Nonequilibrium Thermodynamics

Chapter 1Fundamentals of equilibrium thermodynamics 11.1 Introduction 11.2 Basic definitions 11.3 Reversible and irreversible processes 61.4 Equilibrium 8Example 1.1 Equilibrium in subsystems 91.5 The fundamental equations 101.6 The thermodynamic laws 11Example 1.2 Relationships between the molar heat capacities Cp and Cv 12Example 1.3 Entropy and distribution of probability 141.7 Balance equations 141.8 Entropy and entropy production 16Example 1.4 Entropy production and subsystems 17Example 1.5 Entropy production in a chemical reaction in a closed system 17Example 1.6 Entropy production in mixing 181.9 The Gibbs equation 201.10 Equations of state 22Example 1.7 Heat capacities for real gases 22Example 1.8 van der Waals isotherms 23Example 1.9 Estimation of molar volume of a gas at high pressure 24Example 1.10 Estimation of volume of a gas at high pressure using generic cubic equation of state 25Example 1.11 Entropy of a real gas 26Example 1.12 Chemical potential of a real gas 27Example 1.13 Henry’s law constant 35Example 1.14 Estimation of partial excess properties 37Example 1.15 Binary liquid mixture phase diagrams 39Example 1.16 Estimation of fugacity coefficients from virial equation 40Example 1.17 Heterogeneous azeotrope 431.11 Thermodynamic potentials 461.12 Cross relations 471.13 Extremum principles 48Problems 49References 52References for further reading 52Chapter 2Transport and rate processes 532.1 Introduction 532.2 Nonequilibrium systems 532.3 Kinetic approach 552.4 Transport phenomena 56Example 2.1 Estimation of momentum flow 59 Example 2.2 Estimation of viscosity at specified temperature and pressure 62Example 2.3 Estimation of viscosity of gas mixtures at low density 62Example 2.4 Estimation of heat flow through a composite wall with constant thermal conductivities 64Example 2.5 Estimation of heat flow with temperature-dependent thermal conductivity 66Example 2.6 Estimation of thermal conductivity at specified temperature and pressure 68Example 2.7 Estimation of thermal conductivity of monatomic gases 70Example 2.8 Estimation of thermal conductivity of polyatomic gases 71Example 2.9 Estimation of thermal conductivity of gas mixtures at low density 71Example 2.10 Estimation of thermal conductivity of pure liquids 72Example 2.11 Mass flow across a stagnant film 74Example 2.12 Estimation of diffusivity in a gas mixture at low density 77Example 2.13 Estimation of diffusivity in a gas mixture at low pressure 79Example 2.14 Estimation of diffusivity in a gas mixture of isotopes 79Example 2.15 Estimation of diffusivity in a gas mixture 80Example 2.16 Estimation of diffusivity of a component through a gas mixture 81Example 2.17 Estimation of diffusivity in a dilute liquid mixture 832.5 The Maxwell–Stefan equations 862.6 Transport coefficients 872.7 Electric charge flow 872.8 The relaxation theory 892.9 Chemical reactions 892.10 Coupled processes 90Problems 92References 96References for further reading 96Chapter 3Fundamentals of nonequilibrium thermodynamics 973.1 Introduction 973.2 Local thermodynamic equilibrium 973.3 The second law of thermodynamics 98Example 3.1 Total entropy change of an air flow in a nozzle 102Example 3.2 Total entropy change in a polytropic compressing of methane 103Example 3.3 Energy dissipation in a nozzle 106Example 3.4 Energy dissipation in a compressor 107Example 3.5 Energy dissipation in an adiabatic mixer 108Example 3.6 Energy dissipation in a mixer 109Example 3.7 Energy dissipation in a turbine 110Example 3.8 Entropy production in a composite system 1123.4 Balance equations and entropy production 112Example 3.9 Conservation of energy 1203.5 Entropy production equation 1213.6 Phenomenological equations 1273.7 Onsager’s relations 1323.8 Transformation of forces and flows 133Example 3.10 Relationships between the conductance and resistance phenomenological coefficients 135Example 3.11 Transformation of phenomenological equations: dependent