Fighting Monsters Part 2

All macroscopic systems consist ultimately of atoms obeying the laws of quantum mechanics. That premise forms the basis for this comprehensive text, intended for a first upper-level course in statistical and thermal physics. Reif emphasizes that the combination of microscopic concepts with some statistical postulates leads readily to conclusions on a purely macroscopic level. The author s writing style and penchant for description energize interest in condensed matter physics as well as provide a conceptual grounding with information that is crystal clear and memorable. Reif first introduces basic probability concepts and statistical methods used throughout all of physics. Statistical ideas are then applied to systems of particles in equilibrium to enhance an understanding of the basic notions of statistical mechanics, from which derive the purely macroscopic general statements of thermodynamics. Next, he turns to the more complicated equilibrium situations, such as phase transformations and quantum gases, before discussing nonequilibrium situations in which he treats transport theory and dilute gases at varying levels of sophistication. In the last chapter, he addresses some general questions involving irreversible processes and fluctuations. A large amount of material is presented to facilitate students later access to more advanced works, to allow those with higher levels of curiosity to read beyond the minimum given on a topic, and to enhance understanding by presenting several ways of looking at a particular question. Formatting within the text either signals material that instructors can assign at their own discretion or highlights important results for easy reference to them. Additionally, by solving many of the 230 problems contained in the text, students activate and embed their knowledge of the subject matter. Title Page Preface Contents Chapter 1: Introduction to Statistical Methods Random Walk and Binomial Distribution 1.1 Elementary statistical concepts and examples 1.2 The simple random walk problem in one dimension 1.3 General discussion of mean values 1.4 Calculation of mean values for the random walk problem 1.5 Probability distribution for large N 1.6 Gaussian probability distributions General Discussion of the Random Walk 1.7 Probability distributions involving several variables 1.8 Comments on continuous probability distributions 1.9 General calculation of mean values for the random walk 1.10 Calculation of the probability distribution 1.11 Probability distribution for large N Suggestions for Supplementary Reading Problems Chapter 2: Statistical Description of Systems of Particles Statistical Formulation of the Mechanical Problem 2.1 Specification of the state of a system 2.2 Statistical ensemble 2.3 Basic postulates 2.4 Probability calculations 2.5 Behavior of the density of states Interaction between Macroscopic Systems 2.6 Thermal interaction 2.7 Mechanical interaction 2.8 General interaction 2.9 Quasi-static processes 2.10 Quasi-static work done by pressure 2.11 Exact and "inexact" differentials Suggestions for Supplementary Reading Problems Chapter 3: Statistical Thermodynamics Irreversibility and the Attainment of Equilibrium 3.1 Equilibrium conditions and constraints 3.2 Reversible and irreversible processes Thermal Interaction between Macroscopic Systems 3.3 Distribution of energy between systems in equilibrium 3.4 The approach to thermal equilibrium 3.5 Temperature 3.6 Heat reservoirs 3.7 Sharpness of the probability distribution General Interaction between Macroscopic Systems 3.8 Dependence of the density of states on the external parameters 3.9 Equilibrium between interacting systems 3.10 Properties of the entropy Summary of Fundamental Results 3.11 Thermodynamic laws and basic statistical relations 3.12 Statistical calculation of thermodynamic quantities Suggestions for Supplementary Reading Problems Chapter 4: Macroscopic Parameters and Their Measurement 4.1 Work and internal energy 4.2 Heat 4.3 Absolute temperature 4.4 Heat capacity and specific heat 4.5 Entropy 4.6 Consequences of the absolute definition of entropy 4.7 Extensive and intensive parameters Suggestions for Supplementary Reading Problems Chapter 5: Simple Applications of Macroscopic Thermodynamics Properties of Ideal Gases 5.1 Equation of state and internal energy 5.2 Specific heats 5.3 Adiabatic expansion or compression 5.4 Entropy General Relations for a Homogeneous Substance 5.5 Derivation of general relations 5.6 Summary of Maxwell relations and thermodynamic functions 5.7 Specific heats 5.8 Entropy and internal energy Free Expansion and Throttling Processes 5.9 Free expansion of a gas 5.10 Throttling (or Joule-Thomson) Process Heat Engines and Refrigerators 5.11 Heat engines 5.12 Refrigerators Suggestions for Supplementary Reading Problems Chapter 6: Basic Methods and Results of Statistical Mechanics Ensembles Representative of Situations of Physical Interest 6.1 Isolated system 6.2 System in contact with a heat reservoir 6.3 Simple applications of the canonical distribution 6.4 System with specified mean energy 6.5 Calculation of mean values in a canonical ensemble 6.6 Connection with thermodynamics Approximation Methods 6.7 Ensembles used as approximations 6.8 Mathematical approximation methods Generalizations and Alternative Approaches 6.9 Grand canonical and other ensembles 6.10 Alternative derivation of the canonical distribution Suggestions for Supplementary Reading Problems Chapter 