9.17. A three-cycle cascade refrigeration unit is to use methane (cycle 1), ethy
ID: 1884392 • Letter: 9
Question
9.17. A three-cycle cascade refrigeration unit is to use methane (cycle 1),
ethylene (cycle 2), and ammonia (cycle 3). The evaporators are to operate
at: cycle 1, 115.6 K; cycle 2, 180 K; cycle 3, 250 K. The outlets of the
compressors are to be: cycle 1, 4 MPa; cycle 2, 2.6 MPa; cycle 3, 1.4 MPa.
Use the Peng-Robinson equation to estimate fluid properties. Use stream
numbers from Fig. 5.11 on page 212. The compressors have efficiencies of
80%.
a. Determine the flow rate for cycle 2 and cycle 3 relative to
the flow rate in cycle 1.
b. Determine the work required in each compressor per kg of
fluid in the cycle.
c. Determine the condenser duty in cycle 3 per kg of flow in
cycle 1.
d. Suggest two ways that the cycle could be improved.
Explanation / Answer
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Contents Preface Notes to Students Acknowledgments About the Authors Glossary Notation Unit I First and Second Laws Chapter 1 Basic Concepts 1.1 Introduction 1.2 The Molecular Nature of Energy, Temperature, and Pressure Example 1.1 The energy derived from intermolecular potentials Example 1.2 Intermolecular potentials for mixtures 1.3 The Molecular Nature of Entropy 1.4 Basic Concepts 1.5 Real Fluids and Tabulated Properties Example 1.3 Introduction to steam tables Example 1.4 Interpolation Example 1.5 Double interpolation Example 1.6 Double interpolation using different tables Example 1.7 Double interpolation using Excel Example 1.8 Quality calculations Example 1.9 Constant volume cooling 1.6 Summary 1.7 Practice Problems 1.8 Homework Problems Chapter 2 The Energy Balance 2.1 Expansion/Contraction Work 2.2 Shaft Work 2.3 Work Associated with Flow 2.4 Lost Work versus Reversibility Example 2.1 Isothermal reversible compression of an ideal gas 2.5 Heat Flow 2.6 Path Properties and State Properties Example 2.2 Work as a path function 2.7 The Closed-System Energy Balance Example 2.3 Internal energy and heat 2.8 The Open-System, Steady-State Balance Example 2.4 Pump work for compressing H2O 2.9 The Complete Energy Balance 2.10 Internal Energy, Enthalpy, and Heat Capacities Example 2.5 Enthalpy change of an ideal gas: Integrating CPig(T) Example 2.6 Enthalpy of compressed liquid Example 2.7 Adiabatic compression of an ideal gas in a piston/cylinder 2.11 Reference States Example 2.8 Acetone enthalpy using various reference states 2.12 Kinetic and Potential Energy Example 2.9 Comparing changes in kinetic energy, potential energy, internal energy, and enthalpy Example 2.10 Transformation of kinetic energy into enthalpy 2.13 Energy Balances for Process Equipment 2.14 Strategies for Solving Process Thermodynamics Problems 2.15 Closed and Steady-State Open Systems Example 2.11 Adiabatic, reversible expansion of an ideal gas Example 2.12 Continuous adiabatic, reversible compression of an ideal gas Example 2.13 Continuous, isothermal, reversible compression of an ideal gas Example 2.14 Heat loss from a turbine 2.16 Unsteady-State Open Systems Example 2.15 Adiabatic expansion of an ideal gas from a leaky tank Example 2.16 Adiabatically filling a tank with an ideal gas Example 2.17 Adiabatic expansion of steam from a leaky tank 2.17 Details of Terms in the Energy Balance
