Lecture 13
5.60/
20
.110/2.772
1
•
What is Statistical Mechanics?
•
Brief Review of probability and combinatorics
•
S=k ln
Ω
and S = -k
Σ
p
i
ln p
i
•
What is Statistical Mechanics?
Spontaneous processes:
under certain conditions, know what system would like to maximize/minimize:
()
i
i
i
i
n
P
T
G
n
P
S
H
n
V
T
A
n
V
S
U
,
,
,
,
,
,
,
,
0
0
0
0
,
,
,
,
,
,
,
,
≤
≤
≤
≤
i
i
i
i
n
P
T
n
P
S
n
V
T
n
V
S
dG
dH
dA
dU
These tell you which way a reaction will go, and when it will stop or reach equilibrium.
Want these thermodynamic properties, now in terms of
molecular level picture
.
E
p
Before: ignore molecular properties
Now want to account for it: molecule exists in states, has energy levels (recall 5.111)
If have large number of molecules (N
A
= 6
×
10
23
), it is nearly impossible to track all of the states. Mind
boggling!
How?
: use probability to describe molecule instead of tracking each one
p
i
= probability that molecule will be in i
th
state. The link between microscopic and macroscopic:
20.110J / 2.772J / 5.601J
Thermodynamics of Biomolecular Systems
Instructors: Linda G. Griffith, Kimberly Hamad-Schifferli, Moungi G. Bawendi, Robert W. Field