Basic and Applied Thermodynamics PDF

Second Edition  About the Author P K Nag has been with the Indian Institute of Technology, Kharagpur, for about four decades, almost since his graduation. After retirement from IIT, he was an Emeritus Fellow of AICTE, New Delhi, stationed at Jadavpur University, Kolka...

Second Edition  About the Author P K Nag has been with the Indian Institute of Technology, Kharagpur, for about four decades, almost since his graduation. After retirement from IIT, he was an Emeritus Fellow of AICTE, New Delhi, stationed at Jadavpur University, Kolkata, till June 2005. He was a Visiting Professor in the Technical University of Nova Scotia (now Dalhousie University), Halifax, Canada, for two years during 1985–86 and 1993–94. Dr Nag is the recipient of the President of India medal (1995) from the Institution of Engineers (India). He is a Fellow of the National Academy of Engineers (FNAE) and a Fellow of the Institution of Engineers (India). In his early days, he was also an NCC Officer at IIT, Kharagpur. Besides these, Dr Nag is also a Life Member of the Indian Society for Technical Education, Indian Society for Heat and Mass Transfer, and the Combustion Institute, USA (Indian section). He was formerly a member of the New York Academy of Sciences, USA. His areas of interest include circulating fluidized bed boilers, combined cycle power generation, second law analysis of thermal systems, and waste heat recovery. He has authored four books, including this one, and more than 150 research papers in several national and international journals and proceedings. He has also attended international conferences in the US, Japan, Canada and Bangladesh where he has presented several papers. Other books from the author Engineering Thermodynamics, 4/e Power Plant Engineering, 3/e Heat Transfer, 2/e  Second Edition P K Nag Former Professor Department of Mechanical Engineering Indian Institute of Technology Kharagpur Tata McGraw Hill Education Private Limited NEW DELHI McGraw-Hill Offices New Delhi New York St. Louis San Francisco Auckland Bogotá Caracas Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal San Juan Santiago Singapore Sydney Tokyo Toronto  Tata McGraw Hill Published by the Tata McGraw Hill Education Private Limited, 7 West Patel Nagar, New Delhi 110 008. Copyright © 2010 by Tata McGraw Hill Education Private Limited. No part of this publication may be reproduced or distributed in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise or stored in a database or retrieval system without the prior written permission of the publishers. The program listings (if any) may be entered, stored and executed in a computer system, but they may not be reproduced for publication. This edition can be exported from India only by the publishers, Tata McGraw Hill Education Private Limited ISBN (13): 978-0-07-015131-4 ISBN (10): 0-07-015131-8 Managing Director: Ajay Shukla Head—Higher Education Publishing: Vibha Mahajan Manager—Sponsoring: Shalini Jha Editorial Executive: Surabhi Shukla Asst. Development Editor: Devshree Lohchab Executive—Editorial Services: Sohini Mukherjee Senior Production Manager: P L Pandita General Manager: Marketing—Higher Education: Michael J Cruz Sr. Product Manager: SEM & Tech Ed: Biju Ganesan Asst. Product Manager: Amit Paranjpe General Manager—Production: Rajender P Ghansela Asst. General Manager—Production: B L Dogra Information contained in this work has been obtained by Tata McGraw Hill, from sources believed to be reliable. However, neither Tata McGraw Hill nor its authors guarantee the accuracy or completeness of any information published herein, and neither Tata McGraw Hill nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that Tata McGraw Hill and its authors are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought. Typeset at Mukesh Technologies Pvt. Ltd., #10, 100 Feet Road, Ellapillaichavadi, Pondicherry 605 005 and printed at Sai Printo Pack, A-102/4, Okhla Industrial Area, Phase-II, New Delhi 110 020 Cover: SDR RAXYCRBFDZLAA The McGraw.Hill Companies To My Grandchildren Madhurima Basu Thakur and Abhiroop Guha with love and blessings  Contents Preface xv Content Highlights xvii 1. Introduction 1 1.1 Macroscopic vs Microscopic Viewpoint 1 1.2 Thermodynamic System and Control Volume 1 1.3 Thermodynamic Properties, Processes and Cycles 2 1.4 Homogeneous and Heterogeneous Systems 3 1.5 Thermodynamic Equilibrium 3 1.6 Quasi-Static Process 4 1.7 Pure Substance 5 1.8 Concept of Continuum 5 1.9 Thermostatics 6 1.10 Units and Dimensions 6 1.11 History of Thermodynamics 10 Solved Examples 15 Review Questions 15 Problems 16 2. Temperature 17 2.1 Zeroth Law of Thermodynamics 17 2.2 Measurement of Temperature—The Reference Points 17 2.3 Comparison of Thermometers 19 2.4 Ideal Gas 19 2.5 Gas Thermometers 20 2.6 Ideal Gas Temperature 21 2.7 Celsius Temperature Scale 22 2.8 Electrical Resistance Thermometer 22 2.9 Thermocouple 22 2.10 International Practical Temperature Scale 23 Solved Examples 24 Review Questions 25 Problems 26 3. Work and Heat Transfer 27 3.1 Work Transfer 27 3.2 pdV–Work or Displacement Work 28 3.3 Indicator Diagram 30 3.4 Other Types of Work Transfer 32  viii Contents 3.5 Free Expansion with Zero Work Transfer 35 3.6 Net Work Done by a System 35 3.7 Heat Transfer 36 3.8 Heat Transfer—A Path Function 36 3.9 Specific Heat and Latent Heat 37 3.10 Points to Remember Regarding Heat Transfer and Work Transfer 38 Solved Examples 38 Review Questions 42 Problems 42 4. First Law of Thermodynamics 45 4.1 First Law for a Closed System Undergoing a Cycle 45 4.2 First Law for a Closed System Undergoing a Change of State 46 4.3 Energy—A Property of the System 47 4.4 Different Forms of Stored Energy 47 4.5 Specific Heat at Constant Volume 49 4.6 Enthalpy 50 4.7 Specific Heat at Constant Pressure 50 4.8 Energy of an Isolated System 51 4.9 Perpetual Motion Machine of the First Kind–PMM1 51 4.10 Limitations of the First Law 51 Solved Examples 51 Review Questions 55 Problems 55 5. First Law Applied to Flow Processes 58 5.1 Control Volume 58 5.2 Steady Flow Process 59 5.3 Mass Balance and Energy Balance in a Simple Steady Flow Process 59 5.4 Some Examples of Steady Flow Processes 61 5.5 Comparison of S.F.E.E. with Euler and Bernoulli Equations 64 5.6 Variable Flow Processes 65 5.7 Example of a Variable Flow Problem 66 5.8 Discharging and Charging a Tank 68 Solved Examples 69 Review Questions 77 Problems 77 6. Second Law of Thermodynamics 81 6.1 Qualitative Difference between Heat and Work 81 6.2 Cyclic Heat Engine 82 6.3 Energy Reservoirs 83 6.4 Kelvin–Planck Statement of Second Law 83 6.5 Clausius’ Statement of the Second Law 84 6.6 Refrigerator and Heat Pump 84 6.7 Equivalence of Kelvin–Planck and Clausius Statements 86 6.8 Reversibility and Irreversibility 87 6.9 Causes of Irreversibility 87 6.10 Conditions for Reversibility 91 6.11 Carnot Cycle 91  Contents ix 6.12 Reversed Heat Engine 92 6.13 Carnot’s Theorem 93 6.14 Corollary of Carnot’s Theorem 93 6.15 Absolute Thermodynamic Temperature Scale 94 6.16 Efficiency of the Reversible Heat Engine 96 6.17 Equality of Ideal Gas Temperature and Kelvin Temperature 97 6.18 Types of Irreversibility 98 Solved Examples 99 Review Questions 104 Problems 105 7. Entropy 109 7.1 Introduction 109 7.2 Two Reversible Adiabatic Paths Cannot Intersect Each Other 109 7.3 Clausius’ Theorem 109 7.4 The Property of Entropy 111 7.5 The Inequality of Clausius 114 7.6 Entropy Change in an Irreversible Process 115 7.7 Entropy Principle 116 7.8 Applications of Entropy Principle 117 7.9 Entropy Transfer Mechanisms 122 7.10 Entropy Generation in a Closed System 124 7.11 Entropy Generation in an Open System 126 7.12 First and Second Laws Combined 128 7.13 Reversible Adiabatic Work in a Steady Flow System 129 7.14 Entropy and Direction: The Second Law—A Directional Law of Nature 131 7.15 Entropy and Disorder 131 7.16 Absolute Entropy 132 Solved Examples 132 Review Questions 143 Problems 144 8. Available Energy, Exergy and Irreversibility 150 8.1 Available Energy 150 8.2 Available Energy Referred to a Cycle 150 8.3 Quality of Energy 153 8.4 Maximum Work in a Reversible Process 155 8.5 Reversible Work by an Open System Exchanging Heat only with the Surroundings 156 8.6 Useful Work 159 8.7 Dead State 160 8.8 Availability 161 8.9 Availability in Chemical Reactions 162 8.10 Irreversibility and Gouy–Stodola Theorem 163 8.11 Availability or Exergy Balance 166 8.12 Second Law Efficiency 168 8.13 Comments on Exergy 173 Solved Examples 175 Review Questions 193 Problems 194  x Contents 9. Properties of Pure Substances 198 9.1 p–v Diagram for a Pure Substance 198 9.2 p–T Diagram for a Pure Substance 201 9.3 p–v–T Surface 202 9.4 T–s Diagram for a Pure Substance 203 9.5 h–s Diagram or Mollier Diagram for a Pure Substance 204 9.6 Quality or Dryness Fraction 206 9.7 Steam Tables 208 9.8 Charts of Thermodynamic Properties 209 9.9 Measurement of Steam Quality 211 Solved Examples 214 Review Questions 232 Problems 232 10. Properties of Gases and Gas Mixtures 236 10.1 Avogadro’s Law 236 10.2 Equation of State of a Gas 236 10.3 Ideal Gas 237 10.4 Equations of State 248 10.5 Virial Expansions 249 10.6 Law of Corresponding States 250 10.7 Other Equations of State 255 10.8 Properties of Mixtures of Gases—Dalton’s Law of Partial Pressures 257 10.9 Internal Energy, Enthalpy and Specific Heats of Gas Mixtures 259 10.10 Entropy of Gas Mixtures 260 10.11 Gibbs Function of a Mixture of Inert Ideal Gases 261 Solved Examples 262 Review Questions 274 Problems 275 11. Thermodynamic Relations, Equilibrium