Index

Note: page numbers with “f” indicate figures; those with “t” indicate tables.

Absolute temperature, 23–24

Absolute zero, 22t

Accumulation, 253

Acentric factor, 47–51

defined, 47–48

of simple, normal, and polar fluids, 50–51

Activity, 606–13

chemical potential and, 607

of gas, 607–8, 611

of liquid, 608–9, 611

P°, working with, 608

of solid, 609–10, 612

of solute, 609, 611–12

standard state and, 610, 613

Activity coefficient, 504–11

for data reduction, 512–15

defined, 504

deviations from Raoult’s law, 508–10, 509f

experimental, 510–15

Gibbs free energy and, excess, 505–7, 510–14, 511f

limits of, 505

phase equilibrium and, 507–10

solubility limits using, 547–48

usefulness of, 505

Activity coefficient models, 515–31

Flory-Huggins, 521–22

Margules, 515–19

NRTL, 520–21

UNIFAC, 525–31

UNIQUAC, 522–25

vanLaar, 519

Wilson, 519–20

Adiabatic flame temperature, 605–6

Adiabatic mixing

heat effects of, 497–99

of solutions on enthalpy charts, 503f

in steady-state processes, 276–78, 277f

Adiabatic processes. See Reversible adiabatic processes

Adiabatic production of work, 261, 262

Adiabatic system, 13

Air, chemical potential in, 441–42

American Engineering system of units, 22

pound-mol (lb-mol) in, 24

pressure measured in, 23

temperature measured in, 23

Ammonia refrigerator, 304–6

Analogous relationships, 215, 408

Antoine equation, 38–40

Clausius-Clapeyron equation and, 343

determining phase with, 39–40

units in, 38–39

ASHRAE designation of refrigerants, 307t

Athermal process of mixing, 410

Avogadro’s number, 22t

Azeotropes, 380–81, 380f

Balances in open systems, 251–335

energy balance, 254f, 255–58

entropy balance, 258–66

flow streams, 252–53, 252f

liquefaction, 309–15

mass balance, 253–55, 254f

power generation, 295–300

problems, 324–35

refrigeration, 301–9

summary, 323–24

thermodynamics of steady-state processes, 272–94

unsteady-state balances, 315–23

Bar, 23

Bath

change of, entropy, 159–61

default, exergy and, 189–91

heat, in entropy balance, 265–66

stream acting as, in entropy balance, 264–65

Benedict-Webb-Rubin equation, 67–71, 70f, 71t

Benzene, solubility of, 577–78, 578f

Binary mixtures, 420–21, 423t

Binary VLE using Soave-Redlich-Kwong, 452–53

Boltzmann constant, 8, 22t

Bubble temperature (or point), 371

BWR equation. See Benedict-Webb-Rubin equation

Calorie, 101

Carbon dioxide (CO₂)