2.18 Summary 2.19 Practice Problems 2.20 Homework Problems Chapter 3 Energy Balances for Composite Systems 3.1 Heat Engines and Heat Pumps – The Carnot Cycle Example 3.1 Analyzing heat pumps for housing 3.2 Distillation Columns Example 3.2 Start-up for a distillation column 3.3 Introduction to Mixture Properties 3.4 Ideal Gas Mixture Properties 3.5 Mixture Properties for Ideal Solutions Example 3.3 Condensation of a vapor stream 3.6 Energy Balance for Reacting Systems Example 3.4 Stoichiometry and the reaction coordinate Example 3.5 Using the reaction coordinates for simultaneous reactions Example 3.6 Reactor energy balances 3.7 Reactions in Biological Systems 3.8 Summary 3.9 Practice Problems 3.10 Homework Problems Chapter 4 Entropy 4.1 The Concept of Entropy 4.2 The Microscopic View of Entropy Example 4.1 Entropy change and “lost work” in a gas expansion Example 4.2 Stirling’s approximation in the Einstein solid 4.3 The Macroscopic View of Entropy Example 4.3 Adiabatic, reversible expansion of steam Example 4.4 A Carnot cycle based on steam Example 4.5 Ideal gas entropy changes in an adiabatic, reversible expansion Example 4.6 Ideal gas entropy change: Integrating CPig(T) Example 4.7 Entropy generation and “lost work” Example 4.8 Entropy generation in a temperature gradient 4.4 The Entropy Balance Example 4.9 Entropy balances for steady-state composite systems 4.5 Internal Reversibility 4.6 Entropy Balances for Process Equipment Example 4.10 Entropy generation by quenching Example 4.11 Entropy in a heat exchanger Example 4.12 Isentropic expansion in a nozzle 4.7 Turbine, Compressor, and Pump Efficiency 4.8 Visualizing Energy and Entropy Changes 4.9 Turbine Calculations Example 4.13 Various cases of turbine outlet conditions Example 4.14 Turbine efficiency calculation Example 4.15 Turbine inlet calculation given efficiency and outlet 4.10 Pumps and Compressors Example 4.16 Isothermal reversible compression of steam Example 4.17 Compression of R134a using P-H chart 4.11 Strategies for Applying the Entropy Balance 4.12 Optimum Work and Heat Transfer Example 4.18 Minimum heat and work of purification 4.13 The Irreversibility of Biological Life 4.14 Unsteady-State Open Systems Example 4.19 Entropy change in a leaky tank Example 4.20 An ideal gas leaking through a turbine (unsteady state) 4.15 The Entropy Balance in Brief 4.16 Summary 4.17 Practice Problems 4.18 Homework Problems Chapter 5 Thermodynamics of Processes 5.1 The Carnot Steam Cycle 5.2 The Rankine Cycle
Example 5.1 Rankine cycle 5.3 Rankine Modifications Example 5.2 A Rankine cycle with reheat Example 5.3 Regenerative Rankine cycle 5.4 Refrigeration Example 5.4 Refrigeration by vapor compression cycle 5.5 Liquefaction Example 5.5 Liquefaction of methane by the Linde process 5.6 Engines 5.7 Fluid Flow 5.8 Problem-Solving Strategies 5.9 Summary 5.10 Practice Problems 5.11 Homework Problems Unit II Generalized Analysis of Fluid Properties Chapter 6 Classical Thermodynamics — Generalizations for any Fluid 6.1 The Fundamental Property Relation 6.2 Derivative Relations Example 6.1 Pressure dependence of H Example 6.2 Entropy change with respect to T at constant P Example 6.3 Entropy as a function of T and P Example 6.4 Entropy change for an ideal gas Example 6.5 Entropy change for a simple nonideal gas Example 6.6 Accounting for T and V impacts on energy Example 6.7 The relation between Helmholtz energy and internal energy Example 6.8 A quantum explanation of low T heat capacity Example 6.9 Volumetric dependence of CV for ideal gas Example 6.10 Application of the triple product relation Example 6.11 Master equation for an ideal gas Example 6.12 Relating CP to C V 6.3 Advanced Topics 6.4 Summary 6.5 Practice Problems 6.6 Homework Problems Chapter 7 Engineering Equations of State for PVT Properties 7.1 Experimental Measurements 7.2 Three-Parameter Corresponding States 7.3 Generalized Compressibility Factor Charts