and Third Law 282 11.1 Some Mathematical Theorems 282 11.2 Maxwell’s Equations 283 11.3 TdS Equations 284 11.4 Difference in Heat Capacities 285 11.5 Ratio of Heat Capacities 286 11.6 Energy Equation 287 11.7 Joule-Kelvin Effect 290 11.8 Clausius-Clapeyron Equation 292 11.9 Evaluation of Thermodynamic Properties from an Equation of State 295 11.10 General Thermodynamic Considerations on an Equation of State 297 11.11 Mixtures of Variable Composition 298 11.12 Conditions of Equilibrium of a Heterogeneous System 301 11.13 Gibbs Phase Rule 302 11.14 Types of Equilibrium 303 11.15 Local Equilibrium Conditions 305 11.16 Conditions of Stability 306 Solved Examples 308 Review Questions 322 Problems 323  Contents xi 12. Vapour Power Cycles 328 12.1 Simple Steam Power Cycle 328 12.2 Rankine Cycle 329 12.3 Actual Vapour Cycle Processes 332 12.4 Comparison of Rankine and Carnot Cycles 333 12.5 Mean Temperature of Heat Addition 334 12.6 Reheat Cycle 335 12.7 Ideal Regenerative Cycle 337 12.8 Regenerative Cycle 338 12.9 Reheat-Regenerative Cycle 341 12.10 Feedwater Heaters 343 12.11 Exergy Analysis of Vapour Power Cycles 345 12.12 Characteristics of an Ideal Working Fluid in Vapour Power Cycles 346 12.13 Binary Vapour Cycles 347 12.14 Thermodynamics of Coupled Cycles 349 12.15 Process Heat and By-Product Power 350 12.16 Efficiencies in Steam Power Plant 352 Solved Examples 354 Review Questions 372 Problems 372 13. Gas Power Cycles 378 13.1 Carnot Cycle (1824) 378 13.2 Stirling Cycle (1827) 379 13.3 Ericsson Cycle (1850) 379 13.4 Air Standard Cycles 380 13.5 Otto Cycle (1876) 380 13.6 Diesel Cycle (1892) 382 13.7 Limited Pressure Cycle, Mixed Cycle or Dual Cycle 384 13.8 Comparison of Otto, Diesel, and Dual Cycles 385 13.9 Brayton Cycle 387 13.10 Aircraft Propulsion 396 13.11 Brayton-Rankine Combined Cycle 398 Solved Examples 400 Review Questions 413 Problems 414 14. Refrigeration Cycles 419 14.1 Refrigeration by Non-Cyclic Processes 419 14.2 Reversed Heat Engine Cycle 419 14.3 Vapour Compression Refrigeration Cycle 420 14.4 Selection of a Refrigerant 434 14.5 Absorption Refrigeration Cycle 436 14.6 Electrolux Refrigerator 439 14.7 Steam Jet Refrigeration System 440 14.8 Heat Pump Systems 441 14.9 Gas Cycle Refrigeration 442 14.10 Application to Aircraft Refrigeration 444 14.11 Liquefaction of Gases 446 14.12 Production of Solid Ice 448  xii Contents Solved Examples 450 Review Questions 462 Problems 463 15. Psychrometrics and Air-conditioning Systems 467 15.1 Properties of Atmospheric Air 467 15.2 Psychrometric Properties of Air 468 15.3 Psychrometric Chart 474 15.4 Psychrometric Processes 476 15.5 Simple Air-conditioning System 486 15.6 Load Calculations 489 15.7 Air-conditioning Systems 490 Solved Examples 491 Review Questions 504 Problems 505 16. Reactive Systems 507 16.1 Degree of Reaction 507 16.2 Reaction Equilibrium 509 16.3 Law of Mass Action 510 16.4 Heat of Reaction 511 16.5 Temperature Dependence of the Heat of Reaction 512 16.6 Temperature Dependence of the Equilibrium Constant 512 16.7 Thermal Ionization of a Monatomic Gas 513 16.8 Gibbs Function Change 515 16.9 Fugacity and Activity 517 16.10 Displacement of Equilibrium Due to a Change in Temperature or Pressure 518 16.11 Heat Capacity of Reacting Gases in Equilibrium 519 16.12 Combustion 520 16.13 Enthalpy of Formation 521 16.14 First Law for Reactive Systems 522 16.15 Adiabatic Flame Temperature 523 16.16 Enthalpy and Internal Energy of Combustion: Heating Value 523 16.17 Absolute Entropy and the Third Law of Thermodynamics 525 16.18 Second Law Analysis of Reactive Systems 526 16.19 Chemical Exergy 526 16.20 Second Law Efficiency of a Reactive System 529 16.21 Fuel Cells 529 Solved Examples 531 Review Questions 544 Problems 544 17. Compressible Fluid Flow 548 17.1 Velocity of Pressure Pulse in a Fluid 548 17.2 Stagnation Properties 550 17.3 One-Dimensional Steady Isentropic Flow 550 17.4 Critical Properties–Choking in Isentropic Flow 552 17.5 Normal Shocks 556 17.6 Adiabatic Flow with Friction and Diabatic Flow without Friction 560  Contents xiii Solved Examples 561 Review Questions 566 Problems 566 18. Elements of Heat Transfer 568 18.1 Basic Concepts 568 18.2 Conduction Heat Transfer 568 18.3 Convective Heat Transfer 574 18.4 Heat Exchangers 579 18.5 Radiation Heat Transfer 584 Solved Examples 591 Review Questions 599 Problems 600 19. Gas Compressors 603 19.1 Compression Processes 603 19.2 Work of Compression 603 19.3 Single-Stage Reciprocating Air Compressor 605 19.4 Volumetric Efficiency 607 19.5 Multi-Stage Compression 609 19.6 Air Motors 613 19.7 Rotary Compressor 613 19.8 Blowers and Fans 624 Solved Examples 624 Review Questions 646 Problems 647 20. Internal Combustion Engines 650 20.1 Internal and External Combustion Engines 650 20.2 Classification of IC Engines 650 20.3 An Overview of Reciprocating Engines 652 20.4 Description of an SI Engine 653 20.5 Operating Principles 653 20.6 The Two-Stroke Engine 658 20.7 Engine Performance 659 20.8 Air Standard Cycles 662 20.9 Fuels for IC Engines 666 20.10 Combustion in SI Engines 669 20.11 Simple Float Carburetor 673 20.12 Fuel Injection in CI Engines 676 20.13 Cooling System of IC Engines 680 20.14 Lubricating System 681 20.15 Starting of Engine 685 20.16 Performance Characteristics 685 20.17 Supercharging 688 Solved Examples 691 Review Questions 705 Problems 706  xiv Contents 21. Gas Tubines and Propulsion Systems 708 21.1 Closed Cycle and Open Cycle Plants 708 21.2 Advantages of a GT Plant 708 21.3 Disadvantages of a GT Plant 710 21.4 Analysis of GT Plant 711 21.5 Closed-Cycle Gas Turbine 715 21.6 Semi-Closed Cycle GT Plant 715 21.7 Performance of Gas Turbine Power Plants 715 21.8 Components of a Gas Turbine Plant 718 21.9 Gas Turbine with Water Injection 722 21.10 Gas Turbine Fuels 723 21.11 Gas Turbine Materials 723 21.12 Jet Propulsion System 724 21.13 Propulsive Devices for Aircrafts and Missiles 726 21.14 Turbojet Engine with Afterburner 732 21.15 Turbo-Prop Engine 733 21.16 Bypass Turbo-JET Engine 735 21.17 Athodyds-Ramjets and Pulsejets 736 21.18 Rocket Propulsion 739 21.19 Nuclear Rockets 744 Solved Examples 744 Review Questions 759 Problems 760 22. Transport Processes in Gases 762 22.1 Mean Free Path and Collision Cross-Section 762 22.2 Distribution of Free Paths 763 22.3 Transport Properties 764 Solved Examples 772 Review Questions 778 Problems 779 Appendix A 780 A.1 Steam Tables 780 A.2 Thermodynamic Properties of Refrigerant-12 (Dichlorodifluoromethane) 798 A.3 Thermodynamic Properties of Refrigerant-22 (Monochlorodifluoromethane) 803 A.4 Thermodynamic Properties of Refrigerant-134A (1,1,1,2–Tetrafluoroethane) 810 A.5 Thermodynamic Properties of Ammonia 817 A.6 Variation of − c p with Temperature for Various Ideal Gases 822 A.7 Ideal Gas Specific Heats of Some Common Gases (kJ/kg.K) 822 A.8 Logarithm to the Base 10 of the Equilibrium Constant K 824 A.9 Enthalpy of Formation at 25°C, Ideal Gas Enthalpy, and Absolute Entropy at 0.1 MPa (1 bar) Pressure 826 A.10 Gas Tables 829 A.11 Critical Point Data 831 Appendix B – Charts (Fig. B.1 – Fig. B.6 ) Multiple-Choice Questions 833 Bibliography 840 Index 842  Preface The author feels greatly encouraged at the good response of the book Engineering Thermodynamics. The present book is a further updated and reorganized version, retaining the framework and style of presentation of the earlier book. The last four chapters of the book, viz., Statistical Thermodynamics, Irreversible Thermodynamics, Kinetic Theory of Gases and Transport Properties of Gases are of little relevance in undergraduate courses on Thermodynamics. Hence, the last four chapters of the book and also the topics not important for UG courses have been omitted in this edition and three new chapters on Gas Compressors, Internal Combustion Engines and Gas Turbines and Propulsion Systems have been included instead in this edition in conformity with the UG curricula of many colleges in Applied Thermodynamics and also the recommendation of the reviewers. In addition to contributing as a basic course, the book can be used for a further advanced course at a senior undergraduate or graduate level with topics selectively chosen. The first eight chapters of the book are devoted to a thorough treatment of the basic principles and concepts of classical thermodynamics. The second law and entropy have been introduced using the concept of heat engine. Chapters 9 and 10 present the properties of substances. Chapter 11 gives the general thermodynamic relationships among properties. A detailed analysis of power and refrigeration cycles is given in chapters 12 to 14. Chapter 15 deals with psychrometrics and air-conditioning systems, while reactive systems are analyzed in Chapter 16. Chapters 17 and 18 deal with compressible fluid flow and heat transfer respectively. Gas compressors are discussed in Chapter 19. Internal combustion engines and their operating principles are explained in Chapter 20. Chapter 21 is devoted to gas turbines and propulsion systems. Finally, Chapter 22 discusses the transport processes in gases. The style of presentation and inclusion of short questions, solved and exercise problems have been retained. Many illustrative examples are solved and many problems are provided in each chapter to aid comprehension and to stimulate the interest of the students. Multiple Choice Questions on the subject have been added at the end. Throughout the text, SI units have been used. Tables and charts given in the Appendices are also in SI units. The book also has an accompanying website which can be accessed at