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PROFESSION Fifteen prominent chemical engineers first met in New York more than 60 years ago to plan a continuing literature for their rapidly growing profession From industry came such pioneer practitioners as Leo H Baekeland, Arthur D Little, Charles L Rees.e, John V N Dorr, M C Whitaker, and R S McBride From the universities came such eminent educators as William H Walker, Alfred H White, D D Jackson, J H James, Warren K Lewis, and Harry A Curtis H C Parmelee, then editor of Chemical and Metallurgical Engineering, served as chairman and was joined subsequently by S D Kirkpatrick as consulting editor After several meetings, this committee submitted its report to the McGraw~Hill Book Company in September 1925 In the report were detailed specifications for a correlated series of more than a dozen texts and reference books which have since become the McGraw~Hil1 Series in Chemical Engineering and which became the cornerstone of the chemical engineering curriculum From this beginning there has evolved a series of texts surpassing by far the scope and longevity envisioned by the founding Editorial Board The McGraw~Hill Series in Chemical Engineering stands as a unique historical record of the development of chemical engineer· ing education and practice In the series one finds the milestones of the subject's evolution: industrial chemistry, stoichiometry, unit operations and processes, thermodynamics, kinetics, and trarisfer operations Chemical engineering is a dynamic profession, and its literature continues to evolve McGraw·Hill and its consulting editors remain committed to a publishing policy that will serve, and indeed lead, the needs of the chemical engineering profession during the years to come INTRODUCfION TO CHEMICAL ENGINEERING THERMODYNAMICS Fourth Edition 0"- J M.§Jnith Professor of Chemical Engineering University of California, Davis H C Van Ness Institute Professor of Chemical Engineering Rensselaer Polytechnic Institute McGraw-Hili Book Company London Madrid New York St Louis San Francisco Auckland Bogota Hamburg Mexico Milan Montreal New Delhi Panama Paris Sio Paulo Singapore Sydney Tokyo Toronto 113 :rqo1 F 6000 - S r;;51l (If) - CONTENTS I/S- 1"echnfsche UnI".rsltCit Dr.sa unl".rsltlitsblb~1I th.t· Zw.lgblblloth.t.: 1't FEB 995 10 19 ' This book was set in Times Roman The editors were Sanjeev Rao and John Morriss The production supervisor was Marietta Breitwieser Project supervision was done by Albert Harrison, Harley Editorial Services R R Donnelley & Sons Company was printer and binder Preface I.I 1.2 1.3 INTRODUCTION TO CHEMICAL ENGINEERING THERMODYNAMICS 1.4 Copyright © 1987, 1975, 1959 by McGraw-Hill, Inc All rights reserved Copyright 1949 by McGraw-Hill, Inc AU rights reserved Printed in the United States of America Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher 1.6 1.7 1.8 1.9 1.5 34567890 DOC DOC 898 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 ISBN 0-07-058703-5 Library of Congress Cataloging-in-Publication nata Smith, J M (Joseph Mauck), 1916Introduction to chemical engineering thermodynamics (McGraw-Hill series in chemical engineering) Includes bibliographical references and index Thermodynamics Chemical engineering I Van Ness, H C (Hendrick C.) II Title Ill Series TP149.S582 1987 660.2'969 86-7184 t ~, ISBN 0-07-058703-5 J ~ (1 Introduction The Scope of Thermodynamics Dimensions and Units Force Temperature Defined Quantities; Volume Pressure Work Energy Heat Problems AOj1'/ G1, C01( /' J , ! S II 12 11 19 The First Law and Other Basic Concepts 21 Joule's Experiments Internal Energy Formulation of the First Law of Thermodynamics The Thermodynamic State and State Functions Enthalpy The Steady-State-Flow Process Equilibrium The Phase Rule The Reversible Process Notation; Constant-Volume and Constant-Pressure Processes Heat Capacity Problems 21 22 22 29 30 31 37 39 45 Volumetric Properties of Pure Fluids 3.1 3.2 xi The PVT Behavior of Pure Substances The Virial Equation 46 51 54 54 60 Yij CONtENTS Ix til CONtENTS 3.3 3.4 3.5 3.6 3.7 4.1 4.2 4.3 4.4 4.5 4.6 4.7 The Ideal Gas Application of the Virial Equation Cubic Equations of State Generalized Correlations for Gases Generalized Correlations for Liquids Problems Heat Effects lOS Sensible Heat Effects 106 114 116 118 123 123 123 133 Heat Effects Accompanying Phase Changes of Pure Substances The Standard Heat of ReactiJlD The Standard Heat of Formation The Standard Heat of Combustion Effect of Temperature on the Standard Heat of Reaction Heat Effects of Industrial Reactions Problems The Second Law of Thermodynamics 5.1 5.2 5.3 5.4 Statements of the Second Law The Heat Engine Thermodynamic Temperature Scales Entropy Entropy Changes of an Ideal Gas 139 140 143 145 148 152 Principle of the Increase of Entropy; Mathematical Statement of the Second Law Entropy from the Microscopic Viewpoint (Statistical 5.9 Thermodynamics) The Third Law of Thermodynamics Problems 159 162 163 Thermodynamic Properties of Fluids 166 6.2 6.3 6.4 6.5 6.6 Relationships among Thermodynamic Properties for a Homogeneous Phase of Constant Composition Residual Properties Two-Phase Systems Thermodynamic Diagrams Tables of Thermodynamic Properties Generalized Correlations of Thermodynamic Properties for Gases Problems Thermodynamics of Flow Processes 7.1 7.2 7.3 7.4 Fundamental Equations Flow in Pipes Expansion Processes Compression Processes Problems 8.1 8.2 8.3 8.4 8.5 8.6 9.1 9.2 9.3 9.4 9.5 9.6 9.7 169 173 180 183 187 189 204 209 2\0 218 220 234 242 Conversion of Heat into Work by Power Cycles 247 The Steam POwer Plant 248 Internal-Combustion Engines The Otto Engine The Diesel Engine The Gas-Turbine Power Plant Jet Engines; Rocket Engines Problems 260 261 263 265 269 271 Refrigeration and Liquefaction 274 The Camot Refrigerator The Vapor-Compression Cycle Comparison of Refrigeration Cycles 275 276 278 283 288 290 291 295 The Choice of Refrigerant Absorption Refrigeration The Heat Pump Liquefaction Processes Problems 10 Systems of Variable Composition Ideal Behavior 10.1 10.2 10.3 10.4 10.5 Fundamental Property Relation The Chemical Potential as a Criterion of Phase Equilibrium 297 The Ideal-Gas Mixture The Ideal Solution Raoulfs Law Problems 297 298 300 302 304 316 Systems of Variable Composition Nonideal Behavior 320 Partial Properties ProbleDis 321 325 331 334 343 346 356 Phase Equilibria at Low to Moderate Pressures 361 12.1 12.2 12.3 The Nature of Equilibrium The Phase Rule Duhem's Theorem Phase Behavior for Vapor/Liquid Systems 12.4 Lo"\v-Pressure VLE from Correlations of Data 12.5 12.6 12.7 12.8 Flash Calculations 361 362 363 373 381 393 397 403 408 155 5.8 6.1 138 Camot Cycle for an Ideal Gas; the Kelvin Scale as a Thennodynamic Temperature Scale 5.5 5.6 5.7 63 77 80 85 96 98 11 11.1 11.2 11.3 11.4 11.5 11.6 12 Fugacity and Fugacity Coefficient Fugacity and Fugacity Coefficient for Species i in Solution Generalized Correlations for the Fugacity Coefficient The Excess Gibbs Energy Activity Coefficients from VLE Data Dew-Point and Bubble-Point Calculations it Composition Dependence of Henry's Law as a Model for Ideal Behavior of a Solute Problems x CONTENTS Solution Thermodynamics 416 13.1 Relations among Partial Properties for Constant-Composition Solutions 13.2 The Ideal Solution 416 418 13.3 13.4 13.5 The Fundamental Residual-Property Relation The Fundamental Excess-Property Relation Evaluation of Partial Properties 13.6 Property Changes of Mixing 428 13.7 Heat Effects of Mixing Processes 434 13 13.8 Equilibrium and Stability 13.9 Systems of Limited Liquid-Phase Miscibility Problems 14 Thermodynamic Properties and VLE from Equations of State 420 422 423 447 454 464 471 471 14.1 14.2 Properties of Fluids from the Virial Equations of State Properties of Fluids from Cubic Equations of State 14.3 Vapor/Liquid Equilibrium from Cubic Equations of State Problems 475 480 493 Chemical-Reaction Equilibria 496 15.1 15.2 The Reaction Coordinate Application of Equilibrium Criteria to Chemical Reactions 15.3 The Standard Gibbs Energy Change and the Equilibrium Constant 15.4 15.5 15.6 15.7 15.8 15.9 Effect of Temperature on the Equilibrium Constant Evaluation of Equilibrium Constants Relations between Equilibrium Constants and Composition Calculation of Equilibrium Conversions for Single Reactions The Phase Rule and Duhem's Theorem for Reacting Systems Multireaction Equilibria 497 501 503 507 510 15 16 PREFACE 514 518 529 532 Problems 542 Thermodynamic Analysis of Processes 548 548 16.1 Second-Law Relation for Steady-State Flow Processes 16.2 16.3 Calculation of Ideal Work Lost Work 16.4 Thermodynamic Analysis of Steady-State Flow Processes Problems 554 555 564 Appendices 569 A B Conversion Factors and Values of the Gas Constant