Preview Introduction to Chemical Engineering Thermodynamics, 8th Edition by J.M. Smith, Hendrick Van Ness, Michael Abbott, Mark Swihart (2018) Preview Introduction to Chemical Engineering Thermodynamics, 8th Edition by J.M. Smith, Hendrick Van Ness, Michael Abbott, Mark Swihart (2018) Preview Introduction to Chemical Engineering Thermodynamics, 8th Edition by J.M. Smith, Hendrick Van Ness, Michael Abbott, Mark Swihart (2018) Preview Introduction to Chemical Engineering Thermodynamics, 8th Edition by J.M. Smith, Hendrick Van Ness, Michael Abbott, Mark Swihart (2018) Preview Introduction to Chemical Engineering Thermodynamics, 8th Edition by J.M. Smith, Hendrick Van Ness, Michael Abbott, Mark Swihart (2018)
INTRODUCTION TO CHEMICAL ENGINEERING THERMODYNAMICS EIGHTH EDITION J M Smith Late Professor of Chemical Engineering University of California, Davis H C Van Ness Late Professor of Chemical Engineering Rensselaer Polytechnic Institute M M Abbott Late Professor of Chemical Engineering Rensselaer Polytechnic Institute M T Swihart UB Distinguished Professor of Chemical and Biological Engineering University at Buffalo, The State University of New York INTRODUCTION TO CHEMICAL ENGINEERING THERMODYNAMICS, EIGHTH EDITION Published by McGraw-Hill Education, Perm Plaza, New York, NY 10121 Copyright © 2018 by McGraw-Hill Education All rights reserved Printed in the United States of America Previous editions © 2005, 2001, and 1996 No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning Some ancillaries, including electronic and print components, may not be available to customers outside the United States This book is printed on acid-free paper LCR 21 20 19 18 17 ISBN 978-1-259-69652-7 MHID 1-259-69652-9 Chief Product Officer, SVP Products & Markets: G Scott Virkler Vice President, General Manager, Products & Markets: Marty Lange Vice President, Content Design & Delivery: Kimberly Meriwether David Managing Director: Thomas Timp Brand Manager: Raghothaman Srinivasan/Thomas M Scaife, Ph.D Director, Product Development: Rose Koos Product Developer: Chelsea Haupt, Ph.D Marketing Director: Tamara L Hodge Marketing Manager: Shannon O’Donnell Director of Digital Content: Chelsea Haupt, Ph.D Digital Product Analyst: Patrick Diller Digital Product Developer: Joan Weber Director, Content Design & Delivery: Linda Avenarius Program Manager: Lora Neyens Content Project Managers: Laura Bies, Rachael Hillebrand & Sandy Schnee Buyer: Laura M Fuller Design: Egzon Shaqiri Content Licensing Specialists: Melissa Homer & Melisa Seegmiller Cover Image: © (Richard Megna) FUNDAMENTAL PHOTOGRAPHS, NYC Compositor: SPi Global Printer: LSC Communications All credits appearing on page or at the end of the book are considered to be an extension of the copyright page Library of Congress Cataloging-in-Publication Data Names: Smith, J M (Joseph Mauk), 1916-2009, author | Van Ness, H C (Hendrick C.), author | Abbott, Michael M., author | Swihart, Mark T (Mark Thomas), author Title: Introduction to chemical engineering thermodynamics / J.M Smith, Late Professor of Chemical Engineering, University of California, Davis; H.C Van Ness, Late Professor of Chemical Engineering, Rensselaer Polytechnic Institute; M.M Abbott, Late Professor of Chemical Engineering, Rensselaer Polytechnic Institute; M.T Swihart, UB Distinguished Professor of Chemical and Biological Engineering, University at Buffalo, The State University of New York Description: Eighth edition | Dubuque : McGraw-Hill Education, 2017 Identifiers: LCCN 2016040832 | ISBN 9781259696527 (alk paper) Subjects: LCSH: Thermodynamics | Chemical engineering Classification: LCC TP155.2.T45 S58 2017 | DDC 660/.2969—dc23 LC record available at https://lccn.loc.gov/2016040832 The Internet addresses listed in the text were accurate at the time of publication The inclusion of a website does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites mheducation.com/highered Contents List of Symbols viii Preface xiii 1 INTRODUCTION 1.1 The Scope of Thermodynamics 1.2 International System of Units 1.3 Measures of Amount or Size 1.4 Temperature 1.5 Pressure 1.6 Work 10 1.7 Energy 11 1.8 Heat 16 1.9 Synopsis 17 1.10 Problems 18 THE FIRST LAW AND OTHER BASIC CONCEPTS 2.1 Joule’s Experiments 2.2 Internal Energy 2.3 The First Law of Thermodynamics 2.4 Energy Balance for Closed Systems 2.5 Equilibrium and the Thermodynamic State 2.6 The Reversible Process 2.7 Closed-System Reversible Processes; Enthalpy 2.8 Heat Capacity 2.9 Mass and Energy Balances for Open Systems 2.10 Synopsis 2.11 Problems 24 24 25 25 26 30 35 39 42 47 59 59 VOLUMETRIC PROPERTIES OF PURE FLUIDS 3.1 The Phase Rule 3.2 PVT Behavior of Pure Substances 3.3 Ideal Gas and Ideal-Gas State 3.4 Virial Equations of State 68 68 70 77 89 iii iv Contents 3.5 Application of the Virial Equations 92 3.6 Cubic Equations of State 95 3.7 Generalized Correlations for Gases 103 3.8 Generalized Correlations for Liquids 112 3.9 Synopsis 115 3.10 Problems 116 HEAT EFFECTS 4.1 Sensible Heat Effects 4.2 Latent Heats of Pure Substances 4.3 Standard Heat of Reaction 4.4 Standard Heat of Formation 4.5 Standard Heat of Combustion 4.6 Temperature Dependence of ΔH° 4.7 Heat Effects of Industrial Reactions 4.8 Synopsis 4.9 Problems 133 134 141 144 146 148 149 152 163 163 THE SECOND LAW OF THERMODYNAMICS 5.1 Axiomatic Statements of the Second Law 5.2 Heat Engines and Heat Pumps 5.3 Carnot Engine with Ideal-Gas-State Working Fluid 5.4 Entropy 5.5 Entropy Changes for the Ideal-Gas State 5.6 Entropy Balance for Open Systems 5.7 Calculation of Ideal Work 5.8 Lost Work 5.9 The Third Law of Thermodynamics 5.10 Entropy from the Microscopic Viewpoint 5.11 Synopsis 5.12 Problems 173 173 178 179 180 182 185 190 194 197 198 200 201 THERMODYNAMIC PROPERTIES OF FLUIDS 6.1 Fundamental Property Relations 6.2 Residual Properties 6.3 Residual Properties from the Virial Equations of State 6.4 Generalized Property Correlations for Gases 6.5 Two-Phase Systems 6.6 Thermodynamic Diagrams 6.7 Tables of Thermodynamic Properties 6.8 Synopsis 6.9 Addendum Residual Properties in the Zero-Pressure Limit 6.10 Problems 