http://www.mhhe.com/nag/bat2e. The author hopes that the book will be useful to the students and teachers alike. The study on Steam like Steam Boilers, Steam Turbines and Condensers will be considered for inclusion in future depending on the demand after omitting and editing some of the existing material. I am thankful to Ms Surabhi Shukla and Ms Devshree Lohchab for their arduous task of syllabi research and competitive analysis which helped me a great deal in preparing this revision. I would also like to thank Ms Sohini Mukherjee for her deft editorial services. Mr P L Pandita too deserves a special mention for his efficient handling of the production process. I am also indebted to the following reviewers for taking out time to review the book.  xvi Preface M K Das MNNIT, Allahabad, Uttar Pradesh Ajay Trehan Dr B R Ambedkar National Institute of Technology Jalandhar, Punjab K P Tyagi Krishna Institute of Engineering and Technology UPTU, Ghaziabad, Uttar Pradesh T K Jana Haldia Institute of Technology WBUT, East Midnapur, West Bengal P K Bardhan JIS College of Engineering WBUT, Nadia, West Bengal P S Utgikar JSPM’s Rajarshi Shahu College of Engineering Pune, Maharashtra D A Warke J T Mahajan College of Engineering Jalgaon, Maharashtra R G Kapadia Shri Sad Vidya Mandal Institute of Technology Bharuch, Gujarat P Chitambarnathan Dr Sivanthi Adithanar College of Engineering Thiruchendur, Tamil Nadu A V S Gupta JNTU College of Engineering Hyderabad, Andhra Pradesh S Ramanathan DRK Institute of Science and Technology JNTU, Hyderabad, Andhra Pradesh Y S Varadarajan The National Institute of Engineering Mysore, Karnataka K Chandrashekara Sri Jayachamarajendra College of Engineering Mysore, Karnataka S Makam R V College of Engineering Bangalore, Karnataka M S Bhagya Shekar Don Bosco Institute of Technology Bangalore, Karnataka Sharanabasava C Pilli K L E Society’s College of Engineering and Technology Belgaum, Karnataka V V Bongale Malnad College of Engineering Hassan, Karnataka Any constructive criticism as well as suggestions for improvement of the book will be welcome and gratefully acknowledged. The present edition of the book is being dedicated to my grandchildren, Kumari Madhurima Basu Thakur and Sri Abhiroop Guha, with love and blessings. P K Nag  CONTENT HIGHLIGHTS New Chapters New chapters on Gas Compres- sors, Internal Combustion Engines and Gas Turbines and Propulsion Systems included in the second edition would help engineers comprehend the role of com- pression processes, IC engines and propulsion systems in thermodynamics. New Topics Coverage on Chapter 14 is enhanced by the insertion of the topics of Expansion Device, Multi-Evaporator Sys- tems and Electrolux Refrigera- tor. Two essential topics on Air-Conditioning Systems and Air Washer are included in Chapter 15. Solved Examples Solved examples in various chapters at the end of the theory portion help the students understand the applicability of engineering calculations for thermodynamic applications. Illustrations Detailed illustrations are neces- sary for any book on engineering. Besides the existing ones, 133 new figures have been included in this edition to let students have a clear grasp of the contents. Review Questions Review questions are provided at the end of each chapter. They cover the contents of the entire chapter. These review questions are very helpful to teachers in set- ting up examination papers and class work assignments.  Problems with Answers A set of problems with answers is given in all the chapters. These help the students test their compre- hension of the concepts. Appendices A total of 11 Appendices are given at the end of the book which contain relevant data, charts and tables related to thermodynamics. Multiple-Choice Questions Over 60 MCQs have been added at the end of the book to let students have a quick revision of the fundamental concepts. Bibliography A comprehensive list of refer- ences in the form of textbooks and journals with the title of the article is given at the end of the book.  C H A P T E R 1 Introduction Thermodynamics is the science of energy transfer and its effect on the physical properties of substances. It is based upon observations of common experience which have been formulated into thermodynamic laws. These laws govern the principles of energy conversion. The applications of the thermodynamic laws and principles are found in all fields of energy technology, notably in steam and nuclear power plants, internal combustion engines, gas turbines, air conditioning, refrigeration, gas dynamics, jet propulsion, compressors, chemical process plants, and direct energy conversion devices. 1.1 MACROSCOPIC VS MICROSCOPIC VIEWPOINT There are two points of view from which the behaviour of matter can be studied: the macroscopic and the microscopic. In the macroscopic approach, a certain quantity of matter is considered, without the events occurring at the molecular level being taken into account. From the microscopic point of view, matter is com- posed of myriads of molecules. If it is a gas, each molecule at a given instant has a certain position, velocity, and energy, and for each molecule these change very frequently as a result of collisions. The behaviour of the gas is described by summing up the behaviour of each molecule. Such a study is made in microscopic or statistical thermodynamics. Macroscopic thermodynamics is only concerned with the effects of the action of many molecules, and these effects can be perceived by human senses. For example, the macroscopic quantity, pressure, is the average rate of change of momentum due to all the molecular collisions made on a unit area. The effects of pressure can be felt. The macroscopic point of view is not concerned with the action of indi- vidual molecules, and the force on a given unit area can be measured by using, e.g. a pressure gauge. These macroscopic observations are completely independent of the assumptions regarding the nature of matter. All the results of classical or macroscopic thermodynamics can, however, be derived from the microscopic and statistical study of matter. 1.2 THERMODYNAMIC SYSTEM AND CONTROL VOLUME A thermodynamic system is defined as a quantity of matter or a region in space upon which attention is concentrated in the analysis of a problem. Everything external to the system is called the surroundings or the environment. The system is B nd separated from the surroundings by the system boundary (Fig. 1.1). The boundary may be either fixed or moving. A system and its sur- roundings together comprise a universe. There are three classes of systems: (a) closed system, (b) open system and (c) isolated system. The closed system (Fig. 1.2) is a ndin system of fixed mass. There is no mass transfer across the system boundary. There may be energy transfer into or out of the system. Fig. 1.1 A thermodynamic system  2 Basic and Applied Thermodynamics B nd n in B nd n M ndin ndin ndin n in n n n n M in n Fig. 1.4 An isolated system Fig. 1.2 A closed system Fig. 1.3 An open system A certain quantity of fluid in a cylinder bounded by a piston constitutes a closed system. The open system (Fig. 1.3) is one in which matter crosses the boundary of the system. There may be energy transfer also. Most of the engineering devices are generally open systems, e.g., an air compressor in which air enters at low pressure and leaves at high pressure and there are energy transfers across the system boundary. The isolated system (Fig. 1.4) is one in which there is no interaction between the system and the surroundings. It is of fixed mass and energy, and there is no mass or energy transfer across the system boundary. If a system is defined as a certain quantity of matter, then the system contains the same matter and there can be no transfer of mass Ai across its boundary. However, if a system is defined as a region of space within a prescribed boundary, then matter can cross the system boundary. While the former is called a closed system, the latter is an open system. n M Ai For thermodynamic analysis of an open system, such as an air compressor (Fig. 1.5), attention is focussed on a certain volume in space surrounding the compressor, known as n v the control volume, bounded by a surface called the control surface. Matter as well as energy Ai in crosses the control surface. Fig. 1.5 Control volume and control surface A closed system is a system closed to matter flow, though its volume can change against a flexible boundary. When there is matter flow, then the system is considered to be a volume of fixed identity, the control volume. There is thus no difference between an open system and a control volume. 