Critical Constants and Acentric Factors 569 571 C D E Steam Tables The UNIFAC Method Newton's Method 573 676 685 Index 687 549 The purpose of this text is to provide an introductory treatment of thermodynamics from a chemical-engineering viewpoint We have sought to present material so that it may be readily understood by the average undergraduate, while at the same time maintaining the standard of rigor demanded by sound thermodynamic analysis The justification for a separate text for chemical engineers is no different nOW than it has been for the past thirty-seven years during which the first three editions have been in print The same thermodynamic principles apply regardless of discipline However, these abstract principles are more effectively taught when advantage is taken of student commitment to a chosen branch of engineering Thus, applications indicating the usefulness of thermodynamics in chemical engineering not only stimulate student interest, but also provide a better understanding of the fundamentals themselves The first two chapters of the book present basic definitions and a development of the first law as it applies to nonflow and simple steady-flow processes Chapters and treat the pressure-volume-temperature behavior of Ouids and certain heat effects, allowing early application of the first law to important engineering p,rot,le,ms The second law and some of its applications are considered in Chap A treatment of the thermodynamic properties of pure Ouids in Chap allows ,.allplication in Chap of the first and second laws to Oow processes in general in Chaps and to power production and refrigeration processes Chapters through 15, dealing with Ouid mixtures, treat topics in the special domain of engineering thermodynamics In Chap 10 we present the simplest of mixture behavior, with application to vapor/liquid equiliis expanded in Chaps 11 and 12 to a general treatment ofvapor/liquid !luilibriurn for systems at modest pressures Chapter 13 is devoted to solution ·.'-:~;:~~~:S"':~'~~~i, providing a comprehensive exposition of the thermodynamic !Ii of Ouid mixtures The application of equations of state in thermodycalculations, particularly in vapor/liquid equilibrium, is discussed in xi xii PREFACE Chap 14 Chemical-reaction equilibrium is covered at length in Chap 15 Finally, Chap 16 deals with the thermodynamic analysis of real processes This material affords a review of much of the practical subject matter of thermodynamics Although the text contains much introductory material, and is intended for undergraduate students, it is reasonably comprehensive, and should also serve as a useful reference source for practicing chemical engineers We gratefully acknowledge the contributions of Professor Charles Muckenfuss, of Debra L Saucke, and of Eugene N Dorsi, whose efforts produced computer programs for calculation of the thermodynamic properties of steam and ultimately the Steam Tables of App C We would also like to thank the reviewers of this edition: Stanley M Walas, University of Kansas; Robert G Squires, Purdue University; Professor Donald Sundstrom, University of Connecticut; and Professor Michael Mohr, Massachusetts Institute of Technology Most especially, we acknowledge the contributions of Professor M M Abbott, whose creative ideas are reflected in the structure and character of this fourth edition, and who reviewed the entire manuscript M Smith H C Van Ness INTRODUCTION TO CHEMICAL ENGINEERING THERMODYNAMICS CHAPTER ONE INTRODUCTION 1.1 THE SCOPE OF THERMODYNAMICS The word thermodynamics means heat power, or power developed from heat, rellecting its origin in the analysis of steam engines As a fully developed modem science, thermodynamics deals with transformations of energy of all kinds from one form to another The general restrictions within which all such transformations are observed to occur are known as the first and second laws of thermodynamics These laws cannot be proved in the mathematical sense Rather, their validity rests upon experience Given mathematical expression, these laws lead to a network of equations from which a wide range of practical results and conclusions can be deduced The universal applicability of this science is shown by the fact that it is employed alike by physicists, chemists, and engineers The basic principles are always the same, but the applications differ The chemical engineer must be able to cope with a wide variety of problems Among the most important are the determination of heat and work requirements for physical and chemical processes, and the determination of equilibrium conditions for chemical reactions and for the transfer of chemical species between phases TheQl'odynamic considerations by themselves are not sufficient to allow calculation of the rates of chemical or physical processes Rates depend on both driving force and resistance Although driving forces are thermodynamic variables, resistances are not Neither can thermodynamics, a macroscopic-property formulation, reveal the microscopic (molecular) mechanisms of physical or chemical processes On the other hand, knowledge of the microscopic behavior ] INTRODUCTION 10 CHEMICAL ENGINEERING THERMODYNAMICS of matter can be useful in the calculation of thermodynamic properties Such property values are essential to the practical application of thermodynamics; numerical results of thermodynamic analysis are accurate only to the extent that the required data are accurate The chemical engineer must deal with many chemical species and their mixtures, and experimental data are often unavailable Thus one must make effective use of correlations developed from a limited data base, but generalized to provide estimates in the absence of data The application of thermodynamics to any real problem starts with the identification of a particular body of matter as the focus of attention This quantity of matter is called the system, and its thermodynamic state is defined by a few measurable macrosCopic properties These depend on the fundamental dimensions of science, of which length, time, mass, temperature, and amount of substance are of interest here INTRODUCTION ~ as there are atoms in 0.012 kg of carbon-I This is equivalent to the "gram mole" commonly used by chemists Decimal mUltiples and fractions of SI units are designated by prefixes Those in common use are listed in Table 1.1 Thus we have, for example, that I cm = 10-2 m and I kg = 103 g Other systems of units, such as the English engineering system, use units that are related to SI units by fixed conversion factors Thus, the foot (ft) is defined as 0.3048 m, the pound mass (Ibm) as 0.45359237 kg, and the pound mole (lb mol) as 453.59237 mol 1.3 FORCE The SI unit of force is the newton, symbol N, derived from Newton's second law, which expresses force F as the product of mass m and acceleration a: 1.2 DIMENSIONS AND UNITS The fundamental dimensions are primitives, recognized through our sensory perceptions and not definable in terms of anything simpler Their use, however, requires the definition of arbitrary scales of measure, divided into specific units of size Primary units have been set by international agreement, and are codified as the International System of Units (abbreviated SI, for Systeme International) The second, symbol s, is the SI unit of time, defined as the duration of 9,192,631,770 cycles of radiation associated with a specified transition of the cesium atom The meter, symbol m, is the fundamental unit of length, defined as the distance light travels in a vacuum during 1/299,792,458 of a second The kilogram, symbol kg, is the mass of a platinum/iridium cylinder kept at the International Bureau of Weights and Measures at Sevres, France The unit of temperature is the kelvin, symbol K, equal to 1/273.16 of the thermodynamic temperature of the triple point of water A more detailed discussion of temperature, the characteristic dimension of thermodynamics, is given in Sec 1.4 The measure of the amount of substance is the mole, symbol mol, defined as the amount of substance represented by as many elementary entities (e.g., molecules) Table 1.1 Prefixes for SI units Fraction or multiple Prelix Symbol 10-9 10-6 nano micro n 10-3 10-2 milli 10' 10' 10' centi kilo mega giga P m c k M G F=ma The newton is defined as the force which when applied to a mass of I kg produce, an acceleration of I m s -2; thus the newton is a derived unit representin~ I kgms- In the English engineering system of units, force is treated as an additional independent dimension along with length, time, and mass The pound force (Ib,: is defined as that force which accelerates I pound mass 32.1740 feet per second per second Newton's law must here include a dimensional proportionalit) constant if it is to be