Example 7.1 Application of the generalized charts 7.4 The Virial Equation of State Example 7.2 Application of the virial equation 7.5 Cubic Equations of State 7.6 Solving the Cubic Equation of State for Z Example 7.3 Peng-Robinson solution by hand calculation Example 7.4 The Peng-Robinson equation for molar volume Example 7.5 Application of the Peng-Robinson equation 7.7 Implications of Real Fluid Behavior Example 7.6 Derivatives of the Peng-Robinson equation 7.8 Matching the Critical Point Example 7.7 Critical parameters for the van der Waals equation 7.9 The Molecular Basis of Equations of State: Concepts and Notation Example 7.8 Estimating molecular size Example 7.9 Characterizing molecular interactions 7.10 The Molecular Basis of Equations of State: Molecular Simulation Example 7.10 Computing molecular collisions in 2D Example 7.11 Equations of state from trends in molecular simulations 7.11 The Molecular Basis of Equations of State: Analytical Theories Example 7.12 Deriving your own equation of state 7.12 Summary 7.13 Practice Problems 7.14 Homework Problems
Chapter 8 Departure Functions 8.1 The Departure Function Pathway 8.2 Internal Energy Departure Function Example 8.1 Internal energy departure from the van der Waals equation 8.3 Entropy Departure Function 8.4 Other Departure Functions 8.5 Summary of Density-Dependent Formulas 8.6 Pressure-Dependent Formulas 8.7 Implementation of Departure Formulas Example 8.2 Real entropy in a combustion engine Example 8.3 Compression of methane using the virial equation Example 8.4 Computing enthalpy and entropy departures from the Peng-Robinson equation Example 8.5 Enthalpy departure for the Peng-Robinson equation Example 8.6 Gibbs departure for the Peng-Robinson equation Example 8.7 U and S departure for the Peng-Robinson equation 8.8 Reference States Example 8.8 Enthalpy and entropy from the Peng-Robinson equation Example 8.9 Liquefaction revisited Example 8.10 Adiabatically filling a tank with propane 8.9 Generalized Charts for the Enthalpy Departure 8.10 Summary 8.11 Practice Problems 8.12 Homework Problems Chapter 9 Phase Equilibrium in a Pure Fluid 9.1 Criteria for Phase Equilibrium 9.2 The Clausius-Clapeyron Equation Example 9.1 Clausius-Clapeyron equation near or below the boiling point 9.3 Shortcut Estimation of Saturation Properties Example 9.2 Vapor pressure interpolation Example 9.3 Application of the shortcut vapor pressure equation Example 9.4 General application of the Clapeyron equation 9.4 Changes in Gibbs Energy with Pressure 9.5 Fugacity and Fugacity Coefficient 9.6 Fugacity Criteria for Phase Equilibria 9.7 Calculation of Fugacity (Gases) 9.8 Calculation of Fugacity (Liquids) Example 9.5 Vapor and liquid fugacities using the virial equation 9.9 Calculation of Fugacity (Solids) 9.10 Saturation Conditions from an Equation of State Example 9.6 Vapor pressure from the Peng-Robinson equation Example 9.7 Acentric factor for the van der Waals equation Example 9.8 Vapor pressure using equal area rule 9.11 Stable Roots and Saturation Conditions 9.12 Temperature Effects on G and f 9.13 Summary 9.14 Practice Problems 9.15 Homework Problems Unit III Fluid Phase Equilibria in Mixtures Chapter 10 Introduction to Multicomponent Systems 10.1 Introduction to Phase Diagrams 10.2 Vapor-Liquid Equilibrium (VLE) Calculations 10.3 Binary VLE Using Raoult’s Law 10.4 Multicomponent VLE Raoult’s Law Calculations Example 10.1 Bubble and dew temperatures and isothermal flash of ideal solutions Example 10.2 Adiabatic flash 10.5 Emissions and Safety 10.6 Relating VLE to Distillation 10.7 Nonideal Systems 10.8 Concepts for Generalized Phase Equilibria 10.9 Mixture Properties for Ideal Gases 10.10 Mixture Properties for Ideal Solutions 10.11 The Ideal Solution Approximation and Raoult’s Law
