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| Preface | |
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| The Kinetic Theory of Gases | |
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| Introduction | |
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| Velocity and Position Distributions of Molecules in a Gas | |
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| Avogadro's law, or the equation of state of an ideal gas | |
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| Temperature and thermal equilibrium | |
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| Equipartition of energy per molecule and its constituent parts--a fundamental problem | |
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| The density in an isothermal atmosphere--the Boltzmann factor in the potential energy | |
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| The Maxwell-Boltzmann distribution | |
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| Averages and distributions | |
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| Brownian Motion | |
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| Historical background | |
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| Characteristic scales of Brownian motion | |
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| Random walk | |
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| Brownian motion, random force and friction: the Langevin equation | |
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| Solving the Langevin equation: approximations and orders of magnitude | |
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| Applications and implications | |
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| Transport Coefficients | |
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| Introduction | |
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| The mean free path and mean free time | |
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| Self-diffusion | |
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| The mobility coefficient | |
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| The connection between the diffusion coefficient and the mobility | |
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| Viscosity and thermal conductivity | |
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| Appendix: a more detailed calculation of the diffusion coefficient | |
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| Self-assessment exercises | |
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| Solutions to exercises in the text | |
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| Solutions to self-assessment exercises | |
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| Statistical Physics with Paramagnets | |
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| Introduction | |
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| Essential Background in Thermodynamics | |
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| The first law | |
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| The second law and the entropy | |
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| Thermodynamic potentials | |
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| The third law | |
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| Thermodynamics with Magnetic Variables | |
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| Introduction | |
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| The first law in magnetic variables | |
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| Microscopic States and Averages | |
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| Magnetic states, angular momentum and paramagnetism | |
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| Microscopic states, observables | |
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| Probabilities and averages | |
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| Isolated Paramagnet--Microcanonical Ensemble | |
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| Number of states and probabilities | |
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| Calculating averages and correlations | |
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| Numerical examples and Stirling's formula | |
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| Isolated Paramagnet--Subsystems and Temperature | |
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| Microscopic states and thermodynamic equilibrium | |
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| [beta] and the temperature | |
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| Sharpness of the maximum | |
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| Identification of temperature and entropy | |
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| Negative temperature | |
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| Summary | |
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| Paramagnet at a Given Temperature | |
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| The canonical ensemble | |
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| The partition function and thermodynamic quantities | |
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| Susceptibility and specific heat of a paramagnet | |
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| Paramagnet with J ] 1/2 | |
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| Order, Disorder and Entropy | |
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| Comparison with Experiment | |
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| Summary | |
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| Self-assessment exercises | |
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| Solutions to exercises in the text | |
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| Solutions to self-assessment exercises | |
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| Statistical Physics and Thermodynamics | |
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| Introduction | |
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| The Canonical Ensemble and Thermodynamics | |
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| The partition function and the internal energy | |
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| Thermodynamic work | |
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| Entropy, free energy, the first and second laws | |
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| The paramagnet--revisited | |
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| On the statistical meaning of the free energy | |
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| Harmonic Oscillator and Einstein Solid | |
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| Microscopic states | |
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| Partition function for oscillators | |
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| Einstein's solid | |
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| Statistical Mechanics of Classical Systems | |
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| Statistical mechanics of a single particle | |
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| Statistical mechanics of a classical gas | |
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| Statistical Mechanics of an Ideal Gas | |
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| The ideal gas | |
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| Mixtures of ideal gases--Dalton's law | |
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| Maxwell-Boltzmann distribution and equipartition | |
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| Ideal gas of quantum particles | |
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| The Gibbs Paradox and the Third Law | |
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| Two difficulties | |
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| The Gibbs paradox and its resolution | |
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| Remarks on the third law of thermodynamics | |
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| Summary | |
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| Fluctuations and Thermodynamic Quantities | |
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| Paramagnet: fluctuations in the magnetization | |
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| Energy fluctuations and the specific heat | |
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| Summary | |
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| Self-assessment exercises | |
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| Solutions to exercises in the text | |
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| Solutions to self-assessment exercises | |
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| From Ideal Gas to Photon Gas | |
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| Introduction | |
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| An Ideal Gas of Molecules with Internal Degrees of Freedom | |
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| Center of mass and internal motions | |
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| Kinematics of a diatomic molecule | |
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| Gas of general composite molecules | |
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| Diatomic gas: classical treatment | |
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| Diatomic molecules: vibration and rotation | |
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| The equipartition principle and its violation | |
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| Diatomic gas--quantum calculation | |
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| Gases in Chemical Reactions | |
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| Conditions for chemical equilibrium | |
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| The law of mass action | |
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| Dissociation in a diatomic gas | |
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| Phonon Gas and the Debye Model | |
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| Sound waves in a crystal | |
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| Vibrational modes, phonons and enumeration of states | |
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| The Debye model | |
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| Thermodynamics of Electromagnetic Radiation | |
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| General considerations of radiation at thermal equilibrium | |
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| Radiation density | |
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| Black body radiation | |
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| Absorption and emission of radiation--Kirchhoff's law | |
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| Role of black body radiation in modern physics | |
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| Calculation of Some Integrals | |
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| Self-assessment exercises | |
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| Solutions to exercises in the text | |
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| Solutions to self-assessment exercises | |
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| Of Fermions and Bosons | |
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| Introduction | |
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| Grand Canonical Ensemble | |
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| Definitions and motivation | |
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| Connection to thermodynamics | |
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| Statistical Mechanics of Identical Quantum Particles | |
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| Classification of states--occupation numbers | |
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| Quantum statistics--many-particle states | |
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| Thermodynamics of fermions and bosons | |
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| Average occupation numbers | |
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| Electrical Conductivity in Metals | |
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| The Drude model | |
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| A critique of the Drude model | |
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| The Sommerfeld model | |
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| Electrons at high and low temperatures | |
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| Metals at room temperature | |
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| Thermodynamics of the Sommerfeld model | |
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| Boson Gas | |
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| Bose-Einstein distribution | |
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| Chemical potential at low temperatures | |
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| Bose-Einstein condensation | |
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| Superfluidity | |
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| Bose-Einstein condensation in helium | |
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| Viscosity of a superfluid | |
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| Fermi liquid and superconductivity | |
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| Calculation of Some Integrals | |
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| Self-assessment exercises | |
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| Solutions to exercises in the text | |
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| Solutions to self-assessment exercises | |
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| Index | |