210 210 220 226 228 235 243 245 248 249 250 APPLICATIONS OF THERMODYNAMICS TO FLOW PROCESSES 264 7.1 Duct Flow of Compressible Fluids 265 7.2 Turbines (Expanders) 278 Contents v 7.3 Compression Processes 283 7.4 Synopsis 289 7.5 Problems 290 PRODUCTION OF POWER FROM HEAT 8.1 The Steam Power Plant 8.2 Internal-Combustion Engines 8.3 Jet Engines; Rocket Engines 8.4 Synopsis 8.5 Problems 299 300 311 319 321 321 REFRIGERATION AND LIQUEFACTION 9.1 The Carnot Refrigerator 9.2 The Vapor-Compression Cycle 9.3 The Choice of Refrigerant 9.4 Absorption Refrigeration 9.5 The Heat Pump 9.6 Liquefaction Processes 9.7 Synopsis 9.8 Problems 327 327 328 331 334 336 337 343 343 10 THE FRAMEWORK OF SOLUTION THERMODYNAMICS 10.1 Fundamental Property Relation 10.2 The Chemical Potential and Equilibrium 10.3 Partial Properties 10.4 The Ideal-Gas-State Mixture Model 10.5 Fugacity and Fugacity Coefficient: Pure Species 10.6 Fugacity and Fugacity Coefficient: Species in Solution 10.7 Generalized Correlations for the Fugacity Coefficient 10.8 The Ideal-Solution Model 10.9 Excess Properties 10.10 Synopsis 10.11 Problems 348 349 351 352 363 366 11 MIXING PROCESSES 11.1 Property Changes of Mixing 11.2 Heat Effects of Mixing Processes 11.3 Synopsis 11.4 Problems 400 400 405 415 415 12 PHASE EQUILIBRIUM: INTRODUCTION 12.1 The Nature of Equilibrium 12.2 The Phase Rule Duhem’s Theorem 12.3 Vapor/Liquid Equilibrium: Qualitative Behavior 12.4 Equilibrium and Phase Stability 12.5 Vapor/Liquid/Liquid Equilibrium 421 421 422 423 435 439 372 379 382 385 389 390 vi Contents 12.6 Synopsis 442 12.7 Problems 443 13 THERMODYNAMIC FORMULATIONS FOR VAPOR/ LIQUID EQUILIBRIUM 13.1 Excess Gibbs Energy and Activity Coefficients 13.2 The Gamma/Phi Formulation of VLE 13.3 Simplifications: Raoult’s Law, Modified Raoult’s Law, and Henry’s Law 13.4 Correlations for Liquid-Phase Activity Coefficients 13.5 Fitting Activity Coefficient Models to VLE Data 13.6 Residual Properties by Cubic Equations of State 13.7 VLE from Cubic Equations of State 13.8 Flash Calculations 13.9 Synopsis 13.10 Problems 450 451 453 454 468 473 487 490 503 507 508 14 CHEMICAL-REACTION EQUILIBRIA 14.1 The Reaction Coordinate 14.2 Application of Equilibrium Criteria to Chemical Reactions 14.3 The Standard Gibbs-Energy Change and the Equilibrium Constant 14.4 Effect of Temperature on the Equilibrium Constant 14.5 Evaluation of Equilibrium Constants 14.6 Relation of Equilibrium Constants to Composition 14.7 Equilibrium Conversions for Single Reactions 14.8 Phase Rule and Duhem’s Theorem for Reacting Systems 14.9 Multireaction Equilibria 14.10 Fuel Cells 14.11 Synopsis 14.12 Problems 524 525 529 530 533 536 539 543 555 559 570 574 575 15 TOPICS IN PHASE EQUILIBRIA 15.1 Liquid/Liquid Equilibrium 15.2 Vapor/Liquid/Liquid Equilibrium (VLLE) 15.3 Solid/Liquid Equilibrium (SLE) 15.4 Solid/Vapor Equilibrium (SVE) 15.5 Equilibrium Adsorption of Gases on Solids 15.6 Osmotic Equilibrium and Osmotic Pressure 15.7 Synopsis 15.8 Problems 587 587 597 602 606 609 625 629 629 16 THERMODYNAMIC ANALYSIS OF PROCESSES 16.1 Thermodynamic Analysis of Steady-State Flow Processes 16.2 Synopsis 16.3 Problems 636 636 645 645 Contents vii A Conversion Factors and Values of the Gas Constant 648 B Properties of Pure Species 650 C Heat Capacities and Property Changes of Formation 655 D The Lee/Kesler Generalized-Correlation Tables 663 E Steam Tables 680 F Thermodynamic Diagrams 725 G UNIFAC Method 730 H Newton’s Method 737 Index 741 List of Symbols A Area A Molar or specific Helmholtz energy ≡ U − TS A Parameter, empirical equations, e.g., Eq (4.4), Eq (6.89), Eq (13.29) a Acceleration a Molar area, adsorbed phase a Parameter, cubic equations of state āi Partial parameter, cubic equations of state B Second virial coefficient, density expansion B Parameter, empirical equations, e.g., Eq (4.4), Eq (6.89) Bˆ Reduced second-virial coefficient, defined by Eq (3.58) B′ Second virial coefficient, pressure expansion B0, B1 Functions, generalized second-virial-coefficient correlation Bij Interaction second virial coefficient b Parameter, cubic equations of state b¯i Partial parameter, cubic equations of state C Third virial coefficient, density expansion C Parameter, empirical equations, e.g., Eq (4.4), Eq (6.90) Cˆ Reduced third-virial coefficient, defined by Eq (3.64) C′ Third virial coefficient, pressure expansion C0, C1 Functions, generalized third-virial-coefficient correlation CP Molar or specific heat capacity, constant pressure CV Molar or specific heat capacity, constant volume CP° Standard-state heat capacity, constant pressure ΔCP° Standard heat-capacity change of reaction ⟨CP⟩H Mean heat capacity, enthalpy calculations ⟨CP⟩S Mean heat capacity, entropy calculations ⟨CP°⟩H Mean standard heat capacity, enthalpy calculations ⟨CP°⟩S Mean standard heat capacity, entropy calculations c Speed of sound D Fourth virial coefficient, density expansion D Parameter, empirical equations, e.g., Eq (4.4), Eq (6.91) D′ Fourth virial coefficient, pressure expansion EK Kinetic energy EP Gravitational potential energy F Degrees of freedom, phase rule F Force Faraday’s constant viii List of Symbols ix fi Fugacity, pure species i fi° Standard-state fugacity fˆi Fugacity, species i in solution G Molar or specific Gibbs energy ≡ H − T S G°i Standard-state Gibbs energy, species i Gˉ i Partial Gibbs energy, species i in solution G E Excess Gibbs energy ≡ G − Gid GR Residual Gibbs energy ≡ G − Gig ΔG Gibbs-energy change of mixing ΔG° Standard Gibbs-energy change of reaction ΔG°f Standard Gibbs-energy change of formation g Local acceleration of gravity gc Dimensional constant = 32.1740(lbm)(ft)(lbf)−1(s)−2 H Molar or specific enthalpy ≡ U + P V Henry’s constant, species i in solution i Hi° Standard-state enthalpy, pure species i Hˉi Partial enthalpy, species i in solution H E Excess enthalpy ≡ H − Hid HR Residual enthalpy ≡ H − Hig (HR)0, (HR)1 Functions, generalized residual-enthalpy correlation ΔH Enthalpy change (“heat”) of mixing; also, latent heat of phase transition ͠ ΔH Heat of solution ΔH° Standard enthalpy change of reaction ΔH°0 Standard heat