7: Simple Applications of Statistical Mechanics General Method of Approach 7.1 Partition functions and their properties Ideal Monatomic Gas 7.2 Calculation of thermodynamic quantities 7.3 Gibbs paradox 7.4 Validity of the classical approximation The Equipartition Theorem 7.5 Proof of the theorem 7.6 Simple applications 7.7 Specific heats of solids Paramagnetism 7.8 General calculation of magnetization Kinetic Theory of Dilute Gases in Equilibrium 7.9 Maxwell velocity distribution 7.10 Related velocity distributions and mean values 7.11 Number of molecules striking a surface 7.12 Effusion 7.13 Pressure and momentum transfer Suggestions for Supplementary Reading Problems Chapter 8: Equilibrium between Phases or Chemical Species General Equilibrium Conditions 8.1 Isolated system 8.2 System in contact with a reservoir at constant temperature 8.3 System in contact with a reservoir at constant temperature and pressure 8.4 Stability conditions for a homogeneous substance Equilibrium between Phases 8.5 Equilibrium conditions and the Clausius-Clapeyron equation 8.6 Phase transformations and the equation of state Systems with Several Components; Chemical Equilibrium 8.7 General relations for a system with several components 8.8 Alternative discussion of equilibrium between phases 8.9 General conditions for chemical equilibrium 8.10 Chemical equilibrium between ideal gases Suggestions for Supplementary Reading Problems Chapter 9: Quantum Statistics of Ideal Gases Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac Statistics 9.1 Identical particles and symmetry requirements 9.2 Formulation of the statistical problem 9.3 The quantum distribution functions 9.4 Maxwell-Boltzmann statistics 9.5 Photon statistics 9.6 Bose-Einstein statistics 9.7 Fermi-Dirac statistics 9.8 Quantum statistics in the classical limit Ideal Gas in the Classical Limit 9.9 Quantum states of a single particle 9.10 Evaluation of the partition function 9.11 Physical implications of the quantum-mechanical enumeration of states 9.12 Partition functions of polyatomic molecules Black-Body Radiation 9.13 Electromagnetic radiation in thermal equilibrium inside an enclosure 9.14 Nature of the radiation inside an arbitrary enclosure 9.15 Radiation emitted by a body at temperature T Conduction Electrons in Metals 9.16 Consequences of the Fermi-Dirac distribution 9.17 Quantitative calculation of the electronic specific heat Suggestions for Supplementary Reading Problems Chapter 10: Systems of Interacting Particles Solids 10.1 Lattice vibrations and normal modes 10.2 Debye approximation Nonideal Classical Gas 10.3 Calculation of the partition function for low densities 10.4 Equation of state and virial coefficients 10.5 Alternative derivation of the van der Waals equation Ferromagnetism 10.6 Interaction between spins 10.7 Weiss molecular-field approximation Suggestions for Supplementary Reading Problems Chapter 11: Magnetism and Low Temperatures 11.1 Magnetic work 11.2 Magnetic cooling 11.3 Measurement of very low absolute temperatures 11.4 Superconductivity Suggestions for Supplementary Reading Problems Chapter 12: Elementary Kinetic Theory of Transport Processes 12.1 Collision time 12.2 Collision time and scattering cross section 12.3 Viscosity 12.4 Thermal conductivity 12.5 Self-diffusion 12.6 Electrical conductivity Suggestions for Supplementary Reading Problems Chapter 13: Transport Theory Using the Relaxation-Time Approximation 13.1 Transport processes and distribution functions 13.2 Boltzmann equation in the absence of collisions 13.3 Path integral formulation 13.4 Example: calculation of electrical conductivity 13.5 Example: calculation of viscosity 13.6 Boltzmann differential equation formulation 13.7 Equivalence of the two formulations 13.8 Examples of the Boltzmann equation method Suggestions for Supplementary Reading Problems Chapter 14: Near-Exact Formulation of Transport Theory 14.1 Description of two-particle collisions 14.2 Scattering cross sections and symmetry properties 14.3 Derivation of the Boltzmann equation 14.4 Equation of change for mean values 14.5 Conservation equations and hydrodynamics 14.6 Example: simple discussion of electrical conductivity 14.7 Approximation methods for solving the Boltzmann equation 14.8 Example: calculation of the coefficient of viscosity Suggestions for Supplementary Reading Problems Chapter 15: Irreversible Processes and Fluctuations Transition Probabilities and Master Equation 15.1 Isolated system 15.2 System in contact with a heat reservoir 15.3 Magnetic resonance 15.4 Dynamic nuclear polarization; Overhauser effect Simple Discussion of Brownian Motion 15.5 Langevin equation 15.6 Calculation of the mean-square displacement Detailed Analysis of Brownian Motion 15.7 Relation between dissipation and the fluctuating force 15.8 Correlation functions and the friction constant 15.9 Calculation of the mean-square velocity increment 15.10 Velocity correlation function and mean-square displacement Calculation of Probability Distributions 15.11 The Fokker-Planck equation 15.12 Solution of the Fokker-Planck equation Fourier Analysis of Random Functions 15.13 Fourier analysis 15.14 Ensemble and time averages 15.15 Wiener-Khintchine relations 15.16 Nyquist's theorem 15.17 Nyquist's theorem and equilibrium conditions General Discussion of Irreversible Processes 15.18 Fluctuations and Onsager relations Suggestions for Supplementary Reading Problems Appendices Numerical Constants Bibliography Answers to Selected Problems Index