Thermal and Statistical Physics: Concepts and Applications

Preface
UGC Approved Syllabus for Choice-Based Credit System
Laws of Thermodynamics
Thermodynamic Potentials
Kinetic Theory of Gases
Theory of Radiation
Statistical Mechanics
Thermal and Statistical Physics—Concepts and Applications
Salient Features
Contents
About the Author
1 Introduction
1.1 Origin of Thermodynamics
1.2 A Macroscopic Approach
1.3 The Thermodynamic Limit and Its Consequences
1.3.1 Intensive and Extensive Variables
1.4 System Versus Surrounding
1.4.1 A System in Thermodynamic Equilibrium
1.4.2 Thermodynamic Variables or Functions of State
1.4.3 Equation of a State
1.4.4 Physical Meaning of dV, dP and dT
1.5 Thermodynamic Reversibility
1.6 A Few Important Mathematical Results
1.6.1 The Reciprocal Theorem
1.6.2 Reciprocity Theorem
1.6.3 Perfect Differential
1.7 Solved Problems
1.8 Multiple Choice Questions
2 The Laws of Thermodynamics
2.1 The Zeroth Law
2.2 Concept of Work and Sign Convention
2.2.1 The Sign Convention
2.2.2 P-V Diagrams
2.2.3 Path Dependence of Work Done
2.2.4 Path Dependence of Heat-Transfer
2.3 Work Done in Various Systems
2.3.1 Work Done in Changing the Area of a Surface Film
2.3.2 Work Done in Changing the Area of a Liquid Drop
2.4 Historical Background Related to First Law of Thermodynamics
2.5 First Law of Thermodynamics
2.5.1 Applying First Law to Various Systems
2.5.2 Compression Work and Utility of Eq.2.12
2.6 Heat Capacities
2.6.1 Simpler form of ps: [/EMC pdfmark [/Subtype /Span /ActualText (upper C Subscript upper P) /StPNE pdfmark [/StBMC pdfmarkCPps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark, Definition of Enthalpy
2.6.2 Molar Heat Capacity
2.6.3 Specific Heats of Gas
2.7 Principle of Calorimetry
2.8 Various Thermodynamic Processes, Revisiting the First Law
2.8.1 Isothermal Process
2.8.2 Adiabatic Process
2.8.3 Free Expansion
2.8.4 Cyclic Process
2.8.5 Isochoric Process
2.8.6 Isobaric Process
2.8.7 Quasi-static Process
2.8.8 Reversible Process
2.8.9 Irreversible Process
2.9 Solved Problems
2.10 Multiple Choice Questions
3 Second Law of Thermodynamics
3.1 Converting Work into Heat
3.2 Second Law of Thermodynamics
3.2.1 Kelvin–Planck Statement
3.2.2 Clausius Statement
3.2.3 Equivalence of the Kelvin–Planck and the Clausius Statements
3.3 Carnot Heat Engine
3.3.1 Efficiency of Heat Engine in Terms of Adiabatic Expansion Ratio (ps: [/EMC pdfmark [/Subtype /Span /ActualText (p) /StPNE pdfmark [/StBMC pdfmarkpps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark)
3.3.2 Increasing Efficiency of Heat Engine
3.3.3 Entropy Change During Carnot Cycle
3.3.4 Two Carnot Engines Connected in Series
3.3.5 Carnot Theorem
3.3.6 Two Carnot Engines Operating Between Similar Reservoirs
3.4 Carnot Engine Running Backwards
3.4.1 Carnot Refrigerator
3.4.2 Heat Pump
3.5 The Thermodynamic Temperature Scale
3.5.1 Absolute Zero and Size of a Degree on Absolute Scale of Temperature
3.5.2 Absolute Zero and Efficiency of a Carnot Engine
3.5.3 Feasibility of Negative Temperature on Absolute Scale
3.6 The Equivalence Between Thermodynamic and the Ideal Gas Scales
3.7 Solved Problems
3.8 Multiple Choice Questions
3.9 Exercises
4 Entropy
4.1 Clausius Theorem
4.1.1 Reversible Case
4.1.2 Irreversible Case, Clausius Inequality
4.2 Entropy and Mathematical Form of the Second Law
4.2.1 The Principle of Increasing Entropy, Irreversible Change
4.2.2 Entropy Change in a Reversible Cycle
4.2.3 Entropy Change in an Irreversible Cycle
4.2.4 Entropy Changes and Second Law
4.2.5 Entropy Change of an Isolated System
4.2.6 Free Expansion and Corresponding Entropy Change
4.2.7 Entropy Change for an Inelastic Collision
4.3 Entropy–Temperature Diagrams
4.3.1 Utility of T-S Diagram
4.3.2 Slope of T-S Curve
4.4 Central Equation of Thermodynamics
