Introductory Statistical Thermodynamics

1 IntroductionPart I QUANTUM DESCRIPTION OF SYSTEMS2 Introduction and Basic Concepts2.1 Systems of Identical Particles2.2 Quantum Description of Particles2.3 Problems with Solutions3 Kinetic energy of Translational Motion3.1 Hamiltonian of Translational Motion3.2 Schrödinger Equation for Translational Motion3.4 Normalization of the Wave function3.5 Quantized Energy of Translational Motion3.6 Problems with Solutions4 Energy of Vibrations4.1 Hamiltonian of Vibrations4.2 Solution of the Schrödinger equation4.3 Quantized Energy of Vibrations4.4 Hermite Polynomials4.5 Normalization of the Wave Function4.6 Problems with Solutions5 Kinetic Energy of Rotations5.1 Hamiltonian of Rotations5.1.1 Kinetic Energy and Hamiltonian Operator5.1.2 Angular Momentum Operator5.2 Solution of the Schrödinger equation5.3 Quantized Energy of Rotations5.4 Legendre Polynomials5.5 Normalization of the Wave function5.6 Spin Angular Momentum5.7 Problems with SolutionsPart II THERMODYNAMICS OF SYSTEMS6 Number of accessible states and Entropy6.1 Introduction and Definitions6.2 Calculation of the Number of accessible States6.2.1 Classical Number of Accessible States6.2.2 Number of Accessible States for Bosons6.2.3 Number of Accessible States for Fermions6.3 Problems with Solutions7 Equilibrium States of Systems7.1 Equilibrium Conditions7.2 Occupation Numbers of Energy Levels7.3 Concept of Temperature7.4 Problems with Solutions8 Thermodynamic Variables8.1 Free Energy and the Partition Function8.2 Internal Energy. Caloric State Equation8.3 Pressure. Thermal State Equation8.4 Classification of Thermodynamic Variables8.5 Problems with Solutions9 Macroscopic Thermodynamics9.1 Changes of States. Heat and Work9.2.1 Zeroth Law of Thermodynamics9.2.2 First Law of Thermodynamics9.2.3 Second Law of Thermodynamics9.2.4 Third Law of Thermodynamics9.3 Open Systems9.4 Thermal Properties of Systems9.4.1 Isobaric Expansion9.4.2 Isochoric Expansion9.4.3 Isothermal Expansion9.4.4 Relation between Thermal Coefficients9.5 Caloric Properties of Systems9.5.1 Specific Heat at Constant Volume cV9.5.2 Specific Heat at Constant Pressure cP9.5.3 Relation between Specific Heats9.6 Relations between Thermodynamic Coefficients9.7 Problems with Solutions10 Variable Number of Particles10.1 Chemical Potential10.2 Thermodynamic Potential10.3 Phases and Phase Equilibrium10.3.1 Latent Heat10.3.2 Clausius-Clapeyron Formula10.4 Problems with SolutionsPart III IDEAL AND NON-IDEAL GASES11 Ideal Monoatomic Gases11.1 Continuous Energy Spectrum11.2 Continuous Partition Function11.3 Partition Function of Ideal Monoatomic Gases11.4 Kinetic Theory of Ideal Monoatomic Gases11.4.1 Maxwell-Boltzmann’s Speed Distribution11.4.2 Most probable Speed of Gas Particles11.4.3 Average Speed of Gas Particles11.4.4 Root-Mean-Square Speed of Gas Particles11.4.5 Average Kinetic Energy and Internal Energy11.4.6 Equipartition Theorem11.5 Thermodynamics of Ideal Monoatomic Gases11.5.1 Caloric State Equation11.5.2 Thermal State Equation11.5.3 Universal and Particular Gas Constants11.5.4 Caloric and Thermal Coefficients11.6 Ideal Gases in External Potentials11.6.1 General Maxwell-Boltzmann distribution11.6.2 Harmonic and Anharmonic Oscillators11.6.3 Classical limit of Quantum Partition Function11.7 Problems with Solutions12 Ideal Diatomic Gases12.1 Rotations of Gas Particles12.2 Vibrations of Gas Particles12.3 Problems with Solutions13 Non-ideal Gases13.1 Partition Function for Non-ideal Gases13.2 Free Energy of Non-ideal Gases13.3 Free Energy of Particle Interactions13.4 Van der Waals Equation13.5 Caloric State Equation for Non-ideal Gases13.6 Specific Heats for Non-ideal Gases13.7 Problems with Solutions14 Quasi-static Thermodynamic Processes14.1 Isobaric Process14.2 Isochoric Process14.3 Isothermal Process14.4 Adiabatic Process14.5 Polytropic Process14.6 Cyclic Processes. Carnot Cycle14.7 Problems with SolutionsPart IV QUANTUM STATISTICAL PHYSICS15 Quantum Distribution Functions15.1 Entropy Maximization in Quantum Statistics15.1.1 The Case of Bosons15.1.2 The Case of Fermions15.2 Quantum Equilibrium Distribution15.3 Helmholtz Thermodynamic Potential15.4 Thermodynamics of Quantum Systems15.5 Evaluation of Integrals15.6 Problems with Solutions16 Electron Gases in Metals16.1 Ground State of Electron Gases in Metals16.2 Electron Gases in Metals at Finite Temperatures16.3 Chemical Potential at Finite Temperatures16.4 Thermodynamics of Electron Gases16.5 Problems with Solutions17 Photon Gas in Equilibrium17.1 Planck Distribution17.2 Thermodynamics of Photon Gas in Equilibrium17.3 Problems with Solutions18 Other examples of Boson Systems18.1 Lattice Vibrations and Phonons18.1.1 Vibration Modes18.1.2 Internal Energy of Lattice Vibrations18.2 Bose-Einstein Condensation18.3 Problems with Solutions19 Special Topics19.1 Ultrarelativistic Fermion Gas19.1.1 Ultrarelativistic Fermion Gas19.1.2 Ultrarelativistic Fermion Gas19.2 Thermodynamics of the Expanding Universe19.2.1 Internal Energy of Elementary-Particle Species19.2.2 Entropy per Volume Element19.3 Problems with SolutionsA Physical constantsBibliographyIndex