10.12 Activity Coefficient and Fugacity Coefficient Approaches 10.13 Summary 10.14 Practice Problems 10.15 Homework Problems Chapter 11 An Introduction to Activity Models 11.1 Modified Raoult’s Law and Excess Gibbs Energy Example 11.1 Gibbs excess energy for system 2-propanol + water 11.2 Calculations Using Activity Coefficients Example 11.2 VLE predictions from the Margules equation Example 11.3 Gibbs excess characterization by matching the bubble point Example 11.4 Predicting the Margules parameter with the MAB model 11.3 Deriving Modified Raoult’s Law 11.4 Excess Properties 11.5 Modified Raoult’s Law and Excess Gibbs Energy 11.6 Redlich-Kister and the Two-Parameter Margules Models Example 11.5 Fitting one measurement with the two-parameter Margules equation Example 11.6 Dew pressure using the two-parameter Margules equation 11.7 Activity Coefficients at Special Compositions Example 11.7 Azeotrope fitting with bubble-temperature calculations 11.8 Preliminary Indications of VLLE 11.9 Fitting Activity Models to Multiple Data Example 11.8 Fitting parameters using nonlinear least squares 11.10 Relations for Partial Molar Properties Example 11.9 Heats of mixing with the Margules two-parameter model 11.11 Distillation and Relative Volatility of Nonideal Solutions Example 11.10 Suspecting an azeotrope 11.12 Lewis-Randall Rule and Henry’s Law Example 11.11 Solubility of CO2 by Henry’s Law Example 11.12 Henry’s constant for CO2 with the MAB/SCVP+ model 11.13 Osmotic Pressure Example 11.13 Osmotic pressure of BSA Example 11.14 Osmotic pressure and electroporation of E. coli 11.14 Summary 11.15 Practice Problems 11.16 Homework Problems Chapter 12 Van Der Waals Activity Models 12.1 The van der Waals Perspective for Mixtures 12.2 The van Laar Model Example 12.1 Infinite dilution activity coefficients from the van Laar theory 12.3 Scatchard-Hildebrand Theory Example 12.2 VLE predictions using the Scatchard-Hildebrand theory 12.4 The Flory-Huggins Model Example 12.3 Deriving activity models involving volume fractions Example 12.4 Scatchard-Hildebrand versus van Laar theory for methanol + benzene Example 12.5 Polymer mixing 12.5 MOSCED and SSCED Theories Example 12.6 Predicting VLE with the SSCED model 12.6 Molecular Perspective and VLE Predictions 12.7 Multicomponent Extensions of van der Waals’ Models Example 12.7 Multicomponent VLE using the SSCED model Example 12.8 Entrainer selection for gasohol production 12.8 Flory-Huggins and van der Waals Theories 12.9 Summary 12.10 Practice Problems 12.11 Homework Problems Chapter 13 Local Composition Activity Models Example 13.1 VLE prediction using UNIFAC activity coefficients 13.1 Local Composition Theory Example 13.2 Local compositions in a two-dimensional lattice 13.2 Wilson’s Equation Example 13.3 Application of Wilson’s equation to VLE 13.3 NRTL
13.4 UNIQUAC Example 13.4 Combinatorial contribution to the activity coefficient 13.5 UNIFAC Example 13.5 Calculation of group mole fractions Example 13.6 Detailed calculations of activity coefficients via UNIFAC 13.6 COSMO-RS Methods Example 13.7 Calculation of activity coefficients using COSMO-RS/SAC 13.7 The Molecular Basis of Solution Models 13.8 Summary 13.9 Important Equations 13.10 Practice Problems 13.11 Homework Problems Chapter 14 Liquid-Liquid and Solid-Liquid Phase Equilibria 14.1 The Onset of Liquid-Liquid Instability Example 14.1 Simple vapor-liquid-liquid equilibrium (VLLE) calculations Example 14.2 LLE predictions