density of liquid, 10

ideal-gas state and, 10–11

intermolecular potential of, 6

Pxy graph of CO₂/n-pentane calculated using Soave-Redlich-Kwong, 451f, 452–53

Carnot cycle, 168–77

defined, 169

in entropy, 168–77, 169f

first-law analysis of, 170

ideal gas used in, 173–74

internal combustion engine example of, 173

second-law analysis of, 171

steam used in, 175–76

steps in, 169–70

thermodynamic efficiency of, 171–73

on TS graph, 169f

work value of heat and, 182–83, 182f

Carnot efficiency, 171–72

Celsius scale, 23–24

Chemical engineer, 5

Chemical engineering thermodynamics, 5

Chemical equilibrium, 15

Chemical potential

activity and, 607

in air, 441–42

in fugacity, 444

in Gibbs free energy, 440–42

in ideal-gas state, 440

in real mixture, 440

in theory of VLE, 439–42

Chemical thermodynamics, 3–5, 4f

Classical thermodynamics

laws of, 11–12

vs. statistical thermodynamics, 11–13

Clausius, Rudolph, 178

Clausius-Clapeyron equation in VLE, 341–43

Clausius statement

as alternative statement of second law, 177–82

defined, 178

as equivalent statement of second law, 180–82

Closed systems

defined, 13

first law for, 98–101

second law in, 150–53

Combinatorial molecular interactions, 507

Completely immiscible liquids, 558–61

calculations, limitations of, 563

Pxy graph of, 561–62, 562f

Txy graph of, 559–61, 559f

Composite system, 13

Compressed liquids, 292–94

entropy of, 156

Poynting equation for calculating, 345–47

throttling of, 288–89, 290f

Compressibility factor, 43–45, 45f

in BWR equation, 69

in corresponding states, 45–47, 46f, 51, 52

in Lee-Kesler method, 56, 68

in Peng-Robinson equation, 67

in Pitzer method, 48, 71

in Rackett equation, 73

roots in, acceptable, 63, 66, 67

in Soave-Redlich-Kwong equation of state, 61

in van der Waals equation, 58–60

in virial equation, 53, 54, 56

ZP graph of pure fluids and, 43–45, 45f, 56

Compressor

graphical solution on Molliev chart, 293f

steam/gas, 290–92

Condensed phases, 9

Constant composition, systems of, 407–8

Constant-pressure cooling, 104–5

Constant pressure entropy

change at, 155

no phase change in, 153–54

Constant-pressure heat capacity (C_P), 111–12

vs. constant-volume heat capacity, 111–12, 112f

as state function, 113

of steam, 114–15

Constant-pressure heating, 102–3

Constant-pressure (or isobaric) process, 18–19

Constants, 22t

Constant-temperature (or isothermal) process, 18–19, 107, 108

Constant-volume cooling, 102

Constant-volume heat capacity (C_V), 109

vs. constant-pressure heat capacity, 111–12, 112f

as state function, 113

Constant-volume heating, 101–2

Constant-volume path entropy, no phase change in, 154

Constant-volume process, 18–19

Constrained equilibrium, 15–16

Conversions, 25t

Corresponding states

in compressibility factor, 45–47, 46f, 51, 52

in phase diagrams of pure fluids, 45, 46f

Cubic equations of state

application to, 230–34

fugacity calculated from, 352–53

isotherm, unstable and metastable parts of, 62–63

Peng-Robinson, 61, 66–67

PVT behavior of, 61–63

roots of, 63–65

Soave-Redlich-Kwong, 30f, 60–61, 66

of state, residual properties from, 232t

Van der Waals, 58–60, 65–66

for volume, solving, 65–67

working with, 64

Data reduction, 514

Definitions, 13–17

equilibrium, 15–16

property, 16–17

system, 13–14

Density

empirical equations for, 72–77

of liquid CO₂, 10

Derivatives with functions of multiple variables, 110

Desalination, 585–86

Dew point, 483

Diathermal system, 13

Differentials

exact, 211–12

form of, 209–11

inexact, 212

integration of, 213–14, 214f

Diffusion in osmotic equilibrium, 582–83

Disorder, defined, 196

Distillation, 378, 379f

Double interpolations, 41, 41f, 42

Elementary process, 18–19

Empirical equations, 57

for density, 72–77

summary, 78

Endothermic process, 410

Energy, 24–25, 25t

forms of, 90

heat and, 96–97

ideal-gas state, 124–32

internal, 96

process requirements, calculating, 5

storable, 89

transfer, sign convention for direction of, 89

work and, 88–89, 88f

Energy balance, 254f, 255–58

in closed systems, 257–58

in enthalpy of vaporization, 478–79

entropy used in, 163–66

in heat exchanger, 479–80

in ideal solution, 475–80

irreversible processes and, 133–38

in open systems, 254f, 255–58

steady state, 258

using C_P and ΔH_vap, 122–24

using tables, 121–22

Energy balances in reacting systems, 601–6

adiabatic flame temperature and, 605–6

heat of combustion and, 603–5

setup for energy balance of reactor, 602f

Enthalpy

defined, 103

enthalpy-entropy (Mollier) chart, 244–45, 245f

equations for, 217–19

excess, heat effects of mixing and, 496, 497f

ideal-gas, 234

of ideal-gas mixture, 416

lever rule for, 119–20

of mixing, 425

pressure and temperature effect on, 220–22

pressure-explicit relations, 229

of reactions, standard, 596–601, 599f

residual, 223, 236, 237f

as state function, 103, 125–26

of steam, 103–5

temperature-enthalpy chart, 243–44, 244f

of vaporization, 478–79

Enthalpy charts, 500–504

adiabatic mixing of solutions on, 503f

of hydrazine/water mixtures, 501f

pressure, 242–43, 243f

using, 503–4

Enthalpy-entropy (Mollier) chart, 244–45, 245f

graphical solution of compressed liquids on, 293f

in steam turbine, 285–86, 285f

Entropy

calculation of (See Entropy, calculation of)