1.3 THERMODYNAMIC PROPERTIES, PROCESSES AND CYCLES Every system has certain characteristics by which its physical condition may be described, e.g., volume, temperature, pressure, etc. Such characteristics are called properties of the system. These are all macro scopic in nature. When all the properties of a system have definite values, the system is said to exist at a definite state. Properties are the coordinates to describe the state of a system. They are the state variables of the system. Any operation in which one or more of the properties of a system changes is called a change of state. The succession of states passed through during a change of state is called the path of the change  Introduction 3 of state. When the path is completely specified, the change a of state is called a process, e.g., a constant pressure pro- cess. A thermodynamic cycle is defined as a series of state 1 changes such that the final state is identical with the initial state (Fig. 1.6). p Properties may be of two types. Intensive properties are independent of the mass in the system, e.g. pressure, b temperature, etc. Extensive properties are related to mass, e.g., volume, energy, etc. If mass is increased, the values of 2 the extensive properties also increase. Specific extensive properties, i.e., extensive properties per unit mass, are ν A intensive properties, e.g., specific volume, specific energy, 121A density, etc. Fig. 1.6 A process and a cycle 1.4 HOMOGENEOUS AND HETEROGENEOUS SYSTEMS A quantity of matter homogeneous throughout in chemical composition and physical structure is called a phase. Every substance can exist in any one of the three phases, viz., solid, liquid and gas. A system consisting of a single phase is called a homogeneous system, while a system consisting of more than one phase is known as a heterogeneous system. 1.5 THERMODYNAMIC EQUILIBRIUM A system is said to exist in a state of thermodynamic e uilibrium when no change in any macroscopic prop- erty is registered, if the system is isolated from its surroundings. An isolated system always reaches in course of time a state of thermodynamic equilibrium and can never depart from it spontaneously. Therefore, there can be no spontaneous change in any macroscopic property if the system exists in an equilibrium state. Thermodynamics studies mainly the properties of physical systems that are found in equi- librium states. A system will be in a state of thermodynamic equilibrium, if the conditions for the following three types of equilibrium are satisfied: (a) Mechanical equilibrium (b) Chemical equilibrium (c) Thermal equilibrium In the absence of any unbalanced force within the system itself and also between the system and the sur- roundings, the system is said to be in a state of mechanical e uilibrium. If an unbalanced force exists, either the system alone or both the system and the surroundings will undergo a change of state till mechanical equilibrium is attained. If there is no chemical reaction or transfer of matter from one part of the system to another, such as diffu- sion or solution, the system is said to exist in a state of chemical e uilibrium. When a system existing in mechanical and chemical equilibrium is separated from its surroundings by a diathermic wall (diathermic means which allows heat to flow’) and if there is no spontaneous change in any property of the system, the system is said to exist in a state of thermal e uilibrium. When this is not satisfied, the system will undergo a change of state till thermal equilibrium is restored.  4 Basic and Applied Thermodynamics When the conditions for any one of the three types of equilibrium are not satisfied, a system is said to be in a none uilibrium state. If the nonequilibrium of the state is due to an unbalanced force in the interior of a system or between the system and the surroundings, the pressure varies from one part of the system to another. There is no single pressure that refers to the system as a whole. Similarly, if the nonequilibrium is because of the temperature of the system being different from that of its surroundings, there is a nonuniform temperature distribution set up within the system and there is no single temperature that stands for the system as a whole. It can thus be inferred that when the conditions for thermodynamic equilibrium are not satisfied, the states passed through by a system cannot be described by thermodynamic properties which represent the system as a whole. Thermodynamic properties are the macroscopic coordinates defined for, and significant to, only ther- modynamic equilibrium states. Both classical and statistical thermodynamics study mainly the equilibrium states of a system. 1.6 QUASI-STATIC PROCESS Let us consider a system of gas contained in a cylinder (Fig. 1.7). The system initially is in an equi- librium state, represented by the properties p1, υ1, t1. The weight on the piston just balances the upward force exerted by the gas. If the weight is removed, there will be an unbalanced force between the system and the surroundings, and under gas pressure, the piston will move up till it hits the stops. The system again comes to an equilibrium state, being described by the properties p 2, υ2, t2. But the intermediate states passed through by the Fin system are nonequilibrium states which cannot W i be described by thermodynamic coordinates. Figure 1.8 shows points 1 and 2 as the initial and Pi n final equilibrium states joined by a dotted line, which has got no meaning otherwise. Now if the ni i p1 ν1 single weight on the piston is made up of many t1 very small pieces of weights (Fig. 1.9), and these nd weights are removed one by one very slowly from Fig. 1.7 Transition between two equilibrium the top of the piston, at any instant of the upward states by an unbalanced force travel of the piston, if the gas system is isolated, the departure of the state of the system from the ther modynamic e uilibrium state will be infinitesimally small. So every state passed through by the system 1 p1 will be an equilibrium state. Such a process, which p is but a locus of all the equilibrium points passed through by the system, is known as a uasi static process (Fig. 1.10), quasi’ meaning almost’. p2 2 Infinite slowness is the characteristic feature of a uasi static process. A quasi-static process is thus ν1 ν ν2 a succession of equilibrium states. A quasi-static process is also called a reversible process. Fig. 1.8 Plot representing the transition between two equilibrium states  Introduction 5 1 ii i p i i i Pi n p1 ν1 t1 nd 2 ν Fig. 1.9 Infinitely slow transition of a Fig. 1.10 A quasi-static process system by infinitesimal force 1.7 PURE SUBSTANCE A pure substance is defined as one that is homogeneous and invariable in chemical composition throughout its mass. The relative proportions of the chemical elements constituting the substance are also constant. Atmospheric air, steam-water mixture and combustion products of a fuel are regarded as pure substances. But the mixture of air and liquid air is not a pure substance, since the relative proportions of oxygen and nitrogen differ in the gas and liquid phases in equilibrium. The state of a pure substance of given mass can be fixed by specifying two properties, provided the system is in equilibrium. This is known as the two-property rule’. The state can thus be represented as a point on thermodynamic property diagrams. Once any two properties of a pure substance are known, other properties can be determined from the available thermodynamic relations. 1.8 CONCEPT OF CONTINUUM From the macroscopic viewpoint, we are always concerned with volumes which are very large compared to molecular dimensions. Even a very small volume of a system is assumed to contain a large number of molecules so that statistical averaging is meaningful and a property value can be assigned to it. Disregarding the behaviour of individual molecules, matter is here δm treated as continuous. Let us consider the mass δm in a volume δV surrounding P the point P (Fig. 1.11). The ratio δm δV is the average mass density of the system δV within the volume δV. We suppose that at first δV is rather large, and is subse- quently shrunk about the point P. If we plot δm/δV against δV, the average den- sity tends to approach an asymptote as δV increases (Fig. 1.12). However, when Fig. 1.11 δV becomes so small as to contain relatively few molecules, the average density fluctuates substantially with time as molecules pass into and out of the volume in random motion, and so it is impossible to speak of a definite value of δm/δV. The smallest volume which may be regarded as continuous is δV ′. The density ρ of the system at a point is thus defined as δm ρ = lim (1.1) δV → δV ′ δV  6 Basic and Applied Thermodynamics Similarly, the fluid velocity at a point P is defined as the instantaneous velocity of the centre of in in gravity of the smallest continuous volume δV ′. n in The concept of continuum loses validity when δm δV the mean free path of the molecules approaches the order of magnitude of the dimensions of the vessel, as, for instance, in highly rarefied gases encountered in high vacuum technology, in rocket flights at high altitudes and in electron tubes. In most engineering applications, however, ρ the assumption of a continuum is valid and con- venient, and goes hand in hand with the macro- scopic point of view. δV′ δV 1.9 THERMOSTATICS Fig.1.12 Definition of the macroscopic property, density The science of thermodynamics deals with sys- tems existing in thermodynamic equilibrium states which are specified by properties. Infinitely slow quasi-static processes executed by systems are only meaningful in thermodynamic plots. The name thermodynamics’ is thus said to be a misnomer, since it does not deal with the dynamics of heat, which is nonquasi-static. The name thermostatics’ then seems to be more appropriate. However, most of the real processes are dynamic and nonquasi-static, although the initial and final states of the system might be in equilibrium. Such processes can be successfully dealt with by the subject. Hence, the term thermodynamics’ is not inappropriate. 