Index

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

Absolute temperature, 2324

Absolute zero, 22t

Accumulation, 253

Acentric factor, 4751

defined, 4748

of simple, normal, and polar fluids, 5051

Activity, 60613

chemical potential and, 607

of gas, 6078, 611

of liquid, 6089, 611

, working with, 608

of solid, 60910, 612

of solute, 609, 61112

standard state and, 610, 613

Activity coefficient, 50411

for data reduction, 51215

defined, 504

deviations from Raoult’s law, 50810, 509f

experimental, 51015

Gibbs free energy and, excess, 5057, 51014, 511f

limits of, 505

phase equilibrium and, 50710

solubility limits using, 54748

usefulness of, 505

Activity coefficient models, 51531

Flory-Huggins, 52122

Margules, 51519

NRTL, 52021

UNIFAC, 52531

UNIQUAC, 52225

vanLaar, 519

Wilson, 51920

Adiabatic flame temperature, 6056

Adiabatic mixing

heat effects of, 49799

of solutions on enthalpy charts, 503f

in steady-state processes, 27678, 277f

Adiabatic processes. See Reversible adiabatic processes

Adiabatic production of work, 261, 262

Adiabatic system, 13

Air, chemical potential in, 44142

American Engineering system of units, 22

pound-mol (lb-mol) in, 24

pressure measured in, 23

temperature measured in, 23

Ammonia refrigerator, 3046

Analogous relationships, 215, 408

Antoine equation, 3840

Clausius-Clapeyron equation and, 343

determining phase with, 3940

units in, 3839

ASHRAE designation of refrigerants, 307t

Athermal process of mixing, 410

Avogadro’s number, 22t

Azeotropes, 38081, 380f

Balances in open systems, 251335

energy balance, 254f, 25558

entropy balance, 25866

flow streams, 25253, 252f

liquefaction, 30915

mass balance, 25355, 254f

power generation, 295300

problems, 32435

refrigeration, 3019

summary, 32324

thermodynamics of steady-state processes, 27294

unsteady-state balances, 31523

Bar, 23

Bath

change of, entropy, 15961

default, exergy and, 18991

heat, in entropy balance, 26566

stream acting as, in entropy balance, 26465

Benedict-Webb-Rubin equation, 6771, 70f, 71t

Benzene, solubility of, 57778, 578f

Binary mixtures, 42021, 423t

Binary VLE using Soave-Redlich-Kwong, 45253

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, 1011

intermolecular potential of, 6

Pxy graph of CO2/n-pentane calculated using Soave-Redlich-Kwong, 451f, 45253

Carnot cycle, 16877

defined, 169

in entropy, 16877, 169f

first-law analysis of, 170

ideal gas used in, 17374

internal combustion engine example of, 173

second-law analysis of, 171

steam used in, 17576

steps in, 16970

thermodynamic efficiency of, 17173

on TS graph, 169f

work value of heat and, 18283, 182f

Carnot efficiency, 17172

Celsius scale, 2324

Chemical engineer, 5

Chemical engineering thermodynamics, 5

Chemical equilibrium, 15

Chemical potential

activity and, 607

in air, 44142

in fugacity, 444

in Gibbs free energy, 44042

in ideal-gas state, 440

in real mixture, 440

in theory of VLE, 43942

Chemical thermodynamics, 35, 4f

Classical thermodynamics

laws of, 1112

vs. statistical thermodynamics, 1113

Clausius, Rudolph, 178

Clausius-Clapeyron equation in VLE, 34143

Clausius statement

as alternative statement of second law, 17782

defined, 178

as equivalent statement of second law, 18082

Closed systems

defined, 13

first law for, 98101

second law in, 15053

Combinatorial molecular interactions, 507

Completely immiscible liquids, 55861

calculations, limitations of, 563

Pxy graph of, 56162, 562f

Txy graph of, 55961, 559f

Composite system, 13

Compressed liquids, 29294

entropy of, 156

Poynting equation for calculating, 34547

throttling of, 28889, 290f

Compressibility factor, 4345, 45f

in BWR equation, 69

in corresponding states, 4547, 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, 5860