Carnot cycle in, 168–77, 169f

change of bath, 159–61

in energy balance, 163–66

energy balances using, 163–66

equations for, 217–19

equilibrium and, 191–95

exergy and, 189–91

generation, 167–68

heat calculated using, 166

ideal-gas, 234

of ideal-gas mixture, 416

ideal work in, 183–88

of irreversibility, 168

of liquids, 156, 157

lost work in, 183–88, 191

measurable quantities relating to, 151–53

of mixing, in ideal solution, 463–64

molecular view of, 195–99, 197f

pressure and temperature’s effect on, 220–22

pressure-explicit relations, 229–30

problems, 201–4

residual, 224, 236, 238f

reversibility and, 176–77

second law and, 149–204

of solids, 155–56, 157

stability and, 191–95

as state function, 153

summary, 199–201

temperature and, 153

thermodynamic potentials, 194–95

of universe, 168

of vaporization, 157, 158

Entropy, calculation of, 153–63, 199

basic formula, 154

change at constant pressure, 155

change of bath, 159–61

compressed liquids, 156

constant-pressure path, no phase change, 153–54

constant-volume path, no phase change, 154

energy balances with phase change, using C_P and ΔH_vap, 158–59

ideal-gas state, 161–62, 161f

phase change, 157–58, 157f

solids, 155–56

steam, 163

tabulated values used for, 162

vaporization, 158

Entropy balance, 258–66

heat exchange between streams, 262–63

in open systems, 258–66

processes with entropy generation, 262f

reversible adiabatic process, 260–61

steady state, 260, 261

stream acting as a bath, 264–65

Entropy generation

cooling system, choosing, 269–71

in power plant, 267

processes with, 262f

Equations of state

appeal of, 453

binary VLE using Soave-Redlich-Kwong, 452–53

BWR, 67–71, 70f, 71t

in compressibility factor, 44

cubic, 57–67

defined, 29

fugacity from, 446–48

Henry’s law from, 572–73

ideal-gas law and, 34, 54

interaction parameter, 451–53

Lee-Kesler, 68–70

mathematical representation of, 44

for mixtures, 419–21

other, 67–71

phase diagrams from, 356–58

Pitzer, 71

properties from mixtures, 421–27

saturation pressure from, 353–56

summary, 77

in theory of VLE, 448–53

in truncated virial equation, 54

Equilibrium, 15–16, 545–91. See also Liquid miscibility

chemical, 15

conditions at constant temperature and pressure, 191–94

conditions fulfilled by, 15

constrained, 15–16

entropy and, 191–95

gas liquids, solubility of, 561–74

liquid-liquid (LLE), 369

liquid-liquid-vapor (LLVE), 369

mechanical, 15

osmotic, 580–86

phase splitting and Gibbs free energy, 548–56

problems, 586–91

schematic of, 546f

solids in liquids, solubility of, 575–80

solids involved in, 629–32

vs. steady state, 261

summary, 586

thermal, 15

thermodynamic potentials and, 194–95

Equilibrium composition, 622–24

with multiple reactions, 634–35

pressure in, effect of, 623–24

Equilibrium constant, 614–20, 621

Ethylene, phase diagram of, 356–58

Euler’s theorem, 406

Eutectic point, 579–80

Exact differential, 211–12

Excess properties, 489–96

as mathematical operator, 490

molar, 490–91, 492f

in nonideal solutions, 489–96

Redlich-Kister expansion, 495–96

volume, 494–95, 495f

in volume of mixing, 492–94

Exergy, 189–91

Exothermic process, 410

Expansion, PV work in, 92–93

Expansion and Compression of Liquids, 292–94

Experimental activity coefficient, 510–15

fitting, 512–14

Pxy graph of, 515f

Extensive property, 16–17

Fahrenheit, 23–24

First law

Carnot cycle analyzed by, 170

for closed system, 98–101

defined, 87

energy and, 87–148

history of, 100–101

Joule’s experiment, 100–101

operator Δ used in, 99–100

paths in, 101–8

problems, 140–48

schematic illustration of, 98f

summary, 139–40

Fixed property, 17

Flash separation, 375–76, 376f

Flash units, multiple, 377–78

Flory-Huggins equation, 521–22

Flow streams, 252–53, 252f

Force, 25t

Fugacity, 343–53

chemical potential and, 444

defined, 343–43

from equations of state, 446–48

from experimental data, 445

Gibbs free energy and, 344–45

Henry’s law used to calculate, 573–74, 574f

in ideal-gas state, 344

in ideal solution, 464–65

Lewis-Randall rule used to calculate, 471, 563, 564

in mixture using Soave-Redlich-Kwong, 447–48

of solubility of gases in liquids, 564f

steam, 349

from steam tables, 347

in theory of VLE, 443–48

Fugacity, calculation of, 345–53

compressibility factor used in, 348–49

from cubic equations of state, 352–53

from generalized graphs, 349–52, 350f, 351f

Poynting equation for compressed liquids, 345–47

saturated liquid, 346

from Soave-Redlich-Kwong, 352, 353

tabulated properties used in, 347–48

