Fundamentals of Thermodynamics

A concise treatment of the fundamentals of thermodynamics is presented in this book. In particular, emphasis is placed on discussions of the second law, a unique feature of thermodynamics, which states the limitations of converting thermal energy into mechanical energy. The entropy function that permits the loss in the potential of a real thermodynamic process to be assessed, the maximum possible work in a process, and irreversibility and equilibrium are deduced from the law through physical and intuitive considerations. They are applicable in mitigating waste heat and are useful for solving energy, power, propulsion and climate-related issues. The treatment is not restricted to properties and functions of ideal gases. The ideal gas assumption is invoked as a limiting case. Reversible paths between equilibrium states are obtained using reversible heat engines and reversible heat pumps between environment and systems to determine the entropy changes and the maximum work. The conditions of thermodynamic equilibrium comprising mechanical, thermal, chemical and phase equilibrium are addressed and the species formed at equilibrium in a chemical reaction at a given temperature and pressure are obtained. The molecular basis for the laws of thermodynamics, temperature, internal energy changes, entropy, reversibility and equilibrium are briefly discussed. The book serves as a reference for undergraduate and graduate students alongside thermodynamics textbooks.

1. Fundamental Concepts 1.1 System and Environment 1.2 State of a System 1.3 Simple Systems 1.4 Mass, Molecular Mass and Moles in a System 1.5 Intensive Variables defining a System 1.5.1 Pressure 1.5.2 Temperature a. Empirical temperature b. Absolute temperature c. Temperature in K and oC 1.6 State of a System; State Variables, Thermodynamic Properties 1.7 Change of State of a System: Quasi-static and Reversible Process 1.7.1 Quasi-static Process 1.7.2 Reversible Process 1.7.3 Cyclic Process: Efficiency and coefficient of performance 2. Equation of State 2.1 Introduction 2.2 Equation of State for an Ideal Gas 2.3 Equations of State for Real Gases 2.3.1 Virial Equation of State 2.3.2 van der Waal equation of State 2.3.3 Bethelot and Dieterci Equations of State 2.3.4 Redlich-Kwong Equation of State 2.4 Generalized Compressibility Chart 2.5 Mixture of Ideal Gases 3. First Law of Thermodynamics 3.1 Statement of the First Law 3.2 Internal Energy and Adiabatic Work 3.3 Heat 3.4 Heat Capacities of a System 3.4.1 Heat Capacity at Constant Volume 3.4.2 Heat Capacity at Constant Pressure 3.4.3 Relation between Heat Capacities 3.4.4 Specific heats 3.5 Internal Energy and Enthalpy for an Ideal Gas 3.6 Experimental Verification of Dependence of Internal Energy on Temperature and Pressure 3.7 Experimental Verification of Enthalpy to be independent of Pressure 3.8 First Law Applied to Open Systems 4. Second Law of thermodynamics 4.1 Statements of the Second Law 4.2 Equivalence of Kelvin Plank and Clausius Statements 4.3 Carnot’s Principle 4.3.1 Efficiencies of Reversible Engines 4.4 Ratio of Heat Transfer and Temperature 4.5 Thermodynamic Temperature 4.5.1 Efficiency of reversible engine depends on Temperature of both the Reservoirs 4.5.2 Thermodynamic Temperatures 4.5.3 Thermodynamic or Absolute Temperature Scale 4.6 Clausius Inequality 4.7 Entropy 4.7.1 Entropy Statement of the Second Law 4.7.2 Equivalence of Entropy Statement and Clausius and Kelvin Plank Statements 5. Entropy 5.1 Entropy Change between Two States 5.2 Path Independence 5.2 Generalized Expression for Entropy Change 5.2.1 Entropy from Internal Energy Changes 5.2.2 Entropy from Enthalpy Changes 5.2.3 Entropy changes as a function of Heat capacities 5.3 Entropy Changes for an Ideal Gas 6. Reversible Work, Availability and Irreversibility 6.1 Reversible Work 6.2 Work from Different Reversible Paths between Two States 6.3 Reversible Work of a System Interacting with Environment: Availability 6.4 Reversible Work of a System Interacting with Reservoir and Environment 6.5 Useful Reversible Work when a System Changes its Volume 6.6 Irreversibility of a System Undergoing a Process 6.7 