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Chapter 1. Concepts of Thermodynamics

1.1 Introduction .
1.2 Some Definitions.
1.3 Zeroth Law of Thermodynamics and Concept of Temperature
1.4 Equation of State of an Ideal Gas
1.5 Vanderwaal’s Equation of State
1.6 Concepts of Work, Internal Energy and Heat
1.7 The First Law of. Thermodynamics
1.8 Thermodynamic Processes
1.9 Adiabatic Equation of a Perfect Gas
1.10 Molar Specific Heats Co and Cv
1.11 External Work Done by an Ideal Gas in Isothermal Expansion
1.12 External Work Done by An Ideal Gas in Adiabatic Expansion
1.13 Heat Engine and Efficiency
1.14 Reversible and Irreversible Processes
1.15 Carnot’s Engine and Camot’s Cycle
1.16 Two Carnot Engines Operating in Series
1.17 Second Law of thermodynamics
1.18 Carnot’s Theorem;
1.19 Entropy
1.20 Change In Entropy in Reversible and irreversible Processes
1:21 Principle of Increase of Entropy or Degradation of Energy
1.22 Formulation of the Second Law In Terms of Entropy
1.23 Clausius Insquallty
1.24 Change in Entropy of a Solid or Liquid
1.25 Entropy of Steam..
1.26 Entropy of a Perfect Gas
Exercises with Multiple Choice Questions

Chapter 2. Thermodynamical Relations With Applications

2.1 Thermodynamic Functions and Maxwell’s Relations
2.2 Deduction from Thermodynamical Relations
2.3. Some Other Properties of Thermodynamic Potentials
2.4 Relation of Fand G with the Parameters of the System
2.5 Thermodynamic Equilibria
2.6 Theorem of Maximum Work
2.7. Nernst’s heat Theorem or the Third law of Thermodynamics
2n8 Consequences of the Third Law.
2:9 Phase, Component and Variation
2:10. Gibb’s Phase Rule
2.11 Chemical Potential
2.12 Vapour Pressure Relation: The Chemical Constant
Exercise with Multiple Choice Questions

Chapter 3. Concepts of Thermal Radiation

3.1 Thermodynamics and Radiation
3.3 Some Definitions
3.4 Energy Density of Radiation in an Isothermal (Uniform Temperature) Enclosure
3.5 Black-Body
3.6 Kirchhoff Law and its Important Applications
3.7. Black Body Radiations
3.9 Stefan-Boltzmann Law
3.10 Determination of Stefan’s Constant
3.12 Spectral Distribution of Radiation Energy
3.13 Number of resonators per unit Volume Lying in the Frequency Range vand v + OV
3.14 Rayleigh-Jean’s law of Spectral Distribution of Energy
.3.15 Planck’s Radiation Lsw
3.16 Experimental Verification of Planck’s Radiation Law and Comparison with other Formulae
3.17 Impacts and Utility of Planck’s Law
Exercises with Multiple Choice Questions

Chapter 4. Concepts of Heat Conduction

4.1 Heat Conduction
4.2 Fundamental Equation of Heat Flow
4.3 Thermoelectric Conductivity (or Diffusivity)
4.4 Thermal Resistance
4.5 Temperature of Interface and Net Flow of Heat when Bars are Connected in Series
4.6 Equivalent Thermal Conductivity.
4.7-Rectillnear Flow of Heat Along a Metal Bar: Fourier’s Equation of Heat Flow
4.8 Ingen-hausz’s.Experiment Comparisons of Electrical Conductivities
4.9 Temperature Distribution in a Cylinder Heated Along the Axis (Cylindrical Flow of Heat)
4.10 Temperature Distribution in a spherical Shell Heated at the Centre (Radial Flow of Heat)
4.11 Periodic Flow of Heat
4.12 Relation Between Thermal and Electrical Copnductivity: Wiedemann Franz Law
Exercises with Multiple Choice Questions

