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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 | |