
i
i

Thus, the total energy is:

E = ∑ n ε [A2.3]
ii
i
The number of complexions, i.e. the number of configurations of the set
of elements, is written as Ω.

The mean energy of an element is ε , and by applying relation [2.2], we
find:

E
ε = [A2.4]
N

Thus, for the number of objects in the state i, we obtain:

n = g i exp ( α− )exp ( βε− i ) [A2.5]
i

g is the statistical weight or the coefficient of degeneracy or multiplicity
i
of the energy level ε : it is the number of different states which have the
i
same energy ε .
i
The coefficient β is a universal, whose value is:

β = 1 [A2.6]
k T
B

k is Boltzmann’s constant (quotient of the joule gas constant, R, by
B
Avogadro’s number N a).