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# Thermodynamics and Statistical Mechanics PHY 531

Syracuse

GPA 3.93

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This 10 page Class Notes was uploaded by Ms. Bryce Wisoky on Wednesday October 21, 2015. The Class Notes belongs to PHY 531 at Syracuse University taught by Staff in Fall. Since its upload, it has received 60 views. For similar materials see /class/225629/phy-531-syracuse-university in Physics 2 at Syracuse University.

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Date Created: 10/21/15

Thermodynamics and Statistical Mechanics PHY 531 Revised Schedule Lecture 1 Monday August 28th Syllabus Course Overview Hard copy syllabus Introductory lecture syllabus Introduction in thermodynamics General advise and hints Lecture 2 Wednesday August 30th pp 111 1 The first law of thermodynamics 11 Fundamental definitions 12 Thermometers 13 Different aspects of equilibrium 14 Functions of state Lecture 3 Friday September 1st pp 1321 15 Internal energy 16 Reversible changes 17 Enthalpy 18 Heat capacities Monday September 4 139 Labor Day No Classes Lecture 4 Wednesday September 6th pp 2023 and 2533 18 Heat capacity Continuation Examples for an ideal gas 19 Reversible adiabatic changes in an ideal gas 2 Entropy and the second law of thermodynamics 21 A first look at the entropy Lecture 5 Friday September 8th pp 3342 22 The second law of thermodynamics 23 The Carnot cycle 24 The equivalence of the absolute and the perfect gas scale of temperature Lecture 6 Monday September 1131pp3442 25 Definition of entropy 26 Measuring the entropy Thermodynamic potentials E1 E2 E3 Maxwell relations derived from thermodynamic potentials pp 302 305 Lecture 7 Wednesday September 13th Problems of thermodynamics Thermodynamic transformations Part I Lecture 8 Friday September 15th pp 4246 27 The law of increase of entropy Clausius inequality pp 42 48 28 Calculations of the increase in the entropy in irreversible processes 1 Problems of thermodynamics thermodynamic transformations Part II Lecture 9 Monday September 183 pp 4648 29 The approach to equilibrium Examples Lecture 10 Wednesday September 20th pp 5264 3 Probability and Statistics Lecture 11 Friday September 22nd pp 6770 The ideas of statistical mechanics Introduction Definition of entropy Lecture 12 Monday September 25th pp 8186 The second law of thermodynamics derived from statistical mechanics 14 Wednesday September 27 Exam 1 Lecture 13 Friday September 293 Problems of thermodynamics from Exam 1 Analysis of exam 1 Problems and their solutions 16 Monday October 2nd Yom Kippur No classes Lecture 14 Wednesday October 4th The canonical ensemble pp 9197 51 A system in contact with a heat bath 52 The partition function 53 Definition of the entropy in the canonical ensamble 54 The bridge to thermodynamics through Z Lecture 15 Friday October 6th The canonical ensemble Thermodynamic properties pp 97101 derived from microscopic principles 55 The condition for thermal equilibrium 56 Thermodynamic quantities from partition function 57 Example for two level system Lecture 16 Monday October 9th The canonical ensemble pp 101106 58 Single particle in one dirnensional box 59 Single particle in a three dirnensional box Lecture 17 1 Wednesday October 11th The canonical ensemble 116123 514 Equipartition theorem 515 Minimizing the free energy 5151 Minimizing the Helmholtz free energy 5152 Minimizing the Gibbs free energy Lecture 18 Friday October 1331 Statistical Mechanics of Identical particles pp 128134 61 Identical particles 62 Symmetric and antisymmetric wave functions 63 Bose particles or bosons 64 Fermi particles or fermions 65 Calculating the partition function for identical particles Lecture 19 Monday October 1631 Statistical Mechanics of Identical particles pp 134140 66 Spin 67 Identical particles localized on lattice sites Lecture 20 Wednesday October 18th Maxwell distribution pp 144146 71 The probability that a particle is in a quantum state Homework Problems and their solutions Lecture 21 Friday October 20th MaxwellBoltzmann distribution pp 146154 72 Density of states in k space 73 Single particle density of states in energy Lecture 22 Monday October 23rd MaxwellBoltzmann distribution pp 146154 74 The distribution of speeds of particles