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

Absolute zero, 22t

Accumulation, 253

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

chemical potential and, 607

*P°*, working with, 608

defined, 504

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

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

limits of, 505

solubility limits using, 547–48

usefulness of, 505

Activity coefficient models, 515–31

vanLaar, 519

Adiabatic flame temperature, 605–6

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

Analogous relationships, 215, 408

Clausius-Clapeyron equation and, 343

ASHRAE designation of refrigerants, 307t

Athermal process of mixing, 410

Avogadro’s number, 22t

Balances in open systems, 251–335

thermodynamics of steady-state processes, 272–94

unsteady-state balances, 315–23

Bar, 23

Bath

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 VLE using Soave-Redlich-Kwong, 452–53

Bubble temperature (or point), 371

BWR equation. *See* Benedict-Webb-Rubin equation

Calorie, 101

Carbon dioxide (CO_{2})

density of liquid, 10

intermolecular potential of, 6

*Pxy* graph of CO_{2}/*n*-pentane calculated using Soave-Redlich-Kwong, 451f, 452–53

defined, 169

first-law analysis of, 170

internal combustion engine example of, 173

second-law analysis of, 171

thermodynamic efficiency of, 171–73

on *TS* graph, 169f

work value of heat and, 182–83, 182f

Chemical engineer, 5

Chemical engineering thermodynamics, 5

Chemical equilibrium, 15

Chemical potential

activity and, 607

in fugacity, 444

in ideal-gas state, 440

in real mixture, 440

Chemical thermodynamics, 3–5, 4f

Classical thermodynamics

*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

Combinatorial molecular interactions, 507

Completely immiscible liquids, 558–61

calculations, limitations of, 563

Composite system, 13

entropy of, 156

Poynting equation for calculating, 345–47

Compressibility factor, 43–45, 45f

in BWR equation, 69

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

in Peng-Robinson equation, 67

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

Condensed phases, 9

Constant composition, systems of, 407–8

Constant-pressure cooling, 104–5

Constant pressure entropy

change at, 155

Constant-pressure heat capacity (*C _{P}*), 111–12

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

as state function, 113

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

fugacity calculated from, 352–53

isotherm, unstable and metastable parts of, 62–63

Soave-Redlich-Kwong, 30f, 60–61, 66

of state, residual properties from, 232t

working with, 64

Data reduction, 514

Density

empirical equations for, 72–77

of liquid CO_{2}, 10

Derivatives with functions of multiple variables, 110

Dew point, 483

Diathermal system, 13

Differentials

inexact, 212

Diffusion in osmotic equilibrium, 582–83

Disorder, defined, 196

Double interpolations, 41, 41f, 42

Empirical equations, 57

summary, 78

Endothermic process, 410

forms of, 90

internal, 96

process requirements, calculating, 5

storable, 89

transfer, sign convention for direction of, 89

in enthalpy of vaporization, 478–79

irreversible processes and, 133–38

steady state, 258

using *C _{P}* and Δ

Energy balances in reacting systems, 601–6

adiabatic flame temperature and, 605–6

setup for energy balance of reactor, 602f

Enthalpy

defined, 103

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

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

ideal-gas, 234

of ideal-gas mixture, 416

of mixing, 425

pressure and temperature effect on, 220–22

pressure-explicit relations, 229

of reactions, standard, 596–601, 599f

as state function, 103, 125–26

temperature-enthalpy chart, 243–44, 244f

adiabatic mixing of solutions on, 503f

of hydrazine/water mixtures, 501f

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)

heat calculated using, 166

ideal-gas, 234

of ideal-gas mixture, 416

of irreversibility, 168

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

as state function, 153

temperature and, 153

thermodynamic potentials, 194–95

of universe, 168

Entropy, calculation of, 153–63, 199

basic formula, 154

change at constant pressure, 155

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 Δ

steam, 163

tabulated values used for, 162

vaporization, 158

heat exchange between streams, 262–63

processes with entropy generation, 262f

reversible adiabatic process, 260–61

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

in compressibility factor, 44

defined, 29

mathematical representation of, 44

Pitzer, 71

properties from mixtures, 421–27

saturation pressure from, 353–56

summary, 77

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

gas liquids, solubility of, 561–74

liquid-liquid (LLE), 369

liquid-liquid-vapor (LLVE), 369

mechanical, 15

phase splitting and Gibbs free energy, 548–56

schematic of, 546f

solids in liquids, solubility of, 575–80

*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

as mathematical operator, 490

Redlich-Kister expansion, 495–96

Exothermic process, 410

Expansion and Compression of Liquids, 292–94

Experimental activity coefficient, 510–15

*Pxy* graph of, 515f

First law

Carnot cycle analyzed by, 170

defined, 87

schematic illustration of, 98f

Fixed property, 17

Flash separation, 375–76, 376f

Flory-Huggins equation, 521–22

Force, 25t

chemical potential and, 444

from equations of state, 446–48

from experimental data, 445

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

in ideal-gas state, 344

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

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

change of variables, 217

summary of, 216t

Gas

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-Duhem equation, 406–7, 439–40

