CH353
- Physical Chemistry I Spring 2013, Unique 52575 Lecture Summary, 3 April 2013 |

Statistical
Thermodynamics: The energy of an
individual molecule or atom has 4 contributions: 1) electronic, 2)
translational, 3) rotational, and 4) vibrational. A monatomic
species contains the first two of these energies, and a polyatomic
species contains all four. Today we focused exclusively on
applying the Boltzmann distribution to a monatomic species, making
the additional simplification that the number of energy states
available for the system to fill is dominated by translational
states, and so we can ignore contributions from electronic energy in
our derivation. We were able to determine an expression for
the partition function of this monatomic species, and from there we
were able to derive exact expressions for the system's average
energy, heat capacity, and pressure. We were gratified to see
that all of these expressions were very familiar. We have thus
seen a few simple examples of how statistical mechanics can start
from the energy of an individual atom or molecule (which can be
calculated from quantum mechanics) and using an appropriate
partition function and the Boltzmann distribution, results in a
macroscopic property that results from a collection of atoms or
molecules. Although we have only done this for a simple
example, we could derive expressions for any macroscopic property of
any system we wish, no matter how complex. |