reconciled with this definition Thus, we write I F=-ma go whencet 1(lb,} =.! x 1(lbm} x 32.1740(ft)(s}-2 go and go = 32.1740(lb m)(ft)(lb,}-'(s}-2 The pound force is equivalent to 4.4482216 N Since force and mass are different concepts, a pound force and a pound ma" are different quantities, and their units cannot be cancelled against one another When an equation contains both units, (Ib,) and (Ibm), the dimensional constanl go must-also appear in the equation to make it dimensionally correct Weight properly refers to the force of gravity on a body, and is therefon correctly expressed in newtons or in pounds force Unfortunately, standards 01 t Where English units are employed, parentheses enclose the abbreviations of all units INTRODUCTION TO CHEMICAL ENGINEERING THERMODYNAMICS mass are often called "weights," and the use of a balance to compare masses is called "weighing." Thus, one must discern from the context whether force or mass is meant when the word "weight" is used in a casual or informal way Example 1.1 An astrQnaut weighs 730 N in Houston, Texas, where the local acceleration of gravity is = 9.792 m S-2 What is the mass of the astronaut, and what does he weigh on the moon, where = 1.67 m s- SOLUTION Letting a = g, we write Newton's law as F=mg whence F 730N = 9.792ms' m =- = 74.55 N m- I S' Since the newton N has the units kgms- , this result simplifies to m = 74.55 kg This mass of the astronaut is independent of loc~tion, but his weight depends on the local acceleration of gravity Thus on the moon his weight is Fmoon = mOmoon = 74.55 kg x 1.67 m S-2 Fmoon = 124.5 kg m s-' = 124.5 N or To work this problem in the English epgineering system of units, we convert the astronaut's weight to (lb,) and the values of to (ft)(s)-' Since N is equivalent to O.2248090b,) and m to 3.28084(ft), we have: = 164.1 (lb,) gmoon = 5.48(ft)(s)-' Weight of astronaut in Houston gHn~'nn = 32.13 and Newton's law here gives Fg, m=- 164.1(lb,) x 32.174O(lbm )(ft)(lb,)-'(s)-' 32.13(ft)(s) , or m = 164.3(lbm ) Thus the astronaufs m!1ss in (Ibm) and weight in (lb f ) in Houston are numerically almost the same, but on the moon this is not the case: = mgmoon = (164.3)(5.48) 28 O(lb) F moon g, 32.1740 , INTRODUCTION Thus a uniform tube, partially filled with mercury, alcohol, or some other can indicate degree of "hotness" simply by the length of the fluid column Howev,er, numerical values are assigned to the various degrees of hotness by art,itr,ary definition For the Celsius scale, the ice point (freezing point of water saturated with 'r at standard atmospheric pressure) is zero, and the steam point (boiling point :~pure water at standard atmospheric pressure) is 100 We may give a thermometer a numerical scale by immersing it in an ice bath and making a mark for zero at the fluid level, and then immersing it in boiling water and making a mark for 100 at this greater fluid level The distance between the two marks is divided into 100 equal spaces called degrees Other spaces of equal size may be marked off below zero and above 100 to extend the range of the thermometer All thermometers, regardless of fluid, read the same at zero and 100 if they are calibrated by the method described, but at other points the readings not usually correspond, because fluids vary in their expansion characteristics An arbitrary choice could be made, and for many purposes this would be entirely satisfactory However, as will be shown, the temperature scale of the SI system, with its kelvin unit, symbol K, is based on the ideal gas as thermometric fluid Since the definition of this scale depends on the properties of gases, detailed discussion of it is delayed until Chap We note, however, that this is an absolute scale, and depends on the concept of a lower limit of temperature Kelvin temperatures are given the symbol T; Celsius temperatures, given the symbol t, are defined in relation to Kelvin temperatures by tOC = T K - 273.15 The unit of Celsius temperature is the degree Celsius, nc, equal to the kelvin However, temperatures on the Celsius scale are 273.15 degrees lower than on the Kelvin scale This means that the lower limit of temperature, called absolute zero on the Kelvin scale, occurs at - 273.l5°C In practice it is the International Practical Temperature Scale of 1968 (IPTS-68) which is used for calibration of scientific and industrial instruments.t This scale has been so chosen that temperatures measured on it closely approximate ideal-gas temperatures; the differences are within the limits of present accuracy of measurement The IPTS-68 is based on assigned values of temperature for a number of reproducible equilibrium states (defining fixed points) and on standard instruments calibrated at these temperatures Interpolation between the fixed-point temperatures is provided by formulas that establish the relation between readings of the standard instruments and values of the international practical temperature The defining fixed points are specified phase-equilibrium states of pure substances,* a~ given in Table 1.2 1.4 TEMPERATURE The most common method of temperature measurement is with a liquid-in-glass thermometer This method depends on the expansion of fluids when they are t The English-language text of the definition of IPTS-68, as agreed upon by the International Committee of Weights and Measures, is published in Metralogia, 5:35-44, 1%9; see also ibid., 12:7-17, 1976 t See Sees 2.7 and 2.8 ~ iii TAIILE C.4 SUPERHEATED STEAM ENGLISH UNITS AIlS PRESS PSIA SAT WATER (SAT TEll') t V 2000 (636.80) H 2026 (637.67) H 2060 (639.31) H 2075 (641.04) H U S V U S V U S V U S !l V 2100 (642.76) H 2125 (644.45) H 2150 (646.13) H 2175 (647.80) H U S V U S V U S V U S V 2200 (649.45) H 2225 (661.08) H 2260 (662.70) H 2276 (664.30) H 2300 (666.89) H U S V U S V U S V U S V U S V 23215 (867.47) U H 23110 (869.03) H 2376 (860.157) H 2400 (662.11) U S V U S V U S V H S SAT STEAM (Cant Inued) TEII'ERATURE DEG F 800 820 860 900 1000 1100 1200 0.0266 662.6 672.1 0.8626 0.1883 1068.6 1138.3 1.2881 0.3072 1221 1335.4 1.4578 0.3171 1233.7 1351 1.4701 0.3312 1260.9 1373.6 1.4874 0.3634 1277.9 1408.7 1.6138 0.3942 1328.2 1474.1 1.6603 0.4320 1376.3 1636.2 1.6014 0.4880 1423.7 1696.9 1.6391 0.0268 665.4 675.0 0.6651 0.1849 1067.2 1136.4 1.2866 0.3026 1220.6 1333.9 1.41566 0.3123 1232.6 1349.7 1.4679 0.3263 1249.9 1372.2 1.4863 0.3483 1277.1 1407.6 1.6118 0.3888 1327.6 1473.3 1.6686 0.4263 1375.8 1636.6 1.6997 0.4619 1423.3 1696.3 1.6376 0.0259 668.1 678.0 0.8676 0.1815 1066.6 1134.5 1.2831 0.2978 1219.4 1332.4 1.4532 0.3076 1231.6 1348.3 1.4667 0.3216 1249.0 1371.0 1.4832 0.3434 1276.3 1406.5 1.15099 0.3836 1327.0 1472.5 1.51567 0.4207 1376.3 1534.9 1.5981 0.4669 1422.8 11595·Ls 0.0260 670.9 680.9 0.8702 0.1782 11&4.1 1132.5 1.2805 0.2933 1218.2 1330.8 1.4509 0.3030 1230.5 1346.9 1.4635 0.3168 1248.0 1369.7 1.4811 0.3386 1275.5 1405.5 1.5079 0.3784 1326.4 1471 1.5549 0.4152 1374.8 1534.2 1.5964 0.41501 1422.4 1695.2 1.6343 0.0262 673.6 683.8 0.8727 0.1750 1062.5 1130.5 1.2780 0.2888 1217.1 1329.3 1.4486 0.2986 1229.4 1345.4 1.4613 0.3123 1247.1 1368.4 1.4790 0.3339 1274.6 1404.4 1.5060 0.3734 1325.8 1470.9 1.5532 0.4099 1374.3 1533.6 1.5948 0.4445 1422.0 1594.7 1.6327 0.0263 676.4 686.7 0.8752 0.1718 1060.9 1128.5 1.2754 0.2845 1215.9 1327.8 1.4463 0.2941 1228.4 1344.0 1.4591 0.3078 1246.1 1367.2 1.4770 0.3293 1273.8 1403.3 1.5041 0.3685 1325.1 1470.0 1.51514 0.4046 1373.8 1532.9 1.5931 0.4389 1421.6 1594.2 1.6312 0.0264 679.1 689.6 0.8778 0.1687 1059.3 1126.4 1.2728 0.2802 1214.7 1326.2 1.4440 0.2898 1227.3 1342.6 1.4669 0.3035 1245.1 1385.9 1.4749 0.3248 1273.0 1402.2 1.15022 0.3637 1324.5 1469.2 1.6497 0.3996 1373.3 1532.3 1.69115 0.4336 1421.1 1593.6 1.6296 0.0266 681.9 692.15 0.8803 0.1667 1057.6 1124.3 1.2702 0.2761 1213.5 1324.6 1.4418 0.2866 1226.2 1341 1.41548 0.2992 1244.2 1364.6 1.4729 0.3204 1272.2 1401.1 1.6003 0.3690 1323.9 1468.4 1.15480 0.3946 1372.8 11531.6 1.I58I1II 0.4282 1420.7 11593.1 1.6281 0.0267 684.6 695.6 0.8828 0.1627 1056.9 1122.2 1.2676 0.2720 1212.3 1323.1 1.4395 0.2816 1226.1 1339.7 1.41526 0.2950 1243.2 1363.3 1.4708 0.3161 1271.4 1400.0 1.4984 0.3645 1323.3 1467.6 1.6463 0.3897 1372.3 1530.9 1.6883 0.4231 1420.3 1692.5 1.6285 0.0268 687.3 698.4 0.8863 0.11598 1054.2 1120.0 1.2649 0.2680 1211 1321.6 1.4372 0.2776 1224.0 1338.2 1.41506 0.2910 1242.2 1362.0 1.4888 0.3119 1270.6 1399.0 1.4966 0.31500 1322.6 1466.7 1.6446 0.3860 1371.8 1530.3 1.6867 0.4180 1419.8 11592.0 1.6261 0.0270 890.1 701.3 0.8879 0.1669 1062.4 1117.8 1.2823 0.2641 1209.9 1319.9 1.4360 0.2736 1222.9 1336.8 1.4483 0.2870 1241.2 1360.7 1.4668 0.3078 1289.7 1397.9 1.4946 0.3466 1322.0 1466.9 1.6430 0.3803 1371 11529.6 1.6862 0.4131 1419.4 11591.4 1.6236 0.0271 692.8 704.2 0.8904 0.1641 1060.6 1116.5 