Gibbs free energy, 5, 194–95, 195f

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

in Margules equation, linearized form of excess, 518f

multicomponent equilibrium in, 437–38, 437f

of combustion in reacting systems, 603–5

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

entropy used to calculate, 166

sensible, 109

sign convention for, 97

specific, 111

transfer, in entropy generation, 188

transfer, irreversible processes in, 133

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

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

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

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

Heat effects of mixing, 496–504

Heat of vaporization (Δ*H*_{vap}), 119–24, 120f

*C _{P}* and Δ

latent, 119

Pitzer correlation for, 121–22

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

Helmholtz free energy, 194, 216, 225, 242

from equation of state, 572–73

formal thermodynamics and, 569–70, 571f

fugacity calculated with, 573–74, 574f

*vs.* Lewis-Randall rule, 573–74

in simultaneous dissolution of two gases, 567–69

temperature and pressure effects on, 569

Household refrigerator, 304

dew point, 483

Ideal gas

throttling of, 288

Ideal-gas constant, 22t

Ideal-gas law

calculated isotherms using, 57f

defined, 34

directions to, 34

molar volume calculated with, example of, 55

summary, 78

*vs.* truncated viral equation, 54

Ideal-gas state, 10–11, 124–32

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

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

defined, 462

noncondensable gases in, 480–83

practical significance of, 463

in separation of work, 464

summary, 484

Inexact differential, 212

Integral form of a function, 209–11

Integrals with functions of multiple variables, 110

Integration of differentials, 213–14, 214f

Intermolecular potential, 6–7, 7f

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

accuracy in, 40

example of, using steam tables, 41–43

types of, 41f

Irreversible processes, energy balances and

heat transfer, 133

of ideal gas, 137

against pressure, 138

Isentropic step in Carnot cycle, 170

Isolated system, 13

Isothermal compression of steam

in first law paths, 108

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

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

at zero pressure, 44

Joule, James Prescott, 100–101

Kelvin (K), 23

Kelvin-Plank statement, 178

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

defined, 35

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

Linde process, 310f

Linear interpolations, 41f, 71, 79

of gas, Linde process for, 310f

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

Liquid-liquid-vapor equilibrium (LLVE), 369

partial, equilibrium between, 545–48

Liquids. *See also* Compressed liquids; Vapor-liquid mixture

CO_{2}, density of, 10

constant-pressure cooling of, 115–17

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

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

Gibbs free energy in, 518f

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

Mass, 25t

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

molecular view of, 412f

rules, 419

volume of, excess properties in, 492–95

Mixtures, 401–33. *See also* Mixing

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

mathematical treatment of, 404–9

properties from equations of state, 421–27

real, compression of, 427

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

partial molar property, 405, 408–8

systems of constant composition, 407–8

Molar mass, 23

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

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

Mole, 24

Molecular basis of thermodynamics, 5–11

condensed phases, 9

density of liquid CO_{2}, 10

intermolecular potential, 6–7, 7f

Maxwell-Boltzmann distribution, 8, 9f

Molecular view of entropy, 195–99, 197f

equally probable microstates, 199

Mollier chart. *See* Enthalpy-entropy (Mollier) chart

Multicomponent mixture, state of, 18

equilibrium compositions with, 634–35

number of, determining, 633–34

Naphthalene, solubility of, 577–78, 578f

Newton, 23

Nitrogen

reversible adiabatic compression of, 131–32

Nomenclature, 17

Noncondensable gases. *See also* Humidification

Nonideal solutions, 489–543. *See also* Activity coefficient

heat effects of mixing, 496–504

Nonrandom two liquid model (NRTL). *See* NRTL equation

Open systems. *See also* Balances in open systems

defined, 13

ideal and lost work in, 266–71

Osmotic equilibrium, 580–86, 580f

diffusion in, chemical potential and, 582–83

*P*°, working with, 608

Partially miscible liquids, 384–89

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

Pascal, 23

defined, 18

illustration of, 18f

constant-pressure cooling, 104–5

constant-pressure heating, 102–3

constant-temperature process, 107, 108

constant-volume cooling, 102

constant-volume heating, 101–2

in isothermal compression of steam, 108

compressibility factor in, 67

fugacity calculated from, 352, 353

residual properties from, 232t

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

Phase behavior of mixtures, 369–400

compositions at bubble and dew point, 374f

flash separation, 375–76, 376f

partially miscible liquids, 384–89

summary, 393

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

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 Δ

Phase diagrams. *See also* Pure fluids, phase diagrams of

of acetic acid/water/methylisobutyl ketone, 390f

from equations of state, 356–58

Phase equilibrium

chemical equilibrium and VLE, 625–28

Phases, calculating incompressible, 220–21

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

