Comprehensive lists of topics for the Final Exam
ChemE 240, Spring 2007
Ising model (1-D and 2-D)
Mean field theory and the 2-d Ising model
From Midterm One
From Last Section of Course
First, second, & third law of thermodynamics
Energy minimization, entropy maximization
Intensive vs. extensive variables
Definitions: closed system, subsystem, adiabatic,
reversible
Legendre transforms
Gibbs-Duhem equation
Euler’s equation
Maxwell relations
How to take partial derivatives to obtain quantities of
interest
Conditions for single and multiphase equilibrium
(thermal/mechanical/chemical equilibrium)
Definitions of κT, κS, cV, cP
Stability criteria
Maxwell construction
Interpreting phase diagrams
Gibbs phase rule
Equilibrium and Gibbs surfaces (including first- and
second-order phase transitions)
Clausius-Clapeyron equation
The van der Waals equation of state
P vs. V diagram for VDW (coexistence, metastable,
spinodal region)
Interfaces, surface tension
Gibbs adsorption isotherm
Qualitative Ising Model
Renormalization group theory
Systems with phase changes
Monte Carlo methods
Classical fluids
Model system: 1-d rigid rods
Derivation of the VDW Equation from Chapter 7
equations
Radial distribution functions
Lennard-Jones fluid
Thermodynamic properties from g(r)
Self-diffusion and random walks
Particle on a spring undergoing Brownian motion
From Midterm Two
Microcanonical ensemble (N,V,E)
Canonical ensemble (N,V,T)
Grand canonical ensemble (μ,V,T)
Partition function
Probability of a state v
Connection formula : −βA = ln Q
Generalized ensemble
Gibbs entropy formula
Fluctuations of <(δE)2> (p. 66) and <(δN)2> (p. 71)
Two state model, section 3.4 (nj = 0 or 1)
Spin systems (nj = -1 or 1)
Stirlings approximation, ln N! = N ln N – N
Degeneracy, degenerate energy levels
Independent, identical particles vs. distinguishable
Regular solution theory
Fugacity and phase equilibrium calculations
Raoult’s law (with and without activity/fugacity
coefficients)
Hamiltonians and energies
Conditions about a critical point