of reaction at reference temperature T0 ΔH°f Standard enthalpy change of formation I Represents an integral, defined, e.g., by Eq (13.71) Kj Equilibrium constant, chemical reaction j K i Vapor/liquid equilibrium ratio, species i ≡ yi / xi k Boltzmann’s constant k ij Empirical interaction parameter, Eq (10.71) Molar fraction of system that is liquid l Length lij Equation-of-state interaction parameter, Eq (15.31) M Mach number ℳ Molar mass (molecular weight) M Molar or specific value, extensive thermodynamic property M¯ i Partial property, species i in solution M E Excess property ≡ M − Mid MR Residual property ≡ M − Mig ΔM Property change of mixing ΔM° Standard property change of reaction ΔM°f Standard property change of formation m Mass m˙ Mass flow rate N Number of chemical species, phase rule NA Avogadro’s number 6.9. Addendum Residual Properties in the Zero-Pressure Limit 249 ∙ Explain the origins of the Clapeyron equation and apply it to estimate the change in phase transition pressure with temperature from latent heat data and vice versa ∙ Recognize equality of Gibbs energy, temperature, and pressure as a criterion for phase equilibrium of a pure substance ∙ Read common thermodynamic diagrams and trace the paths of processes on them ∙ Apply the Antoine equation and similar equations to determine vapor pressure at a given temperature and enthalpy of vaporization, via the Clapeyron equation ∙ Construct multi-step computational paths that allow one to compute property changes for arbitrary changes of state of a pure substance, making use of data or correlations for residual properties, heat capacities, and latent heats 6.9 ADDENDUM RESIDUAL PROPERTIES IN THE ZERO-PRESSURE LIMIT The constant J, omitted from Eqs (6.46), (6.48), and (6.49), is the value of G R / RTin the limit as P → The following treatment of residual properties in this limit provides background Because a gas becomes ideal as P → (in the sense that Z → 1), one might suppose that in this limit all residual properties are zero This is not in general true, as is easily demonstrated for the residual volume Written for VR in the limit of zero pressure, Eq (6.41) becomes lim V R = lim V − lim V ig P→0 P→0 P→0 Both terms on the right side of this equation are infinite, and their difference is indeterminate Experimental insight is provided by Eq (6.40): Z − 1 ∂ Z lim V R = RT lim _ = RT lim _ ( ( ) P ∂ p )T P→0 P→0 P→0 The center expression arises directly from Eq (6.40), and the rightmost expression is obtained by application of L’Hôpital’s rule Thus, VR/RT in the limit as P → at a given T is proportional to the slope of the Z-versus-P isotherm at P = Figure 3.7 shows clearly that these values are finite, and not, in general, zero For the internal energy, U R ≡ U − U ig Because Uig is a function of T only, a plot of ig U vs P for a given T is a horizontal line extending to P = For a real gas with intermolecular forces, an isothermal expansion to P → results in a finite increase in U because the molecules move apart against the forces of intermolecular attraction Expansion to P = (V = ∞) reduces these forces to zero, exactly as in an ideal gas, and therefore at all temperatures, lim U = U ig and lim U R = 0 P→0 P→0 From the definition of enthalpy, lim H R = lim U R + lim (P V R) P→0 P→0 P→0 250 CHAPTER 6. Thermodynamic Properties of Fluids Because both terms on the right are zero, lim H R = 0for all temperatures P→0 For the Gibbs energy, by Eq (6.37), G V d _ = _ dP (const T ) ( RT ) RT For the ideal-gas state, V = V ig = RT / P, and this becomes G ig dP d _ = _ (const T ) ( RT ) P Integration from P = 0to pressure P yields P dP G ig G ig G ig _ = _ = _ + _ + ln P + ∞ (const T ) ( RT ) ∫0 P RT ( RT ) P=0 P=0 For finite values of G ig / RT at P > 0, we must have lim (G ig / RT ) = − ∞ We cannot reasonably P→0 expect a different result for lim (G / RT ), and we conclude that P→0 G R G G ig lim _ = lim _ − lim _ = ∞ − ∞ P→0 RT P→0 RT P→0 RT Thus G R / RT(and of course GR) is, like VR, indeterminate in the limit as P → In this case, however, no experimental means exists for finding the limiting value However, we have no reason to presume it is zero, and therefore we regard it like lim V Ras finite, and not in general P→0 zero Equation (6.44) provides an opportunity for further analysis We write it for the limiting case of P = 0: ∂ (G R / RT) H R 2 = − _ ( R T ) [ ∂ T ] P=0 As already shown, H R(P = 0) = 0, P=0 and therefore the preceding derivative is zero As a result, G R _ = J ( RT ) P=0 where J is a constant of integration, independent of T, justifying the derivation of Eq (6.46) 6.10 PROBLEMS 6.1 Starting with Eq (6.9), show that isobars in the vapor region of a Mollier (HS) diagram must have positive slope and positive curvature 6.2 (a) Making use of the fact that Eq (6.21) is an exact differential expression, show that: (∂ CP / ∂ P) T = − T (∂ 2 V / ∂ T 2) P What is the result of application of this equation to an ideal gas? 251 6.10. Problems (b) Heat capacities CV and CP are defined as temperature derivatives respectively of U and H Because these properties are related, one expects the heat capacities also to be related Show that the general expression connecting CP to CV is: ∂ P ∂ V CP = CV + T _ _ ( ∂ T ) ( ∂ T ) V P Show that Eq (B) of Ex 6.2 is another form of this expression 6.3 If U is considered a function of T and P, the “natural” heat capacity is neither CV nor CP, but rather the derivative (∂ U / ∂ T) P Develop the following connections between (∂ U / ∂ T ) P, CP, and CV: ∂ U ∂ V _ = CP − P _ = CP − βPV ( ∂ T ) ( ∂ T ) P P β ∂ P ∂ V = CV + T _ − P _ = CV + (βT − κP)V κ [ ( ∂ T ) ] ( ∂ T ) V P To what these equations reduce for an ideal gas? For an incompressible liquid? 6.4 The PVT behavior of a certain gas is described by the equation of state: P(V − b) = RT where b is a constant If in addition CV is constant, show that: (a) U is a function of T only (b) γ = const (c) For a mechanically reversible process, P (V − b) γ = const 6.5 A pure fluid is described by the canonical equation of state: G = Γ(T ) + RT ln P, where Γ(T ) is a substance-specific function of temperature Determine for such a fluid expressions for V, S, H, U, CP, and CV These results are consistent with those for an important model of gas-phase behavior What is the model? 