using Flory-Huggins theory: Polymer mixing 14.2 Stability and Excess Gibbs Energy 14.3 Binary LLE by Graphing the Gibbs Energy of Mixing Example 14.3 LLE predictions by graphing 14.4 LLE Using Activities Example 14.4 The binary LLE algorithm using MAB and SSCED models 14.5 VLLE with Immiscible Components Example 14.5 Steam distillation 14.6 Binary Phase Diagrams 14.7 Plotting Ternary LLE Data 14.8 Critical Points in Binary Liquid Mixtures Example 14.6 Liquid-liquid critical point of the Margules one-parameter model Example 14.7 Liquid-liquid critical point of the Flory-Huggins model 14.9 Numerical Procedures for Binary, Ternary LLE 14.10 Solid-Liquid Equilibria Example 14.8 Variation of solid solubility with temperature Example 14.9 Eutectic behavior of chloronitrobenzenes Example 14.10 Eutectic behavior of benzene + phenol Example 14.11 Precipitation by adding antisolvent Example 14.12 Wax precipitation 14.11 Summary 14.12 Practice Problems 14.13 Homework Problems Chapter 15 Phase Equilibria in Mixtures by an Equation of State 15.1 Mixing Rules for Equations of State Example 15.1 The virial equation for vapor mixtures 15.2 Fugacity and Chemical Potential from an EOS Example 15.2 K-values from the Peng-Robinson equation 15.3 Differentiation of Mixing Rules Example 15.3 Fugacity coefficient from the virial equation Example 15.4 Fugacity coefficient from the van der Waals equation Example 15.5 Fugacity coefficient from the Peng-Robinson equation 15.4 VLE Calculations by an Equation of State Example 15.6 Bubble-point pressure from the Peng-Robinson equation Example 15.7 Isothermal flash using the Peng-Robinson equation Example 15.8 Phase diagram for azeotropic methanol + benzene Example 15.9 Phase diagram for nitrogen + methane Example 15.10 Ethane + heptane phase envelopes 15.5 Strategies for Applying VLE Routines 15.6 Summary 15.7 Practice Problems 15.8 Homework Problems Chapter 16 Advanced Phase Diagrams 16.1 Phase Behavior Sections of 3D Objects 16.2 Classification of Binary Phase Behavior 16.3 Residue Curves 16.4 Practice Problems
16.5 Homework Problems Unit IV Reaction Equilibria Chapter 17 Reaction Equilibria 17.1 Introduction Example 17.1 Computing the reaction coordinate 17.2 Reaction Equilibrium Constraint 17.3 The Equilibrium Constant 17.4 The Standard State Gibbs Energy of Reaction Example 17.2 Calculation of standard state Gibbs energy of reaction 17.5 Effects of Pressure, Inerts, and Feed Ratios Example 17.3 Butadiene production in the presence of inerts 17.6 Determining the Spontaneity of Reactions 17.7 Temperature Dependence of Ka Example 17.4 Equilibrium constant as a function of temperature 17.8 Shortcut Estimation of Temperature Effects Example 17.5 Application of the shortcut van’t Hoff equation 17.9 Visualizing Multiple Equilibrium Constants 17.10 Solving Equilibria for Multiple Reactions Example 17.6 Simultaneous reactions that can be solved by hand Example 17.7 Solving multireaction equilibria with Excel 17.11 Driving Reactions by Chemical Coupling Example 17.8 Chemical coupling to induce conversion 17.12 Energy Balances for Reactions Example 17.9 Adiabatic reaction in an ammonia reactor 17.13 Liquid Components in Reactions Example 17.10 Oligomerization of lactic acid 17.14 Solid Components in Reactions Example 17.11 Thermal decomposition of methane 17.15 Rate Perspectives in Reaction Equilibria 17.16 Entropy Generation via Reactions 17.17 Gibbs Minimization Example 17.12 Butadiene by Gibbs minimization Example 17.13 Direct minimization of the Gibbs energy with Excel Example 17.14 Pressure effects for Gibbs energy minimization 17.18 Reaction