1 Introduction 1
1.1 The Water–Energy Nexus 1
1.2 Systems and Their Properties 4
1.3 Thermodynamic Concentrations, Constants, Units, and Relationships 6

2 The First Law of Thermodynamics and Energy Balances for Closed Systems 13
2.1 Work and Energy Overview 13
2.2 Internal Energy and the First Law 15
2.3 Expansion Work 19
2.4 Heat Exchange at Constant Volume 22
2.5 Nonexpansion Work 26
2.6 Enthalpy 28
2.7 Enthalpy versus Internal Energy for Ideal Gas 32
2.8 Special Case for Ideal Gas with Little Volume Change 34
2.9 Relating Cp to Cv for an Ideal Gas 34
2.10 Adiabatic Changes for Ideal Gas 35
2.11 Standard Enthalpy Changes 37
2.12 Enthalpies of Chemical Change, that is Reactions 40
2.13 Some Other Useful Relationships 42

3 The First Law of Thermodynamics and Energy Balances for Open Systems 49
3.1 Kinetic and Potential Energies of Moving Water 49
3.2 First Law Applied to Steady Flow Devices 56
3.3 First Law Applied to Unsteady Flow Devices 68
3.4 Major Head Losses in Piping 70
3.5 Minor Head Losses in Piping 80
3.6 Pump and Turbine Energy 81

4 Second and Third Laws of Thermodynamics, Entropy, and Free Energy 95
4.1 Defining Entropy 95
4.2 Entropy and the Heat Engine 98
4.3 Clausius Inequality 107
4.4 Examples of Entropy Change for Specific Processes 109
4.5 Entropy Balances 114
4.6 Helmholtz and Gibbs Energies 120

5 Thermodynamics of Simple Mixtures 137
5.1 Chemical Potential 137
5.2 Thermodynamics of Mixing for Ideal Gases 139
5.3 Thermodynamics of Mixing for Liquids 142
5.4 Application of Thermodynamics of Mixing for Water Desalination 149
5.5 What About When We Have More than One Phase at Equilibrium (No Reaction) 153
5.6 What About When We Have Mixtures that Are Reacting in Solution 154

6 Thermal Distillation 163
6.1 Idealized Distillation Occurring in a Batch Reactor 163
6.2 Overview of Multiple Effect and Multistage Flash Distillation 171
6.3 Design of Forward Feed MED System 176
6.4 Defining the Performance of Thermal Desalination Systems 186
6.5 Quantifying Entropy Change During Desalination 189

7 Membrane Desalination 215
7.1 Overview of Water Treatment Using Membranes 215
7.2 Membrane Operational Parameters 221
7.3 Minimum Isothermal Reversible Work of Membrane Separation 228
7.4 Energy Requirements for Desalination Using a Simple One-Stage Reverse Osmosis Module 233
7.5 Energy Requirements for Desalination Using Reverse Osmosis Modules in Series, With or Without Energy Recovery 238
7.6 A More Practical Approach to Design RO Membrane Desalination that Considers the System Pressure Used to Drive Flow 244
7.7 Entropy Losses During Reverse Osmosis 248

8 Electrodialysis261
8.1 Overview of Water Treatment Using Electrodialysis 261
8.2 Common Terms and Definitions in Electrodialysis 265
8.3 Thermodynamics of a Reversible Electrodialysis Process 267
8.4 Practical Minimum Energy Consumption for Electrodialysis 271
8.5 Designing a Practical Electrodialysis System 273

9 Electrochemical Treatment of Water 301
9.1 Promise of Electrochemistry in Water Treatment 301
9.2 Electrochemical Reactions and Reactors 302
9.3 Anodic Reactions Under Standard Conditions 305
9.4 Cathodic Reactions Under Standard Conditions 305
9.5 Calculating Standard Potentials and Gibbs Free Energy Values for Half Reactions 305
9.6 Full Cell Reactions at Standard Conditions 309
9.7 Full Cell Reactions Under (Standard) Environmental Conditions 312
9.8 Theoretical Current Demand 315
9.9 Actual Current Demand and Current Efficiency 322
9.10 Overpotential and Reaction Kinetics 324
9.11 Energy Consumption for Water Treatment 331

End of Chapter 9 Problems 332
References 336
Appendix A 339
Index 379