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A Textbook of Chemical Engineering Thermodynamics SECOND EDITION

K.V. NARAYANAN Former Professor and Head

Department of Chemical Engineering an d

Former Principal Government Engineering College Thrissur, Kerala

PHI Learning Private Limited Delhi110092 201 3

A Textbook of Chemical Engineering Thermodynamics SECOND EDITION K.V. NARAYANAN Former Professor and Head Department of Chemical Engineering and Former Principal Government Engineering College Thrissur, Kerala

Delhi-110092 2013 A TEXTBOOK OF CHEMICAL ENGINEERING THERMODYNAMICS, Second Edition K.V.

Narayanan © 2013 by PHI Learning Private Limited, Delhi. All rights reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher. ISBN-978-81-203-4747-2 The export rights of this book are vested solely with the publisher. Seventeenth Printing (Second Edition)............................................................May, 2013 Published by Asoke K. Ghosh, PHI Learning Private Limited, Rimjhim House, 111, Patparganj Industrial Estate, Delhi-110092 and Printed by Mohan Makhijani at Rekha Printers Pvt. Ltd., New Delhi-110020.

Contents Preface xiii Preface to the First Edition xv 1. INTRODUCTION AND BASIC CONCEPTS.........1–23 1.1 Scope and Limitations of Thermodynamics ...... 1 1.2 Definitions and Fundamental Concepts......2 1.2.1 Systems and Processes......2 1.2.2 Homogeneous and Heterogeneous Systems......3 1.2.3 Closed and Open Systems......3 1.2.4 State and Properties......3 1.2.5 Intensive and Extensive Properties......4 1.2.6 State and Path Functions......4 1.3 Force, Pressure and Energy......5 1.3.1 Force......5 1.3.2 Pressure......5 1.3.3 Energy......6 1.4 Equilibrium State and the Phase Rule......10 1.4.1 Steady State......10 1.4.2 Equilibrium State......10 1.4.3 Phase Rule......11 1.5 Temperature and Zeroth Law of Thermodynamics......11 1.5.1 Zeroth Law......11 1.5.2 Temperature......11 1.5.3 Ideal Gas Temperature Scale......12 1.6 Heat Reservoirs and Heat Engines......14 1.6.1 Heat Reservoir......14 1.6.2 Heat Engine......14 1.6.3 Heat Pump......15 1.7 Reversible and Irreversible Processes......16 Summary......20 Review Questions......21 Exercises......22 2. FIRST LAW OF THERMODYNAMICS.........24–48 2.1 General Statements of First Law of Thermodynamics......24 2.2 First Law of Thermodynamics for Cyclic Process......25 2.3 Internal

Energy......25 2.4 First Law of Thermodynamics for Non-flow Process......26 2.5 Enthalpy......31 2.6 First Law of Thermodynamics for Flow Process......34 2.7 Heat Capacity......40 Summary......44 Review Questions......44 Exercises......45 3. P-V-T BEHAVIOUR AND HEAT EFFECTS.........49–88 3.1 P-V-T Behaviour of Pure Fluids......49 3.2 Equations of State and the Concept of Ideal Gas......51 3.3 Processes involving Ideal Gases......52 3.3.1 Constant Volume Process......52 3.3.2 Constant Pressure Process......53 3.3.3 Constant Temperature Process......54 3.3.4 Adiabatic Process......55 3.3.5 Polytropic Process......57 3.4 Equations of State for Real Gases......60 3.4.1 Limiting Conditions......61 3.4.2 van der Waals Equation......61 3.4.3 Redlich–Kwong Equation......63 3.4.4 Redlich–Kwong–Soave Equation......64 3.4.5 Peng–Robinson Equation......64 3.4.6 Benedict– Webb–Rubin Equation......64 3.4.7 Virial Equation......65 3.5 Compressibility Charts......67 3.5.1 Principle of Corresponding States......68 3.5.2 Generalised Compressibility Charts......69 3.6 Heat Effects accompanying Chemical Reactions......69 3.6.1 The Standard Heat of Reaction......69 3.6.2 The Standard Heat of Combustion......70 3.6.3 The Standard Heat of Formation......70 3.6.4 Hess’s Law of Constant Heat Summation......71 3.6.5 Effect of Temperature on Standard Heat of Reaction......72 3.6.6 Temperature of Reaction......77 Summary......79 Review Questions......80 Exercises......81 4. SECOND LAW OF THERMODYNAMICS.........89–125 4.1 Limitations of the First Law of Thermodynamics......89 4.1.1 Direction of Change......89 4.1.2 Qualitative Difference between Heat and Work......90 4.2 General Statements of the Second Law of Thermodynamics......90