Function, differential and integral forms of, 209–11

Fundamental relationships

calculating, 214–17

change of variables, 217

summary of, 216t

Gas

activity of, 607–8, 611

Linde process for liquefaction of, 310f

Gases in liquids, solubility of, 563–74. See also Henry’s law

fugate of, 564f

Generalized correlations, calculating, 235–36, 237–38f

Generalized graphs, 77

fugacity calculated from, 349–52, 350f, 351f

Gibbs, J. Willard, 4–5, 4f

Gibbs-Duhem equation, 406–7, 439–40

Gibbs free energy, 5, 194–95, 195f

calculating, 215, 225, 242

chemical potential in, 440–42

excess, activity coefficient and, 505–7, 510–14, 511f

fugacity and, 344–45

in Margules equation, linearized form of excess, 518f

multicomponent equilibrium in, 437–38, 437f

phase rule in, 438–39

phase splitting and, 548–56

in theory of VLE, 435–39

Gibbs’s phase rule, 438–39

Heat, 96–97

capacities, 109–19

of combustion in reacting systems, 603–5

direction of flow, second law to determine, 184–85

entropy used to calculate, 166

as path function, 105–6

sensible, 109

sign convention for, 97

specific, 111

transfer, in entropy generation, 188

transfer, irreversible processes in, 133

of vaporization, 119–24, 120f

of vaporization using Soave-Redlich-Kwong, 338

work and, shared characteristics with, 97

work value of, Carnot cycle and, 182–83, 182f

Heat bath (or heat reservoir), 19

Heat capacity, 109–19

constant-pressure heat capacity, 111–12, 112f

constant-volume heat capacity, 109, 111–12, 112f

defined, 112–13

effect of pressure and temperature on, 113–19, 113f

excess, 499–500

Heat effects of mixing, 496–504

enthalpies, excess, 496, 497f

enthalpy charts, 500–504

excess heat capacity, 499–500

isothermal, 497–99

Heat exchanger, 278–81, 279f

in ideal solution, 479–80

Heat of vaporization (ΔH_vap), 119–24, 120f

C_P and ΔH_vap, energy balances with phase change using, 122–24

latent, 119

Pitzer correlation for, 121–22

tables, energy balances with phase change using, 121–22

Helmholtz free energy, 194, 216, 225, 242

Henry’s law, 564–74

alternative forms of, 566–67

carbonated soda and, 571–72

from equation of state, 572–73

formal thermodynamics and, 569–70, 571f

fugacity calculated with, 573–74, 574f

vs. Lewis-Randall rule, 573–74

other units for, 565–66

in simultaneous dissolution of two gases, 567–69

temperature and pressure effects on, 569

VLE using, 564–65

Household refrigerator, 304

Humidification, 481–83

dew point, 483

relative humidity, 482, 483

Hypothetical states, 476–77

Ideal gas

filling a tank with, 318–18

throttling of, 288

venting, 322–23

Ideal-gas constant, 22t

Ideal-gas law

calculated isotherms using, 57f

defined, 34

directions to, 34

equation of state and, 34, 54

molar volume calculated with, example of, 55

summary, 78

vs. truncated viral equation, 54

Ideal-gas state, 10–11, 124–32

calculating, 219–20

Carnot cycle using, 173–75

chemical potential in, 440

equations, summary of, 219t

fugacity in, 344

hypothetical, 223

irreversible expansion of, 137

in isothermal compression of steam, 126–27

log-x mean, 130

mixtures in, 413–19

paths in, 132f

residual properties of, 225–26

reversible adiabatic compression of nitrogen, 131–32

reversible adiabatic process, 127–30, 131–32, 132f

reversible adiabatic process in, 164–66

triple-product rule in, 207

Ideal solution, 461–88

defined, 462

energy balances in, 475–80

entropy of mixing in, 463–64

fugacity in, 464–65

ideality in, 461–63

noncondensable gases in, 480–83

practical significance of, 463

problems, 484–88

in separation of work, 464

summary, 484

VLE in, Raoult’s law, 466–74

Ideal work, 183–88

for heat transfer, 268–69

in open systems, 266–71

Incompressible phases, 220–21

Inexact differential, 212

Integral form of a function, 209–11

Integrals with functions of multiple variables, 110

Integration of differentials, 213–14, 214f

Integration paths, 109–10

Intensive property, 16–17

Interaction parameter, 451–53

Intermolecular potential, 6–7, 7f

Internal energy, 96, 215, 219, 224–25, 241–42

Interpolations, 40–43, 41f

accuracy in, 40

example of, using steam tables, 41–43

types of, 41f

Irreversible processes, energy balances and

adiabatic mixing, 134–36

heat transfer, 133

of ideal gas, 137

against pressure, 138

against vacuum, 136–37

Isentropic step in Carnot cycle, 170

Isolated system, 13

Isothermal compression of steam

in first law paths, 108

in ideal-gas state, 126–27

in PV work, 94–95, 96f

Isothermal mixing, heat effects of, 497–99