Chapter 5. Kinetic Theory of Gases

5.1 Introduction
5.2 Maxwell-Boltzmann’s Law of Distribution of Velocities
5.3 Experimental Test of Maxwell’s Law
5.4 The Mean Free Path ..
5.5 Order and Variation of Mean Free Path
5.6 Mean Free Path and Collision Probability
5.7 Law of Distribution of Free Path (or the Probability of a Free Path of Given Length)
5.8 Experimental Determination of Mean Free Path a
5.9 Transport Phenomena
5.10 Viscosity
5.11 Agreement between Theory and Observations for the Coefficient of Viscosity
5.12 Thermal Conductivity
5.13 Variation of Conductivity with Pressure and Temperature
5.14 Diffusion
5.15 The Brownian Motion
5.16 Langevin’s Thecry
5.17 Einstein’s Theory of the Translational Brownian Motion
5.18 Experimental Verification of Brownian Movement Equation and Determination of Avogadro Number
5.19 Molecular Diameters
Exercises with Multiple Choice Questions

Chapter 6. Principles of Statistical Mechanics : Classical Statistics

6.1 Introduction to Statistical Mechanics
6.2 Probability
6.3 Probability of Considerations of Tossing of Coins
6.4 Distribution of n molecules in two halves of a box
6.5 Cases with Weightage; General Case
6.6 Phase-Space
6.7 Ensembles
6.8 Density of Distribution in the Phase-Space
6.9 Liouville’s Theorem
6.10 Density of Phase Points in a Classical Ensemble
6.11 Statistical Equilibrium
6.12 Postulate of Equal a Priori Probability
6.13 Microstates and Macrostates
6.14 General Expression for Probability
6.15 Stirling’s Formula
6.16 The Most Probable Distribution
6.17 Fuctuations and their dependence on N
6.18 Time and Ensemble Averages
6.19 Division of Phase.Space into Cells
6.20 Number of Microstates in the Energy Range Eto E+ SE
6.21 Maxwell Boltzmann Distoibution Law
6.22 Maxwell’s Distribution Law of Velocities; the Function F(Vx)
6.23 Maxwell’s Distribution Law of Speeds: The Function Flv
6.24 Most Probable speed, Average speed and Root Mean Square Speed
6.25 Degrees of Freedom:
6.26 Law of Equipartition of Energy
6.27 Atomicity of Gases
6.28 Interpretation of Temperature
6.29 The Condition of Equilibrium between two Systems in Thermal Contact-The B Parameter
6.30 Entropy and Probability
6.31 Probability of Distribution and Entropy of a Two Level System
6.32 Negative Temperature
Exercises with Multiple Choice Questions

Chapter 7. Method of Ensembles : Partition Functions

7.0 Introduction
7.1 Micro Canonical Ensemble
7.2 Entropy in Statistical Mechanics
7.3 Condition for Equilibrium
7.4 Connection between Statistical and Thermodynamic Quantities
7.5 Perfect gas in Microcanonical Ensemble
7.6 Partition Functions
7.7 Partition Function and Thermodynamical Quantities
7.8 Entropy of a Perfect Gas: Gibb’s Paradox
7.9 Gibb’s Canonical Ensemble
7.10 Thermodynamical Functions for the Canonical Ensemble and Partition Function
7.11 Statistical Mechanical Formulation of third Law of Thermodynamics
7.12 Perfect Monatomic gas in Canonical Ensemble
7.13 Maxwellian Velocity Distribution from Canonical Distribution
7.14 Equipartition Theorem
7.15 Grand Caanonical Ensemble
7.16 Partition Function and Thermodynamic Function for Grand Canonical Ensemble
7.17 Perfect Gas in Grand Canonical Ensemble
7.18 Comparison of Various Ensembles
7.19 Separation of Partition Functions
7.20 Partition Functions and Thermodynamic Properties of a Diatomic Molecule
7.21 Theory of Imperfect Gases; Viral Coefficients
7.22 Determination of Virial Coefficients
Exercises with Multiple Choice Questions

