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ASTE 501a


ASTE 501a Fall 2006:
Physical Gas Dynamics


3 units; 6:30-9:10 Monday, VHE 210
Instructor:

Joseph Kunc, RRB 219, (213) 740-5375, kunc@usc.edu.

Office Hours: Tuesdays and Thursdays, 2-4 PM
Text: Course notes. To be posted in pdf form on this website.

Midterm Exam: There will be one midterm exam on a date to be announced.

Final Exam: Monday, December 11, 7:00 PM-9:00 PM.

Homework: Assigned weekly or biweekly. Due in class.

Grading: Homework, 20%; midterm exam, 40%; final exam, 40%.
Course Material:
  1. SOME STATISTICAL CONCEPTS
    • Introduction
    • Discrete random events
      • The concept of probability
      • Normalization of probability
      • Mean value
      • Variance and standard deviation
      • The most probable value
      • Multivariate distributions
    • Continuous random events
      • The concept of probability
      • Density of probability
      • Normalization of probability
      • Mean value
      • Variance and standard deviation
      • The most probable value
      • Multivariate distributions
    • Probability distributions
      • General properties of distribution functions
      • Uniform distribution
      • Delta Distribution
      • Binomial distribution
      • The most probable density of particles in a gas
      • Fluctuations
      • Poisson distribution
      • Gaussian distribution
      • The Chebyshev inequality
      • An angular distribution
    • Importance of distribution functions
    • Some results of combination theory
      • Combinatorics of indistinguishable objects
      • Combinatorics of distinguishable objects
    • The Stirling approximation
  2. SOME PHYSICAL CONCEPTS
    • Introduction
    • Unit systems
    • Macroscopic equilibrium, non-equilibrium and steady-state
    • Thermodynamic equation of state
    • Mean distance between gas particles
    • Flux of particles
    • Need for statistical approach in gas physics
    • Concept of the phase space
  3. STRUCTURE AND DYNAMICS OF PARTICLES
    • Introduction
    • Spatial wave functions
    • Complete wave functions
    • Pauli's Exclusion Principle
    • Heisenberg's Uncertainty Principle
    • Atomic and molecular systems
    • Translational motion of particles
      • Motion of a free particle
      • Particle in a box
    • Motion of electrons in atomic particles
      • The hydrogen-like particles
      • Multi-electron atoms and atomic ions
      • Quantum properties of atomic nuclei
      • Atoms in electric and magnetic fields
    • Electronic configurations in atoms and atomic ions
    • Molecular rotation
      • Rigid rotor
      • Nonrigid rotor
    • Molecular vibration
      • Harmonic oscillator
      • Anharmonic oscillator
      • Rotating Morse oscillator
    • Vibrating and rotating molecule (with no electrons)
      • Vibrating rotor
    • Vibrating and rotating molecule (with electrons)
      • Rigid symmetric top
      • Nonrigid symmetric top
      • Vibrating and rotating symmetric top
    • Electronic configurations in molecules and molecular ions
  4. STATISTICAL MECHANICS
    • Introduction
    • Statistical concept of entropy
    • Microscopic vs. macroscopic equilibrium
    • Models of systems in equilibrium
      • Fixed-energy system
      • Microcanonical system
      • Canonical system
      • Grand canonical system
    • Energy distributions of particles
      • Bose-Einstein distribution
      • Fermi-Dirac distribution
      • Maxwell-Boltzmann distribution
      • Comparisons of the B-E, F-D and M-B distributions
    • Degeneration of quantum statistics
    • Distribution of quantum states of equilibrium systems
    • The concept of the statistical ensemble
      • Probabilities of quantum states in microcanonical system
      • Probabilities of quantum states in grand canonical system
      • Probabilities of quantum states in canonical system
    • Importance of the canonical distribution
    • Classical canonical distribution
    • Averaging over canonical distribution
    • Constants b and g
    • Some applications of statistical mechanics
      • Translational partition function
      • Maxwellian distribution
      • Spatial distribution of particles in external field
    • Partition functions of atoms
      • Translational partition function
      • Electronic partition function
      • Nuclear partition function
    • Partition functions of diatomic molecules
      • Translational partition function
      • Electronic partition function
      • Vibrational partition function
      • Rotational and nuclear partition functions
    • The number of internal energy levels in diatomic molecules
    • Zero-energy level of molecular energy
    • Thermodynamic functions
      • Thermodynamic functions and zero-energy molecular level
      • Gas of monatomic particles
      • Gas of diatomic particles
    • Equipartition of particle energy
  5. FORCES BETWEEN PARTICLES
    • Introduction
    • Chemical bond
    • Atomic and ionic bonds
    • Electric field of a system of charges
    • Long-range interactions
      • Electrostatic forces
      • Induction forces
      • Size of rotationally and vibrationally excited molecules
      • Dispersion forces
      • Van der Waals energy
      • Macroscopic electric properties of gases
    • Short-range interactions
    • Examples of intermolecular potentials
    • Mixture rule
    • Virial theorem
    • Van der Waals molecules