flows 135Example 3.12 Transformation of phenomenological equations: dependent forces 137Example 3.13 Transformation of phenomenological equations: dependent flows and forces 1383.9 Chemical reactions 1393.10 Heat conduction 139Example 3.14 Entropy production and dissipation function in heat conduction 1403.11 Diffusion 1413.12 Validity of linear phenomenological equations 142Example 3.15 Gibbs energy and distance from global equilibrium 1433.13 Curie–Prigogine principle 1433.14 Time variation of entropy production 144Example 3.16 Entropy production and the change of the rate of entropy production withtime in heat conduction 1453.15 Minimum entropy production 146Example 3.17 Minimum entropy production in a two-flow system 147Example 3.18 Minimum entropy production in an elementary chemical reaction system 148Example 3.19 Minimum energy dissipation in heat conduction 149Example 3.20 Minimum entropy production in electrical circuits 151Problems 152References 154References for further reading 154Chapter 4Using the second law: Thermodynamic analysis 1554.1 Introduction 1554.2 Second-law analysis 155Example 4.1 Lost work in throttling processes 158Example 4.2 Dissipated energy in an adiabatic compression 159Example 4.3 Thermomechanical coupling in a Couette flow between parallel plates 161Example 4.4 Thermomechanical coupling in a circular Couette flow 164Example 4.5 Entropy production in a flow through an annular packed bed 166Example 4.6 Entropy production in a packed duct flow 168Example 4.7 Heat and mass transfer 172Example 4.8 Chemical reactions and reacting flows 1744.3 Equipartition principle 176Example 4.9 Entropy production in separation process: distillation 1784.4. Exergy analysis 184Example 4.10 Thermodynamic efficiency in a power plant 1914.5 Applications of exergy analysis 192Example 4.11 Energy dissipation in countercurrent and cocurrent heat exchangers 192Example 4.12 Exergy analysis of a power plant 194Example 4.13 Simple reheat Rankine cycle in a steam power plant 196Example 4.14 Actual reheat Rankine cycle in steam power generation 198Example 4.15 Ideal regenerative Rankine cycle 201Example 4.16 Actual regenerative Rankine cycle 204Example 4.17 Ideal reheat regenerative cycle 208Example 4.18 Actual reheat regenerative Rankine cycle 211Example 4.19 Energy dissipation in a cogeneration plant 215Example 4.20 Energy dissipation in an actual cogeneration plant 218Example 4.21 A steam power plant using a geothermal energy source 222Example 4.22 Exergy analysis of a refrigeration cycle 225Example 4.23 Analysis of the Claude process in liquefying natural gas 227Example 4.24 Power plant analysis 229Example 4.25 Column exergy efficiency 236Example 4.26 Assessment of separation section of a methanol plant 237Example 4.27 Assessment of separation of a 15-component mixture in two columns 239Example 4.28 Assessment of separation section of vinyl chloride monomer (VCM) plant 2414.6 Chemical exergy 2434.7 Depletion number 2444.8 Optimization problem 2454.9 Information capacity and exergy 2454.10 Pinch analysis 246Example 4.29 Minimum utilities by composite curve method 250Example 4.30 Pinch analysis by temperature interval method and grand composite curve 257Example 4.31 Column grand composite curves in a distillation column with a five-component mixture 261Example 4.32 Column grand composite curves in methanol plant 263Problems 264References 273References for further reading 274Chapter 5Thermoeconomics 2755.1 Introduction 2755.2 Thermodynamic cost 275Example 5.1 Cost of power generation 278Example 5.2 Cost of power and process steam generation 278Example 5.3 Thermoeconomic consideration of a refrigeration system 2795.3 Ecological cost 2855.4 Availability 2865.5 Thermodynamic optimum 287Example 5.4 Minimization of entropy production 2875.6 Equipartition and optimization in separation systems 289Example 5.5 Equipartition principle in separation processes: extraction 289Example 5.6 Thermoeconomics