17
T
HERMODYNAMICS IS ONE OF THE FEW TOPICS that one can ap-
proach from two completely different perspectives and arrive at the same
answers. One approach, the phenomenological approach,is the subject of the
first eight chapters of this book. It is based on the observation ofphenomena,
whose behaviors are generalized by various algebraic and calculus expressions.
Over the course of hundreds of thousands of observations, some generalities
have been used as summaries to describe how all known systems should be-
have. These summaries are known as the three laws of thermodynamics.
There is another way to consider thermodynamic properties: a statistical ap-
proach.Years before the quantum theory of matter was formulated, the atomic
theory was becoming the cornerstone of chemistry. Some people—James Clerk
Maxwell, Ludwig Boltzmann, and J. Willard Gibbs among them—thought that
if atoms and molecules were so small, then perhaps their behavior with respect
to energy could be understood statistically. Many of their scientific contempo-
raries rejected the idea. (In fact, Boltzmann’s suicide is blamed partly on the
negative reception given his ideas.) However, it turns out that we canuse sta-
tistics to understand the thermodynamics of atoms and molecules. Ultimately,
we find that the statistical approach allows us to make the same thermody-
namic predictions as with the phenomenological approach. This new approach
is called statistical thermodynamics.17.1 Synopsis
We will begin with a necessary (but nonchemical) review of some statistics that
we later apply to gaseous systems. (We use gases almost exclusively in our dis-
cussion of statistical thermodynamics.) We will see how we can separate, or
partition, a system into smaller units and define an important quantity called
a partition function. In time, we will see that the partition function is related
to the thermodynamic state functions that define our system.
The partition function is defined in terms of the different possible energies
of the individual particles in a system. The developers of statistical thermody-
namics derived their equations without an understanding of the quantum the-
ory of nature. But now, we recognize that atomic and molecular behavior is
described by quantum mechanics, and our development of statistical thermo-586
17.1 Synopsis
17.2 Some Statistics Necessities
17.3 The Ensemble
17.4 The Most Probable
Distribution: Maxwell-
Boltzmann Distribution
17.5 Thermodynamic Properties
from Statistical
Thermodynamics
17.6 The Partition Function:
Monatomic Gases
17.7 State Functions in Terms of
Partition Functions
17.8 Summary