4.5 A Few Other Examples of Entropy Change Calculations
4.5.1 Entropy of a Perfect Gas
4.5.2 The Entropy Change on Heating a Substance
4.5.3 The Entropy Change on Cooling a Substance
4.5.4 Entropy Change of Melting Ice
4.5.5 Entropy Change When Ice is Converted into Steam
4.5.6 Entropy Change on Mixing of Same Liquids at Different Temperatures
4.5.7 Entropy Change on Mixing of Two Different Liquids at Different Temperature
4.5.8 Entropy Change in Expanding a Spring
4.5.9 Entropy Change in Charging a Capacitor
4.6 Nernest Theorem, Third Law of Thermodynamics
4.6.1 Consequences of Third Law
4.6.2 Heat Capacity at Absolute Zero
4.7 Unavailability of Energy; Heat Death of Universe
4.8 Solved Problems
4.9 Multiple Choice Questions
4.10 Exercises
5 Thermodynamic Potentials and Maxwell Relations
5.1 Thermodynamic Potentials
5.1.1 The Internal Energy, U
5.1.2 The Enthalpy, H
5.1.3 The Helmholtz Function, F
5.1.4 The Gibbs Function, G
5.1.5 Physical Meaning of Free Energy
5.2 Maxwell's Relations
5.2.1 First Maxwell Relation Derived from Internal Energy, U
5.2.2 Second Maxwell Relation Derived from Enthalpy, H
5.2.3 Third Maxwell Relation Derived from Helmholtz Free Energy, F
5.2.4 Fourth Maxwell Relation Derived from Gibbs Free Energy, G
5.2.5 A Thermodynamic Mnemonic Diagram
5.3 Clausius–Clapeyron Equation
5.3.1 Effect of Pressure on Boiling Points of Liquids
5.3.2 Effect of Pressure on Melting Points of Solids
5.4 Phase Transformation in Pure Substances, Triple Point of Water
5.5 Thermodynamic Potential with More Than Two Natural …
5.6 Use of Maxwell's Relations in Solving Various Thermodynamic Problems
5.7 The TdS Equations
5.7.1 First TdS Equation
5.7.2 Second TdS Equation
5.7.3 Third TdS Equation
5.8 The Energy Equations
5.8.1 First Energy Equation
5.8.2 Second Energy Equation
5.9 Applications to Various System
5.9.1 Stretching of an Elastic Rod by a Constant Force
5.9.2 Isothermal Stretching of an Elastic Rod
5.9.3 Adiabatic Stretching of a Wire
5.9.4 Temperature Change During Adiabatic Process
5.10 Magneto Caloric Effect
5.11 Solved Problems
5.12 Multiple Choice Questions
5.13 Exercises
6 Kinetic Theory of Gases
6.1 Postulates of Kinetic Theory of Gases
6.2 Pressure Exerted by an Ideal Gas
6.2.1 Kinetic Interpretation of Temperature
6.2.2 Boyle's Law
6.2.3 Gay-Lussac's Law
6.2.4 Charle's Law
6.2.5 Avogadro's Law
6.3 The Maxwell–Boltzmann Law of Distribution of Velocities
6.3.1 The Velocity Distribution
6.3.2 Molecular Distribution of Speed
6.3.3 Evaluating Constants C and B
6.4 A Few Important Deductions from Maxwell's Law
6.4.1 Average or Mean Speed
6.4.2 Root Mean Square Speed
6.4.3 Most Probable Speed
6.5 Experimental Verification of Maxwell's Law
6.5.1 Doppler Broadening of Spectral Lines
6.5.2 Zartman and Ko Experiment
6.5.3 Stern's Experiment
6.6 Heat Capacities of Gases, Classical Approach
6.6.1 Degrees of Freedom
6.6.2 Equipartition Theorem
6.7 Mean Free Path and Transport Phenomena
6.7.1 The Mean Collision Time
6.7.2 The Collision Cross Section
6.7.3 The Mean Free Path, Zeroth-Order Approximation
6.7.4 The Mean Free Path, First-Order Approximation
6.8 Transport Phenomenon
6.8.1 Viscosity, Transport of Momentum
6.8.2 Thermal Conduction, Transport of Energy
6.8.3 Diffusion, Transport of Mass
6.9 Solved Problems
6.10 Multiple Choice Type Questions
6.11 Exercises
7 Real Gases
7.1 Behaviour of Real Gases
7.2 Deviation from Ideal Gas Equation
7.3 Boyle Temperature
7.4 Van der Waals Equation of State for Real Gases
7.4.1 Correction for Volume, Finite Size of Gas Molecule
7.4.2 Correction for Pressure, Intermolecular Forces
7.5 Andrew's Experiment on COps: [/EMC pdfmark [/Subtype /Span /ActualText (Subscript 2) /StPNE pdfmark [/StBMC pdfmark2ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark Gas, Isotherms of a Real Gas