6.6 A pure fluid, described by the canonical equation of state: G = F(T) + KP, where F(T) is a substance-specific function of temperature and K is a substance-specific constant Determine for such a fluid expressions for V, S, H, U, CP, and CV These results are consistent with those for an important model of liquid-phase behavior What is the model? 6.7 Estimate the change in enthalpy and entropy when liquid ammonia at 270 K is compressed from its saturation pressure of 381 kPa to 1200 kPa For saturated liquid ammonia at 270 K, Vl = 1.551 × 10−3 m3·kg−1, and β = 2.095 × 10−3 K−1 6.8 Liquid isobutane is throttled through a valve from an initial state of 360 K and 4000 kPa to a final pressure of 2000 kPa Estimate the temperature change and the 252 CHAPTER 6. Thermodynamic Properties of Fluids entropy change of the isobutane The specific heat of liquid isobutane at 360 K is 2.78 J·g−1·°C−1 Estimates of V and β may be found from Eq (3.68) 6.9 One kilogram of water (V1 = 1003 cm3·kg−1) in a piston/cylinder device at 25°C and bar is compressed in a mechanically reversible, isothermal process to 1500 bar Determine Q, W, ΔU, ΔH, and ΔS given that β = 250 × 10−6 K−1 and κ = 45 × 10−6 bar −1 A satisfactory assumption is that V is constant at its arithmetic average value 6.10 Liquid water at 25°C and bar fills a rigid vessel If heat is added to the water until its temperature reaches 50°C, what pressure is developed? The average value of β between 25 and 50°C is 36.2 × 10−5 K−1 The value of κ at bar and 50°C is 4.42 × 10−5 bar−1, and may be assumed to be independent of P The specific volume of liquid water at 25°C is 1.0030 cm3·g−1 6.11 Determine expressions for GR, HR, and SR implied by the three-term virial equation in volume, Eq (3.38) 6.12 Determine expressions for GR, HR, and SR implied by the van der Waals equation of state, Eq (3.39) 6.13 Determine expressions for GR, HR, and SR implied by the Dieterici equation: RT a P = _ exp (− _ ) V − b VRT Here, parameters a and b are functions of composition only 6.14 Estimate the entropy change of vaporization of benzene at 50°C The vapor pressure of benzene is given by the equation: 2788.51 ln P sat / kPa = 13.8858 − ∘ t / C + 220.79 (a) Use Eq (6.86) with an estimated value of ΔVlv (b) Use the Clausius/Clapeyron equation of Ex 6.6 6.15 Let P1sat and P2sat be values of the saturation vapor pressure of a pure liquid at absolute temperatures T1 and T2 Justify the following interpolation formula for estimation of the vapor pressure Psat at intermediate temperature T: Psat T 2(T − T 1) ln P sat = ln P1sat + _ ln 2sat T( T 2 − T 1) P1 6.16 Assuming the validity of Eq (6.89), derive Edmister’s formula for estimation of the acentric factor: θ ω = _ log Pc − 1 ( 1 − θ ) where θ ≡ Tn / Tc , Tn is the normal boiling point, and Pc is in (atm) 6.10. Problems 253 6.17 Very pure liquid water can be subcooled at atmospheric pressure to temperatures well below 0°C Assume that kg has been cooled as a liquid to −6°C A small ice crystal (of negligible mass) is added to “seed” the subcooled liquid If the subsequent change occurs adiabatically at atmospheric pressure, what fraction of the system freezes, and what is the final temperature? What is ΔS total for the process, and what is its irreversible feature? The latent heat of fusion of water at 0°C is 333.4 J⋅g−1, and the specific heat of subcooled liquid water is 4.226 J⋅g−1⋅°C−1 6.18 The state of 1(lbm) of steam is changed from saturated vapor at 20 (psia) to superheated vapor at 50 (psia) and 1000(°F) What are the enthalpy and entropy changes of the steam? What would the enthalpy and entropy changes be if steam were an ideal gas? 6.19 A two-phase system of liquid water and water vapor in equilibrium at 8000 kPa consists of equal volumes of liquid and vapor If the total volume Vt = 0.15 m3, what is the total enthalpy Ht and what is the total entropy St? 6.20 A vessel contains kg of H2O as liquid and vapor in equilibrium at 1000 kPa If the vapor occupies 70% of the volume of the vessel, determine H and S for the kg of H2O 6.21 A pressure vessel contains liquid water and water vapor in equilibrium at 350(°F) The total mass of liquid and vapor is 3(lbm) If the volume of vapor is 50 times the volume of liquid, what is the total enthalpy of the contents of the vessel? 6.22 Wet steam at 230°C has a density of 0.025 g⋅cm−3 Determine x, H, and S 6.23 A vessel of 0.15 m3 volume containing saturated-vapor steam at 150°C is cooled to 30°C Determine the final volume and mass of liquid water in the vessel 6.24 Wet steam at 1100 kPa expands at constant enthalpy (as in a throttling process) to 101.33 kPa, where its temperature is 105°C What is the quality of the steam in its initial state? 6.25 Steam at 2100 kPa and 260°C expands at constant enthalpy (as in a throttling p rocess) to 125 kPa What is the temperature of the steam in its final state, and what is its entropy change? What would be the final temperature and entropy change for an ideal gas? 6.26 Steam at 300 (psia) and 500(°F) expands at constant enthalpy (as in a throttling process) to 20 (psia) What is the temperature of the steam in its final state, and what is its entropy change? What would be the final temperature and entropy change for an ideal gas? 6.27 Superheated steam at 500 kPa and 300°C expands isentropically to 50 kPa What is its final enthalpy? 6.28 What is the mole fraction of water vapor in air that is saturated with water at 25°C and 101.33 kPa? At 50°C and 101.33 kPa? 254 CHAPTER 6. Thermodynamic Properties of Fluids 6.29 A rigid vessel contains 0.014 m3 of saturated-vapor steam in equilibrium with 0.021 m3 of saturated-liquid water at 100°C Heat is transferred to the vessel until one phase just disappears, and a single phase remains Which phase (liquid or vapor) remains, and what are its temperature and pressure? How much heat is transferred in the process? 