Isothermal step in Carnot cycle, 169–70

Isotherms

critical point and, 33

of Lee-Kesler method, 68

of modified BWR equation, 67, 70f

pressure-volume, of acetone, 74–75, 76f

on PV graph, 31, 33

of Soave-Redlich-Kwong equation, 61–62, 62f

at zero pressure, 44

on ZP graph, 53, 57f

Joule, James Prescott, 100–101

Kelvin (K), 23

Kelvin-Plank statement, 178

K-factors, 382, 449, 468

Kinetic energy, 90

Latent heat of vaporization, 119

Laws of classical thermodynamics, 11–12

Lee-Kesler method

compressibility factor in, 56, 68

in phase diagrams of pure fluids, 48–49, 48f, 49f, 50f

for residual enthalpy, 237f

for residual entropy, 238f

Length, 25t

Lever rule, 34–36, 35f

defined, 35

for enthalpy, 119–20

partially miscible liquids and, 388

in phase behavior of mixtures, 372–73

setup for application of, 35f

state located with, steam table example, 43

using, reasons for, 36

Lewis-Randall rule

defined, 565

fugacity in liquid phase given by, 471, 563, 564

vs. Henry’s law, 573–74

Linde process, 310f

Linear interpolations, 41f, 71, 79

Liquefaction, 309–15

of gas, Linde process for, 310f

of nitrogen, 310f, 311–14

Liquid-liquid equilibrium (LLE), 369, 546f

Liquid-liquid-vapor equilibrium (LLVE), 369

Liquid miscibility

complete, 558–61

partial, equilibrium between, 545–48

temperature and, 556–58

Liquids. See also Compressed liquids; Vapor-liquid mixture

activity of, 608–9, 611

CO₂, density of, 10

constant-pressure cooling of, 115–17

of enthalpy and entropy, pressure and temperature’s effect on, 220–22

entropy of, 156, 157

expansion of, 292–94

fugacity of saturated, 346

gases in, solubility of, 563–74

heat capacities, 114

hypothetical state of, 472

properties, compressed, 117–19, 118f

pump, calculating, 294

solids in, solubility of, 575–80

Log-x mean, 130

Lost work in open systems, 266–71

Magdeburg hemispheres, 27–28

Margules equation, 515–19

Gibbs free energy in, 518f

Pxy graph reconstructed from limited data, 517, 518–19

Mass, 25t

Mass balance, 253–55, 254f

Mathematical conditions for stability, 552

Maxwell-Boltzmann distribution, 8, 9f

Maxwell relationships, 214, 216

Measurable quantities relating to entropy, 151–53

Mechanical equilibrium, 15

Mechanically reversible process, 91–92, 92f

Methane, virial coefficient used for residual properties of, 227–28

Mixing, 411–13. See also Mixtures

athermal process of, 410

endothermic process of, 410

enthalpy of, 425

exothermic process of, 410

heat effects of, 496–504

molecular view of, 412f

non-isothermal, 416–18

properties of, 409–11

rules, 419

separation and, 411–13

separation of air, 418–91

volume of, 409–10

volume of, excess properties in, 492–95

Mixtures, 401–33. See also Mixing

binary, 420–21

composition of, 402–4

equations of state for, 419–21

formation of, at constant pressure and temperature, 410f

fugacity in, using Soave-Redlich-Kwong, 447–48

homogeneous properties of, 403–4

in ideal-gas state, 413–19

mathematical treatment of, 404–9

phase behavior of, 369–400

problems, 428–33

properties from equations of state, 421–27

real, compression of, 427

real, properties of, 424–25

residual properties of, 420, 421

subscripts, 411

summary, 428

VLE of, using equations of state, 448–53

Mixtures, mathematical treatment of, 404–9

Euler’s theorem, 406

Gibbs-Duhem equation, 406–7

partial molar property, 405, 408–8

systems of constant composition, 407–8

Molar mass, 23

Molar property, 16–17

excess, in nonideal solutions, 490–91, 492f

partial, 405, 408–9

residual, 408–9

residual partial, 408–9

Molar volume

of compressed liquid, 73

in compressibility factor, 44

in corresponding states, 51, 52

in cubic equations, 64, 65, 66, 67

ideal-gas, 55

liquid, in Rackett equation, 72–73

mean intermolecular distance and, 29

proper, selecting, 63

in PT graph of pure fluid, 37, 37f

in PV graph of pure fluid, 30f, 31–35

in PVT behavior of pure fluid, 29–30

in Soave-Redlich-Kwong equation, 62

in van der Waals equation, 59

in virial equation, 55, 56

Mole, 24

Molecular basis of thermodynamics, 5–11

condensed phases, 9

density of liquid CO₂, 10

ideal-gas state, 10–11

intermolecular potential, 6–7, 7f

Maxwell-Boltzmann distribution, 8, 9f

phase transitions, 8–9

temperature and pressure, 7–8

Molecular collisions, 7–8, 97

Molecular view of entropy, 195–99, 197f

equally probable microstates, 199

probabilities and, 198–99

Mollier chart. See Enthalpy-entropy (Mollier) chart

Multicomponent mixture, state of, 18

Multiple reactions, 632–35

equilibrium compositions with, 634–35