4.2.1 The Equivalence of the Kelvin and Clausius Statements......91 4.3 Entropy......92 4.3.1 Why the Concept of Entropy?......92 4.3.2 Entropy and Heat......93 4.3.3 Entropy and Temperature......94 4.3.4 Entropy and the Nature of the Process......94 4.4 The Carnot Principle......95 4.4.1 Thermodynamic Temperature Scale......97 4.4.2 Ideal Gas as the Carnot Engine Working Substance......98 4.5 Entropy—A State Function......101 4.6 Calculation of Entropy Changes......103 4.6.1 Phase Change......103 4.6.2 Processes Involving Ideal Gases......103 4.6.3 Adiabatic Mixing Process......105 4.6.4 Isothermal Mixing of ideal Gases......106 4.6.5 Chemical Reactions......107 4.7 Clausius Inequality......108 4.8 Mathematical Statement of the Second Law of Thermodynamics......111 4.9 Entropy and Irreversibility......115 4.10 Statistical Explanation for Entropy......118 4.11 Third Law of Thermodynamics......118 Summary......120 Review Questions......121 Exercises......122 5. SOME APPLICATIONS OF THE LAWS OF THERMODYNAMICS.........126–205 5.1 Flow Processes......126 5.1.1 Continuity Equation......126 5.1.2 Energy Equation......127 5.1.3 Flow in Pipes......135 5.1.4 Flow through Nozzles......137 5.1.5 Ejectors......142 5.1.6 Throttling Process (Joule–Thomson Expansion)......143 5.1.7 Compressors......143 5.2 Refrigeration......151 5.2.1 Coefficient of Performance (COP)......152 5.2.2 Refrigerator Capacity......152 5.2.3 Carnot Cycle......152 5.2.4 Vapour-compression Cycle......154 5.2.5 Choice of Refrigerant......159 5.2.6 Air-refrigeration Cycle......161 5.2.7 Absorption Refrigeration......163 5.2.8 Heat Pumps......165 5.3 Liquefaction Processes......166 5.3.1 Vaporisation of Liquid......166 5.3.2 Free Expansion......167 5.3.3 Isentropic Expansion......168 5.4 The Steam-Power Plant......170

5.4.1 Rankine Cycle......171 5.4.2 Reheat Cycle......174 5.4.3 Regenerative Cycle......177 5.5 Internal Combustion Engines......180 5.5.1 Otto Cycle......180 5.5.2 Diesel Cycle......183 5.5.3 Dual Cycle......187 5.6 Gas-turbine Power Plant......188 5.6.1 Brayton Cycle......189 Summary......191 Review Questions......192 Exercises......193 6. THERMODYNAMIC PROPERTIES OF PURE FLUIDS.........206– 272 6.1 Classification of Thermodynamic Properties......206 6.1.1 Reference Properties......206 6.1.2 Energy Properties......206 6.1.3 Derived Properties......207 6.2 Work Function (Helmholtz Free Energy)......207 6.3 Gibbs Free Energy......208 6.4 Relationships among Thermodynamic Properties......209 6.4.1 Exact Differential Equations......209 6.4.2 Fundamental Property Relations......210 6.4.3 Maxwell’s Equations......211 6.4.4 Clapeyron Equation......213 6.4.5 Entropy–Heat Capacity Relationships......215 6.4.6 Differential Equations for Entropy......216 6.4.7 Modified Equations for U and H......217 6.4.8 Effect of Temperature, Pressure and Volume on U, H and S......220 6.4.9 Relationship between CP and CV......226 6.4.10 Ratio of Heat Capacities......229 6.4.11 Effect of Pressure and Volume on CP and CV......229 6.4.12 Joule– Thomson Coefficient......233 6.4.13 Gibbs–Helmholtz Equation......235 6.5 Method of Jacobians......236 6.5.1 Properties of Jacobians......237 6.5.2 Thermodynamic Relations through the Method of Jacobians......238 6.6 Fugacity......244 6.6.1 Standard State for Fugacity......245 6.6.2 Fugacity Coefficient......246 6.6.3 Effect of Temperature and Pressure on Fugacity......246 6.6.4 Determination of Fugacity of Pure Gases......247 6.6.5 Fugacities of Solids and Liquids......254 6.7 Activity......255