1.10 UNITS AND DIMENSIONS In the present text, the SI (System International) system of units has been used. The basic units in this system are given in Table 1.1. Table 1.1 System: Basic Units Quantity Unit Symbol Length (L) Metre m Mass (M) Kilogramme kg Time (t) Second s Amount of substance Mole mol Temperature (T) Kelvin K Electric current Ampere A Luminous intensity Candela cd Plane angle Radian rad Solid angle Steradian sr  Introduction 7 The dimensions of all other quantities are derived from these basic units which are given in Table 1.2. Table 1.2 SI System: Derived Units Quantity Unit Symbol Alternative unit In basic units Force (F ) Newton N kg m/s2 Energy (E) Joule J Nm kg m2/s2 Power Watt W J/s kg m2/s3 Pressure Pascal Pa N/m2 kg/(ms2) Frequency Hertz Hz s−1 Electric charge Coulomb C As Electric potential Volt V W/A = J/C kg m2/(s3 A) Capacitance Farad F C/V s4 A2/(kg m2) Electrical resistance Ohm Ω V/A kg m2/(s3 A2) Magnetic flux Weber Wb Vs kg m2/(s2 A) Magnetic flux density Tesla T Wb/m2 kg/(s2 A) Inductance Henry H Wb/A kg m2/(s2 A2) It is often convenient and desirable to use multiples of various units, the standard list of which is given in Table 1.3. Table 1.3 SI System: Standard Multipliers Factor Prefix Factor Prefix 1012 tera, T 10−3 milli, m 109 giga, G 10−6 micro, μ 106 mega, M 10−9 nano, n 103 kilo, k 10−12 pico, p 1.10.1 Force The force acting on a body is defined by Newton’s second law of motion. The unit of force is the newton ( N). A force of one newton produces an acceleration of 1 ms−2 when applied to a mass of 1 kg. 1 N = 1 kg m/s2 The weight of a body (W) is the force with which the body is attracted to the centre of the earth. It is the product of its mass (m) and the local gravitational acceleration (g), i.e. W = mg The value of g at sea level is 9.80665 m/s2. The mass of a substance remains constant with elevation, but its weight varies with elevation.  8 Basic and Applied Thermodynamics 1.10.2 Pressure δA Pressure is the normal force exerted by a system against unit area of the bounding surface. If δA is a small area and δA′ is the smallest area from Fn continuum consideration, and δFn is the component of force normal to δA (Fig. 1.13), the pressure p at a point on the wall is defined as δ Fn p= lim Fig. 1.13 Definition of pressure δA → δA ′ δA The pressure p at a point in a fluid in equilibrium is the same in all directions. The unit for pressure in the SI system is the pascal (Pa), which is the force of one newton acting on an area of 1 m2. 1 Pa = 1 N/m2 The unit of pascal is very small. Very often kilo-pascal (kPa) or mega-pascal (MPa) is used. Two other units, not within the SI system of units, continue to be widely used. These are the bar, where 1 bar =105 Pa = 100 kPa = 0.1 MPa and the standard atmosphere, where 1 atm = 101.325 kPa = 1.01325 bar Most instruments indicate pressure relative to the atmospheric pressure, whereas the pressure of a system is its pressure above zero, or relative to a perfect vacuum. The pressure relative to the atmosphere is called gauge pressure. The pressure relative to a perfect vacuum is called absolute pressure. Absolute pressure = Gauge pressure + Atmospheric pressure When the pressure in a system is less than atmospheric pressure, the gauge pressure becomes negative, but is frequently designated by a positive number and called vacuum. For example, 16 cm vacuum will be 76 – 16 × 1.013 = 0.80 bar 76 Figure 1.14 shows a few pressure measuring devices. Figure (a) shows the Bourdon gauge which mea- sures the difference between the system pressure inside the tube and atmospheric pressure. It relies on the deformation of a bent hollow tube of suitable material which, when subjected to the pressure to be measured on the inside (and atmospheric pressure on the outside), tends to unbend. This moves a pointer through a suit- able gear-and-lever mechanism against a calibrated scale. Figure (b) shows an open U-tube indicating gauge pressure, and Fig. (c) shows an open U-tube indicating vacuum. Figure (d) shows a closed U-tube indicating absolute pressure. If p is atmospheric pressure, this is a barometer. These are called U-tube manometers. If is the difference in the heights of the fluid columns in the two limbs of the U-tube Fig. (b) and Fig. (c) , ρ the density of the fluid and g the acceleration due to gravity, then from the elementary principle of hydrostatics, the gauge pressure pg is given by ⎡ kg m ⎤ pg = ρg ⎢ m ⋅ 3 2 ⎥ = ρg N/m2 ⎢⎣ m s ⎥⎦ If the fluid is mercury having ρ = 13,616 kg/m3, one metre head of mercury column is equivalent to a pressure of 1.3366 bar, as shown below 1 m Hg = ρg = 1 × 13616 × 9.81 = 1.3366 × 105 N/m2 = 1.3366 bar The manometer is a sensitive, accurate and simple device, but it is limited to fairly small pressure differ- entials and, because of the inertia and friction of the liquid, is not suitable for fluctuating pressures, unless the rate of pressure change is small. A diaphragm-type pressure transducer along with a cathode ray oscilloscope can be used to measure rapidly fluctuating pressures.  Introduction 9 p p p p v d p p Z Z Z p d Fig. 1.14 Pressure gauges (a) bourdon gauge (b) open U-tube indicating gauge pressure (c) open U-tube indicating vacuum (d) closed U-tube indicating absolute pressure 1.10.3 Specific Volume and Density Volume (V ) is the space occupied by a substance and is measured in m3. The specific volume (υ) of a sub- stance is defined as the volume per unit mass and is measured in m3/kg. From continuum consideration the δV specific volume at a point is defined as υ = lim δV → δV ′ δ m where δV ′ is the smallest volume for which the system can be considered a continuum. Density (ρ) is the mass per unit volume of a substance, which has been discussed earlier, and is given in kg/m3. m ρ= υ In addition to m3, another commonly used unit of volume is the litre (l). 1l = 10−3 m3 The specific volume or density may be given either on the basis of mass or in respect of mole. A mole of a substance has a mass numerically equally to the molecular weight of the substance. One g mol of oxygen has a mass of 32 g and 1 kg mol (or kmol) of nitrogen has a mass of 28 kg. The symbol υ is used for molar specific volume (m3/kmol). 1.10.4 Energy Energy is the capacity to exert a force through a distance, and manifests itself in various forms. Engineering processes involve the conversion of energy from one form to another, the transfer of energy from place to place, and the storage of energy in various forms, utilizing a working substance. The unit of energy in the SI system is Nm or J ( joule). The energy per unit mass is the specific energy, the unit of which is J/kg. 1.10.5 Power The rate of energy transfer or storage is called power. The unit of power is watt (W), kilowatt (kW) or mega- watt (MW). 1 W = 1 J/s = 1 Nm/s 1 kW = 1000 W  10 Basic and Applied Thermodynamics 1.11 HISTORY OF THERMODYNAMICS The latter half of the eighteenth century ushered man into the modern world of machinery and manufacture, and brought about cataclysmic changes in the social, economic and political life of the people. The historians have called it the Industrial Revolution. It began in England due to a fortuitous combination of many factors. There was bustling creative activity in science and technology during this period in England, with the appearance of a galaxy of some brilliant individuals. The invention of the steam engine gave an impetus to this activity, and for the first time made man free from the forces of nature. The name of Savery, Newcomen and notably James Watt are associated with this invention. Watt brought about considerable improvement in the performance of the steam engine, which began to be widely used in coal mines, iron metallurgy and textile mills. George Stephenson introduced steam engine for rail transport, and Robert Fulton used it in steam boats. A variety of industries grew up, and man gradually entered into the modern machine age. The advent of steam engine also gave stimulus to the birth of thermodynamics. Thermodynamics is said to be the daughter of the steam engine. D. Bradley, Thermodynamics – the Daughter of Steam , Engineering Heritage, Vol. 2, I.Mech.E., London, 1966. There was once a young inventor who thought that he could produce energy out of nothing. It is well known , said he, that an electrical motor converts electrical energy into mechanical energy and that an elec- tric generator converts mechanical energy into electrical energy. Why not then, use the motor to run the gen- erator and the generator to run the motor, and create thereby an endless supply of energy But this is never to happen. A hypothetical device which creates energy from nothing is called a perpetual motion machine of the first kind, a PPMI. Like the proverbial touchstone which changes all metals into gold, man attempted to find such a PMMI for long long years, but it turned out to be a wild goose chase. In fact, the development of the principle of conservation of energy has been one of the most significant achievements in the evolution of physical science. The first recognition of this principle was made by Leibnitz in 1693, when he referred to the sum of kinetic energy and potential energy in a gravitational force field. Energy is neither created nor destroyed. Energy manifests in various forms and gets transformed from one form to another. Through gentle metabolic processes, a day labourer gradually transforms the chemical energy of the food he eats and the oxygen he breathes into heat, sound and useful work. Work was always considered a form of energy. The concept of heat was, however a very actively debated scientific topic. Until the middle of the nineteenth century, heat was regarded as an invisible colourless, weightless, odourless fluid that flowed from a body of higher calorie to a body of lower calorie. This was known as the caloric theory