University of California Santa Barbara, Department of Chemical Engineering ChE 210A: Thermodynamics and Statistical Mechanics Problem set #1 Due: Friday, October 2, 2009 Objective: To become familiar with the thermodynamic entropy, its derivatives, and it
University of California Santa Barbara, Department of Chemical Engineering ChE 210A: Thermodynamics and Statistical Mechanics Problem set #2 Due: Friday, October 9, 2009 Objective: To become familiar with the thermodynamic entropy, its derivatives, and it
University of California Santa Barbara, Department of Chemical Engineering ChE 210A: Thermodynamics and Statistical Mechanics Problem set #3 Due: Friday, October 16, 2009 Objective: To understand the properties of the fundamental equation, and the feature
University of California Santa Barbara, Department of Chemical Engineering ChE 210A: Thermodynamics and Statistical Mechanics Problem set #4 Due: Friday, October 23, 2009 Objective: To become comfortable with Legendre transformations, Maxwell relations, a
University of California Santa Barbara, Department of Chemical Engineering ChE 210A: Thermodynamics and Statistical Mechanics Problem set #5 Due: Friday, ctober 30, 2009
Objective: To understand and manipulate the thermodynamic properties of ideal and non
University of California Santa Barbara, Department of Chemical Engineering ChE 210A: Thermodynamics and Statistical Mechanics Problem set #6 Due: Friday, November 6, 2009 Objective: To understand and manipulate the thermodynamic properties of ideal and no
University of California Santa Barbara, Department of Chemical Engineering ChE 210A: Thermodynamics and Statistical Mechanics Problem set #7 Due: Wednesday, November 18, 2009 Objective: To understand microscopic crystals and the third law of thermodynamic
University of California Santa Barbara, Department of Chemical Engineering ChE 210A: Thermodynamics and Statistical Mechanics Problem set #8 Due: Wednesday, November 25, 2009 Objective: To understand the properties of and develop models using the canonica
University of California Santa Barbara, Department of Chemical Engineering ChE 210A: Thermodynamics and Statistical Mechanics Problem set #9 Due: Friday, December 5, 2008 Objective: To understand the properties of and develop models using the isothermal-i
Equilibrium and entropy
What is equilibrium?
ChE210A
At its most basic level, the subject of thermodynamics is the study of the properties of systems and substances at equilibrium. What is meant by equilibrium? A simple way of thinking about equilibrium i
Other ensembles
T he isothermal-isobaric ensemble
ChE210A
In the last few lectures, we derived the microscopic probabilities for systems that are at constant temperature, i.e., coupled to an infinitely large energy bath. We will now find the same probabil
Phase equilibrium
ChE210A
It is a familiar fact that pure substances tend to exist in one of three distinct states: solid, liquid, and gas. Heat a crystal up, and at a specific temperature it suddenly melts into a liquid. Continue heating that liquid, and
How the microscopic world works
ChE210A
In order to understand the molecular origins of thermodynamic equilibrium, it is important to first understand the fundamental principles by which molecules interact. Moreover, as science and technology increasingly
How the macroscopic world works
ChE210A
Previously, we covered how the world works at a microscopic level-how atoms and molecules interact with each other and what laws govern their time evolution. Now, we take a macroscopic point of view. What happens wh
ChE 210B: Advanced Topics in Equilibrium Statistical Mechanics
Glenn Fredrickson
Lecture 1
Reading: 3.1-3.5 Chandler, Chapters 1 and 2 McQuarrie This course builds on the elementary concepts of statistical mechanics that were introduced in ChE 210A and pr
Advanced Topics in Equilibrium Statistical Mechanics
Glenn Fredrickson
2. Classical Fluids
A. Coarse-graining and the classical limit
For concreteness, let's now focus on a fluid phase of a simple monatomic substance, e.g. Argon.
We can write generally th
Advanced Topics in Equilibrium Statistical Mechanics
Glenn Fredrickson
3. Theory of Gases
A. The Ideal Gas
As we shall see, gases are much easier to deal with than liquids, because the low density of gases makes collisions and pair interactions of molecul
Advanced Topics in Equilibrium Statistical Mechanics
Glenn Fredrickson
Lecture 5
Reading: Chandler 7.2, 7.3, 7.4, 7.5 Recap: dilute to moderately dilute gases treated by virial expansions about = 0 (z = 0) state. easily extended to molecular fluids and di
Advanced Topics in Equilibrium Statistical Mechanics
Glenn Fredrickson
5. Computer Simulation Methods
A. General Considerations
We have just seen that successful analytical theories for simple liquids like Argon can be constructed by means of modern pertu
Advanced Topics in Equilibrium Statistical Mechanics
Glenn Fredrickson
6. Statistical Mechanics of Classical Fields
Up to this point we have talked about how to set up and perform equilibrium statistical mechanical calculations of systems with a finite se
Advanced Topics in Equilibrium Statistical Mechanics
Glenn Fredrickson
7. Critical Phenomena
The subject of critical phenomena, i.e., the study of the equilibrium and nonequilibrium properties of systems near a critical point (e.g., a gas-liquid critical
Advanced Topics in Equilibrium Statistical Mechanics
Glenn Fredrickson
Lecture 14 8. Polymer Statistical Mechanics
A. Coarse-Graining
Polymer science is a particularly rich area of application of statistical mechanics. Before we can talk about the statist
Advanced Topics in Equilibrium Statistical Mechanics
Glenn Fredrickson
Lecture 16
Recap: semi-dilute, good solvent
(c) independent of N ! for c b( cb3 )-3/4 c-3/4
p 1
c
b-3
So, b (1A )
kB T 3
(20A )
R (100A )
c9/4
9. Interfacial Statistical Mechanics
T
Advanced Topics in Equilibrium Statistical Mechanics
Glenn Fredrickson
10. Electrolyte and Colloidal Solutions
A. Systems and Models
Thus far, we have restricted our attention to the equilibrium SM of simple fluids and polymers. However, there are many ot
Department of Chemical Engineering University of California, Santa Barbara ChE 210B Instructor: Glenn Fredrickson Homework #1 Homework Due: Friday, January 15, 2010 1. Check out our class web site at http:/www.mrl.ucsb.edu/ghf/che210b/. Familiarize yourse
Department of Chemical Engineering University of California, Santa Barbara ChE 210B Instructor: Glenn Fredrickson Homework #2 Homework Due: Friday, January 29, 2010 1. Prepare solutions to the following problems in your Chandler text: 7.8, 7.9, 7.11, 7.12
Department of Chemical Engineering University of California, Santa Barbara ChE 210B Instructor: Glenn Fredrickson Homework #3 Homework Due: Friday, February 12, 2010 1. Starting from the "virial equation" connecting g(r) to the pressure, show that p =1- 3
Department of Chemical Engineering University of California, Santa Barbara ChE 210B Instructor: Glenn Fredrickson Homework #4 Homework Due: Friday, February 19, 2010 1. For the vibrating elastic string discussed in class, compute the fourth moment of the
Department of Chemical Engineering University of California, Santa Barbara ChE 210B Instructor: Glenn Fredrickson Homework #5 Homework Due: Friday, March 5, 2010 1. Prepare solutions to the following problems in Chandler: 5.15-5.18. 2. The surface area of
Department of Chemical Engineering University of California, Santa Barbara ChE 210B Instructor: Glenn Fredrickson Homework #6 Homework Due: Friday, March 12, 2010 1. The problem of equilibrium phase coexistence between a lamellar mesophase and a liquid ph