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stp_tableofcontents - Contents 1 From Microscopic to...

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Contents 1 From Microscopic to Macroscopic Behavior 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Some Qualitative Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Doing Work and the Quality of Energy . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Some Simple Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.5 Measuring the Pressure and Temperature . . . . . . . . . . . . . . . . . . . . . . . 15 1.6 Work, Heating, and the First Law of Thermodynamics . . . . . . . . . . . . . . . . 19 1.7 *The Fundamental Need for a Statistical Approach . . . . . . . . . . . . . . . . . . 19 1.8 *Time and Ensemble Averages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.9 Models of Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.9.1 The ideal gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.9.2 Interparticle potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.9.3 Lattice models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.10 Importance of Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.11 Dimensionless Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.12 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.13 Supplementary Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.13.1 Approach to equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.13.2 Mathematics refresher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Vocabulary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Additional Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Suggestions for Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2 Thermodynamic Concepts 31 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.2 The System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3 Thermodynamic Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 i
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CONTENTS ii 2.4 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.5 Pressure Equation of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.6 Some Thermodynamic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.7 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.8 The First Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.9 Energy Equation of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.10 Heat Capacities and Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.11 Quasistatic Adiabatic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.12 The Second Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.13 The Thermodynamic Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.14 The Second Law and Heat Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.15 Entropy Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.16 Equivalence of Thermodynamic and Ideal Gas Scale Temperatures . . . . . . . . . 70 2.17 The Thermodynamic Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 2.18 The Fundamental Thermodynamic Relation . . . . . . . . . . . . . . . . . . . . . . 72 2.19 The Entropy of an Ideal Classical Gas . . . . . . . . . . . . . . . . . . . . . . . . . 74 2.20 The Third Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 74 2.21 Free Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 2.22 Thermodynamic Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2.23 *Applications to Irreversible Processes . . . . . . . . . . . . . . . . . . . . . . . . . 84 2.23.1 Joule or free expansion process . . . . . . . . . . . . . . . . . . . . . . . . . 85 2.23.2 Joule-Thomson process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 2.24 Supplementary Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 2.24.1 The mathematics of thermodynamics . . . . . . . . . . . . . . . . . . . . . . 88 2.24.2 Thermodynamic potentials and Legendre transforms . . . . . . . . . . . . . 91 Vocabulary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Additional Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Suggestions for Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 3 Concepts of Probability 106 3.1 Probability in Everyday Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 3.2 The Rules of Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 3.3 Mean Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 3.4 The Meaning of Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 3.4.1
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