Cover
Contents
Preface
About the Author
Chapter 1: Mathematical Preliminaries
1.1 Partial Differentiation
1.1.1 Total Differential of a Function
1.1.2 Total Derivative of a Function
1.1.3 The Perfect or Exact Differential
1.1.4 The Integrating Factor
1.1.5 Geometrical Meaning of Perfect Differential
1.2 Definition of Mechanical Work
1.2.1 Work Done in Rotational Motion
1.3 Energy
1.3.1 Kinetic Energy
1.3.2 Potential Energy
1.4 Conservative Field of Force
1.4.1 The Work Function
1.4.2 The Potential Function
1.4.3 The Energy Equation (for conservative system)
1.5 Non-conservative System of Forces
1.5.1 Principle of Conservation of Energy
1.6 Gamma functions and Some Integrations
Chapter 2: Thermometry
2.1 Introduction
2.2 General Theory of Thermometry
2.3 Liquid Thermometer
2.4 Gas Thermometer
2.4.1 Constant Volume Hydrogen Thermometer
2.4.2 Callendar’s Compensated Constant Pressure Air Thermometer
2.4.3 Limitations of Gas Thermometers
2.5 Resistance Thermometer
2.5.1 Platinum Resistance Thermometer
2.6 Thermocouple Thermometers
2.7 Low and High Temperature Thermometry
Solved Problems
Problems
Questions
Chapter 3: The Mechanical Equivalent of Heat
3.1 On the Nature of Heat: The Caloric Theory of Heat
3.1.1 The Dynamical Theory of Heat
3.2 Friction Methods for Determining J. Joule’s Method
3.2.1 Searle’s Method of Measuring J
3.3 Work Done During Expansion of a Gas at Constant Pressure
3.3.1 Mayer’s Method of Determining J
3.4 Callendar and Barnes’ Steady Flow Method
3.4.1 Other Methods of Determining J
3.5 Newton’s Law of Cooling
3.5.1 Specific Heat at Constant Volume, Cu
3.5.2 Specific Heat at Constant Pressure Cp
3.5.3 Relation Between Cp and Cu
3.5.4 Principle of Calorimetry
3.5.5 Measurement of Specific Heat of Solids
3.5.6 Measurement of Specific Heat of the Liquids
3.6 Specific Heat of a Gas by Joly's Differential Steam Caloriemeter
3.7 Determination of Specific Heat of a Gas at Constant Pressure by Regnault’s Method
3.8 Determination of by Clement and Desorme’s Method
Solved Problems
Problems
Questions
Chapter 4: Kinetic Theory of Gases
4.1 Macroscopic and Microscopic Points of View
4.1.1 The Growth of the Kinetic Theory
4.2 Derivation of the Pressure Exerted by a Perfect Gas
4.2.1 Calculation of Pressure Exerted by a Perfect Gas
4.3 Distribution Function of Velocities
4.3.1 Assumption of Molecular Chaos
4.3.2 The Velocity Space
4.3.3 Maxwell’s Law of Distribution of Velocities
4.3.4 Value of the Constants a and b
4.3.5 Graphical Representation of the Change of the Distribution of Velocity with Temperature
4.3.6 The Average Velocity of the Molecules
4.3.7 Maxwell’s Law
4.4 Elastic Collisions
4.4.1 The Mechanical Laws Obeyed by Collision
4.4.2 Class-A Molecules
4.4.3 Class-B Molecules
4.4.4 Proof of Maxwellian Law of Distribution of Velocities
4.4.5 Calculation of Collisions of Class a
4.4.6 Boltzmann’s H–Function
4.4.7 Experimental Verification of Maxwells’ Law
4.4.8 Mixed Gases and Equipartition of Energy
4.5 Energy of Gas Molecules
4.5.1 Degrees of Freedom of a Molecule
4.5.2 Equipartition of Energy Amongst Different Degrees of Freedom
4.5.3 Molecular Energy and Specific Heat
4.5.4 Dulong and Petit’s Law of Specific Heat of a Monatomic Solid
4.5.5 Kinetic Theory and Variation of Specific Heat
4.6 Finite Volume of a Molecule, Mean Free Path
4.6.1 Definition of Mean Free Path
4.6.2 Calculation of Mean Free Path
4.6.3 Calculation of Mean Free Path on the Assumption of Uniform Molecular Velocity
4.6.4 Maxwell’s Mean Free Path
4.6.5 Tait’s Mean Free Path
4.6.6 Jean’s Mean Free Path
4.6.7 Mean Free Path in a Mixture of Gases