number of, determining, 633–34

Naphthalene, solubility of, 577–78, 578f

Newton, 23

Nitrogen

liquefaction of, 310f, 311–14

reversible adiabatic compression of, 131–32

Nomenclature, 17

Noncondensable gases. See also Humidification

in ideal solution, 480–83

Nonideal solutions, 489–543. See also Activity coefficient

excess properties, 489–96

heat effects of mixing, 496–504

molecular view of, 507, 507f

problems, 533–43

summary, 531–33

Nonrandom two liquid model (NRTL). See NRTL equation

NRTL equation, 520–21

Open systems. See also Balances in open systems

defined, 13

ideal and lost work in, 266–71

Operator Δ, 99–100, 255

Osmotic equilibrium, 580–86, 580f

desalination and, 585–86

diffusion in, chemical potential and, 582–83

pressure in, 584–85

reverse osmosis, 583–84, 584f

Osmotic pressure, 584–85

P°, working with, 608

Partially miscible liquids, 384–89

equilibrium between, 545–48

lever rule and, 388

Pxy graph of, 387f, 552–54, 553f

qualitative-phase diagram of, 388–89, 389f

Txy graph of, 385f, 554–56, 554f, 557f

Partial molar, 405, 408–9

Pascal, 23

Path, 18–19, 18f

defined, 18

illustration of, 18f

Paths in first law, 101–8

alternate, 106–7, 107f

constant-pressure cooling, 104–5

constant-pressure heating, 102–3

constant-temperature process, 107, 108

constant-volume cooling, 102

constant-volume heating, 101–2

enthalpy of steam, 103–5

heat as path function, 105–6

integration, 109–10

in isothermal compression of steam, 108

work as path function, 105–6

Peng-Robinson equation

compressibility factor in, 67

fugacity calculated from, 352, 353

fugacity from, 446–47

residual properties from, 232t

Perry’s Chemical Engineers’ Handbook (Perry), 220, 233, 234, 275, 338, 357, 362t

Phase behavior of mixtures, 369–400

azeotropes, 380–81

compositions at bubble and dew point, 374f

distillation, 378, 379f

flash separation, 375–76, 376f

flash units, multiple, 377–78

lever rule in, 372–73

partially miscible liquids, 384–89

problems, 394–400

Pxy graph, 373–79

summary, 393

ternary systems, 390–93

Txy graph, 370–73

VLE at elevated pressures and temperatures, 383–84, 384f

xy graph, 381–83, 382f

Phase change, entropy and, 153–58, 157f

constant-pressure path, no phase change, 153–54

constant-volume path, no phase change, 154

energy balances with, using C_P and ΔH_vap, 158–59

Phase diagrams. See also Pure fluids, phase diagrams of

of acetic acid/water/methylisobutyl ketone, 390f

from equations of state, 356–58

of ethylene, 356–58

in Raoult’s law, 473–74, 474f

Phase equilibrium

chemical equilibrium and VLE, 625–28

as chemical reaction, 628–29

reactions and, 624–29

Phases, calculating incompressible, 220–21

Phase splitting Gibbs free energy and, 548–56, 550f

equilibrium and stability in, 551–52, 551f

Phase transitions, 8–9

Pipe, flow through, 272–76

energy losses in, schematic for calculating, 273f

pressure drop, 275–76

Pitzer method

compressibility factor in, 48, 71

for heat of vaporization, 121–22

in phase diagrams of pure fluids, 47, 48

Planck, Max, 178

Potential energy, 90

Pound-mol (lb-mol), 24

Power, 25t

Power generation in open systems, 295–300

Poynting equation, 345–47

PR equation. See Peng-Robinson equation

Pressure, 7–8, 22–23, 25t

in equilibrium composition, effect of, 623–24

Henry’s law and, 569

irreversible expansion against, 138

Pressure, effect on heat capacities, 113–19, 113f

compressed liquid properties, 117–19, 118f

constant-pressure cooling of liquid, 115–17

heat capacity of steam, 114–15

ideal-gas heat capacity, 114

liquid heat capacities, 114

Pressure-enthalpy chart, 242–43, 243f

Pressure-explicit relations, 228–30

enthalpy, 229

entropy, 229–30

Pressurizing, 321

Processes, 18–19, 18f

defined, 18

energy requirements of, calculating, 5

entropy and, 176–77

Properties, 16–17

defined, 16–17

extensive and intensive properties, 16–17

fixed, 17

molar, 16–17

nomenclature and, 17

of pure component, 17

specific, 16–17

tabulated values of, 40–43

Properties, calculating, 205

cubic equations, application to, 230–34

differentials, integration of, 213–14

enthalpy, 217–19

entropy, 217–19

fundamental relationships, 214–17

generalized correlations, 235–36, 237–38f

ideal-gas state, 219–20

in compressible phases, 220–21

pressure-explicit relations, 228–30

problems, 246–50

of reference states, 236, 239–42

residual properties, 222–28

summary, 245–46

thermodynamic charts, 242–45

thermodynamics, 205–12

Properties of Gases and Liquids, The (Polling, Prausnitz, and O’Connell), 38, 114, 121

