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E-grāmata: Statistical Theory of Heat

  • Formāts: PDF+DRM
  • Sērija : Graduate Texts in Physics
  • Izdošanas datums: 15-Nov-2016
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783319400495
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Statistical Theory of HeatPalielināt
  • Formāts: PDF+DRM
  • Sērija : Graduate Texts in Physics
  • Izdošanas datums: 15-Nov-2016
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783319400495
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Scheck"s textbook starts with a concise introduction to classical thermodynamics, including geometrical aspects. Then a short introduction to probabilities and statistics lays the basis for the statistical interpretation of thermodynamics. Phase transitions, discrete models and the stability of matter are explained in great detail. Thermodynamics has a special role in theoretical physics. Due to the general approach of thermodynamics the field has as a bridging function between several areas like the theory of condensed matter, elementary particle physics, astrophysics and cosmology. The classical thermodynamics describes predominantly averaged properties of matter, reaching from few particle systems and state of matter to stellar objects. Statistical Thermodynamics covers the same fields, but explores them in greater depth and unifies classical statistical mechanics with quantum theory of multiple particle systems. The content is presented as two tracks: the fast track for mast

er students, providing the essentials, and the intensive track for all wanting to get in depth knowledge of the field. Clearly labelled material and sections guide students through the preferred level of treatment. Numerous problems and worked examples will provide successful access to Statistical Physics and Thermodynamics.

Basic Notions of the Theory of Heat.- Thermodynamics: Classical Framework.- Geometric Aspects of Thermodynamics.- Probabilities, States, Statistics.- Mixed Phases, Phase Transitions, Stability of Matter.- Exercises, Hints and Selected Solutions.
1 Basic Notions of the Theory of Heat
1(38)
1.1 Introduction
1(1)
1.2 First Definitions and Propositions
1(8)
1.3 Microcanonical Ensemble and Ideal Gas
9(3)
1.4 The Entropy, a First Approach
12(6)
1.5 Temperature, Pressure and Chemical Potential
18(7)
1.5.1 Thermal Contact
18(5)
1.5.2 Thermal Contact and Exchange of Volume
23(1)
1.5.3 Exchange of Energy and Particles
24(1)
1.6 Gibbs Fundamental Form
25(2)
1.7 Canonical Ensemble, Free Energy
27(3)
1.8 Excursion: Legendre Transformation of Convex Functions
30(9)
2 Thermodynamics: Classical Framework
39(36)
2.1 Introduction
39(1)
2.2 Thermodynamic Potentials
39(7)
2.2.1 Transition to the Free Energy
39(1)
2.2.2 Enthalpy and Free Enthalpy
40(2)
2.2.3 Grand Canonical Potential
42(4)
2.3 Properties of Matter
46(3)
2.4 A Few Thermodynamic Relations
49(1)
2.5 Continuous Changes of State: First Examples
50(9)
2.6 Continuous Changes of State: Circular Processes
59(7)
2.6.1 Exchange of Thermal Energy Without Work
59(2)
2.6.2 A Reversible Process
61(1)
2.6.3 Periodically Working Engines
62(3)
2.6.4 The Absolute Temperature
65(1)
2.7 The Laws of Thermodynamics
66(6)
2.8 More Properties of the Entropy
72(3)
3 Geometric Aspects of Thermodynamics
75(30)
3.1 Introduction
75(1)
3.2 Motivation and Some Questions
75(2)
3.3 Manifolds and Observables
77(13)
3.3.1 Differentiable Manifolds
77(2)
3.3.2 Functions, Vector Fields, Exterior Forms
79(3)
3.3.3 Exterior Product and Exterior Derivative
82(5)
3.3.4 Null Curves and Standard Forms on Rn
87(3)
3.4 The One-Forms of Thermodynamics
90(5)
3.4.1 One-Forms of Heat and of Work
91(1)
3.4.2 More on Temperature
92(3)
3.5 Systems Depending on Two Variables Only
95(5)
3.6 *An Analogy from Mechanics
100(5)
4 Probabilities, States, Statistics
105(36)
4.1 Introduction
105(1)
4.2 The Notion of State in Statistical Mechanics
105(6)
4.3 Observables and Their Expectation Values
111(3)
4.4 Partition Function and Entropy
114(9)
4.5 Classical Gases and Quantum Gases
123(6)
4.6 Statistics, Quantum and Non-quantum
129(12)
4.6.1 The Case of Classical Mechanics
129(1)
4.6.2 Quantum Statistics
130(4)
4.6.3 Planck's Radiation Law
134(7)
5 Mixed Phases, Phase Transitions, Stability of Matter
141(56)
5.1 Introduction
141(1)
5.2 Phase Transitions
141(18)
5.2.1 Convex Functions and Legendre Transformation
142(9)
5.2.2 Phase Mixtures and Phase Transitions
151(5)
5.2.3 Systems with Two or More Substances
156(3)
5.3 Thermodynamic Potentials as Convex or Concave Functions
159(2)
5.4 The Gibbs Phase Rule
161(2)
5.5 Discrete Models and Phase Transitions
163(15)
5.5.1 A Lattice Gas
163(2)
5.5.2 Models of Magnetism
165(4)
5.5.3 One-Dimensional Models with and Without Magnetic Field
169(3)
5.5.4 Ising Model in Dimension Two
172(6)
5.6 Stability of Matter
178(19)
5.6.1 Assumptions and First Thoughts
179(3)
5.6.2 Kinetic and Potential Energies
182(3)
5.6.3 Relativistic Corrections
185(6)
5.6.4 Matter at Positive Temperatures
191(6)
6 Exercises, Hints and Selected Solutions
197(32)
Literature 229(2)
Index 231
Florian A. Scheck, professor emeritus at University of Mainz, Germany.Born in 1936, diploma degree 1962 , Ph.D. (Dr. rer.nat) 1964, both at U. Freiburg, Germany. Habilitation at U. Heidelberg 1968. Guest scientist at the Weizmann Instituteof Science, Rehovoth, (1964 1966), research assistant U. Heidelberg, (1966  1968), research fellow at CERN, Geneva, (1968 1970), head of theory groupSIN/PSI, lecturer and titular professor at ETH Zurich (1970 1976). Professor of theoretical Physics U. Mainz (1976 2005). Numerous visits as guest scientist or guest professor, Helsinki, Montpellier, Marseille, San José (Costa Rica), Bogota (Columbia).
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