A. THERMODYNAMICS
1.Kinetic Theory of Gasses
Basic assumptions of kinetic theory, Ideal gas approximation, deduction of perfect gas laws. Maxwell’s distribution law (both in terms of velocity and energy), root mean square and most probable speeds. Finite size of molecules : Collision probability, Distribution of free paths and mean free path from Maxwell’s distribution. Degrees of freedom, equipartition of energy (detailed derivation not required).
2 .Real Gases
Nature of intermolecular interaction : isotherms of real gases. Van der-Waals equation of state, Other equations of state (mention only), critical constants of a gas, law of corresponding states; Virial Coefficients, Boyle temperature.
3. Heat transfer
Thermal conductivity, diffusivity, Fourier equation for heat conduction –its solution (steady state) for rectilinear and radial (spherical and cylindrical) flow of heat, Determination of thermal conductivity of solids by Searle’s method, Forbe’s method and Lee’s disc method( for bad conductors).
4. Radiation
Nature of radiant heat, emissive and absorptive power, prevost’s theory of heat exchange, Kirchhoff’s law (simple deduction), Black body radiation, Stefan-Boltzmann law, Planck’s formula for black body radiation (elementary idea).
5. Basic Concepts of Thermodynamics
Microscopic and macroscopic points of view : thermodynamic variables of a system, State function, exact and inexact differentials.
6 . First Law of Thermodynamics
Thermal equilibrium, Zeroth law and the concept of temperature. Thermodynamic equilibrium, internal energy, external work, quasi-static process, first law of thermodynamics and applications including magnetic systems, specific heats and their ratio, isothermal and adiabatic changes in perfect and real gases.
7. Second Law of Thermodynamics
Reversible and irreversible processes, indicator diagram. Carnot’s cycles-efficiency, Carnot’s theorem. Kelvin’s scale of temperature, relation to perfect gas scale, second law of thermodynamics – different formulations and their equivalence, Clausius inequality, entropy, change of entropy in simple reversible and irreversible processes, entropy and disorder; equilibrium and entropy principle, principle of degradation of energy.
8. Thermodynamic Functions
Enthalpy, Helmholtz and Gibbs’ free energies; Legendre transformations, Maxwell’s relations and simple deductions using these relations; thermodynamic equilibrium and free energies.
9. Change of State
Equilibrium between phases, triple point : Gibbs’ phase rule (statement only) and simple applications. First and higher order phase transitions, Ehrenfest criterion. Clausius-Clapeyron’s equation. Joule-Thomson effect.
B. STATISTICAL MECHANICS
1. Phase space
Concept of Microstates and macro states, Basic postulates - equal priori probability and ergodic hypothesis, Liouville theorem and conservation of density in phase space, Statistical ensemble - Micro-canonical, Canonical and Grand canonical ensemble and their partition functions, Relation of statistical mechanics with thermodynamics - Expressions of different thermodynamical quantities (e.g. Free energy, pressure, average energy, entropy, Specific heat) in terms of partition function;
2. Classical statistics
Maxwell-Boltzamann distribution function, Calculation of thermodynamical quantities for ideal gas, Maxwell-Bolzamann velocity distribution law, (Average, most probable velocity and root mean square speed and their relation; Principle of equipartition of energy. )
3. Quantum statistics
Concept of indistinguishability, Entropy of mixing and Gibb's paradox, Resolution of Gibb's paradox introducing indistinguishability; Bose-Einstein distribution function and its behaviour with temperature, Basic idea of phenomenon Bose-Einstein condensation (Qualitative description), Calculation of various thermodynamical quantities of photon gas (black body radiation); Fermi-Dirac distribution function and its behaviour with temperature, Basic idea of Fermi surface and fermi energy, Calculation of various thermodynamical quantities of free electron gas; Classical limits and distinguishing features of classical and quantum statistics.
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