Chemical Engineering Thermodynamics P Liquid P x 1 sat P 1 T sat T 2 T x 1 T x 1 T y 1 Liquid Vapour sat P 2 P x 1 P y 1 P y 1 Vapour sat T 1 x, y 1 1 x, y 1 1 Pradeep Ahuja
Contents CHEMICAL ENGINEERING THERMODYNAMICS i PRADEEP AHUJA Reader Department of Chemical Engineering and Technology Institute of Technology, Banaras Hindu University Varanasi New Delhi-110001 2009
CHEMICAL ENGINEERING THERMODYNAMICS Pradeep Ahuja 2009 by PHI Learning Private Limited, New 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-978-81-203-3637-7 The export rights of this book are vested solely with the publisher. Published by Asoke K. Ghosh, PHI Learning Private Limited, M-97, Connaught Circus, New Delhi-110001 and Printed by Baba Barkha Nath Printers, Bahadurgarh, Haryana-124507.
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Contents Preface Nomenclature xv xvii 1 Introduction 1 37 1.1 Equilibrium State and Steady State 1 1.2 Systems and Surroundings 3 1.3 Processes 3 1.4 Internally Reversible Process 4 1.5 About Steam Tables 6 1.6 Degrees of Freedom 6 1.7 Total Volume and Molar/Specific Volume 7 1.8 Dryness Fraction 8 1.9 Extensive and Intensive Properties 9 1.10 Non-flow and Flow Processes 9 1.11 Work Done During Internally Reversible Non-flow Process 11 1.12 State and Path Functions 14 1.13 Useful Work 15 1.14 Gauge and Vacuum Gauge Pressures 16 1.15 Mechanical Energy of a Fluid 16 1.16 T-V Diagram of a Pure Substance 18 1.17 P-V Diagram of a Pure Substance 20 1.18 P-T Diagram of a Pure Substance 22 1.19 Boiling Point of Pure Substances 25 1.20 Internal Energy and Enthalpy 27 1.21 Heat Capacities 27 1.21.1 Ideal Gases 28 1.21.2 Incompressible Liquids and Solids 29 v
vi Contents 1.22 Enthalpy of Compressed Liquid 30 1.23 Roots of Non-linear Equation 32 Summary 34 Exercises 35 2 Equations of State 38 77 2.1 Virial Gas Equation of State 38 2.2 Law of Corresponding States 41 2.3 Acentric Factor 42 2.4 Molar Volume Calculations Using Virial Equation of State 44 2.5 Virial Equation of State for Binary Mixtures 50 2.5.1 Virial Mixing Rules 50 2.5.2 Pseudo-reduced Method 50 2.6 Conclusions of Virial Equations of State 57 2.7 Cubic Equations of State 59 2.8 van der Waals Equation of State 60 2.9 Redlich Kwong Equation of State 62 2.10 Cubic Equations of State in Cubic Form 62 2.11 Cubic Equations of State for Binary Mixtures 70 Summary 73 Exercises 74 3 The First Law and Its Applications 78 129 3.1 Constant Pressure Process 79 3.2 Constant Volume Process 83 3.3 Constant Temperature Process 84 3.4 Adiabatic Process 91 3.5 Polytropic Process 95 3.6 Steady Flow Process 101 3.7 Work Done in a Flow Process 103 3.8 Bernoulli s Equation 103 3.9 Nozzles and Diffusers 105 3.10 Turbines and Compressors 107 3.11 Polytropic Flow Process 108 3.12 Multi-Stage Compression with Intercooling 109 3.13 Transient Flow Process 114 3.14 Uniform Flow Process 115 3.15 Charging Process 115 3.16 Charging Process with Boundary Work 118 3.17 Discharging Process 120 Summary 124 Exercises 125
Contents vii 4 The Second Law and Its Applications 130 180 4.1 Carnot Cycle (P-V Diagram) 130 4.2 Clausius Inequality 133 4.3 Reversible and Irreversible Processes 135 4.4 Second Law Statements 135 4.5 Limitations of the First Law of Thermodynamics 136 4.5.1 Case I 136 4.5.2 Case II 136 4.5.3 Case III 137 4.6 Entropy Change of an Irreversible Process 138 4.7 Reversible and Irreversible Expansion at Constant Temperature 140 4.8 Irreversibility Due to Heat Transfer Over 141 4.9 Increase of Entropy Principle 144 4.10 Entropy Change of an Ideal Gas 145 4.10.1 Entropy Change for Ideal Gas Undergoing Polytropic Process 145 4.11 Entropy Change for Liquids and Solids 146 4.12 Why Carnot Cycle is Reversible 146 4.13 The Criteria of Equilibrium in Closed Systems 148 4.14 Entropy Balance for Control Volumes 156 4.15 Adiabatic Efficiency of Some Steady-flow Devices 158 4.15.1 Compressors 158 4.15.2 