6.7.1 Effect of Pressure and Temperature on Activity......256 6.8 Departure Functions and Generalised Charts......256 6.9 Thermodynamic Diagrams......259 6.9.1 Types of Diagrams......259 6.9.2 Construction of Thermodynamic Diagrams......262 Summary......265 Review Questions......265 Exercises......267 7. PROPERTIES OF SOLUTIONS.........273–328 7.1 Partial Molar Properties......273 7.1.1 Physical Meaning of Partial Molar Properties......274 7.1.2 Partial Molar Properties and Properties of Solution......276 7.1.3 Determination of Partial Molar Properties......279 7.2 Chemical Potential......284 7.2.1 Effect of Temperature and Pressure on Chemical Potential......285 7.3 Fugacity in Solutions......288 7.3.1 Fugacity in Gaseous Solutions......288 7.3.2 Lewis–Randall Rule......290 7.3.3 Fugacities in Liquid Solutions......291 7.3.4 Ideal Solutions and Raoult’s Law......292 7.4 Henry’s Law and Dilute Solutions......293 7.4.1 Ideal Behaviour of Real Solutions......293 7.4.2 Henry’s Law and Gas Solubility......294 7.5 Activity in Solutions......296 7.5.1 Selection of Standard States......296 7.6 Activity Coefficients......297 7.6.1 Effect of Pressure on Activity Coefficients......299 7.6.2 Effect of Temperature on Activity Coefficients......299 7.7 Gibbs–Duhem Equations......302 7.8 Property Changes of Mixing......307 7.8.1 Activity and Property Change of Mixing......308 7.8.2 Property Changes of Mixing for Ideal Solutions......310 7.9 Heat Effects of Mixing Processes......311 7.10 Excess Properties......317 7.10.1 Excess Gibbs Free Energy......318 Summary......320 Review Questions......321 Exercises......322 8. PHASE EQUILIBRIA.........329–424

8.1 Criteria of Phase Equilibrium......330 8.2 Criterion of Stability......332 8.3 Phase Equilibria in Single-component Systems......335 8.4 Phase Equilibria in Multicomponent Systems......338 8.5 Phase Rule for Non-reacting Systems......341 8.6 Duhem’s Theorem......343 8.7 Vapour–Liquid Equilibria......344 8.8 Phase Diagrams for Binary Solutions......346 8.8.1 Constant-pressure Equilibria......346 8.8.2 Constant-temperature Equilibria......350 8.9 Vapour–Liquid Equilibria in Ideal Solutions......351 8.10 Non-ideal Solutions......361 8.10.1 Azeotropes......364 8.11 Vapour–Liquid Equilibria (VLE) at Low Pressures......368 8.11.1 Activity Coefficient Equations......369 8.12 Vapour–Liquid Equilibria involving High Pressures and Multicomponent Systems......386 8.12.1 Equations of State Approach......386 8.12.2 Vaporisation Equilibrium Constants......387 8.12.3 Bubble-point Equilibria......389 8.12.4 Dew-point Equilibria......389 8.12.5 Flash Vaporisation......390 8.13 Consistency Test for VLE Data......395 8.13.1 Using Slope of ln g Curves......395 8.13.2 Using Data at the Mid-point......396 8.13.3 Redlich–Kister Method......396 8.13.4 Using the Coexistence Equation......398 8.13.5 Using the Partial Pressure Data......399 8.14 Calculation of Activity Coefficients using Gibbs– Duhem Equation......401 8.15 VLE for Systems of Limited Miscibility......403 8.15.1 Partially Miscible Systems......403 8.15.2 Immiscible Systems......405 8.16 Liquid–Liquid Equilibrium Diagrams......408 8.16.1 Binary Liquid–Liquid Equilibria......408 8.16.2 Ternary Equilibrium Diagrams......408 Summary......411 Review Questions......412 Exercises......413 9. CHEMICAL REACTION EQUILIBRIA.........425–481 9.1 Reaction Stoichiometry......426 9.2 Criteria of Chemical Reaction Equilibrium......429 9.3 Equilibrium Constant......431 9.4 Equilibrium Constant and Standard Free Energy Change......433

