Building up gradually from first principles, this unique introduction to modern thermodynamics integrates classical, statistical and molecular approaches and is especially designed to support students studying chemical and biochemical engineering. In addition to covering traditional problems in engineering thermodynamics in the context of biology and materials chemistry, students are also introduced to the thermodynamics of DNA, proteins, polymers and surfaces. It includes over 80 detailed worked examples, covering a broad range of scenarios such as fuel cell efficiency, DNA/protein binding, semiconductor manufacturing and polymer foaming, emphasizing the practical real-world applications of thermodynamic principles; more than 300 carefully tailored homework problems, designed to stretch and extend students' understanding of key topics, accompanied by an online solution manual for instructors; and all the necessary mathematical background, plus resources summarizing commonly used symbols, useful equations of state, microscopic balances for open systems, and links to useful online tools and datasets.

Preface page xv

Acknowledgments xviii

Definitions xix

1 Introduction 1

1.1 Relevant questions for thermodynamics 2

1.2 Work and energy 4

Exercises 5

2 The postulates of thermodynamics 7

2.1 The postulational approach 7

2.2 The first law: energy conservation 8

2.3 Definition of heat 10

2.4 Equilibrium states 15

2.5 Entropy, the second law, and the fundamental relation 15

2.6 Definitions of temperature, pressure, and chemical potential 22

2.7 Temperature differences and heat flow 33

2.8 Pressure differences and volume changes 35

2.9 Thermodynamics in one dimension 37

Summary 40

Exercises 41

3 Generalized thermodynamic potentials 52

3.1 Legendre transforms 53

3.2 Extremum principles for the potentials 58

3.3 The Maxwell relations 66

3.4 The thermodynamic square 68

3.5 Second-order coefficients 70

3.6 Thermodynamic manipulations 78

3.7 One- and two-dimensional systems 83

      3.7.1 A non-ideal rubber band 83

      3.7.2 Unzipping DNA 85

      3.7.3 Langmuir adsorption 90

Summary 96

Exercises 97

4 First applications of thermodynamics 112

4.1 Stability criteria 112

      4.1.1 Entropy 113

      4.1.2 Internal energy 116

      4.1.3 Generalized potentials 116

4.2 Single-component vapor–liquid equilibrium 118

      4.2.1 The spinodal curve of a van der Waals fluid 118

      4.2.2 The binodal (or coexistence) curve of a van der Waals fluid 122

      4.2.3 The general formulation 126

      4.2.4 Approximations based on the Clapeyron equation 127

4.3 Crystallization of solids 128

4.4 Thermodynamic diagrams 129

      4.4.1 Construction of fundamental relations from two equations of state for single-component systems 131

      4.4.2 Residual properties 135

Summary 141

Exercises 141

5 Application to process design: flow systems 149

5.1 Macroscopic mass, energy, and entropy balances 150

      5.1.1 The throttling process 154

      5.1.2 Specifications for a turbine generator 156

      5.1.3 Work requirements for a pump 158

      5.1.4 The Ranque–Hilsch vortex tube 159

      5.1.5 Fuel cells 162

5.2 Cycles 166

      5.2.1 The Carnot cycle 167

      5.2.2 The Rankine power cycle 169

      5.2.3 The refrigeration cycle 173

Summary 177

Exercises 178

6 Statistical mechanics 181

6.1 Ensemble and time averages 181

6.2 The canonical ensemble 184

6.3 Ideal gases 187

      6.3.1 A simple ideal gas 187

      6.3.2 A general ideal gas 190

6.4 Langmuir adsorption 192

6.5 The grand canonical ensemble 194

6.6 An elastic strand 196

6.7 Fluctuations 199

Summary 204

Exercises 205

7 Molecular interactions 211

7.1 Ideal gases 211

7.2 Intermolecular interactions 212

      7.2.1 The significance of “kBT” 212

      7.2.2 Interactions at long distances 213

      7.2.3 Interactions at short distances 219

      7.2.4 Empirical potential-energy functions 220

      7.2.5 Hydrogen bonds 224

7.3 Molecular simulations 225

7.4 The virial expansion 227

7.5 Equations of state for liquids 230

7.6 Experimental manifestations of intermolecular interactions 231

Conclusions 235

Exercises 236

8 Fugacity and vapor–liquid equilibrium 246

8.1 General equations of phase equilibria 247

8.2 Mixtures of ideal gases 247

8.3 Mixtures: partial molar properties 249

      8.3.1 Definition of a partial molar property 249

      8.3.2 General properties of partial molar quantities 251

      8.3.3 Residual partial molar quantities 255

8.4 Fugacity 257

      8.4.1 Definition of fugacity 257

      8.4.2 Properties of fugacity 258

      8.4.3 Estimating the fugacity of a pure vapor or liquid 259

8.5 Calculation of fugacity coefficients of mixtures from PVT equations of state 263

8.6 Fugacity in ideal or Lewis mixtures 267