6.30 A vessel of 0.25 m3 capacity is filled with saturated steam at 1500 kPa If the vessel is cooled until 25% of the steam has condensed, how much heat is transferred, and what is the final pressure? 6.31 A vessel of m3 capacity contains 0.02 m3 of liquid water and 1.98 m3 of water vapor at 101.33 kPa How much heat must be added to the contents of the vessel so that the liquid water is just evaporated? 6.32 A rigid vessel of 0.4 m3 volume is filled with steam at 800 kPa and 350°C How much heat must be transferred from the steam to bring its temperature to 200°C? 6.33 One kilogram of steam is contained in a piston/cylinder device at 800 kPa and 200°C (a) If it undergoes a mechanically reversible, isothermal expansion to 150 kPa, how much heat does it absorb? (b) If it undergoes a reversible, adiabatic expansion to 150 kPa, what is its final temperature and how much work is done? 6.34 Steam at 2000 kPa containing 6% moisture is heated at constant pressure to 575°C How much heat is required per kilogram? 6.35 Steam at 2700 kPa and with a quality of 0.90 undergoes a reversible, adiabatic expansion in a nonflow process to 400 kPa It is then heated at constant volume until it is saturated vapor Determine Q and W for the process 6.36 Four kilograms of steam in a piston/cylinder device at 400 kPa and 175°C undergoes a mechanically reversible, isothermal compression to a final pressure such that the steam is just saturated Determine Q and W for the process 6.37 Steam undergoes a change from an initial state of 450°C and 3000 kPa to a final state of 140°C and 235 kPa Determine ΔH and ΔS: (a) From steam-table data (b) By equations for an ideal gas (c) By appropriate generalized correlations 6.38 A piston/cylinder device operating in a cycle with steam as the working fluid executes the following steps: ∙ Steam at 550 kPa and 200°C is heated at constant volume to a pressure of 800 kPa ∙ It then expands, reversibly and adiabatically, to the initial temperature of 200°C ∙ Finally, the steam is compressed in a mechanically reversible, isothermal process to the initial pressure of 550 kPa What is the thermal efficiency of the cycle? 6.10. Problems 255 6.39 A piston/cylinder device operating in a cycle with steam as the working fluid executes the following steps: ∙ Saturated-vapor steam at 300 (psia) is heated at constant pressure to 900(°F) ∙ It then expands, reversibly and adiabatically, to the initial temperature of 417.35(°F) ∙ Finally, the steam is compressed in a mechanically reversible, isothermal process to the initial state What is the thermal efficiency of the cycle? 6.40 Steam entering a turbine at 4000 kPa and 400°C expands reversibly and adiabatically (a) For what discharge pressure is the exit stream a saturated vapor? (b) For what discharge pressure is the exit stream a wet vapor with quality of 0.95? 6.41 A steam turbine, operating reversibly and adiabatically, takes in superheated steam at 2000 kPa and discharges at 50 kPa (a) What is the minimum superheat required so that the exhaust contains no moisture? (b) What is the power output of the turbine if it operates under these conditions and the steam rate is kg⋅s−1? 6.42 An operating test of a steam turbine produces the following results With steam supplied to the turbine at 1350 kPa and 375°C, the exhaust from the turbine at 10 kPa is saturated vapor Assuming adiabatic operation and negligible changes in kinetic and potential energies, determine the turbine efficiency, i.e., the ratio of actual work of the turbine to the work of a turbine operating isentropically from the same initial conditions to the same exhaust pressure 6.43 A steam turbine operates adiabatically with a steam rate of 25 kg⋅s−1 The steam is supplied at 1300 kPa and 400°C and discharges at 40 kPa and 100°C Determine the power output of the turbine and the efficiency of its operation in comparison with a turbine that operates reversibly and adiabatically from the same initial conditions to the same final pressure 6.44 From steam-table data, estimate values for the residual properties VR, HR, and SR for steam at 225°C and 1600 kPa, and compare with values found by a suitable generalized correlation 6.45 From data in the steam tables: (a) Determine values for Gl and Gv for saturated liquid and vapor at 1000 kPa Should these be the same? (b) Determine values for ΔHlv/T and ΔSlv at 1000 kPa Should these be the same? (c) Find values for VR, HR, and SR for saturated vapor at 1000 kPa (d) Estimate a value for dPsat/dT at 1000 kPa and apply the Clapeyron equation to evaluate ΔSlv at 1000 kPa Does this result agree with the steam-table value? Apply appropriate generalized correlations for evaluation of VR, HR, and SR for saturated vapor at 1000 kPa Do these results agree with the values found in (c)? 256 CHAPTER 6. Thermodynamic Properties of Fluids 6.46 From data in the steam tables: (a) Determine values for Gl and Gv for saturated liquid and vapor at 150(psia) Should these be the same? (b) Determine values for ΔHlv/T and ΔSlv at 150(psia) Should these be the same? (c) Find values for VR, HR, and SR for saturated vapor at 150(psia) (d) Estimate a value for dPsat/dT at 150(psia) and apply the Clapeyron equation to evaluate ΔSlv at 150(psia) Does this result agree with the steam-table value? Apply appropriate generalized correlations for evaluation of VR, HR, and SR for saturated vapor at 150(psia) Do these results agree with the values found in (c)? 