Lecture 1 Notes: Idealized Systems
This is a course in building microscopic models for macroscopic
phenomena. Most of first half involves idealized systems, where interparticle interactions can be ignored and where individual particles are
adequately desc
Lecture 3 Notes: Boltzmann Factor
e
P j
E kT
Canonical
j
eEm
Distribution
Function
kT
m
Denominator of canonical distribution function has a special name .
Q(N,V,T) eEj
kT
j
CANONICAL PARTITION FUNCTION
Sum of "Boltzmann factor", e
Ej/kT
, over states of
Lecture 6 Notes: Implicitly Values
Transformed Q from sum over states of an entire Nmoleculeassembly to sum over states of an individual molecule
Qe
E kT
j
sum over states
of assembly
n
j
n
j
j kT N
q
sum over states
i
j
e
N
of a molecule
E n kT
e j
Lecture 4 Notes: Microphysical Framework
P(E)(N,V,E)e
E/kT
Q(N,V,T)
probability of finding an assembly state with energy E in the ensemble
probability of finding the gas with energy E
A physical picture that describes the canonical framework is
Gas
Heat
Lecture 2 Notes: Ensemble Theory
microscopic impulses of each molecule impacting the vessel's
walls. The positions and velocities of each molecule change on a
1013s time scale (the duration of a collision)!
Possible Solution:
TIME AVERAGE the microscopic
Lecture 5 Notes: Assembly Descriptions
Overview: We've learned to calculate thermodynamic (macroscopic) properties of a
system from the partition function. However, the partition function, as it is presently
written, depends on the energy levels available
Lecture 10 Notes: Harmonic Approximation
T0
T0
rot
lim
lim CV
T0
12Nkr
T
T0
2
2
e
2r T
0
1.0
rot
C
V
nR
1.0
Low T Limit
CVrot 12r2 e
E
rot
nR
Note maximum in
2 T
r
r
v
T/rot
Cvrot 1
nR
6re2 T
C
nR
rot
High T Limit
T2
nR
E
E
rot
T
nR
1.624 at T 1.0 if we
Lecture 9 Notes: Partition Function
Nuclear hyperfine? [Nuclear spin degeneracy factors. LATER.]
Internal energy adds to translational energy to get total energy
=trans
int
+
quantum #'s
internal quantum #'s
N,M,L
where int = energy from internal degrees
Lecture 8 Notes: Macroscopic Properties
The macroscopic thermodynamic properties are written in terms of Q. Q is
related to the single-molecule partition function q, which is the sum over the molecular
energy levels or states. Atoms and molecules have dif
Lecture 7 Notes: Molecular
Properties
CANONICAL PARTITION FUNCTION FOR INDEPENDENT,
INDISTINGUISHABLE MOLECULES
N
Q(N,V,T) = q /N!
approximation valid for q N, not assured to be always valid
corrected Boltzmann statistics
where q ei
/kT
molecular partitio