in a classical gas Lecture 23 Wednesday October 25th Homework problems and their solutions Chapter 7 Lecture 24 October 27th Chapter 8 Plank s distribution 81 Blackbody radiation pp 160166 83 Plank s distribution pp 167168 28 Monday October 30 139 Exam 2 Lecture 25 Wednesday November 1st Plank s distribution pp 172176 85 Derivation of the Plank distribution 86 The free energy Lecture 26 Friday November 3rd Chapter 9 Systems with variable number of particles pp 188193 91 Systems with variable number of particles 92 The condition for chemical equilibrium 93 The approach to chemical equilibrium Lecture 27 Monday November 63 Chapter 9 Systems with variable number of particles pp 193197 94 The chemical potential Lecture 28 Wednesday November 83 Chapter 9 Systems with variable number of particles pp 202207 97 The grand canonical ensemble 98 Absorption of atoms on surface sites 99 The grand potential Lecture 29 Friday November 103 Chapter 10LII Fermi and Bose particles pp 210215 101 Introduction 102 The statistical mechanics of identical particles Lecture 30 Monday November 133 Chapter 10LII Fermi and Bose particles pp 215222 103 The thermodynamic properties of a Fermi gas Lecture 31 Wednesday November 153 Chapter 10LII Fermi and Bose particles pp 229233 105 The thermodynamic properties of a non interacting Bose gas Lecture 32 Friday November 1731 Present Homework Problems of Chapter 9LII Lecture 33 Monday November 203 Chapter 11 Phase transitions pp 236239 111 Phases 112 Thermodynamic potential 38 Wednesday November 22 Thanksgiving Holiday 39 Friday November 24 1 Thanksgiving Holiday Lecture 34 Monday November 273 Chapter 11 Phase transitions pp 239244 113 Approxilnation 114 First order phase transition 115 Clapeyron equation Lecture 35 Wednesday November 293 Chapter 11 Phase transitions pp 245248 116 Phase separation 42 Friday December 15 Exam 3 Lecture 36 Monday December 43 Chapter 12 Continuous phase transitions pp 255 256 258 121 Introduction 122 lsing model 1221 Mean field theory Lecture 37 Wednesday December 6th Surprise lecture The unexpected quiz Are we prepared for the final exam Lecture 38 Friday December 83 Review Meeting for the final exam Final exam Friday December 15 1 800 1000 AM There will be three parts that will follow Bowley amp Sanchez Part I Thermodynamics Chapters 1 3 Part 11 Statistical mechanics I Chapters 4 8 Part III Statistical mechanics 11 Chapters 9 12 Thermodynamics and Statistical Mechanics PHY 531 Revised Schedule Lecture 1 Monday August 28th Syllabus Course Overview Hard copy syllabus Introductory lecture syllabus Introduction in thermodynamics General advise and hints Lecture 2 Wednesday August 30th pp 111 1 The first law of thermodynamics 11 Fundamental definitions 12 Thermometers 13 Different aspects of equilibrium 14 Functions of state Lecture 3 Friday September 1st pp 1321 15 Internal energy 16 Reversible changes 17 Enthalpy 18 Heat capacities Monday September 4 139 Labor Day No Classes Lecture 4 Wednesday September 6th pp 2023 and 2533 18 Heat capacity Continuation Examples for an ideal gas 19 Reversible adiabatic changes in an ideal gas 2 Entropy and the second law of thermodynamics 21 A first look at the entropy Lecture 5 Friday September 8th pp 3342 22 The second law of thermodynamics 23 The Carnot cycle 24 The equivalence of the absolute and the perfect gas scale of temperature Lecture 6 Monday September 1131pp3442 25 Definition of entropy 26 Measuring the entropy Thermodynamic potentials E1 E2 E3 Maxwell relations derived from thermodynamic potentials pp 302 305 Lecture 7 Wednesday September 13th Problems of thermodynamics Thermodynamic transformations Part I Lecture 8 Friday September 15th pp 4246 27 The law of increase of entropy Clausius inequality pp 42 48 28 Calculations of the increase in the entropy in irreversible processes 1 Problems of thermodynamics thermodynamic transformations Part II Lecture 9 Monday September 183 pp 4648 29 The approach to equilibrium Examples Lecture 10 Wednesday September 20th pp 5264 3 Probability and Statistics Lecture 11 Friday September 22nd pp 6770 The ideas of statistical mechanics Introduction Definition of entropy Lecture 12 Monday September 25th pp 8186 The second law of thermodynamics derived from statistical mechanics 14 Wednesday September 27 Exam 1 