1.2696 1~.7 18.3 4328 0.2603 0.2897 1221.1 13315 1.4462 0.2831 1240.2 1369.4 1.41548 0.3038 1268.9 1396.8 1.4928 0.3414 1321.4 1466.1 1.6413 0.3768 1370.7 1628.9 1.15836 0.4083 1419.0 1590·1 221 0.0273 895.6 707.2 0.8929 0.11513 1048.8 1113.2 1.21589 0.2685 1207.6 1316.7 1.4306 0.2860 1220.6 1333.8 1.4441 0.2793 1239.2 1368.1 1.4628 0.2999 1268.0 1395.7 1.4910 0.3372 1320.7 1464.2 1.6397 0.3714 1370.2 1628.3 1.15821 0.4035 1418.6 1690.3 1.6207 0.0274 898.3 710.1 0.89154 0.1486 1046.9 111 O 0.21529 1206.2 131&.1 1.4283 ::!1p 0.2823 133 1.4420 0.2765 1238.2 13118.8 1.4808 0.2960 1287.2 1394.5 1.4891 0.3331 1320.1 1483.4 1.5380 0.31170 lm· 115 7.8 1.6806 0.3989 1418.1 11589.8 1.8192 0.0276 701.1 713.1 0.8980 0.1460 1046.1 1108.6 215115 ~93 12\1 131 1.4281 lm·1.4398 0.2719 1237.2 13&11.15 1.4188 0.2923 1=.3 1.4873 0.3291 1lm·.8 1.153114 0.31127 lm· 115 7.0 1.15791 0.3944 1417.7 0.0277 703.9 716.0 0.9005 0.1433 1043.1 1106.1 1.2488 0.24158 1203.7 1311.8 1.4239 0.28151 1217.2 1329.4 1.4377 0.2813 1238.2 13114.1 1.4169 0.2886 1lm·.3 1.4865 0.32152 1318.8 1481 1.15348 0.31186 115 lm·1.5776 O·roo 1417 1188.7 1.6164 0.0279 106.8 719.0 0.903t 0.1408 1041.2 1103.7 1.2460 0.2424 1202.6 1310.1 1.4217 0.21517 1216.1 1327.9 1.4357 1311 1.4649 12ft:~8 0.2850 1264.6 1391.2 1.4837 0.3214 1318.2 1480.9 1.5332 0.r'15 1368 1152&.6 1.5761 0.381S6 1lm·.1 1.8149 Is 0.2887 1~:i178 ~ TABLE C.4 SUPERHEATED STEAM ASS PRESS PSIA SAT WATER (SAT TEMP) 2460 (1166.14) 21500 (668.11) t 26150 (671.04) 2600 (673.91) 2860 (676.74) 2700 (679.63) 2760 (882.28) (u ~96) m TEMPERATURE DEG F 880 700 720 740 760 780 800 0.0282 712., 726 0.90815 0.1367 1037.1 1098.6 1.2403 0.1660 1072.8 1143.6 1.2801 0.1762 1104.9 1184.3 1.3166 0.1906 1130.0 1216.4 1.3429 0.2037 1160.8 1243.2 1.36156 0.2163 1168.9 1266.6 1.3M8 0.2269 1185.1 1287.6 1.4019 0.2367 1199.9 1306.8 1.4173 0.0286 718.15 731 0.9139 0.1307 1032.9 1093.3 1.2346 0.1481 1064.4 1132.9 1.2696 0.1681 1098.9 1176.7 1.3076 0.1839 1125.3 1210.4 1.3364 0.1972 1147.0 1238.2 1.3698 0.2089 1165.6 1262.3 1.3797 0.2196 1182.2 1283.7 1.3972 0.2293 1197.4 1303.4 1.4129 0.0290 724.4 738 I 0.9194 0.1268 1028.4 1087'1 286 0.1401 1066.2 1121.1 1581 0.1612 1092.6 1168.7 1.2993 0.1774 1120.4 1204.1 1.3297 0.1909 1143.0 1233.1 1.3640 0.2027 1162.3 1267.9 1.3745 0.2133 1179.3 1279.9 1.3925 0.2231 1194.7 1300.0 1.4086 0.0294 730.3 744.6 0.9247 0.1211 1023.8 1082.0 1.2226 0.0313 747.9 762.9 0.9410 0.1644 1086.9 1160.2 1.2908 0.1711 1116.4 1197.7 1.3228 0.1848 1138.9 1227.8 1.3482 0.1967 1168.8 1263.6 1.3694 0.2073 1176.3 1276.0 1.3878 0.2171 1192.1 1296.6 1.4042 0.0298 736.2 760.9 0.9301 0.1165 1018.9 1076.0 1.2162 0.0308 743.9 769.0 0.9373 0.1477 1078.9 1161.4 1.2820 0.1649 1110.1 1191.0 3168 0.1789 1134.7 1222.4 1.3423 0.1909 1166.3 1248.9 1.3642 0.2016 1173.3 1272.1 1.3830 0.2113 1189.4 1293.0 1.3998 0.0303 742.2 767.3 0.9366 0.1119 1013.7 1069.7 1.2097 0.0304 740.6 766.7 0.9342 0.1411 1071.6 1142.0 1.2727 0.1688 1104.7 1184.0 1.3087 0.1731 1130.4 1216.9 1.3363 0.1862 1161 1244.3 1.3690 0.1960 1170.2 1268.1 1.3783 0.2068 1186.7 1289.6 1.3964 S 0.0308 748.2 763.9 0.9411 0.1076 1008.3 1063.0 1.2029 0.1346 1063.6 1132.0 1.2631 0.1629 1099.0 1176.8 1.3013 0.1676 1126.0 1211.2 1.3302 0.1798 1148.0 1239.6 1.3637 0.1906 1167.0 1264.0 1.3736 0.2004 1183.9 1285.9 1.3911 V U H S 0.0313 764.4 770.7 0.9468 0.1030 1002.4 1066.8 1.1,968 0.1278 1066.0 1121.2 1.2627 0.1471 1=.0 11 1.2t38 0.1620 1121.4 1206.3 1.3241 0.17415 1144.3 1234.7 1.3484 0.1863 1163'1 1269 V U H S V U H S V U H S V U H S V U H S V U H S V U H I.'" lm·1•.2l•7 0.1962 H S 0.0319 760.9 777.7 0.9626 0.0986 996.1 1048.2 1.1883 0.1209 1045.2 1109.0 1.2411 0.1414 1086.8 1161.4 1.2860 0.1667 1116.6 1199.2 3178 0.1693 1140.4 1229.7 1.3430 0.1803 1160.6 1266.6 1.3640 0.1901 1178.2 1278.6 1.3824 2900 (690.22) V U H S 0.0326 767.6 786.1 0.9688 0.0942 989.3 1039.8 1.1803 0.1138 1034.2 1096.2 1.2283 0.1368 1080.3 1163.2 1.2779 0.1616 1111 1193.0 1.3114 0.1643 1136.4 1224.6 3376 0.1764 1167.2 1261.3 1.3692 0.1863 1176.3 1274.7 1.3780 (62fzO 2.79) V U H S 0.0334 774.9 793.1 0.9666 0.0897 981 1030.6 1.1716 0.1063 1021.4 1079.6 1.2139 0.1303 1073.5 1144.6 1.2896 0.1464 1106.6 1186.6 1.3048 0.1694 1132.4 1219.4 1.3320 0.1706 1163.8 1246.9 1.3644 0.1806 1172.4 1270.9 1.3736 3000 (696.33) V U H S 0.0343 782.8 801.8 O 728 0.0860 973.1 1020.3 1.1619 0.0982 1006.0 1060.6 1.1966 0.1248 1066.3 1136.6 1.2610 0.1414 1101 1179.8 1.2982 0.11546 1128.2 1214.0 1.3286 0.1659 1160.3 1242.4 1.3496 0.1769 1169.4 1267.0 1.3692 0150 ( 97.82) V U H S 0.0364 791.9 811.8 0.9812 0.0800 963.0 1008.2 1.1608 0.0884 986.2 1036.1 1740 0.1193 10158.6 1126.0 1.2618 0.13615 1096.9 1172.9 1.2913 0.1600 1123.9 1208.6 1.3208 0.1614 1146.7 1237.9 1.3446 0.1716 1166.3 1263.1 1.3648 3100 (700.28) V U H 0.0368 02 24.0 0.9914 au 0.1137 1060.1 1116.4 1.2419 0.1317 1090.2 1165.7 1.2843 0.1466 1119.6 1202.9 3161 0.1670 1143.1 1233.2 1.3397 0.1671 1163.2 1269.1 1.3604 3160 (702.70) H V U 0.0390 817.8 840.6 1.0063 0.0878 933.4 972.9 1.1192 0.1081 1040 • 1103 1.2314 0.1270 1084.3 1168.3 1.2771 0.1411 1114.9 1197.2 1.3093 0.1628 1139.4 1228.4 1.3347 0.1629 1180.1 1265.0 1.3660 3200 (706.08) V U H S 0.0447 H9.0 76.6 1.0361 89831.7 1.0832 0.1024 1030.7 1091.3 1.2199 0.1224 1078.2 1160.6 1.2698 0.1367 1110.3 1191.2 1.3033 0.1488 1136.6 1223.6 1.3297 0.1688 1165.9 1260.9 1.3616 3208.2 (706.47) V U H S 0.0608 876.9 906.0 0612 0.0608 876.9 906.0 1.0612 0.1014 1028.9 1089.1 1.2178 0.1216 1077 I 1149.3 1.2686 0.1360 1109.6 1190.2 1.3024 0.1479 1136.0 1222.8 1.3288 0.1682 1166'1 1260 .1.3608 o ~ SAT STEAM (Continued) 7.61) ( CoO ENGLISH UNITS V U S S 0.0746 1373 0.0!586 TABlE C.4 SUPERHEATED STEAM ASS PRESS PSIA SAT WATER (SAT TEMP) 2450 (665.14) 2500 (668.11) t ~ uo V U H S V U H S V 2560 (671.04) H 2500 (673.91) H 2650 (676.74) H 2700 (679.63) H 2750 (682.26) H 2800 (684.96) H U S V U S V U S V U S V U S V U S ENGLISH UNITS SAT STEAM (Continued) TEMPERATURE DEG F 820 860 900 950 1000 1100 1200 0.0282 712.5 725.3 0.9085 0.1357 1037.1 1098.6 1.2403 0.2449 1213.8 1324.8 1.4316 0.2579 1233.2 1360.1 1.4610 0.2780 1262.9 1389.0 1.4801 0.2965 1290.6 1425.0 1.5062 0.3139 1316.9 1469.2 1.5300 0.3466 1367.1 1624.3 1.6732 0.3772 1416.0 1587.0 1.6122 0.0286 718.6 731.7 0.9139 0.1307 1032.9 1093.3 1.2346 0.2386 1211.4 1321.8 1.4273 0.2514 1231.1 1347.4 1.4472 0.2712 1251.2 1386.7 1.4766 0.2896 1289.1 1423.1 1.5029 0.3068 1315.6 1457.5 1.5259 0.3390 1366.1 1522.9 1.5703 0.3692 1415.1 1585.9 1.6094 0.0290 724.4 738.1 0.9194 0.1258 1028.4 1087.8 1.2286 0.2322 1209.1 1318.7 1.4232 0.2451 1229.0 1344.7 1.4433 0.2648 1259.5 1384.4 1.4731 0.2829 1287.6 1421 1.4996 0.2999 1314.3 1455.8 1.5238 0.3317 1365.1 1521.6 1.5674 0.3614 1414.3 1564.8 1.6067 0.0294 730.3 744.5 0.9247 0.1211 1023.8 1082.0 1.2226 0.2252 1206.7 1316.5 1.4191 0.2390 1226.9 1341 1.4395 0.2585 1257.7 1382.1 1.4696 0.2765 1286.1 1419.2 1.4964 0.2933 1313.0 1454.1 1.5208 0.3247 1364.0 1520.2 1.5646 0.3640 1413.4 1583.7 1.6040 0.0298 736.2 760.9 0.9301 0.1165 1018.9 1076.0 1.2162 0.2204 1204.2 1312.4 1.4150 0.2332 1224.8 1339.1 1.4367 0.2526 1256.0 1379.8 1.4662 0.2703 1284.6 1417.2 1.4932 0.2870 1311 1452.4 1.5177 0.3179 1363.0 1518.9 1.5618 0.3468 1412.5 1582.6 1.6014 0.0303 742.2 757.3 0.9366 0.1119 1013.7 1069.7 1.2097 0.2149 1201.8 1309.1 1.4109 0.2275 1222.7 1336.3 1.4319 0.2468 1254.2 1377.5 1.4628 0.2644 1283 1415.2 1.4900 0.2809 1310.3 1460.7 1.6148 0.3114 1361 1517.6 1.5591 0.3399 1411 1581.5 1.5988 0.0308 748.2 763.9 0.9411 0.1075 1008.3 1063.0 1.2029 0.2095 1199.3 1305.9 1.4069 0.2221 1220.S 1333.5 1.4282 0.2412 1252.4 1375.1 1.4594 0.2587 1281.6 1413.2 1.4869 0.2760 1309.0 1449.0 1.5118 0.3052 1360.9 1516.2 1.5564 0.3333 1410.8 1580.4 1.5963 0.0313 754.4 770.7 0.9468 0.1030 1002.4 1055.8 1.1958 0.2043 1196.8 1302.6 1.4028 0.2168 1218.3 1330.7 1.4245 0.2368 1250.6 1372.8 1.4661 0.2531 1280.1 1411.2 1.4838 0.2693 1307.7 1447.2 1.6089 0.2991 1369.8 1614.8 1.6637 0.3268 1409.9 1579.3 1.5938 2860 (687.61) V U H 0.0319 760.9 777.7 0.9626 0.0986 996.1 1048.2 1.1883 0.1992 1194.2 1299.3 1.3988 0.2118 1216.1 1327.8 1.4208 0.2306 1248.8 1370.4 1.4527 0.2478 1278.6 1409.2 1.4807 0.2638 1306.4 1445.5 1.5060 0.2933 1358.8 1513.5 1.6511 0.3207 1409.1 1578.2 1.5913 2900 (690.22) V U H 0.0326 767.6 786.1 0.9588 0.0942 989.3 1039.8 1.1803 0.1943 1191 1296.0 1.3947 0.2068 1213.9 1324.9 1.4171 0.2256 1247.0 1368.0 1.4494 0.2427 1277.0 1407.2 1.4777 0.2686 1306.0 1443.7 1.5032 0.2877 1357.7 1512.1 1.6485 0.3147 1408.2 1577.0 1.6889 2950 (692.79) V U H 0.0334 774.9 793.1 0.9656 0.0897 981 1030.6 1.1716 0.1896 1189.1 1292.6 1.3907 0.2021 1211.6 1322.0 1.4134 0.2208 1245.1 1365.6 1.4461 0.2377 1275.4 1405.2 1.4747 0.2634 1303.7 1442.0 1.5004 0.2822 1366.7 1510.7 1.6459 0.3089 1407.3 1575.iI 1.5865 3000 (695.33) V U H 0.0343 782.8 