7.5.1 Continuity of Liquid and Gaseous States
7.6 Critical Constants of a Gas
7.6.1 Critical Coefficient
7.7 Van der Waals Equation and Boyle Temperature
7.8 Limitations of Van der Waals Equation
7.9 Reduced Equation of State and Law of Corresponding States
7.10 Multiple Choice Type Questions with Explanations
7.11 Exercises
8 Applications to Some Irreversible Changes, Cooling of Real Gases
8.1 The Joule Expansion
8.1.1 Isothermal Expansion
8.1.2 Entropy Change Accompanying Joule Expansion
8.1.3 The Joule Coefficient for an Ideal Gas
8.1.4 The Joule Coefficient for Real Gas
8.1.5 Why Real Gases Produce Cooling on Expansion?
8.2 Joule–Kelvin Expansion
8.2.1 The Joule–Kelvin Coefficient for an Ideal Gas
8.2.2 The Joule–Kelvin Coefficient for a Real Gas
8.2.3 Relation Between Boyle Temperature, Temperature of Inversion and Critical Temperature
8.2.4 Entropy Change Accompanying Joule–Kelvin Expansion
8.3 Distinction Between Adiabatic Expansion, Joule Expansion …
8.4 Multiple Choice Questions
8.5 Exercises
9 Theory of Radiation
9.1 Transfer of Thermal Energy
9.2 Thermal Radiation
9.3 A Few Important Definitions
9.3.1 Total Energy Density (u)
9.3.2 Spectral Energy Density (ups: [/EMC pdfmark [/Subtype /Span /ActualText (Subscript lamda) /StPNE pdfmark [/StBMC pdfmarkλps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark)
9.3.3 The Spectral Absorptivity (ps: [/EMC pdfmark [/Subtype /Span /ActualText (alpha Subscript lamda) /StPNE pdfmark [/StBMC pdfmarkαλps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark)
9.3.4 Emissivity (e)
9.3.5 Relative Emittance (ps: [/EMC pdfmark [/Subtype /Span /ActualText (epsilon) /StPNE pdfmark [/StBMC pdfmarkεps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark)
9.3.6 The Spectral Emissive Power (ps: [/EMC pdfmark [/Subtype /Span /ActualText (e Subscript lamda) /StPNE pdfmark [/StBMC pdfmarkeλps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark)
9.4 Kirchhoff's Law
9.5 Blackbody
9.5.1 A Blackbody in Practice
9.5.2 Energy Distribution in a Blackbody Radiation Spectrum
9.6 Radiation Emitted from a Blackbody and Other Objects (Stefan–Boltzmann Law)
9.6.1 Newton's Law of Cooling from Stefan's Law
9.7 Pressure Exerted by Radiation
9.8 Classical Thermodynamics of Electromagnetic Radiation
9.8.1 Isothermal Expansion of Blackbody Radiation
9.8.2 Adiabatic Expansion of Blackbody Radiation
9.9 Wien's Displacement Law
9.10 Rayleigh–Jeans Law
9.10.1 Ultraviolet Catastrophe
9.11 Planck's Law
9.11.1 Deduction of Rayleigh–Jeans Law
9.11.2 Deduction of Wien's Distribution Law
9.11.3 Deduction of Wien's Displacement Law
9.11.4 Deduction of Stefan's Law
9.12 Solved Problems
9.13 Multiple Choice Questions
9.14 Exercises
10 Elementary Statistical Mechanics
10.1 Probability
10.1.1 Probability of Two Independent Events
10.1.2 Principle of Equal a Priori Probability
10.1.3 Permutations and Combinations
10.2 Phase Space
10.2.1 Division of Phase Space into Cells
10.2.2 Constraints on a System and Accessible States
10.3 Macrostates and Microstates
10.3.1 Distribution of Four Distinguishable Particles in Two Identical Boxes
10.3.2 Distribution of Four Indistinguishable Particles in Two Identical Boxes
10.4 Static and Dynamic Systems
10.5 Thermodynamic Probability
10.5.1 Probability of a Macrostate
10.6 Three Kinds of Statistics
10.7 The Distribution Functions
10.7.1 Maxwell–Boltzmann Distribution
10.7.2 Fermi–Dirac Distribution
10.7.3 Bose–Einstein Distribution
10.8 Approach to Obtain the Most Probable Distribution in Different Statistics
10.8.1 The Most Probable Distribution, Maxwell–Boltzmann Statistics
10.8.2 Determination of Unknown Coefficients
10.8.3 Maxwell–Boltzmann's Law of Distribution of Energy and Velocity
10.8.4 The Most Probable Distribution, Fermi–Dirac Statistic
10.8.5 The Most Probable Distribution, Bose–Einstein Statistic
10.8.6 Comparison Between Three Statistics
10.9 Solved Problems
10.10 Multiple Choice Questions
10.11 Exercises
Index