of extraction 291Example 5.7 Equipartition principle: heat exchanger 292Example 5.8 Characterization of the deviation from equipartition 294Example 5.9 Distribution of driving forces 295Example 5.10 Variance and heat exchangers 295Example 5.11 Hot fluid flow rate effect 296Example 5.12 Equipartition principle in an electrochemical cell with a specified duty 297Example 5.13 Optimal distillation column: diabatic configuration 298Example 5.14 Optimal feed state for a binary distillation 299Example 5.15 Retrofits of distillation columns by thermodynamic analysis 3005.7 Thermoeconomics of latent heat storage 307Example 5.16 Cash flow diagram for seasonal latent heat storage 312Problems 315References 318References for further reading 318Chapter 6Diffusion 3196.1 Introduction 3196.2 Maxwell–Stefan equation 319Example 6.1 Maxwell-Stefan equation for binary mixtures 322Example 6.2 Diffusion in a ternary ideal gas mixture 330Example 6.3 Diffusion of species from a gas mixture to a falling liquid film 332Example 6.4 Wetted wall column with a ternary liquid mixture 3336.3 Diffusion in nonelectrolyte systems 3356.4 Diffusion in electrolyte systems 336Example 6.5 Diffusion in aqueous solutions 338Example 6.6 Diffusion across a membrane 3396.5 Diffusion without shear forces 344Example 6.7 Binary and ternary isothermal gas mixtures 346Example 6.8 Diffusion in a dilute isothermal gas mixture 3476.6 Statistical rate theory 351Example 6.9 Transport in biological cells: osmotic and pressure driven mass transport across a biological cell membrane 351Example 6.10 Prediction of diffusion coefficients of macromolecules 359Example 6.11 Diffusion of solutes in biological cells 359Problems 360References 362References for further reading 362Chapter 7Heat and mass transfer 3637.1 Introduction 3637.2 Coupled heat and mass transfer 3637.3 Heat of transport 3697.4 Degree of coupling 3717.5 Coupling in liquid mixtures 372Example 7.1 Mass diffusion flow in term of mole fractions 3727.6 Coupled mass and energy balances 3847.7 Separation by thermal diffusion 387Example 7.2 Separation by thermal diffusion 388Example 7.3 Total energy flow and phenomenological equations 389Example 7.4 Modified Graetz problem with coupled heat and mass flows 390Example 7.5 Cooling nuclear pellets 3917.8 Nonlinear approach 394Example 7.6 Fokker-Planck equation for Brownian motion in a temperature gradient:short-term behavior of the Brownian particles 395Example 7.7 Absorption of ammonia vapor by lithium nitrate-ammonia solution 3997.9 Heat and mass transfer in discontinuous system 4017.10 Thermoelectric effects 406Problems 410References 413References for further reading 413Chapter 8Chemical reactions 4158.1 Introduction 4158.2 Chemical reaction equilibrium constant 415Example 8.1 Equilibrium constant of a reaction 416Example 8.2 Equilibrium compositions 416Example 8.3 Temperature effect on equilibrium conversion 4188.3 The principle of detailed balance 4198.4 Dissipation for chemical reactions 4238.5 Reaction velocity (flow) 425Example 8.4 Affinity and heat of reaction 4268.6 Multiple chemical reactions 426Example 8.5 Conservation of mass in chemical reactions 428Example 8.6 Calculation of entropy production for a reversible reaction 4298.7 Stationary states 430Example 8.7 Entropy production for series of reactions at stationary state 433Example 8.8 Entropy production in a homogeneous chemical system 435Example 8.9 Chemical reactions far from global equilibrium 437Example 8.10 Time variation of affinity 440Example 8.11 Time variation of entropy production in simultaneous chemical reactions 441Example 8.12 Minimum entropy production 4428.8 Michaelis–Menten kinetics 443Example 8.13 Growth of a pathogenic bacterium Brucella abortus 4458.9 Coupled chemical reactions 447Problems 449References 451Chapter 9Coupled systems of chemical reactions and transport processes 4539.1 Introduction 4539.2 Nonisothermal reaction–diffusion systems 453Example 9.1 Effective