CM7043 2016
2. Determination of P(Ek) and f(E)
Two macroscopic systems A and B in equilibrium with heat reservoir.
We denote by PA(EA) the probability of finding A
in a particular (micro)state with en
CM7043 2016
1. Probability
1. Frequency and probability
event a specific outcome of a trial.
Index the event with i.
In coin tossing, i = h, t.
In rolling a die, i = 1, 2, 3, 4, 5, 6.
Consider a total
CM7043 2016
2. Energy
1. Introduction
Statistical mechanics consider the energy of each molecule, not the internal energy of the system
2. Kinetic energy and potential energy
(1)
equation of motion:
(
CM7043 2016
8. Open systems
An open system with temperature and chemical potential specified:
Another assumption of statistical mechanics:
All (micro)states with the same energy E and the same number
CM7043 2016
3. Internal Energy
An example of calculating a thermodynamic variable (macroscopic quantity) from Z.
Ek fluctuates from time to time as it exchanges
heat with the heat reservoir.
The inter
CM7043 2016
4. Identification of
Consider a perfect gas consisting of N monatomic molecules of mass m:
(20)
For this system,
(21)
and
(22)
Let
molecular partition function
Then,
(23)
and
(25)
where
T
CM7043 2016
0. Introduction
Classical thermodynamics
Assumptions:
1. dQ + dW = dU
2. TdS = dQ for reversible processes
We obtain some of the relationships between macroscopic variables S, T, U, V, and
CM7043 2016
7. Fluctuations of the energy
(41)
We calculate
.
Therefore,
Recall:
. Therefore,
Since
and
Therefore,
Then,
(42)
In eq 42, only T is changed in U/T. No change in the volume, polarization,
CM7043 2016
4.5 Imperfect gas
Perfect gas equation of state
(5.1)
A deviation from the ideality is represented in the virial expansion:
(5.14)
B2: second virial coefficient (B in the Textbook)
B3: thi
CM7043 2016
4. Applications of Statistical Mechanics
4.2 Maxwell distribution functions
We consider translational motion of molecules in perfect gas.
We do not consider rotational or vibrational energ
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6. Another look at entropy
Since
and
(const. is dropped)
, eq 35 is rewritten to
(35)
Here,
Therefore,
(39)
cf. uncertainty:
. Therefore,
(entropy) = kB (uncertainty of microstates)
(40)
C
CM7043 2016
Appendix 3A
General formula for (E) in a system consisting of N non-interacting particles, each having i =
ni0 with ni = 0, 1, 2, Total energy is E =1 + 2 + + N = 0(n1 + n2 + + nN).
Let us
CM7043 2016
5. Remaining thermodynamic functions
We will obtain expressions of S, F, etc. as a function of Z.
We have already seen
which uses the dependence of U on (or T).
Z depends on V:
or
There is
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3. Statistical Mechanics
1. Basic assumption of statistical mechanics
Consider a closed system consisting of N particles.
The textbook uses v. We switch from v to p = mv.
The microscopic s
CM1004
Lecture Notes
03FEB15
Chapter 1
- Derived unit
o Volume = 1m^3 x 10^-2 cm^3 = 1 cucm = 1 cc = 1 mL
Water has a max density at 4 degC
Volume of a cylinder = infinite number of circles (area of
The Basics of General, Organic, and Biological
Chemistry
3-1
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Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.
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The Basics of General, Organic, and Biological
Chemistry
4-1
This work is licensed under the
Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.
To view a copy of this license
CHA P TER
4
Covalent Bonding and
Simple Molecular
Compounds
1.
2.
1.
2.
9.
1.
3.
5.
7.
32
THE BASICS OF GENERAL, ORGANIC, AND BIOLOGICAL CHEMISTRY
11.
13.
15.
17.
CHAPTER 4
COVALENT BONDING AND SIMPLE
CHA P TER
3
Ionic Bonding and Simple
Ionic Compounds
1.
Fluorine atom
Fluorine ion
1.
2.
3.
5.
1.
22
THE BASICS OF GENERAL, ORGANIC, AND BIOLOGICAL CHEMISTRY
1.
1.
2.
3.
1.
CHAPTER 3
3.
IONIC BONDING
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11. Use the localized electron model to describe the bonding in H2O.
O
H
1O x 6e- = 6e4 groups of electrons (P)
2H x 1e-= 2e2 atoms, 2 lone pairs
H
Total
8e
Trigonal