Modeling with Limited Data 17.19 Simultaneous Reaction and VLE Example 17.15 The solvent methanol process Example 17.16 NO2 absorption 17.20 Summary 17.21 Practice Problems 17.22 Homework Problems Chapter 18 Electrolyte Solutions 18.1 Introduction to Electrolyte Solutions 18.2 Colligative Properties Example 18.1 Freezing point depression Example 18.2 Example of osmotic pressure Example 18.3 Example of boiling point elevation 18.3 Speciation and the Dissociation Constant 18.4 Concentration Scales and Standard States 18.5 The Definition of pH 18.6 Thermodynamic Network for Electrolyte Equilibria 18.7 Perspectives on Speciation 18.8 Acids and Bases Example 18.4 Dissociation of fluconazole 18.9 Sillèn Diagram Solution Method Example 18.5 Sillèn diagram for HOAc and NaOAc Example 18.6 Phosphate salt and strong acid Example 18.7 Distribution of species in glycine solution 18.10 Applications Example 18.8 Dissociation and solubility of fluconazole 18.11 Redox Reactions Example 18.9 Alkaline dry-cell battery
18.12 Biological Reactions Example 18.10 ATP hydrolysis Example 18.11 Biological fuel cell 18.13 Nonideal Electrolyte Solutions: Background 18.14 Overview of Model Development 18.15 The Extended Debye-Hückel Activity Model 18.16 Gibbs Energies for Electrolytes 18.17 Transformed Biological Gibbs Energies and Apparent Equilibrium Constants Example 18.12 Gibbs energy of formation for ATP 18.18 Coupled Multireaction and Phase Equilibria Example 18.13 Chlorine + water electrolyte solutions 18.19 Mean Ionic Activity Coefficients 18.20 Extending Activity Calculations to High Concentrations 18.21 Summary 18.22 Supplement 1: Interconversion of Concentration Scales 18.23 Supplement 2: Relation of Apparent Chemical Potential to Species Potentials 18.24 Supplement 3: Standard States 18.25 Supplement 4: Conversion of Equilibrium Constants 18.26 Practice Problems 18.27 Homework Problems Chapter 19 Molecular Association and Solvation 19.1 Introducing the Chemical Contribution 19.2 Equilibrium Criteria 19.3 Balance Equations for Binary Systems 19.4 Ideal Chemical Theory for Binary Systems Example 19.1 Compressibility factors in associating/solvating systems Example 19.2 Dimerization of carboxylic acids Example 19.3 Activity coefficients in a solvated system 19.5 Chemical-Physical Theory 19.6 Wertheim’s Theory for Complex Mixtures Example 19.4 The chemical contribution to the equation of state 19.7 Mass Balances for Chain Association Example 19.5 Molecules of H2O in a 100 ml beaker 19.8 The Chemical Contribution to the Fugacity Coefficient and Compressibility Factor 19.9 Wertheim’s Theory of Polymerization Example 19.6 Complex fugacity for the van der Waals model Example 19.7 More complex fugacity for the van der Waals model 19.10 Statistical Associating Fluid Theory (The SAFT Model) Example 19.8 The SAFT model 19.11 Fitting the Constants for an Associating Equation of State 19.12 Summary 19.13 Practice Problems 19.14 Homework Problems Appendix A Summary of Computer Programs A.1 Programs for Pure Component Properties A.2 Programs for Mixture Phase Equilibria A.3 Reaction Equilibria A.4 Notes on Excel Spreadsheets A.5 Notes on MATLAB A.6 Disclaimer Appendix B Mathematics B.1 Important Relations B.2 Solutions to Cubic Equations B.3 The Dirac Delta Function Example B.1 The hard-sphere equation of state Example B.2 The square-well equation of state Appendix C Strategies for Solving VLE Problems C.1 Modified Raoult’s Law Methods C.2 EOS Methods C.3 Activity Coefficient (Gamma-Phi) Methods Appendix D Models for Process Simulators D.1 Overview
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