6.47 Propane gas at bar and 35°C is compressed to a final state of 135 bar and 195°C Estimate the molar volume of the propane in the final state and the enthalpy and entropy changes for the process In its initial state, propane may be assumed an ideal gas 6.48 Propane at 70°C and 101.33 kPa is compressed isothermally to 1500 kPa Estimate ΔH and ΔS for the process by suitable generalized correlations 6.49 A stream of propane gas is partially liquefied by throttling from 200 bar and 370 K to bar What fraction of the gas is liquefied in this process? The vapor pressure of propane is given by Eq (6.91) with parameters: A = –6.72219, B = 1.33236, C = –2.13868, D = –1.38551 6.50 Estimate the molar volume, enthalpy, and entropy for 1,3-butadiene as a saturated vapor and as a saturated liquid at 380 K The enthalpy and entropy are set equal to zero for the ideal-gas state at 101.33 kPa and 0°C The vapor pressure of 1,3-butadiene at 380 K is 1919.4 kPa 6.51 Estimate the molar volume, enthalpy, and entropy for n-butane as a saturated vapor and as a saturated liquid at 370 K The enthalpy and entropy are set equal to zero for the ideal-gas state at 101.33 kPa and 273.15 K The vapor pressure of n-butane at 370 K is 1435 kPa 6.52 The total steam demand of a plant over the period of an hour is 6000 kg, but instantaneous demand fluctuates from 4000 to 10,000 kg⋅h−1 Steady boiler operation at 6000 kg⋅h−1 is accommodated by inclusion of an accumulator, essentially a tank containing mostly saturated liquid water that “floats on the line” between the boiler and the plant The boiler produces saturated steam at 1000 kPa, and the plant operates with steam at 700 kPa A control valve regulates the steam pressure upstream from the accumulator and a second control valve regulates the pressure downstream from the accumulator When steam demand is less than boiler output, steam flows into and is largely condensed by liquid residing in the accumulator, in the process increasing the pressure to values greater than 700 kPa When steam demand is greater than boiler output, water in the accumulator vaporizes and steam flows out, thus reducing the pressure to values less than 1000 kPa What accumulator volume is required for this service if no more that 95% of its volume should be occupied by liquid? 6.10. Problems 257 6.53 Propylene gas at 127°C and 38 bar is throttled in a steady-state flow process to bar, where it may be assumed to be an ideal gas Estimate the final temperature of the propylene and its entropy change 6.54 Propane gas at 22 bar and 423 K is throttled in a steady-state flow process to bar Estimate the entropy change of the propane caused by this process In its final state, propane may be assumed to be an ideal gas 6.55 Propane gas at 100°C is compressed isothermally from an initial pressure of bar to a final pressure of 10 bar Estimate ΔH and ΔS 6.56 Hydrogen sulfide gas is compressed from an initial state of 400 K and bar to a final state of 600 K and 25 bar Estimate ΔH and ΔS 6.57 Carbon dioxide expands at constant enthalpy (as in a throttling process) from 1600 kPa and 45°C to 101.33 kPa Estimate ΔS for the process 6.58 A stream of ethylene gas at 250°C and 3800 kPa expands isentropically in a turbine to 120 kPa Determine the temperature of the expanded gas and the work produced if the properties of ethylene are calculated by: (a) Equations for an ideal gas; (b) Appropriate generalized correlations 6.59 A stream of ethane gas at 220°C and 30 bar expands isentropically in a turbine to 2.6 bar Determine the temperature of the expanded gas and the work produced if the properties of ethane are calculated by: (a) Equations for an ideal gas; (b) Appropriate generalized correlations 6.60 Estimate the final temperature and the work required when mol of n-butane is compressed isentropically in a steady-flow process from bar and 50°C to 7.8 bar 6.61 Determine the maximum amount of work obtainable in a flow process from kg of steam at 3000 kPa and 450°C for surrounding conditions of 300 K and 101.33 kPa 6.62 Liquid water at 325 K and 8000 kPa flows into a boiler at a rate of 10 kg⋅s−1 and is vaporized, producing saturated vapor at 8000 kPa What is the maximum fraction of the heat added to the water in the boiler that can be converted into work in a process whose product is water at the initial conditions, if Tσ = 300 K? What happens to the rest of the heat? What is the rate of entropy change in the surroundings as a result of the work-producing process? In the system? Total? 6.63 Suppose the heat added to the water in the boiler in the preceding problem comes from a furnace at a temperature of 600°C What is the total rate of entropy generation as a ∙ result of the heating process? What is W lost? 258 CHAPTER 6. Thermodynamic Properties of Fluids 6.64 An ice plant produces 0.5 kg⋅s−1 of flake ice at 0°C from water at 20°C (Tσ) in a continuous process If the latent heat of fusion of water is 333.4 kJ⋅kg−1 and if the thermodynamic efficiency of the process is 32%, what is the power requirement of the plant? 6.65 An inventor has developed a complicated process for making heat continuously available at an elevated temperature Saturated steam at 100°C is the only source of energy Assuming that there is plenty of cooling water available at 0°C, what is the maximum temperature level at which heat in the amount of 2000 kJ can be made available for each kilogram of steam flowing through the process? 6.66 Two boilers, both operating at 200(psia), discharge equal amounts of steam into the same steam main Steam from the first boiler is superheated at 420(°F) and steam from the second is wet with a quality of 96% Assuming adiabatic mixing and negligible changes in potential and kinetic energies, what is the equilibrium condition after mixing and what is SG for each (lbm) of discharge steam? 6.67 A rigid tank of 80(ft)3 capacity contains 4180(lbm) of saturated liquid water at 430(°F) This amount of liquid almost completely fills the tank, the small remaining volume being occupied by saturated-vapor steam Because a bit more vapor space in the tank is wanted, a valve at the top of the tank is opened, and saturated-vapor steam is vented to the atmosphere until the temperature in the tank falls to 420(°F) Assuming no heat transfer to the contents of the tank, determine the mass of steam vented 6.68 A tank of 50 m3 capacity contains steam at 4500 kPa and 400°C Steam is vented from the tank through a relief valve to the atmosphere until the pressure in the tank falls to 3500 kPa If the venting process is adiabatic, estimate the final temperature of the steam in the tank and the mass of steam vented 6.69 A tank of m3 capacity contains 1500 kg of liquid water at 250°C in equilibrium with its vapor, which fills the rest of the tank A quantity of 1000 kg of water at 50°C is pumped into the tank How much heat must be added during this process if the temperature in the tank is not to change? 