of heat, first proposed in 1789 by Antoine Lavoisier (1743–1794), the father of modern chemistry. When an object became full of caloric, it was then said to be saturated with it. This was the origin of the terms saturated liquid , saturated vapour etc, that we use in thermodynamics today. The caloric was said to be conserved and it was indestructible. The caloric theory was, however, refuted and heat was confirmed as a form of energy in the middle of the nine- teenth century leading to the formulation of the first law of thermodynamies. The names which stand out in the establishment of the first law were Benjamin Thompson (1753–1814), James Prescott Joule (1818–1889) and Julius Robert Mayer (1814 –1878). Benjamin Thompson, and American born in Massachusetts, did not support the revolt against the British during the American war of independence, and in 1775 he left for England where he took up government service. On a trip to Germany, he met the prince of Bavaria who offered him a job. He introduced many reforms in the government for which the title of Count von Rumford was conferred on him. While boring brass cannon hole, Count Rumford noticed that there was a continuous heat realease. How could the caloric fluid be conserved, when it was being produced continuously by mechanical friction From the established principle of conserva- tion of mass, a true fluid can be neither created nor destroyed, so heat could not be a fluid if it could be continu- ously created in an object by mechanical friction. Rumford conceived that heat was a kind of motion and the hotness of an object was due to the vibrating motion of the particles in the objects. On his return to England, he  Introduction 11 became a member of the Royal Society, and later founded the Royal Institution for the Advancement of Science. Rumford married the widow of Lavoisier and lived in Paris for the rest of his eventful life. In the early forties of the nineteenth century, James P. Joule and Julius R. Mayer almost simultaneously set forth the idea that heat transfer and mechanical work were simply different forms of the same quantity, which we now recognize as energy in transit. In some modern treatments of engineering thermodynamies, Joule’s name alone is attached to the establishment of the equivalence of heat and work. The published record, however, shows that the idea of convertibility of heat into work was published independently by Mayer in May, 1842 and Joule in August, 1843. For an important aspect in the history of the first law, is the fact that both Mayer and Joule had difficulty in getting their papers published and in being taken seriously by their established contemporaries. Robert Mayer was a doctor in a ship in the East Indies and from physiological observations, he believed in a principle of conservation of energy. He derived theoretically, the mechanical heat equivalent based on the calorimetric data of Joseph Black of Glasgow University. Mayer tried to publish his paper but remained unsuc- cessful for a long time. His despair was so great that he attempted suicide by jumping from a window, but he only broke his two legs. He was placed in an asylum for some time. In later years, however, he was given some measure or recognition and honoured equally with Joule in establishing the mechanical theory of heat. Mayer argued that an amount of gas needs to be heated more at constant pressure than at constant volume, because at constant pressure it is free to dilate and do work against the atmosphere, which in today’s notations becomes mcp ΔT − mcv ΔT = Patm ΔV (1.2) Using the cp and cp/cv constants that were known in his time, he estimated the left-hand side of the equa- tion in calories, while the right-hand side was known in mechanical units. He thus established numerically the equivalence between these units. If the relation Pυ = RT (1.3) is used in Eq. (1.2), Mayer’s argument reduces to c p − cv = R (1.4) This classic relationship between the specific heats of an ideal gas is called Mayer’s equation: while the ideal gas equation of state, Eq. (1.3), was first derived by Clapeyron Bejan, 1988. Joule was the ultimate experimentalist. His experiments seem to be the direct continuation of those of Rumford and the gap of some forty years between the two investigations appeared puzzling to some authors. Joule’s first discovery from his measurements was that the flow of current in a resistance, is accompanied by the development of heat proportional to the resistance. He concluded that caloric was indeed created by the flow of current. He was firmly convinced that there existed some conservation law of a general nature and hence set out to investigate whether the conversion of the various forms of energy is governed by definite conversion factors. He considered the conversion of chemical, electric, caloric, and mechanical energy forms in all combinations. The determination of the mechanical equivalent of heat forms the central part of his experiments, the results of which can be summed up in the general relation: W = JQ (1.5) where J is the mechanical equivalent of heat. Joule’s experiments suggested that this relation may have uni- versal validity with the same numerical value of J under all conditions. Joule communicated the results of his experiments to the British Association for the Advancement of Science in 1843. It was received with entire incredulity and general silence. In 1844 a paper by Joule on the same subject was rejected by the Royal Society. To convince the skeptics, he produced a series of nakedly simple experiments whose message proved impossible to refute. From the point of view of mechanical engineers, the most memorable among these experiments was the heating of a pool of water by an array of paddle wheels driven by falling weights. He discussed in 1847, before the British Association at Oxford, his Adrian Bejan, Research into the Origins of Engineering Thermodynamics , Int. Comm. Heat Mass Transfer, Vol. 15, No. 5, 1988, pp 571–580.  12 Basic and Applied Thermodynamics experimental results in which he suggested that the water at the bottom of the Niagara waterfall (160 feet high) should be warmer than at the top (by 0.2°F). From the thermal expansion of gases Joule deduced that there should be a zero of temperature , 480°F below the freezing point of ice. This was the first suggestion of absolute zero. Although these results failed to provoke further discussion, it created interest in a young man who only two year ago had passed from the University of Cambridge with the highest honour. The young man was William Thomson, who later became Lord Kelvin. He somewhere stated that it was one of the most valuable recollections of his life. Michael Faraday was also present in the 1844 Oxford meeting, and he communicated Joule’s paper On the Mechanical Equivalent of Heat to the Royal Society in 1849. The paper ultimately appeared in its Philosphical Transactions in 1850. Even while Joule was perfecting the experimental basis of the energy law now called the Mayer-Joule principle, Herman Ludwig von Helmohltz (1821–1894) published in 1847, his famous essay on the conser- vation of force. In this work, he advanced the conservation of energy as a unifying principle extending over all branches of physics. Helmholtz, like Mayer, was a physician by profession and self-taught in Physics and Mathematics. He also faced great difficulties in getting his paper published in professional journals. In the history of classical thermodynamics, one thinks of only the closed system formulations of the first law which were deliberated by the pioneers as stated above. In engineering thermodynamics, however, open system formulations are of prime interest. The first law for open systems was first stated by Gustave Zeuner, as part of the analysis of flow systems that operate in the steady state. Zeuner’s formula for the heat transfer rate to a stream m in steady flow and without shaft work in present notations is given to be: dQ / m = d (u + Pυ + V 2 / 2 + gz ) (1.6) The reference of this formula is found in Stodola’s classic treatise on steam turbines, first published in the German language in 1903. The first person to invent a theory simultaneously involving the ideas of conservation and conversion of energy was the young French military engineer Nicolas Leonard Sadi Carnot (1796–1832). The strikingly origi- nal ideas of Carnot’s work make it among the most brilliant new departures in theoretical physics. Sadi Carnot was the son of Napoleon’s general, Lazare Carnot, and was educated at the famous Ecole Polytechnique in Paris. Between 1794 and 1830, Ecole Polytechnique had such famous teachers as Lagrange, Fourier, Laplace, Ampere, Cauchy, Coriolis, Poisson. Gay-Lussac, and Poiseuille. After his formal education Carnot chose a career as an army officer. Britain was then a powerful military force, primarily as a result of the industrial rev- olution brought about by the steam engine. French technology was not developing as fast as Britain’s. Carnot was convinced that France’s inadequate utilization of steam power had made it militarily inferior. He began to study the fundamentals of steam engine technology, and in 1824 he published the results of his study in the form of a brochure Reflection on the Motive Power of Heat and on Machines Fitted to Develop that Power. Carnot was trained in the basic principles of hydraulics, pumps and water wheels at the Ecole Polytechnique. During Carnot’s time, caloric theory of heat was still persisting, and the water wheel as the major source of