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

1.5 Real Fluids and Tabulated Properties

*Example 1.3 Introduction to steam tables*

*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*

2.1 Expansion/Contraction Work

2.4 Lost Work versus Reversibility

*Example 2.1 Isothermal reversible compression of an ideal gas*

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 H _{2}O*

2.9 The Complete Energy Balance

2.10 Internal Energy, Enthalpy, and Heat Capacities

*Example 2.5 Enthalpy change of an ideal gas: Integrating C _{P}^{ig}(T)*

*Example 2.6 Enthalpy of compressed liquid*

*Example 2.7 Adiabatic compression of an ideal gas in a piston/cylinder*

*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

**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*

*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

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 C _{P}^{ig}(T)*

*Example 4.7 Entropy generation and “lost work”*

*Example 4.8 Entropy generation in a temperature gradient*

*Example 4.9 Entropy balances for steady-state composite systems*

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

*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*

*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

**Chapter 5 Thermodynamics of Processes**

*Example 5.2 A Rankine cycle with reheat*

*Example 5.3 Regenerative Rankine cycle*

*Example 5.4 Refrigeration by vapor compression cycle*

*Example 5.5 Liquefaction of methane by the Linde process*

5.8 Problem-Solving Strategies

**Unit II Generalized Analysis of Fluid Properties**

**Chapter 6 Classical Thermodynamics — Generalizations for any Fluid**

6.1 The Fundamental Property Relation

*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 C _{V} 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 C _{P} to C_{V}*

**Chapter 7 Engineering Equations of State for PVT Properties**

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*

7.6 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*

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

8.5 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*

*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

**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*

**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*

10.6 Relating VLE to Distillation

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

**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

11.5 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 CO _{2} by Henry’s Law*

*Example 11.12 Henry’s constant for CO _{2} with the MAB/SCVP+ model*

*Example 11.13 Osmotic pressure of BSA*

*Example 11.14 Osmotic pressure and electroporation of E. coli*

**Chapter 12 Van Der Waals Activity Models**

12.1 The van der Waals Perspective for Mixtures

*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*

*Example 12.3 Deriving activity models involving volume fractions*

*Example 12.4 Scatchard-Hildebrand versus van Laar theory for methanol + benzene*

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

**Chapter 13 Local Composition Activity Models**

*Example 13.1 VLE prediction using UNIFAC activity coefficients*

*Example 13.2 Local compositions in a two-dimensional lattice*

*Example 13.3 Application of Wilson’s equation to VLE*

*Example 13.4 Combinatorial contribution to the activity coefficient*

*Example 13.5 Calculation of group mole fractions*

*Example 13.6 Detailed calculations of activity coefficients via UNIFAC*

*Example 13.7 Calculation of activity coefficients using COSMO-RS/SAC*

13.7 The Molecular Basis of Solution Models

**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*

*Example 14.4 The binary LLE algorithm using MAB and SSCED models*

14.5 VLLE with Immiscible Components

*Example 14.5 Steam distillation*

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

*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*

**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

**Chapter 16 Advanced Phase Diagrams**

16.1 Phase Behavior Sections of 3D Objects

16.2 Classification of Binary Phase Behavior

**Chapter 17 Reaction Equilibria**

*Example 17.1 Computing the reaction coordinate*

17.2 Reaction Equilibrium Constraint

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 *K _{a}*

*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

*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 NO*_{2} *absorption*

**Chapter 18 Electrolyte Solutions**

18.1 Introduction to Electrolyte Solutions

*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

18.6 Thermodynamic Network for Electrolyte Equilibria

18.7 Perspectives on Speciation

*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*

*Example 18.8 Dissociation and solubility of fluconazole*

*Example 18.9 Alkaline dry-cell battery*

*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

18.22 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

**Chapter 19 Molecular Association and Solvation**

19.1 Introducing the Chemical Contribution

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*

19.6 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 H _{2}O 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)

19.11 Fitting the Constants for an Associating Equation of State

**Appendix A Summary of Computer Programs**

A.1 Programs for Pure Component Properties

A.2 Programs for Mixture Phase Equilibria

A.4 Notes on Excel Spreadsheets

B.2 Solutions to Cubic Equations

*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.3 Activity Coefficient (Gamma-Phi) Methods

**Appendix D Models for Process Simulators**

**Appendix E Themodynamic Properties**

E.4 Henry’s Constant with Water as Solvent

E.5 Dielectric Constant for Water

E.6 Dissociation Constants of Polyprotic Acids

E.7 Standard Reduction Potentials

E.10 Pressure-Enthalpy Diagram for Methane

E.11 Pressure-Enthalpy Diagram for Propane

E.12 Pressure-Enthalpy Diagram for R134a (1,1,1,2-Tetraflouroethane)

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