PT graph of pure fluid, 36–40, 37f

Pure component

multicomponent mixture, state of, 18

property of, 17

state of, 17–18

Pure fluid, 337–66

fugacity, 343–53

phase diagrams from equations of state, 356–58

problems, 360–66

saturation pressure from equations of state, 353–56

summary, 358–60

two-phase systems, 337–40

VPE of, 340–43

Pure fluids, phase diagrams of, 29–85

compressibility factor, 43–45, 45f

corresponding states, 45, 46f

empirical equations, 57

PVT behavior of, 29–40

tabulated values of properties, 40–43

virial equation, 53

PV graph of pure fluid, 31–36, 31f

critical point, 33

ideal-gas state, 33–34

two-phase region and lever rule, 34–36, 35f

PVT behavior

boiling in open air, 32

PT graph of pure fluid, 36–40, 37f

of pure fluids, phase diagrams of, 29–40

PV graph of pure fluid, 31–36, 31f

PVT surface of pure fluid, 30f

PVT surface of pure fluid, 30f

PV work, 90–96, 91f

equation for, obtaining, 90–91

in expansion, 92–93

in isothermal compression of steam, 94–95, 96f

reversible, 91–92, 92f

Soave-Redlich-Kwong equation used for, 93–94

Pxy graph, 373–79

of CO₂/n-pentane calculated using Soave-Redlich-Kwong, 451f, 452–53

of completely immiscible liquids, 561–62, 562f

of ethanol/water at elevated temperatures, 384f

of experimental activity coefficient, 515f

of heptane and decane, 375f

forisobutane/furfural system, 389f

of partially miscible liquids, 387f, 552–54, 553f

reconstructing from limited data, 517, 518–19

for UNIFAC equation, 530f, 531f

UNIQUAC equation used to calculate, 524–25, 526f

Quantities relating to entropy, measurable, 151–53

Quasi-static process, 19–22, 20f

example of, 21–22

explained, 21

reversible, 20–21

Rackett equation, 73

Rankine (R), 23

Rankine power plant, 295–300, 295f

Raoult’s law, 466–74

bubble and dew pressure in, 469–70

bubble T calculation in, 467

deviations from, 508–10, 509f

dew P calculation in, 467–68

dew T calculation in, 468

flash calculation in, 468–69

fugacity and, 470–71

hypothetical liquid state in, 472

phase diagram in, 473–74, 474f

Reactions, 593–645

activity, 606–13

energy balances in, 601–6

equilibrium composition, 622–24

equilibrium constant, 614–20

equilibrium involving solids, 629–32

multiple, 632–35

phase equilibrium and, 624–29

problems, 637–45

standard enthalpy of, 596–601, 599f

stoichiometry, 593–96

summary, 636–37

Real mixtures

chemical potential in, 440

compression of, 427

properties of, 424–25

Redlich-Kister expansion, 495–96

Reference states

calculating, 236, 239–42

using, 240–41

Refrigerants, 307–9

ASHRAE designation of, 307t

environment and, 308–9

saturation pressure of, 308f

Refrigeration, 301–9

ammonia refrigerator, 304–6

cycle on PH graph, 303f

household refrigerator, 304

refrigerants, 307–9

thermodynamic analysis of, 302–6

vapor-compression refrigeration cycle, 301f

Relative humidity (RH), 482, 483

Relative volatility, 382

Residual molar, 408–9

Residual molecular interactions, 507

Residual partial molar, 408–9

Residual properties, 222–28

applications, 225–28

from corresponding states, 235–36

from cubic equations of state, 232–34, 232t

defined, 22

enthalpy, 223

entropy, 224

in ideal-gas state, 225–26

of methane, using virial coefficient, 227–28

of mixtures, 420, 421

other, 224–25

from truncated virial equation, 226–27

volume, 224

Reverse osmosis, 583–84, 584f

Reversible PV work, 91–92, 92f

Reversibility, entropy and, 176–77

Reversible adiabatic processes, 127–30, 131–32, 132f

in entropy balance, 260–61

in ideal-gas state, 164–66

in mixing, 134–36

in nitrogen compression, 131–32

in steam compression, 165

Reversible quasi-static process, 20–21

Roots

in compressibility factor, acceptable, 63, 66, 67

of cubic equation of state, 63–65

Saturated liquid, fugacity of, 346

Saturation pressure from equations of state, 353–56, 354f, 355f

Second law

alternative statements of, 177–82

Carnot cycle analyzed by, 171

in closed system, 150–53

consequences of, 180, 200–201

defined, 149

direction of heat flow determined by, 184–85

entropy and, 149–204

in feasibility of process, 185–87

Sensible heat, 109

Separation of work, ideal solution in, 464

Separation units, 4f, 5

Shaft work, 90, 91f

Sign convention

for heat, 97

for transfer energy, direction of, 89

for work, 89

Simple interpolations, 41, 41f

Simple system, 13

SI system of units, 22

energy measured in, 24

mole, 24

pressure measured in, 22–23

temperature measured in, 23

Soave-Redlich-Kwong equation

binary mixture properties using, 423t

binary VLE using, 452–53

calculation of Henry’s law constant, 569–70, 571f

CO₂/n-pentane calculated using, 451f, 452–53

coefficient of thermal expansion using, 207–9

compressibility factor in, 61

fugacity from, 352, 353, 446–48

heat of vaporization using, 338

for PV work, 93–94

residual properties from, 232–34, 232t

vapor-liquid mixture calculated by, 339–40

Solids

activity of, 609–10, 612

entropy of, 155–56, 157

in liquids, solubility of, 575–80

Solubility

of benzene, 577–78, 578f

eutectic point, 579–80

of gases in liquids, 563–74

limits using activity coefficients, 547–48

of naphthalene, 577–78, 578f

of solids in liquids, 575–80

Solute, activity of, 609, 611–12

Specific energy, 25t

Specific heat, 111

Specific property, 16–17

SRK equation. See Soave-Redlich-Kwong equation

Stability, 355–56

entropy and, 191–95

equilibrium and, in phase splitting, 551–52, 551f

mathematical conditions for, 552

Standard state, activity and, 610, 613

State function, 17

constant-volume heat capacity as, 109, 113

enthalpy as, 103, 125–26

entropy as, 153

heat capacity as, 109

internal energy as, 89, 96, 107

Statistical thermodynamics, 11–13

Steady state

energy balance, 258

entropy balance, 260, 261

vs. equilibrium, 261

Steam

in Carnot cycle, 175–76

Carnot cycle using, 175–76

compression of, 291–92

entropy of, 163

filling a tank with, 317–18

fugacity of, 349

tables, 663–75

tables, fugacity from, 347