801.8 0.9728 0.0860 973.1 1020.3 1.1619 0.1860 1186.4 1289.1 1.3866 0.1975 1209.4 1319.0 1.4097 0.2161 1243.3 1363.2 1.4429 0.2329 1273.8 1403.1 1.4717 0.2484 1302.3 1440.2 1.4976 0.2770 1356.6 1609.4 1.5434 0.3033 1406.4 1574.8 1.5841 3060 (697.82) V U H S 0.0364 791.9 811.8 0.9812 0.0800 963.0 1008.2 1.1608 0.1806 1183.7 1286.6 1.3825 0.1930 1207.1 1316.0 1.4061 0.2116 1241.4 1360.8 1.4396 0.2282 1272.3 1401.1 1.4687 0.2436 1301.0 1438.5 1.4948 0.2719 1354.6 1508.0 1.6409 0.2979 1406.5 1673.7 1.6817 3100 (700.28) V U H 10224.0 0.0368 0.9914 0.0745 950.6 993.3 1373 0.1763 1181.0 1282.1 1.3786 0.1881 1204.7 1313.0 1.4024 0.2071 1239.5 1368.4 1.4364 0.2237 1270.7 1399.0 1.4668 0.2390 1299.6 1436.7 1.4920 0.2570 1363.6 1506.6 1.5384 0.2927 1404.7 1572.6 1.5794- 3150 (702.70) V U H 0.0390 817.8 840.6 1.0063 0.0678 933.4 972.9 1.1192 0.1721 1178.2 1278.5 1.3745 0.1845 1202.4 1310.0 1.3988 0.2029 1237.6 1365.9 1.4332 0.2193 1.259.1 1396.9 1.4629 0.2345 1298.2 1434.9 1.4893 0.2522 1362.4 1506.2 1.5369 0.2876 1403.8 1571.5 1.5771 3200 (706.08) V U H 0.0447 849.0 876.5 1.0361 0.0666 898.1 931 1.0832 0.1680 1175.4 1274'B 706 0.1804 1200.0 1306.9 1.3961 0.1987 1236.7 1353.4 1.4300 0.2151 1257.6 1394.9 1.4600 0.2301 129&.8 1433.1 1.4866 0.2576 1351.3 1603.8 1.5336 0.2827 1402.9 1570.3 1.6749 3208.2 (706.47) V U H 0.0608 876.9 906.0 1.0612 0.0608 876.9 906.0 0612 0.1874 1176.0 1274.3 1.3898 0.1798 1199.8 1306.4 1.3945 0.1981 1236.4 1353.0 1.4296 0.2144 1257.2 1394.6 1.4595 0.2294 1296.6 1432.8 1.4862 0.2568 1351 1603.6 1.5331 820 1402 1570.2 1.5745 S S S S S S S S -0'1 THE UNIFAC METHOD APPENDIX D THE UNIFAC METHOD 677 all species, and '1jj = I for i = j In these equations rj (a relative molecular volume) and qi (a relative molecular surface area) are the pure-species parameters The temperature dependence of enters in Eq (D.3) through the '1j;, which are given by Tji - Uii) = exp- ( UjiRT (D.4) The interaction parameters for the UNIQUAC equation are the differences (Uji - Ujj) An expression for In 'Yi is found by application of Eq (I1.62) to the UNIQUAC equation for [Eqs (D.I) through (D.3)] The result is given by the following equations: In 'Yi In 'YiC = In 'Yf + In 'Y~ = 1- 1.i + In Ji - (D.5) (1;Li + Li1;) 5qj - - In- (D.6) and (D.7) E e UNIQUAC equiltiont treats 55 G / RT as comprised of two additive parts, "combinatorial" part gC to account for molecular size and shape differences, nd a "residual" part gR to account for molecular interactions: = gC + gR where gC =L i Xi In -2 + Xi i i L-=-L (D.9) Lj rjxj (D.I) (J L qiJCi In -.! (D.8) r· Function gC contains pure-species parameters only, whereas function gR neludes two interaction parameters for each pair of constituent molecules For multi component system, 1;= ', (D.2) Lj fJ.;Xj (J =L qiXi (D.10) Sji =L qiTmj (D.1 I) SjiXi (D.12) m nd 'TIj =L i (D.3) here and Tmj and j ubscript i identifies species, and j is a dummy index All summations t D S Abrams and J M Prausnitz, AIChE I., 21: 116, 1975 76 fUR over = exp -(Umj - Uii) RT (D.13) Again subscript i identifies species, and j and m are dummy indices All summations are over all species, and Tmj = I for m = j Values for the parameters rio q;, and (u"!i - u.ij) are given by Gmehling et al.t t J Gmehling, U Onken, and W Arlt, Vapor-Liquid Equilibrium Data Collection, Chemistry Data Series, vol I, parts 1-8, DECHEMA, Frankfurt/Main, 1977-1984 678 INTRODUCTION TO CHEMICAL ENGINEERING THERMODYNAMICS THE UNIFAC METHOD 679 Table D.I UNIFAC-VLE subgroup volume and surface-area parametent Main group k Rk Qk I 0.9011 0.6744 0.4469 0.2195 0.848 0.540 0.228 0.000 "ACH" ACH (AC = aromatic carbon) 10 0.5313 "ACCH " ACCH3 ACCH2 12 13 "OH" OH "H2 O" "CH CO" I "CH " 13 "CH O" 15 "CNH" 19 "CCN" , , Subgroup CH3 CH2 CH C from more than one set of subgroups, the set containing the least number of different subgroups is the correct set The great advantage of the UNIFAC method is that a relatively small number of subgroups combine to form a very large number of molecules Activity coefficients depend not only on the subgroup properties Rk and Ok, but also on interactions between subgroups Here, similar subgroups are assigned to a main group, as shown in the first column of Table 0.1 The designations of these groups, such as "CH2 ," "ACH," etc., are descriptive only All subgroups belonging to the same main group are considered identical with respect to group interactions Therefore parameters characterizing group interactions are identified with pairs of main groups Parameter values amk for a few such pairs are given in Table 0.2 The UNIFAC method is based on the UNIQUAC equation, for which the activity coefficients are given by Eq (0.5) When applied to a solution of groups, Eqs (0_6) and (0.7) are written: Examples of molecules and their constituent groups n-Butane: Isobutane: 2,2-Dimethyl propane: 2CH ,2CH 3CH3 ,ICH 4CH ,IC 0.400 Benzene: 6ACH 1.2663 1.0396 0.968 0.660 Toluene: Ethylbenzene: 5ACH, IACCH3 ICH 3,5ACH,IACCH 15 1.0000 1.200 Ethanol: ICH3, ICH 20 IOH H2O 17 0.9200 1.400 Water: IH CH 3CO 19 1.6724 1.488 CH2 CO 20 1.4457 1.180 Used when CO is attached to CH3 Acetone: ICH3CO,ICH3 3-Pentanone: 2CH3,ICH2 CO,ICH2 CH 30 CH2 CH-O 25 26 27 1.1450 0.9183 0.6908 1.088 0.780 0.468 Dimethyl ether: ICH 3,ICH3O Diethyl ether: 2CH3, ICH2 , ICH2 Diisopropyl ether: 4CH3, ICH, ICH-O CH3NH CH2 NH CHNH 32 33 34 1.4337 1.2070 0.9795 1.244 0.936 0.624 Dimethylamine: ICH3,ICH3NH Diethylamine: 2CH3, ICH , ICH NH DiisopropyJamine: 4CH3, I CH, I CHNH CH3CN CH2 CN 41 42 1.8701 1.6434 1.724 1.416 Acetonitrile: Propionitrile: In 'Yf = - ] Ji + In Ji - 5qi ( - ~i Ji ) + In Li (0.14) and (0.15) The quantities Ji and Li are still given by Eqs (0.8) and (0.9) In addition, the following definitions apply: (0.16) qi ICH 3CN ICH3 , ICH2 CN = L Vk(i) Ok (0.17) = V~)Ok (0.18) k Oki t J Gmehling, P Rasmussen, and Aa Fredenslund, Ind Eng Chem Process Des Dev., 21: 118, 1982 (0.19) (0.20) The UNIFAC method for evaluation of activity coefficientst depends on the concept that a liquid mixture may be considered a solution of the structural units from which the molecules are formed rather than a solution of the molecules themselves These structural units are called subgroups, and a few of them are listed in the second column of Table 0.1 An identifying number, represented by Ie, is associated with each subgroup_ The relative volume Rk and relative surface area Ok are properties of the subgroups, and values are listed in columns and of Table 0.1 Also shown (column 6) are examples of the subgroup compositions of molecular species When it is possible to construct a mohicule t Aa Fredenslund, R L Jones, and J M Prausnitz, AIChE 1.,21: 1086, 1975 (0.21) I and -amk Tmk =exPr (0.22) Subscript i identifies species, and j is a dummy index running over all species Subscript k identifies subgroups, and m is a dummy index running over all subgroups The quantity v~) is the number of subgroups of type k in a molecule of species i Values of the subgroup parameters Rk and Ok and of the group THE UNIFAC METHOD 681 interaction parameters amk come from tabulations in the literature.t Tables 0.1 and 0.2 show a few parameter values; the number designations of the complete tables are retained The equations for the UNIFAC method are presented here in a form convenient for computer programming In the following example we run through a set of hand calculatiops to demonstrate their application Example 0.1 For the binary system diethylamine(1)/n-heptane(2) at 308.15 K., find 'YI and 'Y2 when XI = 0.4 and X2 = 0.6 SOLUTION The subgroups involved are indicated by the chemical formulas: CH -CH2NH -CH 2-CH ( 1)/ CH - ( CH 2)s-CH The following table shows the subgroups, their identification numbers, values of parameters Rk and Qk (from Table D.1), and the numbers of each subgroup in each molecule: k N ~ of- ; ] 0.9011 0.848 2 0.6744 33 1.2070 0.540 0.936 o 1:1 By Eq (D.16), 'I = (2)(0.9011) + (1)(0.6744) + (1)(1.2070) Similarly, '2 = (2)(0.9011) + (5)(0.6744) 'I = 3.6836 '2 = 5.1742 Thus, In like manner by Eq (D.17), q2 = 4.3960 ql = 3.1720 Application of Eq (D.8) for i = I now gives 3.6836 + (5.1742)(0.6) J I = (3.6836)(0.4) Quantity J2 is expressed similarly; thus, J I = 0.8046 J2 = 1.1302 Equation (D.9), applied in exactly the same way, yields ::r:: o uo ::r::u ",,,,::r::Z ::r::UU::r:: ,,::r::::r::ZU U«O::r::UUUU LI = 0.8120 1.1253 t J Gmehling, P Rasmussen, and Aa Fredenslund, IntI Eng Chern Process Des Dev.,21: 118, 1982 680 ~ = 68l INTRODUCTION TO CHEMICAL ENGINEERING THERMODYNAMICS The results of substitution into Eq (0.18) are as follows: THE UNIFAC METHOD The activity coeffi,cients may now be calculated By Eq (0.14), = -0.0213 and In 'Yf In 'Yf = 0.1463 and In 'Y: = 0.0537 and 'Y2 = 1.047 In 'Yf By Eq (0.15), °ki k i=2 