4.6.8 Correction for Mean Free Path on Account of Finite Size of Molecules
4.6.9 The Collision Rate
4.6.10 Correction for Relative Velocity
4.6.11 Pressure-Volume Relation of Clausius
4.6.12 Number of Molecules Striking Unit Area of a Surface per Second
4.6.13 The Probability of a Free Path
4.6.14 Experimental Determination of Mean Free Path
4.7 The Transport Phenomena
4.7.1 Experimental Definition of Viscosity of a Gas
4.7.2 Experimental Definition of Heat Conductivity of a Gas
4.7.3 Experimental Definition of Coefficient of Self-Diffusion
4.7.4 The Transport Theorem
4.7.5 Evaluation of Viscosity Coefficient
4.7.6 Evaluation of Heat Conductivity of a Gas
4.7.7 Evaluation of Coefficient of Self-Diffusion
4.7.8 Maxwell’s Method of Evaluation of h
4.7.9 Other Expressions for the Numerical
4.7.10 Agreement of the Approximate Theory with Observation
4.7.11 Sutherland’s Formula for Variation of Viscosity with Temperature
4.8 Viscosity of Gases at Low Pressures
4.8.1 Evaluation of the Coefficient of Slip
4.9 Collisions with a Solid Boundary: Pressure Exerted by a Gas Introducing Mean Free Path Concept
4.9.1 Knudsen’s Cosine Law
4.9.2 Knudsen’s Experiment
4.10 Kinetic Theory of Conduction of Heat Through a Gas
4.10.1 Evaluation of Coefficient of Heat Conduction Considering the Distribution of Free Path and Velocities
4.10.2 Conduction of Heat Through Rarefied Gases
4.10.3 The Accommodation Coefficient
4.10.4 Knudsen’s Absolute Manometer
4.11 Theory of Self-Diffusion in a Gas
4.11.1 Pressure and Thermal Diffusion
4.12 Thermal Transpiration
Thermal Creep and the Radiometer In
4.13 Evidences of Molecular Motion
4.13.1 Characteristic Features of Brownian Motion
4.13.2 Einstein and Smoluchowski’s Equation for Brownian Motion
4.13.3 Brownian Motion in Gases
Solved Problems
Problems
Questions
Chapter 5: Equations of State
5.1 Equation of State of Perfect Gas
5.2 Van der Waals’ Equation of State
5.3 Determination of the Constants a and b
5.4 Discussions on Van der Waals’ Equation
5.5 Comparison of Van der Waals’ Equation with Andrews’ Experimental Curves
5.6 Experimental Determination of Critical Constants
5.7 Reduced Equation of State and Law of Corresponding States
5.8 Merits and Demerits of Van der Waals’ Equation
5.9 Boyle Temperature from Van der Waals’ Equation
5.10 Other Equations of State
Solved Problems
Problems
Questions
Chapter 6: Change of State
6.1 Deduction of Clausius–Clapeyron’s Equations
6.2 Specific Heat of Saturated Vapours
6.3 Internal and External Latent Heats
6.4 Deduction of Clapeyron’s Equations from Thermodynamic Potential
6.5 The Steam Line, the Hoar Frost Line and the Ice Line
6.6 The Phase Rule
6.7 Thermodynamics of Solutions
6.7.1 Raoult’s Law
Solved Problems
Problems
Questions
Chapter 7: The Joule–Thomson Cooling Effect
7.1. Introduction
7.2 The Theory of The Experiment
7.3 Calculation of Amount of Cooling
7.4 Calculation of Cooling Co-efficient from Van Der Waals’ Equation
7.5 Condition for Liquefaction of Gases
7.6 Regenerative Cooling
7.6.1 Efficiency of the Liquefier
7.7 Method of Adiabatic Demagnetization
7.7.1 Theory of the Method
7.8 Liquefaction of Air
7.8.1 Linde’s Process
7.8.2 Claude’s Method
7.8.3 Heylandt’s Method
7.9 Liquefaction of Hydrogen
7.10 Liquefaction of Helium
7.10.1 Simon’s Single Expansion Method of Liquefaction of Helium
7.11 Properties of Liquid Helium
7.12 Measurement of Low Temperature
7.12.1 Secondary Thermometers
7.13 Measurement of Specific Heat at Low Temperatures
7.13.1 Measurement of Specific Heat of Gases at Low Temperatures
7.14 Refrigerating Mechanism
