ASTE 501a Fall 2006:

Physical Gas Dynamics

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

- 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

- 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

- 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

- 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

- 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