6.70 Liquid nitrogen is stored in 0.5 m3 metal tanks that are thoroughly insulated Consider the process of filling an evacuated tank, initially at 295 K It is attached to a line containing liquid nitrogen at its normal boiling point of 77.3 K and at a pressure of several bars At this condition, its enthalpy is –120.8 kJ⋅kg−1 When a valve in the line is opened, the nitrogen flowing into the tank at first evaporates in the process of cooling the tank If the tank has a mass of 30 kg and the metal has a specific heat capacity of 0.43 kJ⋅kg−1⋅K−1, what mass of nitrogen must flow into the tank just to cool it to a temperature such that liquid nitrogen begins to accumulate in the tank? Assume that the nitrogen and the tank are always at the same temperature The properties of saturated nitrogen vapor at several temperatures are given as follows: 259 6.10. Problems T /K P /bar 80 85 90 95 100 105 110 1.396 2.287 3.600 5.398 7.775 10.83 14.67 Vv /m3⋅kg−1 Hv /kJ⋅kg−1 0.1640 0.1017 0.06628 0.04487 0.03126 0.02223 0.01598 78.9 82.3 85.0 86.8 87.7 87.4 85.6 6.71 A well-insulated tank of 50 m3 volume initially contains 16,000 kg of water distributed between liquid and vapor phases at 25°C Saturated steam at 1500 kPa is admitted to the tank until the pressure reaches 800 kPa What mass of steam is added? 6.72 An insulated evacuated tank of 1.75 m3 volume is attached to a line containing steam at 400 kPa and 240°C Steam flows into the tank until the pressure in the tank reaches 400 kPa Assuming no heat flow from the steam to the tank, prepare graphs showing the mass of steam in the tank and its temperature as a function of pressure in the tank 6.73 A m3 tank initially contains a mixture of saturated-vapor steam and saturated-liquid water at 3000 kPa Of the total mass, 10% is vapor Saturated-liquid water is bled from the tank through a valve until the total mass in the tank is 40% of the initial total mass If during the process the temperature of the contents of the tank is kept constant, how much heat is transferred? 6.74 A stream of water at 85°C, flowing at the rate of kg⋅s−1 is formed by mixing water at 24°C with saturated steam at 400 kPa Assuming adiabatic operation, at what rates are the steam and water fed to the mixer? 6.75 In a desuperheater, liquid water at 3100 kPa and 50°C is sprayed into a stream of superheated steam at 3000 kPa and 375°C in an amount such that a single stream of saturated-vapor steam at 2900 kPa flows from the desuperheater at the rate of 15 kg⋅s−1∙ Assuming adiabatic operation, what is the mass flow rate of the water? What is S Gfor the process? What is the irreversible feature of the process? 6.76 Superheated steam at 700 kPa and 280°C flowing at the rate of 50 kg⋅s−1 is mixed with liquid water at 40°C to produce steam at 700 kPa and 200°C Assuming adiabatic ∙ operation, at what rate is water supplied to the mixer? What is S Gfor the process? What is the irreversible feature of the process? 6.77 A stream of air at 12 bar and 900 K is mixed with another stream of air at bar and 400 K with 2.5 times the mass flow rate If this process were accomplished reversibly and adiabatically, what would be the temperature and pressure of the resulting air stream? Assume air to be an ideal gas for which CP = (7/2)R 260 CHAPTER 6. Thermodynamic Properties of Fluids 6.78 Hot nitrogen gas at 750(°F) and atmospheric pressure flows into a waste-heat boiler at the rate of 40(lbm)s−1, and transfers heat to water boiling at 1(atm) The water feed to the boiler is saturated liquid at 1(atm), and it leaves the boiler as superheated steam at 1(atm) and 300(˚F) If the nitrogen is cooled to 325(˚F) and if heat is lost to the surroundings at a rate of 60(Btu) for each (lbm) of steam generated, what is the ∙ steam-generation rate? If the surroundings are at 70(°F), what is S G for the process? Assume nitrogen to be an ideal gas for which CP = (7/2)R 6.79 Hot nitrogen gas at 400°C and atmospheric pressure flows into a waste-heat boiler at the rate of 20 kg⋅s−1, and transfers heat to water boiling at 101.33 kPa The water feed to the boiler is saturated liquid at 101.33 kPa, and it leaves the boiler as superheated steam at 101.33 kPa and 150°C If the nitrogen is cooled to 170°C and if heat is lost to the surroundings at a rate of 80 kJ for each kilogram of steam generated, what is ∙ the steam-generation rate? If the surroundings are at 25°C, what is S G for the process? Assume nitrogen to be an ideal gas for which CP = (7/2)R 6.80 Show that isobars and isochores have positive slopes in the single-phase regions of a TS diagram Suppose that CP = a + bT, where a and b are positive constants Show that the curvature of an isobar is also positive For specified T and S, which is steeper: an isobar or an isochore? Why? Note that CP > CV 6.81 Starting with Eq (6.9), show that isotherms in the vapor region of a Mollier (HS) diagram have slopes and curvatures given by: 1 ∂ H ∂ 2 H ∂ β _ = (βT − 1) _ 2 = − ( ∂ S ) β ( ∂ S ) β V ( ∂ P ) T T T Here, β is volume expansivity If the vapor is described by the two-term virial equation in P, Eq (3.36), what can be said about the signs of these derivatives? Assume that, for normal temperatures, B is negative and dB/dT is positive 6.82 The temperature dependence of the second virial coefficient B is shown for nitrogen in Fig 3.8 Qualitatively, the shape of B(T ) is the same for all gases; quantitatively, the temperature for which B = corresponds to a reduced temperature of about Tr = 2.7 for many gases Use these observations to show by Eqs (6.54) through (6.56) that the residual properties GR, HR, and SR are negative for most gases at modest pressures and normal temperatures What can you say about the signs of VR and CPR ? 