9.4.1 Choice of Standard State......434 9.4.2 Feasibility of a Reaction......434 9.5 Effect of Temperature on Equilibrium Constant......436 9.5.1 Evaluation of Equilibrium Constants......440 9.5.2 Giauque Functions......440 9.6 Effect of Pressure on Equilibrium......446 9.6.1 Effect of Pressure on Equilibrium Constant......446 9.6.2 Effect of Pressure on Equilibrium Composition......446 9.7 Other Factors Affecting Equilibrium Conversion......450 9.7.1 Presence of Inert Materials......451 9.7.2 Presence of Excess of Reactants......454 9.7.3 Presence of Products......457 9.8 Liquid-phase Reactions......459 9.9 Heterogeneous Reaction Equilibria......461 9.9.1 Reactions in Solutions......461 9.9.2 Equilibria involving Pure Solids and Liquids......461 9.9.3 Pressures of Decomposition......462 9.10 Simultaneous Reactions......465 9.11 Phase Rule for Reacting Systems......468 Summary......470 Review Questions......471 Exercises......472 Appendixes.........483–534 A. Table for Thermodynamic Properties of Saturated Steam......483 B. Table for Thermodynamic Properties of Superheated Steam......485 C. Aptitude Test in Chemical Engineering Thermodynamics......491 References.........535–536 Answers to Exercises.........537–544 Index.........545–552

Preface The main concern of the author while writing the first edition of A Textbook of Chemical Engineering Thermodynamics was to provide a student-friendly book on the subject of thermodynamics which was considered by many in the academic circles, as a difficult subject consisting of abstract and difficult-to-conceptualize ideas, principles and variables. Within a very short period after its publication, the book received wide acceptance among the faculty and students of

Chemical Engineering and related disciplines. This prompted the author to bring out this second edition retaining the basic structure, sequence, philosophy and style of presentation. Several changes and corrections were made in previous reprints of the first edition based on readers’ feedback. Suggestions have also been made to include more number of worked-out examples illustrating the applications of the laws of thermodynamics. Therefore, in this edition, worked-out examples have been added in almost all Chapters to make the abstract concepts of thermodynamics more clear to the readers. More than 25 such worked-out numerical examples and a few exercise problems are incorporated in the new edition. The Chapter on Phase Equilibria is revised recognizing the importance that the Equations of State Approach and vaporization equilibrium constants for solving vapour-liquid-equilibrium problems have attained recently due to the increased use of simulation packages in the design of process units. More than 90 GATE questions with answers have been added to the Appendix in Objective Type Questions on Chemical Engineering Thermodynamics, taking the total number of such questions to 236, which will definitely be a boon to the candidates preparing for competitive examinations. The author believes that with the improvements made, the second edition will retain the strength of the first edition that so many people have appreciated and commented. Many Universities have accepted the earlier edition as a textbook or reference book for their course study in Chemical Engineering or related branches of Engineering, such as Biotechnology and Biochemical Engineering, Petroleum Engineering, Fire and Safety Engineering, Electrochemical Engineering, Polymer Science and Engineering, Environmental Engineering etc. The author is grateful to all the academicians who have shown interest in the book and the faculties who have come forward with valuable suggestions for improvement and hope their continued patronage for the present work as well. He would also like to acknowledge the valuable service of the

editorial and marketing team at PHI Learning, Delhi for making the work a commendable success. The author is also grateful to the readers for their interest and hope that they will continue to make suggestions for improvement of the book. K.V. NARAYANAN