diffusivity 455Example 9.2 Maximum temperature difference in the hydrogenation of benzene 459Example 9.3 Effectiveness factor for first-order irreversible reaction-diffusion system 459Example 9.4 Effectiveness for a first-order reversible reaction 462Example 9.5 Maximum overall temperature difference in the hydrogenation of benzene 4649.3 Chemical reaction with coupled heat and mass flows 465Example 9.6 Coupled heat and mass flows in oxidation of CH3OH to CH2O 4679.4 Coupled system of chemical reaction and transport processes 470Example 9.7 Diffusion in a liquid film with a reversible homogeneous reaction 473Example 9.8 Stationary coupling of chemical reactions with heat and mass flows 481Example 9.9 Chemical reaction velocity coupled to mass flow 482Example 9.10 Chemical reaction velocity coupled to heat flow 482Example 9.11 Modeling of a nonisothermal plug flow reactor 4839.5 Evolution of coupled systems 4849.6 Facilitated transport 485Example 9.12 Steady-state substrate flow in a facilitated transport 487Example 9.13 Effect of temperature on myoglobin-facilitated transport 489Example 9.14 Nonisothermal facilitated transport 4929.7 Active transport 495Example 9.15 Long-term asymptotic solution of reversible reaction diffusion system 496Example 9.16 Nonisothermal heterogeneous autocatalytic reactions-diffusion system 4999.8 Nonlinear macrokinetics in a reaction–diffusion system 500Problems 501References 503References for further reading 504Chapter 10Membrane transport 50510.1 Introduction 50510.2 Membrane equilibrium 505Example 10.1 Membrane equilibrium 50710.3 Passive transport 508Example 10.2 Gas permeation in a binary gas mixture 509Example 10.3 Time necessary to reach equilibrium in a membrane transport 514Example 10.4 Diffusion cell with electrolytes 518Example 10.5 Diffusion cell and transference numbers 519Example 10.6 Estimation of flow in a diffusion cell 520Example 10.7 Energy conversion in the electrokinetic effect 52410.4 Facilitated and active transports in membranes 52510.5 Biomembranes 526Example 10.8 Coupled system of flows and a chemical reaction 534Example 10.9 A representative active transport and energy conversions 537Problems 538References 539References for further reading 540Chapter 11Thermodynamics and biological systems 54111.1 Introduction 54111.2 Simplified analysis in living systems 541Example 11.1 Cell electric potentials 542Example 11.2 Excess pressure in the lungs 542Example 11.3 Enthalpy and work changes of blood due to the pumping work of the heart 543Example 11.4 Energy expenditure in small organisms 544Example 11.5 Energy expenditure in an adult organism 545Example 11.6 Oxidation of glucose 546Example 11.7 Unimolecular isomerization reaction 54711.3 Bioenergetics 548Example 11.8 Efficiency of energy conversion of photosynthesis 55611.4 Proper pathways 557Example 11.9 A linear pathway 562Example 11.10 Sensitivity of the rate of the enzymatic reaction to substrate concentration 56311.5 Coupling in mitochondria 56711.6 Regulation in bioenergetics 574Example 11.11 Approximate analysis of transport processes in a biological cell 57911.7 Exergy use in bioenergetics 581Example 11.12 Exergy efficiency 590Example 11.13 Approximate exergy balances in a representative active transport 59211.8 Molecular evolution 59311.9 Molecular machines 59311.10 Evolutionary criterion 595Problems 596References 597References for further reading 598Chapter 12Stability analysis 59912.1 Introduction 59912.2 The Gibbs stability theory 59912.3 Stability and entropy production 604Example 12.1 Distance of a chemical reaction from equilibrium 606Example 12.2 Stability of chemical systems 60712.4 Thermodynamic fluctuations 607Example 12.3 Stability under both dissipative and convective effects 60812.5 Stability in nonequilibrium systems 608Example 12.4 Stability of an autocatalytic reaction 610Example 12.5 Macroscopic behavior in systems far from equilibrium 61312.6 Linear stability analysis 614Example 