7.14.1 Electrolux Refrigerator: Absorption Type
7.14.2 Frigidaire Refrigerator: Compression Type
7.15 Air Conditioning Machine
7.15.1 Summer Air Conditioning
7.15.2 Winter Air Conditioning
7.16 Effects of Chlorofluoro Carbons (CFCS) on Ozone Layer
7.17 Applications of Substances at Low Temperature
Solved Problems
Problems
Questions
Chapter 8: First Law of Thermodynamics
8.1 Principle of Conservation of Energy
8.2 The Thermodynamic State and Thermodynamic Co-ordinates
8.2.1 Thermodynamic Equilibrium
8.2.2 Zeroth Law of Thermodynamics
8.3 Specific Heats and Latent Heats
8.4 The Energy Equation
8.4.1 dU is a Perfect Differential
8.4.2 dQ is Not a Perfect Differential
8.4.3 Joule’s Experiment
8.4.4 Forms of Energy Equation
8.4.5 Dependence of Cp and Cv of a Perfect Gas on Pressure and Volume at Constant Temperature
8.4.6 Meyer’s Method of Determining J
8.5 Atmosphere in Convective Equilibrium
8.6 The Isothermal and Adiabatic Curves
8.6.1 Work Done in Isothermal Expansion
8.6.2 Work Done in Adiabatic Expansion
8.6.3 Adiabatic and Isothermal Elasticities of a Perfect Gas
8.6.4 The Most General Equation Relating to Specific Heats of a Substance
Solved Problems
Problems
Questions
Chapter 9: The Second Law of Thermodynamics
9.1 Limitations of the First Law of Thermodynamics
9.2 The Spontaneous Process
9.3 The Heat Engine
9.3.1 How to Obtain Maximum Amount of Work?
9.3.2 Conditions of Obtaining Maximum Amount of Work
9.3.3 Reversible Operation
9.3.4 Cyclic Operation
9.3.5 The Carnot’s Engine
9.3.6 Are Spontaneous Processes Reversible?
9.4 The Second Law of Thermodynamics
9.4.1 Kelvin’s Statement of the Second Law
9.4.2 Planck’s statement
9.4.3 Kelvin Planck’s Statement
9.4.4 Clausius’ Statement of the Second Law
9.5 Carnot’s Theorem
9.6 Efficiency of a Carnot’s Engine is Independent of Nature of the Working Substance
9.7 The Thermodynamic or Kelvin Scale of Temperature
9.7.1 Thermodynamic Absolute Temperature
9.8 Centigrade Scale and Absolute Scale
9.8.1 The Centigrade Scale of Temperature
9.9 Conversion of Real-Gas Thermometer Scale to Perfect-
Gas Thermometer Scale or Absolute Thermodynamic Scale
9.9.1 Extension of Carnot’s Cycle
9.10 Entropy
9.10.1 Entropy of a Heterogeneous System
9.10.2 The Integrating Factor
9.10.3 Change of Entropy Along an Adiabatic
9.10.3 Clausius’ Theorem Considered as Second Law
9.10.4 Changes of Entropy in Irreversible and Reversible Processes
9.10.5 Entropy and Available Energy
9.10.6 Entropy of an Ideal Gas
9.10.7 Entropy of Mixture of Perfect Gases
9.10.8 Changes of Entropy in Spontaneous Processes
9.10.9 The Temperature–Entropy Diagram
9.11 Calculation of Efficiency of Rankine’s Cycle
9.11.1 Calculation of Heat Drawn
9.12 Efficiency of Diesel Cycle
9.12.1 Ideal Diesel Cycle
9.12.2 Actual Diesel Cycle
9.13 Efficiency of Otto Cycle
9.14 Third Law of Thermodynamics
Solved Problems
Problems
Questions
Chapter 10: Thermodynamic Relations
10.1 Maxwell’s Relations
10.1.1 Gibb’s Heat Functions
10.1.2 Alternative Method of Deduction of Maxwell’s Relations
10.2 Relation Between the Thermodynamic Functions
10.3 Specific Heat Equations
10.3.1 Specific Heat of Saturated Vapour
Solved Problems
Problems
Questions
Chapter 11: Conduction of Heat
11.1 Introduction
11.2 Rectilinear Flow of Heat
11.3 Ingen-Hausz’s method
11.4 Experiment of Despretz, Wiedemann and Franz for Comparison of Conductivities of Two Different Materials
11.5 Forbes’ Method
11.6 Conductivity of Poor Conductors
11.6.1 Lees’ Disc Method
11.7 Spherical Shell Method
11.7.1 Temperature Distribution at a Point at a Certain Time
11.8 Cylindrical Shell Method