Preface to the First Edition The field of chemical engineering is conventionally classified into two broad categories: the unit operations and the unit processes. The former involves physical transformation and the latter chemical changes. The chemical engineer, whether he is concerned with the unit operations or with the unit processes has to evaluate the energy requirements for initiating these transformations, study the energy changes involved in such processes, and determine the extent to which these transformations can be carried out. The science of thermodynamics deals exactly with these problems and a strong foundation in thermodynamics is therefore a must for the success of a chemical engineer in his professional life. Chemical engineering thermodynamics is one of the core courses in the undergraduate chemical engineering curriculum. In this course, more emphasis is given to the treatment of properties of solutions, phase equilibria and chemical reaction equilibria, all coming under the realm of ‘chemical thermodynamics’ rather than on the thermodynamic analysis of heat engines and heat-power cycles. The conventional textbooks on thermodynamics are, therefore, inadequate to meet these requirements. Hence the need for a book on thermodynamics that deals exclusively with the theory and applications of chemical engineering thermodynamics. During the several years of my experience in teaching thermodynamics to the undergraduate students, I have come across students who have strong ‘likes’ and ‘dislikes’ toward the subject. Unfortunately, the latter frequently outnumber the former. The seemingly abstract nature of

thermodynamic principles is only partly to blame for this scenario. The major reason is the dearth of student-friendly textbooks that help the student in providing a sound basis and act as catalysts for going deeper into the subject. An unwilling student should not be compelled to studying the vast subject of thermodynamics, without giving him or her a proper orientation. These inadequacies of the existing books on the subject have been kept in mind while writing this book. An earnest attempt has been made to eliminate avoidable rigour and intricacies that usually make the subject dry. Instead, the book tries to provide a firm foundation in the theory through the application of the fundamentals to solve practically important problems. This book is intended to serve as a textbook for the undergraduate students in chemical engineering and other related branches of engineering such as polymer engineering, petroleum engineering, and safety and environmental engineering. Numerical examples given under each section would help the student gain a better insight into the theory. In this text, only SI units used. Review questions at the end of the chapters would help the student check his/her understanding of the topics discussed in each chapter before going to the next. Each chapter is provided with a number of exercise problems, and answers to all of them are given at the end of the book. A number of objectivetype questions are included in the Appendix: ‘An Aptitude Test in Chemical Engineering Thermodynamics’. The student would find these very helpful in preparing for competitive examinations. Most of the questions presented in this section are taken from earlier Graduate Aptitude Test in Engineering (GATE) question papers. This book is the outgrowth of the several lectures I have delivered to the chemical engineering students in the Government Engineering College, Thrissur. The response from the students who benefitted from these lectures was a major source of inspiration for writing this book. Valuable help and suggestions at various stages in its evolution have contributed

towards bringing it out in the present form. My colleagues at the Government Engineering Colleges at Thrissur and Calicut provided a helpful environment for undertaking this work and I am very grateful towards all of them. I recall with gratitude the stimulating experience I spent at IIT Madras during my research work under Prof. M.S. Ananth, which contributed much in sustaining my interest in the subject of thermodynamics. I am thankful to the Director of Technical Education, Kerala and the Government of Kerala for granting me permission to publish the book. And my special thanks are due to my wife Lakshmi for her suggestions for improving the quality and content of the book as also for the cooperation in accommodating the lengthy hours that I spent during the preparation of the manuscript. Thanks are also due to my daughter Aparna for her patience and understanding even when I could not attend to her due to my preoccupation in this book-writing project. Comments, constructive criticism and suggestions for improving the quality of the book would be gratefully accepted. K.V. NARAYANAN

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