      8.6.1 Lewis mixing 267

      8.6.2 Properties of Lewis (ideal) mixtures 268

      8.6.3 A simple application of Lewis (ideal) mixing: Raoult’s law 270

8.7 Solubility of solids and liquids in compressed gases 271

      8.7.1 Phase equilibria between a solid and a compressed gas 271

      8.7.2 Phase equilibria between a liquid and a compressed gas 272

      Summary 273

      Exercises 275

9 Activity and equilibrium 282

9.1 Excess properties and activities 282

9.2 A summary of fugacity and activity 285

9.3 Correlations for partial molar excess Gibbs free energy 286

      9.3.1 Simple binary systems 286

      9.3.2 Thermodynamic consistency 291

9.4 Semi-theoretical expressions for activity coefficients 292

      9.4.1 The van Laar equation 293

      9.4.2 Wilson’s equation 293

      9.4.3 The NRTL equation 294

      9.4.4 The UNIQUAC model 295

9.5 Dilute mixtures: Henry’s constants 296

      9.5.1 Measurement of activity coefficients 299

9.6 The blood–brain barrier 303

9.7 Partial miscibility 305

      9.7.1 Thermodynamic stability 305

      9.7.2 Liquid–liquid equilibria in ternary mixtures 310

      9.7.3 Critical points 311

9.8 Simple free-energy models from statistical mechanics 313

      9.8.1 Lewis mixing 314

      9.8.2 The Margules model 315

      9.8.3 Exact solution of the lattice model 316

Summary 316

Exercises 317

10 Reaction equilibrium 328

10.1 A simple picture: the reaction coordinate 328

10.2 Extent of reaction 330

10.3 The equilibrium criterion 332

10.4 The reaction equilibrium constant 333

10.5 Standard property changes 334

10.6 Estimating the equilibrium constant 335

10.7 Determination of equilibrium compositions 340

10.8 Enzymatic catalysis: the Michaelis–Menten model 342

10.9 Denaturation of DNA and polymerase chain reactions 343

      10.9.1 Denaturation 344

      10.9.2 Polymerase chain reaction 346

10.10 Statistical mechanics of reactions and denaturation 347

      10.10.1 Stochastic fluctuations in reactions 347

      10.10.2 DNA denaturation 353

Summary 355

Exercises 356

11 Thermodynamics of polymers 365

11.1 Solubility and miscibility of polymer solutions 365

11.2 Generalizations of the Flory–Huggins theory 370

      11.2.1 The generalization of Qian et al. 370

      11.2.2 The Sanchez–Lacombe equation of state 374

      11.2.3 The BGY model 380

11.3 Block copolymers 383

11.4 Derivation of the Flory–Huggins theory 386

Summary 390

Exercises 390

12 Thermodynamics of surfaces 393

12.1 The interfacial tension of a planar interface 393

12.2 The Gibbs free energy of a surface phase and the Gibbs–Duhem relation 395

12.3 Curved interfaces 396

12.4 Solid–liquid interfaces: wetting 401

12.5 Capillary forces 403

12.6 Solid–gas interfaces: adsorption 409

12.7 The temperature dependence of surface tension 410

12.8 Interfaces in mixtures 411

      12.8.1 Vapor–liquid interfaces 412

      12.8.2 Monolayer formation on liquid surfaces 416

Summary 419

Exercises 420

Appendix A Mathematical background 426

A.1 Taylor’s series expansion 426

A.2 The chain rule 427

A.3 Jacobian transformations 429

A.4 The fundamental theorem of calculus 431

A.5 Leibniz’s rule 431

A.6 The Gauss divergence theorem 432

A.7 Solutions to cubic equations 432

A.8 Combinatorics 434

      A.8.1 The binomial theorem 434

      A.8.2 The multinomial theorem 435

Appendix B Fluid equations of state 437

B.1 A general ideal gas 437

B.2 The virial equation of state 438

B.3 The van der Waals fluid 440

B.4 The Carnahan–Starling equation of state 441

B.5 The Redlich–Kwong equation of state 442

B.6 The Peng–Robinson equation of state 444

B.7 Martin’s generalized cubic equation of state 445

B.8 The Benedict–Webb–Rubin equation of state 446

B.9 The Anderko–Pitzer equation of state 447

Appendix C Microscopic balances for open systems 451

C.1 Mass: the continuity equation 451

C.2 Momentum: the equation of motion 453

C.3 Energy: the microscopic energy balance 454

C.4 Entropy: the microscopic entropy balance 455

C.5 Entropy flux and generation in laminar flow 458

Appendix D Physical properties and references 461

D.1 Websites with data and programs 461

D.2 Entropy and properties of formation 462

D.3 Physical constants 468

D.4 Steam tables 469

References 470

Index 477

Jay D. Schieber is Professor of Chemical Engineering in the Department of Chemical and Biological Engineering and the Department of Physics, and Director of the Center for Molecular Study of Condensed Soft Matter, at the Illinois Institute of Technology. He has been a visiting professor at universities in both Europe and Asia, holds numerous teaching awards, and was the 2004 Hougen Scholar at the University of Wisconsin, Madison.

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