12.6 Evolution in chemical systems 61512.7 Oscillating systems 616Example 12.7 Linear stability analysis: Brusselator scheme 617Example 12.8 Linear stability analysis with two variables 618Example 12.9 Chemical instability 623Example 12.10 Multiple steady states 624Example 12.11 Reaction–diffusion model 626Example 12.12 Adiabatic stirred flow reactor 627Problems 628References 629References for further reading 629Chapter 13Organized structures 63113.1 Introduction 63113.2 Equilibrium and nonequilibrium structures 63113.3 Bifurcation 63213.4 Limit cycle 63313.5 Order in physical structures 634Example 13.1 Lorenz equations: The strange attractor 635Example 13.2 Van der Pol’s equations 63713.6 Order in chemical systems 638Example 13.3 The Brusselator system and oscillations 638Example 13.4 Order in time and space with the Brusselator system 640Example 13.5 The Belousov–Zhabotinsky reaction scheme 643Example 13.6 Order in time: Thermodynamic conditions for chemical oscillations 64413.7 Biological structures 650Example 13.7 Chiral symmetry breaking 652Example 13.8 Prey–predator system: Lotka–Volterra model 654Example 13.9 Sustained oscillations of the Lotka–Volterra type 656Example 13.10 Lotka–Volterra model 657Example 13.11 Enzymatic reactions: Oscillations in the glycolytic cycle 657Example 13.12 Long-wavelength instability in bacterial growth 660Example 13.13 Instability in a simple metabolic pathway 661Example 13.14 A model for an enzyme reaction inhibited by the substrate and product 662Problems 663References 668References for further reading 669Chapter 14Nonequilibrium thermodynamics approaches 67114.1 Introduction 67114.2 Network thermodynamics with bond graph methodology 67114.3 Mosaic nonequilibrium thermodynamics 67814.4 Rational thermodynamics 67914.5 Extended nonequilibrium thermodynamics 68014.6 Generic formulations 68314.7 Matrix model 68414.8 Internal variables 685References 686References for further reading 686Appendix 687Appendix A 687Tensors 687Appendix B 688Table B1 Lennard-Jones (6-12) potential parameters and critical properties 688Table B2 Collision integrals for predicting transport properties of gases at low densities 688Table B3 Heat capacities of gases in the ideal-gas state 689Table B4 Heat capacities of solids 690Table B5 Heat capacities of liquids 691Table B6 Properties of some common liquids 691Table B7 Standard enthalpies and Gibbs energies of formation at 298.15K 692Table B8 Selected state properties 694Table B9 Approximate standard reaction enthalpy and standard reaction Gibbs energy for some selected reactions at standard state T5258C, P51atm 694Appendix C 695Table C1 Parameters for the thermal conductivity of alkanes in chloroform 695Table C2 Parameters for the mutual diffusion coefficients of alkanes in chloroform 695Table C3 Parameters for the heats of transport of alkanes in chloroform 695Table C4 Parameters for the thermal conductivity of alkanes in carbon tetrachloride 696Table C5 Parameters for the mutual diffusion coefficients of alkanes in carbon tetrachloride 696Table C6 Parameters for the heats of transport of alkanes in carbon tetrachloride 696Appendix D 696Table D1 Saturated water-temperature table 696Table D2 Superheated steam 698Appendix E 704Table E1 Saturated refrigerant-134a properties-Temperature 704Table E2 Saturated refrigerant-134a properties-Pressure 705Table E3 Superheated refrigerant-134a 706Table E4 Ideal-gas properties of air 709Table E5 Ideal-gas properties of carbon dioxide, CO2 711Appendix F 713Table F1 Values of Z0 713Table F2 Values of Z1 714Table F3 Values of Z0 714Table F4 Values of Z1 715Table F5 Values of (HR)0/RTc 716Table F6 Values of (HR)1/RTc 717Table F7 Values of (HR)0/RTc 718Table F8 Values of (HR)1/RTc 719Table F9 Values of (SR)0/R 719Table F10 Values of (SR)1/R 720Table F11 Values of (SR)0/R 721Table F12 Values of (SR)1/R 722Table F13 Values of f0 723Table F14 Values of f1 724Table F15 Values of f0 724Table F16 Values of f1 725