mechanical power was gradually getting replaced by the steam engine. Carnot conceived that the power of a steam engine was released, as the heat fluid or caloric fell from the high temperature of the boiler to the lower temperature of the condenser, in much the same way that water falls through a water wheel to produce mechanical shaft work output. Carnot stated, The motive power of a water wheel depends on its height and the quantity of liquid. The motive power of heat also depends on the quantity of caloric used and on the height of its fall, i.e., the difference of temperatures of the bodies between which the exchange of caloric is made. Till Carnot’s time thermodynamics was developed primarily on an empricial basis provided by chemistry. Carnot approached an engineering problem, the efficiency of heat engines, in terms of entirely new concepts with the steam engine serving as the stimulus. Carnot observed that the existence of temperature differences is a necessary condition for producing mechanical work by means of a heat engine. He simplified the problem to its bare essentials and stipulates, that this system, consisting essentially of a working substance, should  Introduction 13 exchange heat with its surroundings only at two fixed temperatures. In order to conceptualize such a situa- tion, he introduces the idea of heat reservoirs. Two important conclusions emerged from Carnot’s work. 1. No one could build a water wheel that would produce a continuous work output unless water actually entered and exited the wheel. If water with a certain kinetic and potential energy entered the wheel, then the same amount of water with a lower energy must also exit the wheel. It is thus impossible to make a water wheel that converts all the energy of the inlet water into shaft work output. There must be an ourflow of water form the wheel. If this idea is extended to a steam engine by replacing the water by heat fluid caloric, it can be concluded that when caloric at a certain energy level (temperature) enters a work producing heat engine, it must also exit the heat engine at a low energy level (temperature). Thus a continuously operating heat engine that converts all of its caloric (heat) input directly into work output is not possible. This is very close to the Kelvin-Planck statement of second law as it is known today. 2. The maximum efficiency of a water wheel was independent of the type of the liquid and depended only on the inlet and outlet flow energies. The maximum efficiency of the steam engine (or any heat engine) depends only on the temperatures of the high and low temperature thermal reservoirs of the engine and is independent of the working fluid. To achieve the maximum efficiency there must not be any mechanical friction or other losses of any kind. Only at the age of 36, Sadi Carnot died of cholera following an attack of scarlet fever. The significance of Carnot’s work was not recognized until 1850, when Rudolf Clausius (1822–1888) and William Thomson (1824–1907) worked out a clear formulation of the conservation of energy principle. Carnot’s first conclusion was then called the second law of thermodynamics by Clausius, and Thomson used Carnot’s second conclu- sion to develop the concept of absolute temperature scale. Thermodynamics is thus said to have originated from the clumsy puffing of the early steam engines and is often called the daughter of steam engine. Carnot’s ideas were so revolutionary that they were largely ignored. Soon after Carnot’s death, Emile Clapeyron (1799–1864), a French mining engineer, strengthened Carnot’s ideas by using more precise math- ematical derivation. Clapeyron constructed its thermodynamic cycle by deducing that it must be composed of two reversible isothermal processes and two reversible adiabatic processes. It is now known as Carnot’s cycle. It was the first heat engine cycle to be conceptualized. No other heat engine can equal its efficiency. Clapeyron was later able to derive a relation for the enthalpy change of the liquid to vapour phase (hf g) in terms of pressure, temperature and specific volume. This provided the first equation, now called the Clausius- Clapeyron equation, representing the first order phase transition, which could be used to estimate a property that is nor directly measurable in terms of properties that are directly measurable. Clapeyron’s equation is now most easily derived from one of Maxwell’s equations. William Thomson (1824–1907), who became a professor of natural philosophy at the University of Glasgow in 1848 at the age of 24 only, rejected the caloric theory of heat and for the first time used the terms thermodynamics and mechanical energy. Apart from the deduction of the absolute temperature scale, Thomson worked with Joule from 1852 to 1862 in a series of experiments to measure the temperature of gas in a controlled expansion and propounded the Joule-Thomson effect for real gases. Rudolf Julius Emanuel Clausius (1822–1888) realized that there were two distinct laws at work, the first law due to Joule and Mayer and the second law as expounded by Carnot. He defined the internal energy U. Although both Kelvin and Clausius used the function Qrev /T for some years, Clausius recognized the value of this function and to describe it he coined the word entropy from the Greek work tropee meaning transformation and assigned it the symbol S. Clausius in 1865, summarized the first and second laws of thermodynamics in the following words: Die Energie der Welt ist konstant. Die Entropie der Welt strebt einem Maximum zu which is translated as The energy of the world is constant.  14 Basic and Applied Thermodynamics The entropy of the world tends toward a maximum The world here means the universe, the system and the surroundings together. These statements made a strong impression upon a young student, Max Karl Ernst Ludwig Planck (1858– 1947). He was educated at the universities of Munich and Berlin. In his autobiography he stated, One day I hap- pened to come across the treatises of Rudolf Clausius, whose lucid style and enlightening clarity of reasoning made an enormous impression on me, and I became deeply absorbed in his articles, with an ever increasing enthusiasm. I appreciated especially his exact formulation of the two laws of thermodynamics, and the sharp distinction, which he was the first to establish between them. In 1897, Planck1 demonstrated the close con- nection between the second law and the concept of reversibility. He stated the second law as the impossibility of a cyclic device which produces positive work and exchanges heat with a single reservoir. Similar statement was also made by Kelvin, and is now recognized as Kelvin-Planck statement of second law. Poincare2 in 1908, extended the work of Planck and prescribed a complete structure of classical thermodynamics. The property, entropy, plays a stellar role in thermodynamics. It was introduced via the concept of heat engines. In 1909, the Greek mathematician Caratheodory proved the existence of entropy function mathe- matically without the aid of Carnot engines and refrigerators. Caratheodory’s statement of second law may be stated as: In the neighbourhood of any arbitrary state P0 of a physical system, there exist neighbouring states which are not accessible from P0 along quasi-statie adiabatic paths. From the standpoint of the engineer and physicist it is entirely mathematical in form and devoid of physical insight. William John Macquorn Rankine (1820–1872) defined the thermodynamic efficiency of a heat engine and showed the usefulness of p–υ diagrams as related to work. He wrote the first text book on thermodynamics3, and was the first to work out the thermodynamic cycle for the adiabatic cylinder steam engine, now known as Rankine cycle for a vapour power cycle. In 1862, the cycle used in modern gasoline-powered I.C engines was proposed in a patent issued to Alphonse Beau de Rochas (1815–1893). The first practical engine was, however, built by Nikolous August Otto (1832–1891) which was demonstrated at the Paris Exposition in 1878. Otto fought many legal battles with Beau de Rochas for production of these engines, but finally lost to him. Captain John Ericsson (1803–1889) was a Swedish engineer who marketed small solar-powered and coal- fired hot air engines. Rev. Robert Stirling (1790–1879), an English parish minister, patented a practical heat engine in 1816 that used air as the working fluid. In theory, the cycle used the Stirling engine approaches the ideal cycle later proposed by Carnot (1824). George Bailey Brayton (1830–1892), an American engineer, marketed an I.C. engine with a separate com- bustion chamber, where combustion of fuel occurred at about constant pressure. This cycle later formed the basis for modern gas turbine plants. Gottlieb Daimler (1834–1900) obtained a patent in 1879 for a multicylinder automotive engine, which was commercially successful. Dr. Rudolf Christian Karl Diesel (1858–1913) studied at Technische Hochschule in Munich. He designed large steam engines and boilers. He later developed in 1897 an I.C. engine with fuel injec- tion which resembled the modern diesel engine. Failing health, continuing criticism and serious financial set- backs beset Diesel who in 1913 disappeared from a boat crossing the English channel in a moonlit night. Josiah Willard Gibbs (1839–1903) is often regarded as the most brilliant thermodynamicist produced in the USA. He received the first doctorate degree in engineering in the USA (Yale University). He contributed significantly in many areas of thermodynamics like heterogeneous systems, phase rule, physical chemistry and statistical ther- modynamics. Some of his very important papers were published in obseure journals like Connecticut Academy of Sciences, and remained unknown to most scientists. Only after his death, these were discovered. 