Two Examples Illustrating Irreversibility 6.7.1 Expansion of an Ideal gas into Vacuum 6.7.2 Cooling of a cup of hot coffee 6.8 Irreversibility in Open Systems 7. Thermodynamic State Functions 7.1 Introduction 7.2 State Functions 7.2.1 Internal Energy 7.2.2 Entropy 7.2.3 Enthalpy 7.2.4 Helmholtz and Gibbs Free Energies 7.3 Derivation of State Functions using Legendre Transform 7.4 Maxwell’s Relationships 7.5 Thermodynamic Potentials and Forces 7.6 Determination of State Functions 7.6.1 Internal Energy 7.6.2 Enthalpy 7.6.3 Entropy 7.7 Thermodynamic Functions for Dense Gases 7.8 Generalized Enthalpy and Entropy Charts 8. Thermodynamic Coefficients and Specific Heats 8.1 Thermodynamic Coefficients 8.1.1 Coefficient of Volume Expansion 8.1.2 Isothermal and Isentropic Compressibility 8.1.3 Pressure Coefficient 8.1.4 Relation among Coefficients and Acoustic Impedance 8.2 Specific Heats 8.2.1 Specific Heats at Constant Pressure and Constant Volume 8.2.2 Ratio of Specific Heats 8.2.3 Variation of Specific Heats with Specific Volume and Pressure 8.3 Joule Thomson Coefficient 8.4 Thermodynamic Coefficient for Dense Gases 9. Thermodynamic Equilibrium 9.1 Introduction 9.2 Criterion for Thermodynamic Equilibrium 9.3 Thermal equilibrium 9.4 Mechanical Equilibrium 9.5 Equilibrium with Mass Exchange 9.6 Multicomponent Systems 9.6.1 Additional Reversible Work from Change of Components 9.6.2 Helmholtz Function and Chemical Potential at Constant Volume 9.6.3 Gibbs Free energy and Chemical Potential at Constant Pressure 9.6.4 Chemical Potential from Enthalpy 9.6.5 Equilibrium of a Multicomponent Gas 9.7 Equilibrium of Phases 9.8 Multiple Components and Multiple Phases in Equilibrium: Gibbs Phase Rule 9.8.1 Clausius-Claypeyron Equation 10. Equilibrium of Species in a Chemically Reacting System 10.1 Introduction 10.2 Choice of Basic datum for State Functions 10.3 Entropy of Species in a Chemical Reaction: Third law of Thermodynamics 10.4 Enthalpy Changes 10.5 Product Species in a Chemical reaction at Given Temperature and Pressure 10.6 Example of Determining Equilibrium Composition 10.7 Chemical equilibrium of Species at a Given Temperature and Volume 10.8 Corrections for Real Gas: Fugacity 11. Statistical Thermodynamics 11.1 Introduction 11.2 Distribution of Particles and Energy Levels: Bose Einstein, Fermi-Dirac and Boltzmann Statistics 11.3 Maxwell-Boltzmann Distribution: Partition Function 11.4 Boltzmann’s Formula 11.5 Partition Function for Monoatomic Gas: Internal Energy, Pressure, Equation of State and Entropy of an Ideal Gas 11.6 Reversible Heat Transfer and Work; The First and Second Laws of Thermodynamics

Professor John Lee is Emeritus Professor of Mechanical Engineering at McGill University, Montreal. He has been carrying out fundamental and applied research in combustion, detonation, shock-wave physics, and high pressure and temperature phenomenon for the past sixty years. As a consultant, Lee has served on a large number of government and industrial committees not only in Canada but in US and other parts of the world. Among the prizes that he has received are the silver medal from the Combustion Institute (1980), the Dionizy Smolensnki Medal from Polish Academy of Sciences (1988), and the Numa Manson gold medal (1991) for his outstanding contributions to the fundamentals and applied aspects of explosion and detonation phenomenon. He is a Fellow of the Royal Society of Canada. Professor K. Ramamurthi completed his Ph. D with Professor John Lee at McGill as a Commonwealth Scholar in 1976. He worked as deputy director in the Indian Space Research Organization and as a professor in the Mechanical Engineering Department at the Indian Institute of Technology Madras. His notable contributions to research have been in instability phenomenon, rocket propulsion, and explosion safety. He has been on several national and international committees and panels on propulsion, combustion and shock waves and is chairman of the Combustion, Detonics and Shock Wave (CDSW) Panel of the Defense Research and Development Organization in India. He continues to teach thermodynamics and is an honorary fellow of the High Energy Material Society.