Course Details

Subject {L-T-P / C} : PH3001 : Thermal and Statistical Physics { 3-1-0 / 4}

Subject Nature : Theory

Coordinator : Prof. Sidhartha S. Jena

Syllabus

Thermodynamic limit, extensive and intensive variables. Zeroth law of thermodynamics and thermal equilibrium. Brief discussion on microstates, macrostates, statistical definition of temperature. Qualitative idea of microcanonical, canonical ensembles. Boltzmann factor from canonical ensemble. Kinetic theory and transport properties of gases: Maxwell-Boltzmann (MB) speed distribution and mean kinetic energy of an ideal gas, most probable velocity, ideal gas law, molecular flux and effusion rate, van der Waals equation of state, critical constants, law of corresponding states. Collision cross section, mean collision time and mean free path, coefficient of viscosity, thermal conductivity, coefficient of self-diffusion, diffusion equation, thermal diffusivity, 1D thermal diffusion equation. Kinetic theory of real gases. Equilibrium and work: thermodynamic equilibrium, state function, definition of work, quasi-static, isobaric and isochoric processes, work in a hydrostatic system, isothermal compressibility. First law: statement of first law, heat capacity of an ideal and non-ideal gas, reversibility, quasi-static isothermal expansion or compression of an ideal gas, adiabatic expansion of an ideal gas. Second law: various statements and equivalence, Carnot engine and theorem, heat engines, refrigerator, heat pump, Clausius’s theorem, definition of entropy, irreversible changes and entropy, Joule expansion. Formal structure: Entropic and energetic fundamental relations, intensive parameters, equation of state, entropic intensive parameters, Gibbs-Duhem relations. Thermodynamic Potentials: Legendre transformation and thermodynamic potentials, Helmholtz, Enthalpy, Gibbs, grand potential, condition of equilibrium, Maxwell’s relations, stability of equilibrium state. Third law: unattainability of absolute zero and different statements of third law, consequences of third law. First order phase transition single component systems, Clausius-Clapeyeron equation, phase diagrams, multicomponent systems, Gibbs phase rule. Statistical Thermodynamics of classical systems: ergodicity, phase space and ensemble averages, Liouville’s theorem. Microcanonical ensemble: microstates and definition of entropy, classical ideal gas, statement of Gibbs paradox and correct enumeration of microstates, thermodynamics of classical non-interacting harmonic oscillators. Canonical ensemble: canonical distribution function, partition function and connection to thermodynamics, classical ideal gas and harmonic oscillators. Grand canonical ensemble: grand partition function and connection to thermodynamics, classical ideal gas.

Course Objectives

Course Outcomes

At the end of this course students should be comfortably placed to study more advance course on statistical mechanics.

Essential Reading

Supplementary Reading