Pumps 159 4.15.3 Turbines 159 4.15.4 Nozzles 160 4.16 Statistical Interpretation of Entropy 172 Summary 173 Exercises 174 5 Exergy (Availability) 181 205 5.1 Exergy of Heat 182 5.2 First and Second Law Efficiency of a Heat Engine 184 5.3 Reversible Useful Work of Non-flow Processes 185 5.4 Exergy of Non-flow Processes 186 5.5 Ú PdV Versus Reversible Work for Non-flow Processes 186 5.6 Irreversibility of Non-flow Processes 187 5.7 Reversible Useful Work of Non-flow Processes while Exchanging Heat with a Reservoir 189 5.8 Reversible Work of Steady-flow Processes 195 5.9 Irreversibility of Heat Exchangers 199 Summary 203 Exercises 204
viii Contents 6 Chemical Reactions 206 232 6.1 Standard Enthalpy Change of Reaction 206 6.2 Standard State 209 6.3 Standard Enthalpy Change of Reaction and Heat Exchange with Surroundings 210 6.4 Heat of Reaction in Case of Incomplete Conversion and Excess Reactants under Isothermal Conditions 211 6.5 About Basic Elements and Molecules 212 6.6 Standard Enthalpy Change of Reaction as a Function of Temperature 213 6.7 Standard Entropy Change of Reaction as a Function of Temperature 216 6.8 Standard Gibbs Free Energy Change of Reaction as a Function of Temperature 217 6.9 Gas Phase Reactions 217 6.10 Gas Solid Reactions 225 Summary 229 Exercises 229 7 Thermodynamic Property Relations of Pure Substances 233 283 7.1 Partial Derivatives and Associated Relations 234 7.2 Maxwell Relations 237 7.3 General Equation for du 237 7.4 General Equation for dh 238 7.5 General Equations for ds 239 7.6 Volume Expansivity and Isothermal Compressibility 242 7.7 General Equations for Heat Capacities 251 7.8 The Joule Thomson Coefficient 258 7.9 The Clapeyron Equation 264 7.10 Application of Stability Criteria to Cubic EOS 271 7.11 Residual Property 272 7.12 Calculations of DH and DS 273 7.13 Fugacity 274 7.14 Fugacity of Superheated Steam, Saturated Steam and Compressed Liquid 275 Summary 279 Exercises 281 8 Thermodynamic Cycles 284 310 8.1 Carnot Cycle 284 8.2 Rankine Cycle 286 8.3 Coefficient of Performance 289 8.4 Reversed Carnot Cycle 290 8.5 Vapour-Compression Refrigeration Cycle 292
Contents ix 8.6 Ammonia-Absorption Refrigeration Cycle 296 8.6.1 Simple Ammonia-Absorption Refrigeration Cycle 296 8.6.2 Ammonia-Absorption Refrigeration Cycle with Analyzer and Heat Exchangers 297 8.7 Linde Hampson Liquefaction Cycle 299 8.8 Claude Liquefaction Cycle 302 Summary 308 Exercises 309 9 General Residual Property Relations 311 319 9.1 General Residual Enthalpy Relation for Z(T, P) Type EOS 311 9.2 General Residual Internal Energy Relation for Z(T, P) Type EOS 312 9.3 General Residual Entropy Relation for Z(T, P) Type EOS 312 9.4 General Residual Gibbs Free Energy Relation for Z(T, P) Type EOS 313 9.5 General Fugacity Relation for Z(T, P) Type EOS 314 9.6 General Residual Internal Energy Relation for Z(T, V) Type EOS 315 9.7 General Residual Enthalpy Relation for Z(T, V) Type EOS 316 9.8 General Residual Entropy Relaton for Z(T, V) Type EOS 316 9.9 General Residual Gibbs Free Energy Relation for Z(T, V) Type EOS 317 9.10 General Fugacity Relation for Z(T, V) Type EOS 318 Summary 319 10 Residual Properties by Equations of State 320 379 10.1 Residual Property Relations for Z = 1 + BP 320 RT 10.2 Calculation of db for Virial Gas Equation of State 322 dt 10.3 Fugacity of Saturated and Compressed Liquid (Vapour Following Virial Gas Equation of State) 323 10.4 Residual Property Relations for Z = 1 + B V 324 10.4.1 Residual Internal Energy Relation for Z = 1 + B V 324 10.4.2 Residual Enthalpy Relation for Z = 1 + B V 10.4.3 Residual Entropy Relation for Z = 1 + B V 325 325 10.4.4 Residual Gibbs Free Energy Relation for Z = 1 + B 325 V 10.5 Residual Property Relations for van der Waals Equation of State 326 10.5.1 Residual Internal Energy Relation for van der Waals Equation of State 326
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