equilibrium and stability in, 551–52, 551f

energy losses in, schematic for calculating, 273f

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

PR equation. *See* Peng-Robinson equation

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

Pressurizing, 321

defined, 18

energy requirements of, calculating, 5

extensive and intensive properties, 16–17

fixed, 17

nomenclature and, 17

of pure component, 17

Properties, calculating, 205

cubic equations, application to, 230–34

differentials, integration of, 213–14

fundamental relationships, 214–17

generalized correlations, 235–36, 237–38f

in compressible phases, 220–21

pressure-explicit relations, 228–30

of reference states, 236, 239–42

*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

phase diagrams from equations of state, 356–58

saturation pressure from equations of state, 353–56

Pure fluids, phase diagrams of, 29–85

compressibility factor, 43–45, 45f

empirical equations, 57

tabulated values of properties, 40–43

virial equation, 53

*PV* graph of pure fluid, 31–36, 31f

critical point, 33

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

equation for, obtaining, 90–91

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

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

of CO_{2}/*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

explained, 21

Rackett equation, 73

Rankine (R), 23

Rankine power plant, 295–300, 295f

bubble and dew pressure in, 469–70

bubble *T* calculation in, 467

dew *T* calculation in, 468

hypothetical liquid state in, 472

phase diagram in, 473–74, 474f

equilibrium composition, 622–24

equilibrium involving solids, 629–32

standard enthalpy of, 596–601, 599f

Real mixtures

chemical potential in, 440

compression of, 427

Redlich-Kister expansion, 495–96

Reference states

ASHRAE designation of, 307t

saturation pressure of, 308f

cycle on *PH* graph, 303f

household refrigerator, 304

thermodynamic analysis of, 302–6

vapor-compression refrigeration cycle, 301f

Relative humidity (RH), 482, 483

Relative volatility, 382

Residual molecular interactions, 507

from corresponding states, 235–36

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

defined, 22

enthalpy, 223

entropy, 224

of methane, using virial coefficient, 227–28

from truncated virial equation, 226–27

volume, 224

Reversible *PV* work, 91–92, 92f

Reversibility, entropy and, 176–77

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

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

defined, 149

direction of heat flow determined by, 184–85

in feasibility of process, 185–87

Sensible heat, 109

Separation of work, ideal solution in, 464

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

temperature measured in, 23

binary mixture properties using, 423t

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

CO_{2}/*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

residual properties from, 232–34, 232t

vapor-liquid mixture calculated by, 339–40

Solids

in liquids, solubility of, 575–80

Solubility

limits using activity coefficients, 547–48

Solute, activity of, 609, 611–12

Specific energy, 25t

Specific heat, 111

SRK equation. *See* Soave-Redlich-Kwong equation

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

entropy as, 153

heat capacity as, 109

internal energy as, 89, 96, 107

Statistical thermodynamics, 11–13

Steady state

energy balance, 258

*vs.* equilibrium, 261

Steam

entropy of, 163

fugacity of, 349

tables, fugacity from, 347

venting, 322

actual operation, 283

ideal and lost work in, 286–87

Mollier graph used in, 285–86, 285f

reversible operation, 283

Storable energy, 89

Subscripts, 411

Successive interpolations, 42

Summary, 26

Surroundings, in system, 13

adiabatic, 13

closed, 13

composite, 13

diathermal, 13

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

Temperature

defined, 8

entropy and, 153

in heat transfer, 20f

Henry’s law and, 569

liquid miscibility and, 556–58

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

Thermal equilibrium, 15

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

Thermodynamic analysis

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

multicomponent mixture, state of, 18

pure component, state of, 17–18

quasi-static process, 19–22, 20f

statistical *vs.* classical, 11–13

summary, 26

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

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

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

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

detailed calculation using, 528–30

group contribution method in, 523–24

*Pxy* graph calculated from, 524–25, 526f

constants, 22t

conversions, 25t

mole, 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 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

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

Vapor-liquid equilibrium, theory of, 435–59

using equations of state, 448–53

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

condensing, 340

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

Variables

change of, in fundamental relationships, 217

derivatives and integrals with functions of multiple, 110

Venting, 321

steam, 322

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

Volume, 25t

excess properties in, 494–95, 495f

residual, 224

adiabatic production of, 261, 262

heat and, shared characteristics with, 97

maximum, in feasibility design, 186–87

separation of, ideal solution in, 464

sign convention for, 89

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

*x, y, z*, convention for, 372

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