58363 - Statistical Physics

Learning outcomes

The course aims to provide students with basicelements of  the probabilistic  theory  and with the abilityof approaching the equilibrium thermodynamics of non-degenerate gases, by means of the statistical thermodynamics.

Course contents

The notion of probability. Random variables. Cumulative probability and density of probability. Dirac's delta function. Sum of random variables. The central limit theorem.
Classical equartions of motions. The phase space. Simple elements of quantum mechanics: states and cells in phase space. The Planck constant. The particles' indistinguishability. Discrete spectra and states' degeneration. The three principles of thermodynamics. Time averages of dynamical variables. Ergodic hypothesis. Phase space averages. Micro-canonic and canonic systems. Heat exchanges. Canonic distribution function. Canonic partition function for discrete spectra. The relationship between beta and T and Boltzmann's principle. The Helmholtz free energy. Continuum limit and semi-classical limit. Canonic partition function of an ideal non-degenerate (perfect) gas. Thermodynamic functions of the perfect gases. Gibb's paradox. The Maxwell-Boltzmann distribution. Rarefied gases and internal degrees of freedom. Atomic gases. Saha's formula for weakly ionized atomic gases. Perfect gases in an external field. The barometric formula. Theorem of equipartition of the energy. Bi-atomic molecular gases. Thermal equilibrium of the chemical reactions.

Readings/Bibliography

Dispense fornite dal docente.
Toda, Kubo, Saito: Statistical Physics Vol. I (Springer-Verlag).
S.K. Ma: Statistical mechanics (World Scientific Publ.)

Office hours

See the website of Loris Ferrari