Chapter 8. Quantum Statistics

8.1 Introduction
8.2 Basic Concepts of Quantum Mechanics
8.3 Postulates of Quantum Mechanics
8.4 Quantum Statistics of Identical Particles (Indistinguishability and Quantum Statistics)
8.5 Symmetric and Antisymmetric Wave Functions
8.6 Construction of Symmetric and Anti-Symmetric wave Functions from Unsymmetrized Function;
Exchange Degeneracy
8.7 Average Value and Quantum Statistics
8.8 Statistical Weight or a Priori Probability
8.9 Density Matrix
8.10 Time Dependence of Density Matrix
8.11 Density Matrix in Microcanonical, Canonical and Grand Canonical Ensembles
8.12 Bose Einstein Statistics : Bose Einstein Distribution Law
8.13 Fermi-Dirac Statistics : Femi Dirac Distribution Law .
8.14 Maxwell-Boltzmann Statistics : Maxwell’s Boltzmann’s Distribution Law
8.15 Evaluation of the Constants d and B.
8.16 Results and Comparision of Three Statistics
-8.18 Grand Canonical Ensemble and Quantum Statistics
(Bose-Einstein and Fermi-Dirac Grand Partition Functions)
8.19 Bose-Einstein Gas
8.19 (a) Maxwell-Boltzmann Distribution as a Limiting Case of Bose-Einstein Distribution
8.19 (b) Degeneracy and Bose-Einstein Condensation
8.20 Fermi-Dirac Gas
8.20 (a) Degeneracy
8.21 Thermodynamic Properties of Degenerate Fermi-Dirac Gas
8.22 Electron Gas in Metals
8.23 Specific Heat Anomaly of Metals and its Solution
8.24 Thermionic Emission
8.25 Magnetic Susceptibility of Free Electrons
8.26 White Dwarts
8.27 Quantum Theory of Diatomic Molecules
8.28 Nuclear Spin Statistics : Ortho and Para Hydrogen
Exercises with Multiple Choice Questions

Chapter 9. Quantum Theory of Specific Heats

9.1 Introduction : The Dulong and Petit’s Law
9.2 Einstein’s Theory of Specific Heat of Solids..
9.3 Deby’s Theory of Specific Heat of Solids
9.4 Comparison of the Debye Formulla with Experiments
9.5 Criticism of Debye’s Theory
9.6 Improvement upon Debye’s Theory (Bom-Karman Theory)
9.7 Spécific Heat of Gases
9.8 Variation of Specific Heat of Diatomic Gases with Temperature
9.9 Quantization of Rotational Motion and its Contribution to Specific Heats
9.10 Quantization of Vibrational Motion and its Contribution to Specific irleats
9.11 Calculation of Specific heat of Diatomic Gases
9.12 Variation of Specific Heat of Hydrogen
Exercises with Multiple Choice Questions
10. Low Temperature Physics
10.1 Introduction
10.2 Production of Low Temperatures
10.3 Approach to Absolute zero by Adiabatic Demagnetization
10.4 Liquefaction of Gases
10.5 Measurement of Low Temperatures
10.6 Gonversion of Magnetic Temperature to Kelvin Temperature
10.7 Helium I and II.
10.8 Some Peculiar Properties of Helium Ii
10.9 Attempted Explanation of the Properties of Liquid Helium !!
10.10 Landau’s Theory
10.11 London’s Theory
10.12 Tiszas’s two Fluid Model
10.13 Second Sound
10.14 Feynmann’s Theory
10.15 Superconductivity
Exercises with Multiple Choice Questions

Chapter 11. Transport Theory

11.1 Introduction
11.2 Distribution Function
11.3 Boltzmann Transport Equation
11.4 Kinetic Formulation of Transport Problems: Chamber’s Equation
11.5 Electrical and Thermal Conductivities in an Electron Gas
11.6 Magneto-Resistance
11.7 Viscosity from Boltzmann Equation
Exercises with Multiple Choice Questions

Chapter 12. Fluctuations and Irreversible Processes

12.1 Introduction
12.2 An illustration of Fluctuation : Molecules in two halves of a box
12.3 Fluctuations in Ensembles
12.4 Probability of one-Dimensional Random Walk
12.5 Motion Due to Fluctuating Force : Fokker Planck Equation.
12.6 Fourier Analysis of Random Function: Wiener-Khintchine Theorem
12.7 Electrical Noise (Nyquist Theorem)
12.8 Thermodynamic Irreversible Processes
12.9 Proof of Onsager Reciprocal Relations
12.10 Applications of Onsager Relation
Exercises with Multiple Choice Questions

Chapter 13. Phase Transitions

13.1 Triple Point
13.2 Vander Waal’s Equation and Phase Transition
13.3 Matter Near the Critical Point
13.4 First and Second Order Phase Transitions
13.5 Ehrenfe’st’s Equations”:
13.6 Critical Exponent
13.7 Ising Model ..
13.8 One Dimensional Ising Model
13.9 Yang and Lee Theory of Phase Transitions
13.10 Landau Theory of Phase Transitions
Exercises with Multiple Choice Questions
INDEX

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