i= = -0.0076 Finally, by Eq (0.5) 33 1.696 2.700 0.000 1.696 0.540 0.936 'YI = 1.133 By Eq (0.19), we have = (1.696)(0.4) + (1.696)(0.6) This and similar expressions for 82 and 833 give 82 = 1.836 = 1.696 833 = 0.3744 The following interaction parameters are found from Table 0.2: al.1 = al.2 = a2,1 = a2.2 = a33,33 = K al.33 = a2.33 = 255.7 K a33.1 = a33.2 = 65.33 K Substitution of these values into Eq (0.22) with T = 308.15 K gives '7'1,33 = '7'2.33 = 0.4361 '7'33,; "" '7'33,2 = 0.8090 The results of application of Eq (0.20) are as follows: Ski k i= i=2 33 2.993 2.993 1.911 4.396 4.396 1.917 Application of Eq (0.21) for k = gives 711 = (2.993)(0.4) This and similar expressions for 712 and 7133 + (4.396)(0.6) give 711 = 3.835 712 = 3.835 7133 = 1.915 683 NEWTON'S METHOD 685 y APPENDIX E NEWTON'S METHOD 0r L~ ~~~~~ x ylr -~_ Numerical techniques are sometimes required in the solution of thermodynamics problems Particularly useful is an iteration procedure that generates a sequence of approximations which rapidly converges on the exact solution of an equation One such procedure is Newton's method, a technique for finding a root X = X, of the equation Y(X) =0 Figure E.1 Graphical construction showing Newton's method for finding a root X of the equation Y(X) = O Another application of this procedure yields a better estimate X of the solution X = X, Thus, at (X Y l ), we write (E.1) The basis for the method is shown graphically by Fig E.l, a sketch of Yvs X for the region that includes the point where Y(X) = O We let X = Xo be an initial estimate of a solution to Eq (E.1), and by constru9tion we identify the corresponding value of Yo = Y(Xo) A tangent drawn to the curve at (Xo, Yo) determines by its intersection with the X axis a new estimate Xl of the solution X = X, The value of Xl is directly related to the slope of the tangent line, which is equal to the derivative of Y with respect to X Thus, at (Xo , Yo), we may write r from which I x =X _ Yl (dY/dX)l (B) By induction, we obtain as a generalization of Eqs (A) and (B) the following recursion formula: from which (A) 684 \}INTRODUCTION TO CHEMICAL ENGINEERING THERMODYNAMICS Equation (E.2) is the mathematical statement of Newton's method Given estimate ~ to the solution of Eq (E.l), it provides a better estimate Xj+l The procedure is repeated until computed values of Y differ from zero by less than some preset tolerance Given an analytical expression for Y, the derivative on the right-hand side of Eq (E.2) is evaluated analytically A major advantage of Newton's method is that it converges rapidly A major disadvantage is that if the function Y exhibits an extremum, the derivative in the denominator of the last term of Eq (E.2) passes through zero and the term itself becomes infinite In this case, Newton's method may still be satisfactory if the initial estimate Xo is properly chosen Fortunately, many problems in thermodynamics involve functions Y(X) that are monotonic in X, and then Newton's method is usually suitable INDEX NAME INDEX Abbott, M M., 84, 92, 221, 341, 379, 425, 475 Abrams, D S., 379, 676 Adler, S B., 97 Alani, G H., 572 Allawi, A J., 458 Arlt, W., 388, 677 Barker, J A., 356 Barr-David, F H., 369, 370 Bennett, C 0., 209 Besserer, G H., 493 Bird, R B., 209 Black, J., 18 Boltzmann, L., 160 Boublik, T., 183 Brewer, L., 86, 510 Camot, N L S., 141 Clausius, R., 13 Compostizo, A" 347 Coriolis, G G., 12 Crespo Colin, A., 347 Dadyburjor, D B., 483 Danner, R P., 108,342,572 Daubert, T E., 108 Davy, H., 18 DePriester, C L., 483-485 deSantis, R., 472 Diaz Peiia, M., 357 Dodds, W S., 292 Duhem, P.-M.-M., 324 Fahien, R W., 209 Fredenslun~, A~., 379, 678, 680-681 Fried, Y., 183 Gallagher, J S., 283 Gibbs, J W., 38, 160 Gmehlipg, J., 379, 388, 677, 680-681 Goodwin, R D., 178 Grande, B., 472 Greell, D., 113, 115,218,283,289,294,446, 562 Greenkom, R A., 97, 98 Haar, L., 283 Hila, E., 183 Harriott, P., 218 Hayden, J G., 342, 387 Haynes, W M., 178 Hougen, O A., 97, 98 Huang, P K., 108 Hurd, C 0., 186 Jones, R L., 379, 678 Joule, J P., 17, 18,21-22 Kelley, K K., 109, 113 Kesler, M G., 88-91, 191-198,336-339 Kister, A T., 377 Kudchadker, A P., 572 Kwong, J N S., 82 Lammers, H B., 248 Lammers, T S., 248 690 INDEX Landsbaum, E M., 292 Lee, B I., 88-91, 191-198,336-339 Lewis, G N., 86, 162,326, 510 Li, Y.-K., 491 Lightfoot, E N., 209 Litvinov, N D., 359 Lydersen, A L., 97, 98 McCabe, W L., 218, 444 McCann, D W., 342 McCracken, P G., 371 McGlashan, M L., 352 Margu1es, M., 351 Maripuri, V C., 354 Mathews, C S., 186 Mathews, J F., 572 Maxwell, J C., 169 Miller, J W., Jr., 114 Missen, R W., 497 Myers, J E., 209 Newton, I., 12 Nghiem, X L., 491 O'Connell, J P., 342, 387 Ohe, S., 183 Onken, U., 388, 677 Orbey, H., 472 Otsuki, H., 528 Pankratz, L B., 109, 113 Passut, C A., 108,572 Peng, D.- Y., 493 Perry, R H., 113, 115,218,283,289,294,446, 562 Pitzer, K S.,,86, 510 Ponce1et, J V., 12 Poynting, J H., 329 Prausnitz, J M., 110,342,379,387, 510, 572, 678 'Rachford, H H., Jr., 394 Rackett, H G., 97 Randall, M., 86, 162, 510 Rankine, W., 14 Raoult, F M., 304 Rasmussen, P., 379, 680-681 Rastogi, R P., 352 Ratcliff, G A., 354 Redlich, 0., 82, 377 Reid, R C., 110,387,510,572 Renon, H., 379 Rice, J D., 394 Riedel, L., 115 Robinson, D B., 493 Rock, H., 360 Ross, W D., 441 SUBJECT INDEX Schorr, G R., 114 Schroder, W., 360 Sherwood, T K., 110,387,510, 572 Sinor, J E., 387 Smith, J C., 218 Smith, J M., 371 Smith, W R., 497 Soave, G., 491 Sollami, B J., 292 Spencer, C F., 97 Spencer, H M., 109 Stevens, W F., 292 Stewart, W E., 209 Stutzman, L F., 292 Taylor, C F., 248 Taylor, E S., 248 Thompson, B., (Count Rumford), 18 Thomson, W (Lord Kelvin), 13 Turnquist, C E., 377 van der Waals, J D., 80 van Laar, J J., 378 Van Ness, H C., 159,221,341,379,425, 4!i8, 475 Vera, J H., 472 Villamaiian, M A., 458 Watson, K M., 116 Watt, J., 18 Weber, J H., 387 Williams, F C., 528 Wilson, G M., 379 Wilson, R H., 444 Woodruff, E B., 248 Yaws, C L., 114 Zwolinski, B J., 572 Acentric factor, 86 table of values for, 571-572 Activity, 503 and chemical-reaction equilibrium constant, 504,516-518 Activity coefficient, 345-357, 376-381, 403-408 analytical representation of, 351, 377-381, 407-408,458-460 effect of T and P on, 423 and the excess Gibbs energy, 345, 406-408, 422 from experimental data, 346-357 infinite-dilution values of, 349-351, 405-408 by the UNIFAC method, 379, 457, 678-683 Adiabatic, process, 66-68, 155-156 Air, TS diagram, 292 Ammonia: PH diagram, 284 thermodynamic properties of, 285-286 Analysis of processes, 555-564 Antoine equation, 182-183 Azeotropes, 373, 392-393, 453, 456 Barker's method, 356 Benedict/Webb/Rubin equation of state, 84 Bernoulli equation, 217-218 Bubble point, 307, 309, 365, 454 Bubble-point calculations, 307-316, 381-393, 482-486,490-493 Calorimeter, flow, 33-35, 117 Carnot cycle, 141-148,248-250,274-276 for power plants, 250 for refrigeration, 275-276 (See also Heat engine; Heat pump) Carnot's equations, 146-147 Carnot's theorem, 142-143 Chemical potential, 298, 302, 303 as equilibrium criterion, 298-299, 503 for ideal gas, 302 for ideal solution, 303 Chemical reaction: equilibrium constant for, 504-516 equilibrium conversion of, 518-528, 533-542 heat effects of, 116-133 reaction coordinate for, 497-501 reversible,41-42,505-507 standard property changes for, 12S, 505 stoichiometry, 497-501 Chemical-reaction equilibrium, 501-528, S32542 calculation of constant for, 510-514 criteria for, 449, 501-503 effect of pressure on, 514-S1S effect of temperature on, S07-S09, SIS in heterogeneous systems, S2S-S28 for multiple reactions, 532-S42 set of independent reactions for, S29-S31 Clapeyron equation, 114-11S, 181 691 692 INDEX Clausius/Clapeyron equation, 182 Coefficient of performance, 275-279, 282-283 Combustion, standard heat of, 123 Compressibility, isot!termal, 58-59, 171-172 Compressibility factor, 62-63, 176 generalized correlations for, 85-96 for mixtures, 471-472, 476-477 Compression, in flow processes, 234-241 Conservation of energy, 12-17,212-217 (See also First law of thermodynamics) Consistency, of VLE data, 355-357 Continuity equation, 211 Control volume, 210-211, 548-550 Conversion factors, taple of, 570 Corresponding states: Correlations, 87-92, 189-199,334-343 theorem of, 86 Critical point, 54-57, 81-82, 184-185,364-368 Critical properties, values of, 571-572 Critical-solution temperature, 455-456 Cubic equation of state, 80-84, 475-493 parameters for, 83-84, 476, 488-489, 491, 493 vapor pressure from, 480-482 Density, generalized correlation for liquids, 97-98 Dew point, 307, 310, 365, 454, 462 Oew-point calculations, 307-316, 381-393, 482486, 490-493 Diesel cycle, 263-265 Differential, exact, 168-169 Dimensions and units, 2-15, 19 Duhem's theorem, 363, 532 Efficiency: Carnot engine, 147,249 