MAJOR-VIII: PHYS8011: STATISTICAL MECHANICS
Classical Statistics: Macrostate & Microstate, Phase Space, Concept of Ensemble – Micro-canonical, canonical and Grand-canonical ensembles. Entropy and Thermodynamic Probability, Maxwell-Boltzmann Distribution Law, Partition Function,Thermodynamic parameters in terms of Partition Function,Ortho- and Para-Hydrogen, Thermodynamic Functions of an Ideal Gas, Classical Entropy Expression using Micro-canonicalensemble, Gibbs Paradox, Sackur Tetrode equation, Law of Equipartition of Energy (with proof) – Applications to Specific Heat and its Limitations, Thermodynamic Functions of a Two-Energy Levels System, Negative Temperature.
Quantum Theory of Radiation: Spectral Distribution of Black Body Radiation. Planck‘s Quantum Postulates. Planck’s Law of Blackbody Radiation, Experimental Verification. Deduction of (1) Wien’s Distribution Law, (2) Rayleigh-Jeans Law, (3) Stefan-Boltzmann Law, (4) Wien‟s Displacement law from Planck‘s law.
Bose-Einstein Statistics: B-E distribution law, Thermodynamic functions of a strongly Degenerate Bose Gas, Bose Einstein condensation, properties of liquid He (qualitative description), Radiation as a photon gas and Thermodynamic functions of photon gas. Bose derivation of Planck‘s law.
Fermi-Dirac Statistics: Fermi-Dirac Distribution Law, Thermodynamic functions of a Completely and strongly Degenerate Fermi Gas, Fermi Energy, Electron gas in a Metal, Thermionic emission and Richardson-Dushman equation, Specific Heat of Metals, Relativistic Fermi gas, White Dwarf Stars, Chandrasekhar Mass Limit.
MAJOR-VIII:PHYS8011: STATISTICAL MECHANICS
Use C/C++/Scilab/Python/other numerical simulations for solving the problems based on Statistical Mechanics like
Computational analysis of the behavior of a collection of particles in a box that satisfy Newtonian mechanics and interact via the Lennard-Jones potential, varying the total number of particles N and the initial conditions:
Study of local number density in the equilibrium state (i) average; (ii)fluctuations
Study of transient behavior of the system (approach to equilibrium)
Relationship of large N and the arrow of time
Computation of the velocity distribution of particles for the system and comparison with the Maxwell velocity distribution
Computation and study of mean molecular speed and its dependence on particle mass
Computation of fraction of molecules in an ideal gas having speed near the most probable speed
Computation of the partition function Z(β) for examples of systems with a finite number of single particle levels (e.g., 2 level, 3 level, etc.) and a finite number of non-interacting particles N under Maxwell-Boltzmann, Fermi-Dirac and Bose- Einstein statistics:
Study of how Z(β), average energy <E>, energy fluctuation ΔE, specific heat at constant volume Cv,depend upon the temperature, total number of particles N and the spectrum of single particle states.
Ratios of occupation numbers of various states for the systems consideredabove
Computation of physical quantities at large and small temperature T andcomparison of various statistics at large and small temperature T.
Plot Planck‟s law for Black Body radiation and compare it with Raleigh-JeansLaw at high temperature and low temperature.
Plot Specific Heat of Solids (a) Dulong-Petit law, (b) Einstein distribution function, (c) Debye distribution function for high temperature and low temperature and compare them for these two cases.
Plot the following functions with energy at different temperatures
Maxwell-Boltzmann distribution b) Fermi-Dirac distribution c) Bose-Einstein distribution