Page 266 - Instant notes

G8
STATISTICAL THERMODYNAMICS

Key Notes
Statistical thermodynamics attempts to both qualitatively and
quantitatively explain measurable properties obtained through
classical thermodynamics (entropy, heat capacity, etc.) by
analyzing the quantized behavior of systems at the molecular
level.
The Boltzmann distribution is a statistical approach which
describes the distribution of the components of a system,
molecules or atoms, for example, over the available states of that
system. The most probable configuration of any system is given
when the population of each state, n i , is given by the Boltzmann
law:

By defining the lowest energy level to be equal to zero, the
population in a level of energy ε j above this is given by
n j =n 0 g j exp(−ε j /k B T) where g j is the degeneracy of level j.
The partition function, q, is defined as:

q is a temperature-dependent dimensionless number which
provides a measure of the ability of molecules to access energy
levels above the ground state. The larger the value of q, the more
molecules access energy levels above ε 0 . q varies from 1 at
absolute zero (n 0 =N) to an exceedingly large value where the
energy levels are closely spaced and at high temperature (n 0 →0).
The total partition function for a molecule is obtained from the
product of the individual terms: q=q trans .q rot .q vib .q elec . Each
partition function may be calculated from knowledge of the
energy spacings of the individual terms. q elec is approximately
equal to 1 for most materials, with the remaining terms being
2 1/2
given by the relationships: q trans =(2πmk B T/h ) V, q rot (diatomic
2
2
molecule)=8π Ik B T/σh and .