6.83 An equimolar mixture of methane and propane is discharged from a compressor at 5500 kPa and 90°C at the rate of 1.4 kg⋅s−1 If the velocity in the discharge line is not to exceed 30 m·s−1, what is the minimum diameter of the discharge line? 6.84 Estimate VR, HR, and SR for one of the following by appropriate generalized correlations: (a) 1,3-Butadiene at 500 K and 20 bar (b) Carbon dioxide at 400 K and 200 bar (c) Carbon disulfide at 450 K and 60 bar 261 6.10. Problems (d) n-Decane at 600 K and 20 bar (e) Ethylbenzene at 620 K and 20 bar (f) Methane at 250 K and 90 bar (g) Oxygen at 150 K and 20 bar (h) n-Pentane at 500 K and 10 bar (i) Sulfur dioxide at 450 K and 35 bar (j) Tetrafluoroethane at 400 K and 15 bar 6.85 Estimate Z, HR, and SR for one of the following equimolar mixtures by the Lee/Kesler correlations: (a) Benzene/cyclohexane at 650 K and 60 bar (b) Carbon dioxide/carbon monoxide at 300 K and 100 bar (c) Carbon dioxide/n-octane at 600 K and 100 bar (d) Ethane/ethylene at 350 K and 75 bar (e) Hydrogen sulfide/methane at 400 K and 150 bar (f) Methane/nitrogen at 200 K and 75 bar (g) Methane/n-pentane at 450 K and 80 bar (h) Nitrogen/oxygen at 250 K and 100 bar 6.86 For the reversible isothermal compression of a liquid for which β and κ may be assumed independent of pressure, show that: V 2 − V 1 (a) W = P 1 V 1 − P 2 V 2 − _ κ β (b) ΔS = (V 2 − V 1) κ 1 − βT (c) ΔH = _ ( V 2 − V 1) κ Do not assume that V is constant at an average value, but use Eq (3.6) for its P dependence (with V2 replaced by V) Apply these equations to the conditions stated in Prob 6.9 What the results suggest with respect to use of an average value for V? 6.87 In general for an arbitrary thermodynamic property of a pure substance, M = M(T, P); whence ∂ M ∂ M dM = dT + _ dP ( ∂ T ) ( ∂ P ) P T For what two distinct conditions is the following equation true? T 2 ∂ M ΔM = _ dT ∫ T 1 ( ∂ T ) P 6.88 The enthalpy of a pure ideal gas depends on temperature only Hence, Hig is often said to be “independent of pressure,” and one writes (∂ H ig / ∂ P) T = 0 Determine expressions for ( ∂ H ig / ∂ P) Vand ( ∂ H ig / ∂ P) S Why are these quantities not zero? 262 CHAPTER 6. Thermodynamic Properties of Fluids 6.89 Prove that CV ∂ T CP ∂ T dS = _ _ _ dP + _ dV T ( ∂ P ) T ( ∂ V ) V P For an ideal gas with constant heat capacities, use this result to derive Eq (3.23c) 6.90 The derivative (∂ U / ∂ V) Tis sometimes called the internal pressure and the product T(∂ P / ∂ T ) V the thermal pressure Find equations for their evaluation for: (a) An ideal gas; (b) A van der Waals fluid; (c) A Redlich/Kwong fluid 6.91 (a) A pure substance is described by an expression for G(T, P) Show how to determine Z, U, and CV, in relation to G, T, and P and/or derivatives of G with respect to T and P (b) A pure substance is described by an expression for A(T, V) Show how to determine Z, H, and CP, in relation to A, T, and V and/or derivatives of A with respect to T and V 6.92 Use steam tables to estimate a value of the acentric factor ω for water Compare the result with the value given in Table B.1 6.93 The critical coordinates for tetrafluoroethane (refrigerant HFC-134a) are given in Table B.1, and Table 9.1 shows saturation properties for the same refrigerant From these data determine the acentric factor ω for HFC-134a, and compare it with the value given in Table B.1 6.94 As noted in Ex 6.6, Δ H lvis not independent of T; in fact, it becomes zero at the critical point Nor may saturated vapors in general be considered ideal gases Why is it then that Eq (6.89) provides a reasonable approximation to vapor-pressure behavior over the entire liquid range? 6.95 Rationalize the following approximate expressions for solid/liquid saturation pressures: (a) Pslsat = A + BT ; (b) Pslsat = A + BlnT 6.96 As suggested by Fig 3.1, the slope of the sublimation curve at the triple point is generally greater than that of the vaporization curve at the same state Rationalize this observation Note that triple-point pressures are usually low; hence assume for this exercise that ΔZ sv ≈ ΔZ lv ≈ 1. 263 6.10. Problems 6.97 Show that the Clapeyron equation for liquid/vapor equilibrium may be written in the reduced form: sat ^lv lv d ln Pr _ ΔH ΔH _ = where ^ ≡ _ ΔH d Tr lv R Tc r ΔZ lv T 6.98 Use the result of the preceding problem to estimate the heat of vaporization at the normal boiling point for one of the substances listed below Compare the result with the value given in Table B.2 of App B Ground rules: Represent P rsat with Eqs (6.92), (6.93), and (6.94), with ω given by Eq (6.95) Use Eqs (3.57), (3.58), (3.59), (3.61), and (3.62) for Zv, and Eq (3.69) for Zl Critical properties and and normal boiling points are given in Table B.1 (a) Benzene; (b) iso-Butane; (c) Carbon tetrachloride; (d) Cyclohexane; (e) n-Decane; (f) n-Hexane; (g) n-Octane; (h) Toluene; (i) o-Xylene 6.99 Riedel proposed a third corresponding-states parameter αc, related to the vapor-pressure curve by: d ln P sat α c ≡ _ [ d ln T ] T=Tc For simple fluids, experiment shows that α c ≈ 5.8 ;for non-simple fluids, αc increases with increasing molecular complexity How well does the Lee/Kesler correlation for Prsat accommodate these observations? 6.100 Triple-point coordinates for carbon dioxide are Tt = 216.55 K and Pt = 5.170 bar Hence, CO2 has no normal boiling point (Why?) Nevertheless, one can define a hypothetical normal boiling point by extrapolation of the vapor-pressure curve (a) Use the Lee/Kesler correlation for Prsat in conjunction with the triple-point coordinates to estimate ω for CO2 Compare it with the value in Table B.1 (b) Use the Lee/Kesler correlation to estimate the hypothetical normal boiling point for CO2 Comment on the likely reasonableness of this result ... Names: Smith, J M (Joseph Mauk), 1916-2009, author | Van Ness, H C (Hendrick C.), author | Abbott, Michael M. , author | Swihart, Mark T (Mark Thomas), author Title: Introduction to chemical. . .INTRODUCTION TO CHEMICAL ENGINEERING THERMODYNAMICS EIGHTH EDITION J M Smith Late Professor of Chemical Engineering University of California, Davis H C Van Ness Late Professor of Chemical Engineering. .. . of Introduction to Chemical Engineering Thermodynamics.” I met with Hank and with Mike Abbott in summer 2004, and began working with them on the eighth edition in earnest almost immediately