11.8.1 Determination of Thermal Conductivity of Rubber
11.8.2 Determination of Thermal Conductivity of Glass
11.8.3 Conductivity of Gas
11.9 Periodic Flow of Heat
11.10 Angstrom’s Experiment
11.11 Conductivity of Earth’s Crust
11.12 Wiedemann–Franz Law
11.13 Jaeger and Diesselhorst Method
Solved Problems
Problems
Questions
Chapter 12: Radiation
12.1 Introduction
12.2 Some Fundamental Concepts and Definitions
12.3 Prevost’s Theory of Exchanges
12.4 Kirchhoff’s Law of Radiation
12.5 Analogy Between Black Body Radiation and Perfect Gas
12.6 Boltzmann’s Ether Engine
12.7 Thermodynamics of Radiation
12.7.1 Reversible Isothermal Change of Volume Occupied by Radiation
12.7.2 Reversible Adiabatic Change of Volume Occupied by Radiation
12.8 The Wavelength–Temperature Displacement Law
12.8.1 Wien’s Energy–Temperature Displacement Law
12.9 Forms of the Distribution Function f
12.9.1 Wien’s Formula
12.9.2 Rayleigh’s Formula
12.9.3 Planck’s Radiation Formula
12.10 The Equipartition Principle
12.11 The Rayleigh–Jeans Radiation Formula
12.12 The Dynamical and Thermodynamical State of a System
12.13 Planck’s Radiation Formula
12.14 Jean’s Method of Deduction of Planck’s Radiation Formula
12.15 Specific Heats of Substances
12.16 Deviations from Dulong and Petit’s Laws
12.17 Einstein’s Theory of Specific Heat
12.17.1 The Characteristic Temperature
12.17.2 Characteristic Frequency
12.18 Debye’s Theory of Specific Heat
12.19 Specific Heat of Gases
12.19.1 Calculation of Specific Heat Due to Translational Motion
12.19.2 Calculation of Specific Heat Due to Rotational Motion
12.19.3 Calculation of Specific Heat Due to Vibrational Motion
12.19.4 Specific Heat of Hydrogen
12.20 Experimental Determination of Stefan’s Constant
12.21 Measurement of High Temperatures by Radiation
12.21.1 The Optical Pyrometer
12.21.2 The Disappearing Filament Pyrometer
12.21.3 The Total Radiation Pyrometer
12.21.4 Methods of Determination of High Temperature Melting Points
12.22 Determination of Solar Constant
12.22.1 Solar Constant and its Determination
12.22.2 Temperature of the Sun
12.22.3 Some Everyday Applications
Solved Problems
Problems
Questions
Chapter 13: Introduction to Statistical Thermodynamics
13.1 Significance of Statistics
13.2 Some Basic Concepts
13.2.1 Probability
13.2.2 Complexion and Statistical State
13.2.3 Statistical Weight
13.2.4 Probability of a Composite Event
13.2.5 The Postulate of Equal a Priori Probability
13.3 Stirling’s Theorem
13.4 Mathematical Probability
13.5 Statistical Methods of a Molecular System
13.6 Liouville’s Theorem
13.7 Boltzmann’s Relation Between Entropy and Probability
13.8 Calculation of Statistical Probability and Number of Cells According to Quantum Statistics
13.9 Bose–Einstein, Fermi–Dirac and Classical Statistics
13.9.1 Calculation of Pt According to Bose–Einstein Method
13.9.2 Calculation of Pt According to Fermi–Dirac Method
13.9.3 Calculation of Pt According to Maxwell and Boltzmann Method
13.10 Distribution Law According to the Three Statistics
13.10.1 Maxwell–Boltzmann Distribution Law
13.10.2 Bose–Einstein Distribution Law
13.10.3 Fermi–Dirac Distribution Law
13.11 Equilibrium State According to the Three Statistics
13.11.1 Value of b
13.12 Law of Distribution of Molecular Velocities According to Classical or Maxwell–Boltzmann Statistics
13.13 Application of Bose–Einstein Distribution Law to Photon Gas
13.14 Application of Fermi–Dirac Distribution Law to Electron Gas
13.15 Comparison of the Three Statistics
13.16 Criticism of the Three Statistics
Solved Problems
Problems
Questions
Index