compressor and turbine, 226-227, 235 of heat engines, 140-141 of internai-combustion ~ngines, 262-269 of Irreversible processes, 69 qf power plants, 252-254 thermal, 140-141, 147,249 thermodynamic, 551 Electrolytic cell, 42, 248 Energy, 12-17 conservation of, 12-17,212 ,217 (See also First law of thermodynamics) external,22 internal (see Internal energy) kinetic, 13-17,22-24,31-33,212-213,216217 potential, 14-17,22-24,31-33,212-213 Engines: Carnot, 141-144 Diesel, 263-265 INDEX Engines: gas-turbine, 265-269 heat, 140-143 internal-combustion, 260-271 jet, 269-270 Otto, 261-263 rocket, 270-271 Enthalpy, 29-30, 33-35 calculation of values for, 177-180, 199-204 differential expression for, 168, 170-172 effect of T and P on, 169-172 excess, 422 experimental determination of, 33-35 ideal-gas, 171, 177-178, 199-200,300-301, 419 ideal-solution, 303, 419, 440 residual, 175-178,421 generalized correlations for, 189-194, 198199 (See also Excess properties; Residual enthalpy; Property relations; Stan4ard heat of reaction) Enthalpy/concentration diagram, 440-447 for sodium hydroxide/water, 444 for sulfuric acid/water, 441 Enthalpy/entropy (Mollier diagram), 183, 185 for steam (see back endpapers) Entropy, 148-163 absolute, 162-163 calculation of values for, 177-180, 199-204 effect of T and P on, 169-172 excess, 422 ideal-gas, 152-155, 171, 177-178, 199-200, 301,419 ideal-solution, 303, 419 and irreversibility, 155-157,554 residual, 176-178,421 generalized correlations for, 189-190, 195199 and second law, 155-159,548-549 statistical interpretation of, 159-162 (See also Excess properties; Residual entropy; Property relations) Entropy generation, 549, 555, 560, 563 Equation of stat~, 58, 60-64, 77-85, 340-343, 471-493 Benedict/Webb/Rubin, 84 cubic, 80-84, 475-482, 487-493 fugacity coefficients from, 340-343, 472, 475 generalized, 115 ' mixing rules for parameters in, 472, 415-477, 488,493 Peng/ Robinson, 493 Redlich/Kwong, 82-86, 487-489 Soave modification of, 491-492 Equation of state: thermodynamic properties from, 471480 van der Waals, 80-81, 83 virial, 60-63, 77-80, 340-341, 471-475 VLE from, 480-493 Equilibrium, 37, 346, 361-362, 447-449 chemical-reaction (see Chemical-reaction eqUilibrium) criteria for, 298-299, 328, 332, 449 phase (see Phase equilibrium) Equilibrium constant for chemical reaction, 504-516 graph for selected reactions, 509 Exact differential expression, 168-169 Excess Gibbs energy: and the activity coefficient, 344-345, 377-381, 403-408, 422 empirical expressions for: Margules, 351-356, 378 NRTL,380 Redlich/Kister, 377 UNIQUAC, 379, 676-677 van Laar, 378 Wilson, 379-381 Excess properties, 344, 422-423, 428-433 partial, 422-425 and property changes of mixing, 428-429 relations among, 422 Expansion, in flow processes, 220-234 Expansivity, volume, 58-59, 171-173 Extensive property, 26 First law of thermodynamics: for closed systems, 22-24, 45-46 as applied to ideal gases, 64-77 for flow processes, 30-35, 212-217 Flame temperature, 127n Flash calculation for VLE, 314-316, 393-397, 486-487,490 Flow processes, 30-35, 209-241 Bernoulli equation for, 217-218 continuity equation for, 211 energy equations for, 30-35, 212-218 friction in, 217 maximum velocity in, 219-222 mechanical-energy balance for, 217 momentum principle for,209 in nozzles, 220-225 thermodynamic analysis of, 555-564 Formation reaction, 118 standard Gibbs-energy change of, 510, 512513 standard heat of, 118-123 693 Freon-I 2: PH diagram for, 282 thermodynamic properties of, 280-281 Fugacity, 325-334 calculation of, 328-331 in chemical-reaction equilibrium, 504, 506507,514 ideal-gas, 327, 334 in ideal solutions, 345, 398-402 and phase equilibrium, 332 of species in solution, 331-334 effect of composition on, 397-402 and stability, 451-452 Fugacity coefficient, 325-343 calculation of, 327-331, 334, 376, 475, 487 from cubic equations of state, 476, 488490 from generalized correlations, 334-343, 477-480 from the virial equation of state, 340-343, 472 effect of T and P on, 421 and the residual Gibbs energy, 326-327, 333, 421 Fundamental excess-property relation, 422-423 Fundamental property relation, 168, 174,297298 Fundamental residual-property relation, 175, 420-421 Fusion, latent heat of 114 Gas constant, 61-62 table of values for, 570 Gas liquefaction, 291:.295 Gas-turbine power plant, 265-269 Gases: critical constants for, 571-572 generalized correlations for, 85-96, 189-199, 334-343 heat-capacity data for, 109 ideal, 61, 63-77, 300-302, 419 PVT relations for, 54-63,77-96,471-493 Generalized correlations: compressibility factor, 85-96, 477 fugacity coefficient, 334-343, 477 liquid density, 96-98 residual enthalpy and entropy, 189-199,477 second virial coefficient, 89, 92-93, 342, 473 Gibbs/Duhem equation, 324, 334, 345, 350, 354-355, 4Ol, 427, 551-552 Gibbs energy, 167 for change of phase, 181 differential expression for, 168, 174, 298, 420 INPl3X _ 694 INDEX Gibbs energy: and equilibrium, 181,448-449,501-503,538539 as generating function, 174-175 for an ideal gas, 301, 419 for an ideal solution, 303, 419 (See also Excess Gibbs energy; Residual Gibbs energy; Standard Gibbs-energy change) Gibbs's theorem, 300 Heat, 17-19,21-26,45-48, 138-139 of combustion, 123 and entropy, 148-152 of formation, 118-123 latent, 114-116, 181 of mixing, 430, 434-447 ofreaction, 116-133 reservoir, 140, 147 reversible transfer of, 41, ISS, 549-550 sign convention for, 23-24 of solution, 434-437 data for HCI and LiCI in water, 436 specific (see Heat capacity) of transition, 162 Heat capacity, 46-48, 106-114 at constant P or V, 47-48, 64-66, 106-114 difference, 65-66 as function of T, \07-114 ideal-gas, 107-110 mean: for enthalpy calculations, 111-112 for entropy calculations, 153-155 ratio, 66-68 of solids and liquids, 113-114 standard.change of reaction, 125 Heat effects, 105-133 of chemical reactions, 116-133 at constant P or V, 47-48, 64-66 latent, 114-116, 181 of mixing, 434-447 Heat engine, 140-143 Heat pump, 290 Heat transfer, 105-106 irreversible, ISS reversible, 41, ISS, 549-550 Helmholtz energy, 167 differential expression for, 168 Henry's constant, 400-402, 405 Henry's law, 400-408, 517 as basis for activity coefficients, 403-406 and Lewis/Randall rule, 401-402 and solution ideality, 403-408 and standard states, 399-400, 517-518 Ideal gas, 61, 63-77 Carnot cycle for, 145-147 equation of state for, 64 entropy changes for, 152-155 fugacity of, 327, 334 heat capacity of, 64-68, 107-113 internal energy and enthalpy changes for, 64-77 property changes of mixing for, 301, 429 property relations for, 171, 177-178, 199-200, 300-302,419 reaction equilibrium for, SIS and residual properties, 175, 177, 199-200 temperature scale, 61 Ideal-gas state, 61, 107, 171 Ideal solution, 302-304, 398-408, 418-419, 428, 440 chemical-reaction equilibrium for, 515-517 and excess properties, 422, 429 Henry's law as model for, 403-408 K-values based on, 482-483 and Lewis/Randall rule, 345, 398-402, 418 properties of, 302-304, 418-419 property changes of mixing for, 429 and Raoult's law, 304 and standard states, 399-400 Ideal work, 549-554 Immiscible systems, 461-464 Incompressible ftuid, 58, 172 Intensive property, 26 Intensive state, 38 Internal-combustion engines, 260-271 Internal energy, 22-24 differential expression for, 167 of ideal gases, 64-65 International Practical Temperature Scale, 5-6 Irreversibility, 40-41, 554-555 and entropy changes, 155-157,554 Isentropic process, 153-155, 187-189,223-231, 235-240 Isobaric process, 65-66 Isothermal compressibility, 58-59, 171-172 ' Isothermal process, 66 Jet engine, 269-270 Joule/Thomson expansion (see Throttling process) K-values for VLE, 315, 394-396, 482-487 Kinetic energy, 13-17,22-24,31-33,212-213, 216-217 • Latent heat, 114-116, 181 Riedel equation for, 115-116 Watson correlation for, 116 Lewis/Randall rule, 345, 398-402, 418-419 and Henry's law, 401:"402 and Raoult's law, 304 Liquefaction processes, 291-295 Liquid/liquid equilibrium, 454-464 Liquid/vapor equilibrium (see Vapor/liquid equilibrium) Liquids: fugacities of, 328-331 generalized density correlation for, 97-98 heat capacities for, 113-114 incompressible, 58, 172 property changes of, 58-60,171-173 PVf behavior of, 80-84, 96-98 standard states for, 117-118,399-400,50450S, 515-518 Lost work 554-555 Mach number, 223 Margules equation, 351, 378 Maximum velocity in ftow, 219-222 Maxwell equations, 169 Mechanical-energy balance, 217 Methane, PH diagram for, 186 Mixing processes: entropy changes for, 429 Gibbs energy change for, 449-452 heat effects of, 434-447 in ideal gases and ideal solutions, 300-304, 418-419 property changes for, 428-431 Mixing rules, 472, 475-477, 488, 493 Mollier diagram, 183, 185 for steam (see back endpapers) Momentum principle, 209 Newton's second law, 3, 12-13 Nozzle, 220-225 