Lecture 13 Friday September 293 Problems of thermodynamics from Exam 1 Analysis of exam 1 Problems and their solutions 16 Monday October 2nd Yom Kippur No classes Lecture 14 Wednesday October 4th The canonical ensemble pp 9197 51 A system in contact with a heat bath 52 The partition function 53 Definition of the entropy in the canonical ensamble 54 The bridge to thermodynamics through Z Lecture 15 Friday October 6th The canonical ensemble Thermodynamic properties pp 97101 derived from microscopic principles 55 The condition for thermal equilibrium 56 Thermodynamic quantities from partition function 57 Example for two level system Lecture 16 Monday October 9th The canonical ensemble pp 101106 58 Single particle in one dirnensional box 59 Single particle in a three dirnensional box Lecture 17 1 Wednesday October 11th The canonical ensemble 116123 514 Equipartition theorem 515 Minimizing the free energy 5151 Minimizing the Helmholtz free energy 5152 Minimizing the Gibbs free energy Lecture 18 Friday October 1331 Statistical Mechanics of Identical particles pp 128134 61 Identical particles 62 Symmetric and antisymmetric wave functions 63 Bose particles or bosons 64 Fermi particles or fermions 65 Calculating the partition function for identical particles Lecture 19 Monday October 1631 Statistical Mechanics of Identical particles pp 134140 66 Spin 67 Identical particles localized on lattice sites Lecture 20 Wednesday October 18th Maxwell distribution pp 144146 71 The probability that a particle is in a quantum state Homework Problems and their solutions Lecture 21 Friday October 20th MaxwellBoltzmann distribution pp 146154 72 Density of states in k space 73 Single particle density of states in energy Lecture 22 Monday October 23rd MaxwellBoltzmann distribution pp 146154 74 The distribution of speeds of particles in a classical gas Lecture 23 Wednesday October 25th Homework problems and their solutions Chapter 7 Lecture 24 October 27th Chapter 8 Plank s distribution 81 Blackbody radiation pp 160166 83 Plank s distribution pp 167168 28 Monday October 30 139 Exam 2 Lecture 25 Wednesday November 1st Plank s distribution pp 172176 85 Derivation of the Plank distribution 86 The free energy Lecture 26 Friday November 3rd Chapter 9 Systems with variable number of particles pp 188193 91 Systems with variable number of particles 92 The condition for chemical equilibrium 93 The approach to chemical equilibrium Lecture 27 Monday November 63 Chapter 9 Systems with variable number of particles pp 193197 94 The chemical potential Lecture 28 Wednesday November 83 Chapter 9 Systems with variable number of particles pp 202207 97 The grand canonical ensemble 98 Absorption of atoms on surface sites 99 The grand potential Lecture 29 Friday November 103 Chapter 10LII Fermi and Bose particles pp 210215 101 Introduction 102 The statistical mechanics of identical particles Lecture 30 Monday November 133 Chapter 10LII Fermi and Bose particles pp 215222 103 The thermodynamic properties of a Fermi gas Lecture 31 Wednesday November 153 Chapter 10LII Fermi and Bose particles pp 229233 105 The thermodynamic properties of a non interacting Bose gas Lecture 32 Friday November 1731 Present Homework Problems of Chapter 9LII Lecture 33 Monday November 203 Chapter 11 Phase transitions pp 236239 111 Phases 112 Thermodynamic potential 38 Wednesday November 22 Thanksgiving Holiday 39 Friday November 24 1 Thanksgiving Holiday Lecture 34 Monday November 273 Chapter 11 Phase transitions pp 239244 113 Approxilnation 114 First order phase transition 115 Clapeyron equation Lecture 35 Wednesday November 293 Chapter 11 Phase transitions pp 245248 116 Phase separation 42 Friday December 15 Exam 3 Lecture 36 Monday December 43 Chapter 12 Continuous phase transitions pp 255 256 258 121 Introduction 122 lsing model 1221 Mean field theory Lecture 37 Wednesday December 6th Surprise lecture The unexpected quiz Are we prepared for the final exam Lecture 38 Friday December 83 Review Meeting for the final exam Final exam Friday December 15 1 800 1000 AM There will be three parts that will follow Bowley amp Sanchez Part I Thermodynamics Chapters 1 3 Part 11 Statistical mechanics I Chapters 4 8 Part III Statistical mechanics 11 Chapters 9 12

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