venting, 322

Steam turbine, 282–87

actual operation, 283

ideal and lost work in, 286–87

Mollier graph used in, 285–86, 285f

reversible operation, 283

steam tables used in, 283–84

Stoichiometry, 593–96

Storable energy, 89

Subscripts, 411

Successive interpolations, 42

Summary, 26

Surroundings, in system, 13

System, 13–14

adiabatic, 13

classifying, 13–14

closed, 13

composite, 13

diathermal, 13

equilibriumin, 15–16

examples of, 14f

isolated, 13

open, 13

simple, 13

surroundings in, 13

universe in, 13

Tabulated properties

entropy calculated using, 162

fugacity calculated using, 347–48

interpolations, 40–43, 41f

Temperature

adiabatic flame, 605–6

defined, 8

entropy and, 153

in heat transfer, 20f

Henry’s law and, 569

liquid miscibility and, 556–58

measuring, 23–24

in molecular collision, 7–8

upper consolute, 557

Temperature, effect on heat capacities, 113–19, 113f

compressed liquid properties, 117–19, 118f

constant-pressure cooling of liquid, 115–17

heat capacity of steam, 114–15

ideal-gas heat capacity, 114

liquid heat capacities, 114

Temperature-enthalpy chart, 243–44, 244f

Ternary systems, 390–93

Thermal equilibrium, 15

Thermal expansion coefficient using Soave-Redlich-Kwong, 207–9

Thermodynamic analysis

of processes, 314–15

of refrigeration, 302–6

Thermodynamic charts, 242–45

enthalpy-entropy (Mollier chart), 244–45, 245f

pressure-enthalpy, 242–43, 243f

temperature-enthalpy, 243–44, 244f

Thermodynamic cycle, notion of, 169

Thermodynamic potential function, 195

Thermodynamic potentials, 194–95, 195f

Thermodynamics

chemical, 3–5, 4f

definitions, 13–17

development of, 12–13

how and why in, 12–13

introduction, 3–5

molecular basis of, 5–11

multicomponent mixture, state of, 18

problems, 26–28

process and path, 18–19, 18f

pure component, state of, 17–18

quasi-static process, 19–22, 20f

statistical vs. classical, 11–13

summary, 26

units, 22–25

Thermodynamics, calculus of, 205–12

differential and integral forms of a function, 209–12

thermal expansion coefficient using Soave-Redlich-Kwong, 207–9

triple-product rule in ideal-gas state, 207

Thermodynamics of steady-state processes, 272–94

adiabatic mixing, 276–78, 277f

expansion and compression of liquids, 292–94

flow through pipe, 272–76

gas compression, 290–92

heat exchanger, 278–81, 279f

power generation, 295–300

steam turbine, 282–87

throttling, 287–90

Thomson, William, 100, 178

Throttling, 287–90

of compressed liquid, 288–89, 290f

of ideal gas, 288

Time, 25t

Torr, 23

Triple-product rule in ideal-gas state, 207

Truncated virial equation, residual properties from, 226–27

Turbines, gas/steam, 282–87

Two-phase systems, pure fluid in, 337–40

condensing a vapor-liquid mixture, 340

heat of vaporization using Soave-Redlich-Kwong, 338

vapor-liquid mixture calculated by Soave-Redlich-Kwong, 339–40

Txy graph, 370–73, 379f

of completely immiscible liquids, 559–61, 559f

of ethanol/water at elevated temperatures, 384f

of heptane and decane, 370f

of partially miscible liquids, 385f, 554–56, 554f, 557f

UNIFAC equation, 525–31

detailed calculation using, 528–30

Pxy graph for, 530f, 531f

terms calculated by, 527–28

using, 530, 532

UNIQUAC equation, 522–25

group contribution method in, 523–24

Pxy graph calculated from, 524–25, 526f

Units, 22–25

constants, 22t

conversions, 25t

energy, 24–25, 25t

mole, 24

pressure, 22–23, 25t

temperature, 23–24

Universal Functional Activity Coefficient (UNIFAC). See UNIFAC equation

Universe

entropy of, 168

in system, 13

Unsteady-state balances, 315–23

filling a tank with ideal gas, 318–18

filling a tank with steam, 317–18

pressurizing a tank, 315–19, 315f

venting a tank, 319–23

venting ideal gas, 322–23

venting steam, 322

Upper consolute temperature (UCT), 557

Vacuum, irreversible expansion against, 136–37

Van der Waals equation

compressibility factor in, 58–60

residual properties from, 232t

Van der Waals forces, 6

Van Laar equation, 519

Vaporization. See also Vapor-liquid mixture

enthalpy of, 478–79

entropy of, 157, 158

heat of, using Soave-Redlich-Kwong, 338

Vapor-liquid equilibrium (VLE), 369. See also Henry’s law; Vapor-liquid equilibrium (VLE)

Antoine equation, 343

binary, using Soave-Redlich-Kwong, 452–53

chemical equilibrium and, 625–28

chemical potential, 341

Clausius-Clapeyron equation, 341–43

elevated pressures and temperatures, 383–84, 384f

at elevated pressures and temperatures, 383–84, 384f

equations in, solving, 449–50, 451f

in ideal solution, 466–74 (See also Raoult’s law)

problems in, classification of, 448–49

of pure fluid, 340–43

Vapor-liquid equilibrium, theory of, 435–59

chemical potential in, 439–42

fugacity in, 443–48

Gibbs free energy in, 435–39

using equations of state, 448–53

Vapor-liquid-liquid equilibrium (VLLE), 546f

Vapor-liquid mixture

condensing, 340

Soave-Redlich-Kwong equation used to calculate, 339–40

Vapor-liquid separator, 4f, 5

Variables

change of, in fundamental relationships, 217

derivatives and integrals with functions of multiple, 110

Venting, 321

ideal gas, 322–23

steam, 322

a tank, 319–23

Virial equation

Benedict-Webb-Rubin equation and, 68

calculated isotherms using, 57f

compressibility factor in, 53, 54, 56

molar volume calculated with, example of, 55–56

residual properties of methane using, 227–28

second virial coefficient, 53–54, 55

summary, 78

truncated, 54, 226–27

Volume, 25t

excess properties in, 494–95, 495f

residual, 224

Volume of mixing, 409–10

Von Guericke, Otto, 27–28

Wilson equation, 519–20

Work, 88–89, 88f

adiabatic production of, 261, 262

heat and, shared characteristics with, 97

ideal, 183–88

lost, in entropy, 183–88, 191

maximum, in feasibility design, 186–87

as path function, 105–6

PV, 90–96, 91f

separation of, ideal solution in, 464

shaft, 90, 91f

sign convention for, 89

value of heat, Carnot cycle and, 182–83, 182f

x, y, z, convention for, 372

xy graph, 381–83, 382f

ZP graph of pure fluids, 43–45, 45f, 56