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1 Content-Thermodynamics & Statistical Mechanics 1. Kinetic theory of gases..(1-13) 1.1 Basic assumption of kinetic theory Pressure exerted by a gas 1.2 Gas Law for Ideal gases: Boyle s Law Charle s Law Avogadro s Law Graham s Law of Diffusion Ideal Gas Equation: 1.3 Kinetic Interpretation of Temperature 1.4 Maxwell-Boltzmann Distribution Law The Distribution in term of Magnitude To Determine Value of β in term of Temperature T Average Velocity Root Mean Square Velocity Most Probable Velocity 2. Real Gases.(14-20) 2.1 Andrew s Experiment on Carbon Dioxide 2.2 van der Waals Equation of State. 2.3 Correction in Ideal Gas Equation to Achieve van der Waals Gas Equation of State Correction for Finite Size Correction for Intermolecular Attraction Maxwell Equal Area Critical Point van der Waals Equation of State and Virial Coefficient, H.No. 40-D, G.F, Jia Sarai, Website: .physics@gmail.com i
2 3. Basics of Thermodynamics and Laws of Thermodynamics (21-30) 3.1 Mathematical Formulations of thermodynamics Some important Formulas 3.2 Fundamental Concept System Isolated System Thermodynamical State State Function Intensive and Extensive Properties 3.3 The Ideal Gas: 3.4 Laws of Thermodynamics Zeroth law of Thermodynamics: First law of Thermodynamics: Work Done during Different Process Specific Heat Heat Capacity of Ideal Gas: Molar Heat Capacity Coefficient of Volume Expansion or Expansivity Isothermal Elasticity and Isothermal Compressibility 3.5 Different Types of Thermo Dynamical Process and use of First Law of Thermodynamics Isochoric Process: Isobaric Process Isothermal Process Adiabatic Process, H.No. 40-D, G.F, Jia Sarai, Website: ii
3 4. Second Law of Thermodynamics and Entropy...(31-41) 4.1 Second Law of Thermodynamics 4.2 Heat Engines 4.3 Entropy Heat Reservoir Efficiency of Heat Engine (η) Carnot Cycle Inequality of Clausius 5. Maxwell relation and Thermodynamic Potential.(42-58) 5.1 Maxwell relations 5.2 Different types of thermodynamic potential and Maxwell relation Internal Energy Enthalpy Helmholtz Free Energy Gibbs Energy 5.3 Application of Maxwell Relation First T ds Second T ds Equation Equation Third T-dS Equation: First Energy Equation Second Energy Equation 6. Postulates of Statistical Mechanics. (59-63) 6.1 Basic Definition, Mathematical Tools 6.2 Postulates of Statistical Mechanics 7. Micro Canonical Ensemble.(64-66) 7.1 Definition of Micro Canonical Ensemble Ergodic hypothesis Entropy, H.No. 40-D, G.F, Jia Sarai, Website: .physics@gmail.com iii
4 8. Canonical Ensemble.(67-85) 8.1 Partition function for canonical ensemble 8.2 Relation between macroscopic variable and canonical partition function Z 8.3 The Second law of Thermodynamics and Thermal Interaction Between Systems and Temperature 8.4 Relation Between Entropy and Probability 8.5 Different system for Canonical ensemble One Dimensional Free Particle Classical Harmonic Oscillator Quantum Harmonic Oscillator Classical Paramagnetic substance: Quantum Mechanical Treatment of Spin Half Paramagnetic Substance 9. Grand Canonical Ensemble (86-93) 9.1 Grand Canonical Partition Function : Thermo dynamical quantities in grand canonical ensemble: 9.2 Classical system in a grand canonical ensemble: Classical Grand Canonical Partition Function of an Ideal Gas Grand Canonical Partition Function for Classical Harmonic Oscillator 9.3 Quantum Mechanical Grand Canonical Partition Grand Canonical Partition Function for Quantum Harmonic Oscillator 10. Maxwell-Boltzmann Distribution.(94-97) 10.1 The total no of arrangements of the particles in the given distributions Derivation of Maxwell-Boltzmann Distribution 10.2 Energy Distribution Function Energy distribution in different dimension Average Energy, H.No. 40-D, G.F, Jia Sarai, Website: .physics@gmail.com iv
5 11. Bose Einstein Distribution...(98-105) 11.1 The Bose-Einstein Energy Distribution 11.2 Bose-Einstein Gas at High Temperature 11.3 Bose Einstein gas at low temperature 11.4 Bose Einstein Condensation 12. Fermi Dirac Distribution..( ) 12.1 Fermi Dirac Distribution 12.2 Fermions at High Temperature 12.3 Fermions at Low Temperature 13. Phase Transition and Low Temperature Physics..( ) 13.1 Third Law of Thermodynamics and Attainable of Low Temperature Production of Low Temperature: The Joule Kelvin Expansion: 13.2 Phase Transition First Order Phase Transition Equilibrium Between Two Phases Clapeyron-Clausius equation Liquid-Vapour Phase Transition Properties of First Order Phase Transition 13.3 Second Order Phase Transition 13.4 Landau Theory of Phase Transition Dimensional Analysis: 13.5 Landau Theory of Second Order Phase Transitions Order Parameter Free energy expansion Minimum Free Energy 13.6 Ising model One-dimensional Ising model Renormalization One-dimensional Ising chain, H.No. 40-D, G.F, Jia Sarai, Website: v
6 14. Random Walk Problem.. ( ) 14.1 Types of Distribution function Binomial distribution Gaussian Distribution: Center limit theorem 14.2 One Dimensional Random Walk Problem 14.3 Ficks Law For three dimensional system For two dimensional system For one dimensional system 14.4 Langevin Equation, H.No. 40-D, G.F, Jia Sarai, Website: vi
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