1 M. Planck, Treatise on Thermodynamics (1897), translated by A. Ogg, Longman and Green London, 1927. 2 H. Poincare, Thermodynami ue, Gauthier-Villars, Paris, 1908. 3 W.J.M. Rankine, Manual of the Steam Engine and other Prime Movers , 1859 going through 17 editions, as mentioned by Robert Balmer in Thermodynamics , West Publishing Co., 1990, page 399.  Introduction 15 Solved Examples Example 1.1 The pressure of gas in a pipe line is measured with a mercury manometer having one limb open to the atmosphere (Fig. Ex. 1.1). If the difference in p the height of mercury in the two limbs is 562 mm, calculate the gas pres- sure. The barometer reads 761 mm Hg, the acceleration due to gravity is p0 9.79 m/s2, and the density of mercury is 13,640 kg/m3. z Solution At the plane AB, we have p = p0 + ρgz A B Now p0 = ρgz0 where z0 is the barometric height, ρ the density of mercury and p0 the atmospheric pressure. Fig. Ex. 1.1 Therefore p = ρg (z + z0) = 13,640 kg/m3 × 9.79 m/s2 (0.562 + 0.761) m = 177 × 103 N/m2 = 177 kPa = 1.77 bar = 1.746 atm Ans. Example 1.2 A turbine is supplied with steam at a gauge pressure of 1.4 MPa. After expansion in the turbine the steam flows into a condenser which is maintained at a vacuum of 710 mm Hg. The barometric pressure is 772 mm Hg. Express the inlet and exhaust steam pressure in pascals (absolute). Take the density of mer- cury as 13.6 × 103 kg/m3. Solution The atmospheric pressure p0 = ρgz0 = 13.6 × 103 kg/m3 × 9.81 m/s2 × 0.772 m = 1.03 × 105 Pa Inlet steam pressure = (1.4 × 106) + (1.03 × 105) Pa = 15.03 × 105 Pa = 1.503 MPa Ans. Condenser pressure = (0.772 − 0.710) m × 9.81 m/s2 × 13.6 × 103 kg/m3 = 0.827 × 104 Pa = 8.27 kPa Ans. Review Questions 1.1 What do you understand by macroscopic and 1.8 Define an isolated sysetm. microscopic viewpoints 1.9 Distinguish between the terms change of state’, 1.2 Is thermodynamics a misnomer for the subject path’, and process’. 1.3 How does the subject of thermodynamics differ 1.10 What is a thermodynamic cycle from the concept of heat transfer 1.11 What are intensive and extensive properties 1.4 What is the scope of classical thermodynamics 1.12 What do you mean by homogeneous and hetero- 1.5 What is a thermodynamic system geneous systems 1.6 What is the difference between a closed system 1.13 Explain what you understand by thermodynamic and an open system equilibrium. 1.7 An open system defined for a fixed region and a 1.14 Explain mechanical, chemical and thermal control volume are synonymous. Explain. equilibrium. 16 Basic and Applied Thermodynamics 1.15 What is a quasi-static process/What is its charac- 1.17 What is vacuum How can it be measured teristic feature 1.18 What is a pressure transducer 1.16 What is the concept of continuum How will you define density and pressure using this concept Problems 1.1 A pump discharges liquid into a drum at the rate 1.7 Assume that the pressure p and the specific of 0.0032 m3/s. The drum, 1.50 m in diameter and volume v of the atmosphere are related accord- 4.20 m in length, can hold 3000 kg of the liquid. ing to the equation pv1.4 = 2.3 × 103, where p is Find the density of the liquid and the mass flow in N/m2 abs and v is in m3/kg. The acceleration rate of the liquid handled by the pump. due to gravity is constant at 9.81 m/s2. What is the 1.2 The acceleration of gravity is given as a function depth of atmosphere necessary to produce a pres- of elevation above sea level by sure of 1.0132 bar at the earth’s surface Consider the atmosphere as a fluid column. Ans. 64.8 km g = 980.6 − 3.086 × 10−6 H 1.8 The pressure of steam flowing in a pipe line is where g is in cm/s2, and H is in cm. If an aero- measured with a mercury manometer, shown in plane weighs 90,000 N at sea level, what is the Fig. P. 1.8. Some steam condenses into water. gravity force upon it at 10,000 m elevation What Estimate the steam pressure in kPa. Take the is the percentage difference from the sea-level density of mercury as 13.6 × 103 kg/m3, density weight of water as 103 kg/m3, the barometer reading as 1.3 Prove that the weight of a body at an elevation H 76.1 cm Hg, and g as 9.806 m/s2. above sea-level is given by mg ⎛ d ⎞⎟2 p W= ⎜⎜ ⎟ g0 ⎜⎝ d + 2H ⎟⎟⎠ p0 where d is the diameter of the earth. 1.4 The first artificial earth satellite is reported to have encircled the earth at a speed of 28,840 km/h 50 2 and its maximum height above the earth’s surface 3 was stated to be 916 km. Taking the mean diam- eter of the earth to be 12,680 km, and assuming the orbit to be circular, evaluate the value of the gravitational acceleration at this height. The mass of the satellite is reported to have been 86 kg at sea-level. Estimate the gravitational force Fig. P.1.8 acting on the satellite at the operational altitude. 1.9 A vacuum gauge mounted on a condenser reads Ans. 8.9 m/s2 765 N 0.66 m Hg. What is the absolute pressure in the 1.5 Convert the following readings of pressure to condenser in kPa when the atmospheric pressure kPa, assuming that the barometer reads 760 mm is 101.3 kPa Ans. 8.8 kPa Hg: 1.10 The basis barometer can be used to measure the (a) 90 cm Hg gauge, (b) 40 cm Hg vacuum, height of a building. If the barometric readings at (c) 1.2 m H2O gauge, (d) 3.1 bar. the top and at the bottom of a building are 730 and 1.6 A 30 m high vertical column of a fluid of density 760 mm Hg, respectively, determine the height of 1878 kg/m3 exists in a place where g = 9.65 m/s2. the building. Assume an average air density of What is the pressure at the base of the column. 1.18 kg/m3. Ans. 544 kPa  C H A P T E R 2.1 ZEROTH LAW OF THERMODYNAMICS 2 Temperature The property which distinguishes thermodynamics from other sciences is temperature. One might say that temperature bears as important a relation to thermodynamics as force does to statics or velocity does to dynamics. Temperature is associated with the ability to distinguish hot from cold. When two bodies at different temperatures are brought into contact, after some time they attain a common temperature and are then said to exist in thermal equilibrium. When a body A is in thermal e uilibrium with a body B, and also separately with a body C, then B and C will be in thermal e uilibrium with each other. This is known as the zeroth law of thermodynamics. It is the basis of temperature measurement. In order to obtain a quantitative measure of temperature, a reference body is used, and a certain physical characteristic of this body which changes with temperature is selected. The changes in the selected char- acteristic may be taken as an indication of change in temperature. The selected characteristic is called the thermometric property, and the reference body which is used in the determination of temperature is called the thermometer. A very common thermometer consists of a small amount of mercury in an evacuated capillary tube. In this case the extension of the mercury in the tube is used as the thermometric property. There are five different kinds of thermometer, each with its own thermometric property, as shown in Table 2.1. Table 2.1 Thermometers and Thermometric Properties Thermometer Thermometric property Symbol 1. Constant volume gas thermometer Pressure p 2. Constant pressure gas thermometer Volume V 3. Electrical resistance thermometer Resistance R 4. Thermocouple Thermal e.m.f. ε 5. Mercury-in-glass thermometer Length L 2.2 MEASUREMENT OF TEMPERATURE—THE REFERENCE POINTS The temperature of a system is a property that determines whether or not a system is in thermal equilibrium with other systems. If a body is at, say, 70°C, it will be 70°C, whether measured by a mercury-in-glass ther- mometer, resistance thermometer or constant volume gas thermometer. If is the thermometric property, let  18 Basic and Applied Thermodynamics us arbitrarily choose for the temperature common to the thermometer and to all systems in thermal e uilib rium with it the following linear function of : θ ( ) = a , where a is an arbitrary constant. θ( 1 ) If 1 corresponds to θ ( 1), then 2 will correspond to ⋅ 2 1 θ( 1 ) that is θ ( 2)= ⋅ 2 (2.1) 1 Two temperatures on the linear scale are to each other as the ratio of the corresponding ’s. 2.2.1 Method Used Before 1954 The thermometer is first placed in contact with the system whose temperature θ ( ) is to be measured, and then in contact with an arbitrarily chosen standard system in an easily reproducible state where the tempera- θ( 1) ture is θ ( 1). Thus = 1 (2.2) θ( ) Then the thermometer at the temperature θ ( ) is placed in contact with another arbitrarily chosen standard system in another easily reproducible state where the temperature is θ ( 2). It gives θ( ) 2 = 2 (2.3) θ( ) θ( ) – θ( 1 2 ) – From Eqs (2.2) and (2.3) = 1 2 θ( ) θ( ) – θ( ) or θ( )= 1 2 ⋅ (2.4) 1 – 2 If we assign an arbitrary number of degrees to the temperature interval θ ( 1)− θ ( 2), then θ ( ) can be calculated from the measurements of , 1 and 2. An easily reproducible state of an arbitrarily chosen standard system is called a fixed point. Before 1954, there were two fixed points: (a) the ice point, the temperature at which pure ice coexisted in equilibrium with air-saturated water at one atmosphere pressure, and (b) the steam point, the temperature of equilibrium between pure water and pure steam at one a