Open system, 298 Otto cycle, 261-263 Partial pressure, 300, 333 Partial properties, 321-325, 416-418 calculation of, 423-428 excess, 422-425 graphical interpretation, for binary system, 425-426 for an ideal solution, 418-419 relations among, 416-418 Partially miscible systems, 454-461 Path functions, 24-25 Phase, 38, 54-58 Phase change, 56-57, 180-181 Phase diaarams: for binary VLB, 306, 309-310, 348, 353, 356, 364-375 for binary systems of limited miscibility, 455-459,461, 463 for a pure species, 55-57 Phase equilibrium, 304-316,346-357, 361-408, 454-464,480-493 criteria for, 298-299, 333, 449 (See also Vapor/liquid equilibrium) Phase rule, 37-39, 362-363, 529-532 Pitzer correlations (see Generalized correlations) Polytropic process, 68-69 Potential energy, 14-17,22-24,31-33,212-213 Power-plant cycles, 247-271 Rankine, 250-253 regenerative, 255-256 thermodynamic analysis of, 556-561 Poynting factor, 329 Pressure, 9-11 critical, 55-56, 571-572 partial, 300 pseudocritical,477-479 reduced,85 Pressure/composition (P,xy) diagram, 306, 348, ·353,356,366,372,457-459,463,492 Pressure/enthalpy (PH) diagram, 183-187 Pressure/temperature (PT) diagram, 55, 57, 367-369, 371 Pressure/volume (PV) diagram, 56, 81, 481 Probability, thermodynamic, 160-161 Process: adiabatic, 66-68, 155-156 constant-pressure, 65-66 constant-volume, 64-65 isentropic, 153-155, 187-189,223-231,235240 isothermal, 66 polytropic, 68-69 thermodynamic analysis of, 555-564 throttling, 77, 232-234, 291-292 Properties: critical, 54-57 from equations of state, 471-480 excess (see Excess properties) extensive and intensive, 26 generalized correlations for, 85-98, 189-199, 334-343 of ideal-gas mixtures, 112-113,300-302,419 of ideal solutions, 302-304, 418-419 notation for, 45-46, 324-325 partial (see Partial properties) reduced, 85, 477 696 INDEX Properties: residual (see Residual properties) of single-phase systems, 167-173 of solutions, 416-419 of two-phase systems, 180-183 (See also Thermodynamic properties) Property changes of mixing, 428-431 and excess properties, 428-429 for ideal gases and ideal solutions, 429 Property changes of reaction, 125, 505 Property relations, 167-183,297-298,416-423 for constant-composition phase, 167-173, 416-418 fUQdamental, 168, 174,298,420-423 Pseudocritical pressure and temperature, 477, 479 PVT relationships, 54-64, 77-98, 471-493 equations of state as, 58, 60-64, 77-85, 471493 for gas mixtures, 340-343, 471-477, 487-493 generalized, 85-98, 473, 477 thermodynamic properties from, 471-480 Quality, 183 Rackett equation, 97 Rankine cycle, 250-253 Raoult's law, 304-316 deviations from, 348-349, 352 modified, for low pressures, 351-356, 388393 Reaction coordinate, 497-501 Redlich/Kister expansion, 377 Redlich/Kwong equation of state, 82-86,487489 Soave modification of, 491-492 Reduced coordinates, 85, 477 Refrigeration, 274-290 Refrigeration cycles: absorption, 288-289 Carnot, 275-276 cascade, 286-287 vapor-compression, 276-279, 282-283 Relative volatility, 392 Residual enthalpy, 175-176,421 from equations of state, 473-479 Residual entropy, 176 from equations of state, 473-479 Residual Gibbs energy, 175-176,326-327,333, 420-421 Residual properties, 173-180,420-421,473-479 Residual volume, 175, 421 Retrograde condensation, 368-369 Reversibility, 39-45, 155-157, 549-551 mechanical,43, lSI INDEX Reversible chemical reaction, 41-42, 505-506 Riedel equation: for latent heat of vaporization, 115-116 for vapor pressure, 183 Rocket engine, 270-271 Saturated liquid and vapor, 56, 185,328,364, 481-482 Second law of thermodynamics, 138-163 in analysis of processes, 548-549, 554-555 statements of, 139-140, 156 statistical interpretation of, 159-162 Second virial coefficient, generalized correlation for, 89, 92-93, 342, 473 Shaft work, 32-33, 213, 216-217 Soave/Redlich/Kwong equation of state, 491492 Sonic velocity in flow, 220-223 Specific heat (see Heat capacity) Stability criteria, 449-454 Standard Gibbs-energy change: of formation, 510, 512-513 of reaction, 504-510 effect of temperature on, 507-508 Standard heat (enthalpy change): of formation, 118-123 of reaction, 116-133, 505, 507-508 effect of temperature on, 123-127, 508 Standard state, 117-118,399-400,504-505, 515-518 for species in chemical reaction, 117-118, 504-505, 515-518 for species in solution, 399-400 State function, 24-26 Statistical thermodynamics, 159-162 Steady-state flow processes, 30-37, 216-218, 548-564 Steam: Mollier diagram for (see back endpapers) tables, 573-675 Steam power plant, 248-260, 556-561 Steam turbine, 225-228 Stoichiometric number, 124,497-501 Superheat, 185 Surroundings, 15-16,22-23 temperature of, 549-550 System, 2, 15-16, 22-24 closed,23 heterogeneous, 525-528 open, 298 Temperature, 4-8, 60-62 absolute zero of,S, 147 critical, 55-56, 571-572 Temperature: critical-solution, 455-456 pseudocritical, 477, 479 reduced, 85, 342, 473 surroundings, 549-550 Temperature/composition (txy) diagram, 310, 366,374,454-456,461-462 Temperature/ entropY (TS) diagram, 183-185, 187 Temperature scales, 4-7 ideal~gas, 61 International Practical, 5-6 Kelvin, 5-7, 64, 146-147 thermodynamic,) 143-144, 146-147 Thermodynamic analysis of processes, 555-564 Thermodynamic consistency, 355-357 Thennodynamic properties: of air, 292 of ammonia, 284-286 of Freon-12, 280-282 of methane, 186 of steam, 573-675 (See also back endpapers) (See also Properties) Third law of thermodynamics, 162-163 Throttling process, 77, 232-234, 291-292 Tie line, 365, 454-455 Triple point, 54,61-62, 184-185 Turbine, 225-23.1 Tul"bojet, 2(;9-270 Two-phase systems, 180-183 Clapeyron equation for, 114-115 qulllity in, 183 (See also Phase equilibria) UNIFAC method, 379, 457, 678-683 UNIQUAC equation, 379, 676-677 Units, 2-15, 19 conversion factors for, 570 Universal gas constant, 61-62 table of values for, 579 Unsteady-statll-flow processes, 210-216 van der Waals equation of state, 80-81, 83 van Laar equations, 378 van't Hoff equilibri\lm box, 505-506 Vapor/liquid equilibrium (VLE): and activity coefficients, 346-357, 376-381 i~finite-dilution values of, 349-351, 377380 binary-system phase diagrams for, 306, 310, 348, 353, 356, 364, 366-372, 374-375, 455-459,461,463,492 Vapor/liquid equilibrium (VLE): block diagrams for, 382-386, 39(i, 490 conditions for stability in, 452-454 correl!ltion through excess Gibbs energy, 351-357,377-381 by Margules equ!ltion, 351-357 by NRTL equation, 380 by Redlich/Kister expansion, 377 by the UNIfAC method, 379, 457, 678683 by UNIQUAC equation, 3.79, 676-677 by van Laar eqllation, 378 by Wilson equation, 379-381 dew- and bubble-point calculations for, 30~ 314,381-393,482-486,490-493 equations, 346-347, 375-381, 480 for high pressure, 480, 482-483, 486-493 for idea! solutions, 482-483 for low to moderate pressure, 347, 375-3: flash calculations for, 314-316, 393-397, 481 487,490 and the Gibbs/Ouhem ",quation, 353-355, 401,451 for immiscible systems, 461-464 K-values for, 315, 394-396, 482-487 nomographs for light hydrocarbons, 484485 for partially miscible systems, 454-461 for pure species, 181,328,480-482 by Raoulfs law, 304-316 reduction of experimental data for, 346-357 and thermodynamic consistency, 355-357 Vapor pressure, 54-57, 86, 115,480-483 empirical eXPressions for, 182-183 Vaporization, 55-57, 114-116, 181-182 latent heat of, 114.,.116, 181-182 from Clapeyron equation, 114-115 from Riedel equation, 115-116 from Watson correlation, 116 Velocity, 13, 211-212, 216-217 average value in pipes, 211 maximum in pip~s, 219-220 profiles in pipes, 211, 216 sonic, 220-223 Virial coefficients, 62-63, 340-342, 472 generalized correlation of second, 89, 92-93 342,473 for mixtures, 340-342, 472 Virial equation of state, 60, 63, 77-80, 340-341 471-475 Yoillme, 8-9 change of mixing, 429-439 critical, 56-58, 571-572 residual, 175-176 Volume expansitivity, 58-59 698 INDEX Watson correlation for latent heat, 116 Wilson equation, 379-381 Work, 11-14,23-26, 138 of adiaba* compression, 67-68, 23S-238 ideal, S49-S54 of isothermal compression, 66 lost, SS4-SSS for pumps, 239-240 Work: and reversibility, 43 shaft, 32-33, 213, 216-217 sign convention for, 23-24 from turbines and expanders, 22S-226 yx diagrams, 370-375 ... consulting editors remain committed to a publishing policy that will serve, and indeed lead, the needs of the chemical engineering profession during the years to come INTRODUCfION TO CHEMICAL ENGINEERING. .. piston is evacuated A pan is attached to the piston rod and a mass m of 45 kg is fastened to the pan The piston, piston rod, and pan together have a mass of 23 kg The latches holding the piston... Unit Operations of Chemical Engineering Mickley, Sherwood, aod Reed: Applied Mathematics in Chemical Engineering Nelson: Petroleum Refinery Engineering Perry aod Green (Editors): Chemical Engineers'