in virial equation, 53, 54, 56

ZP graph of pure fluids and, 4345, 45f, 56

Compressor

graphical solution on Molliev chart, 293f

steam/gas, 29092

Condensed phases, 9

Constant composition, systems of, 4078

Constant-pressure cooling, 1045

Constant pressure entropy

change at, 155

no phase change in, 15354

Constant-pressure heat capacity (CP), 11112

vs. constant-volume heat capacity, 11112, 112f

as state function, 113

of steam, 11415

Constant-pressure heating, 1023

Constant-pressure (or isobaric) process, 1819

Constants, 22t

Constant-temperature (or isothermal) process, 1819, 107, 108

Constant-volume cooling, 102

Constant-volume heat capacity (CV), 109

vs. constant-pressure heat capacity, 11112, 112f

as state function, 113

Constant-volume heating, 1012

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

Constant-volume process, 1819

Constrained equilibrium, 1516

Conversions, 25t

Corresponding states

in compressibility factor, 4547, 46f, 51, 52

in phase diagrams of pure fluids, 45, 46f

Cubic equations of state

application to, 23034

fugacity calculated from, 35253

isotherm, unstable and metastable parts of, 6263

Peng-Robinson, 61, 6667

PVT behavior of, 6163

roots of, 6365

Soave-Redlich-Kwong, 30f, 6061, 66

of state, residual properties from, 232t

Van der Waals, 5860, 6566

for volume, solving, 6567

working with, 64

Data reduction, 514

Definitions, 1317

equilibrium, 1516

property, 1617

system, 1314

Density

empirical equations for, 7277

of liquid CO2, 10

Derivatives with functions of multiple variables, 110

Desalination, 58586

Dew point, 483

Diathermal system, 13

Differentials

exact, 21112

form of, 20911

inexact, 212

integration of, 21314, 214f

Diffusion in osmotic equilibrium, 58283

Disorder, defined, 196

Distillation, 378, 379f

Double interpolations, 41, 41f, 42

Elementary process, 1819

Empirical equations, 57

for density, 7277

summary, 78

Endothermic process, 410

Energy, 2425, 25t

forms of, 90

heat and, 9697

ideal-gas state, 12432

internal, 96

process requirements, calculating, 5

storable, 89

transfer, sign convention for direction of, 89

work and, 8889, 88f

Energy balance, 254f, 25558

in closed systems, 25758

in enthalpy of vaporization, 47879

entropy used in, 16366

in heat exchanger, 47980

in ideal solution, 47580

irreversible processes and, 13338

in open systems, 254f, 25558

steady state, 258

using CP and ΔHvap, 12224

using tables, 12122

Energy balances in reacting systems, 6016

adiabatic flame temperature and, 6056

heat of combustion and, 6035

setup for energy balance of reactor, 602f

Enthalpy

defined, 103

enthalpy-entropy (Mollier) chart, 24445, 245f

equations for, 21719

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

ideal-gas, 234

of ideal-gas mixture, 416

lever rule for, 11920

of mixing, 425

pressure and temperature effect on, 22022

pressure-explicit relations, 229

of reactions, standard, 596601, 599f

residual, 223, 236, 237f

as state function, 103, 12526

of steam, 1035

temperature-enthalpy chart, 24344, 244f

of vaporization, 47879

Enthalpy charts, 500504

adiabatic mixing of solutions on, 503f

of hydrazine/water mixtures, 501f

pressure, 24243, 243f

using, 5034

Enthalpy-entropy (Mollier) chart, 24445, 245f

graphical solution of compressed liquids on, 293f

in steam turbine, 28586, 285f

Entropy

calculation of (See Entropy, calculation of)

Carnot cycle in, 16877, 169f

change of bath, 15961

in energy balance, 16366

energy balances using, 16366

equations for, 21719

equilibrium and, 19195

exergy and, 18991

generation, 16768

heat calculated using, 166

ideal-gas, 234

of ideal-gas mixture, 416

ideal work in, 18388

of irreversibility, 168

of liquids, 156, 157

lost work in, 18388, 191

measurable quantities relating to, 15153

of mixing, in ideal solution, 46364

molecular view of, 19599, 197f

pressure and temperature’s effect on, 22022

pressure-explicit relations, 22930

problems, 2014

residual, 224, 236, 238f

reversibility and, 17677

second law and, 149204

of solids, 15556, 157

stability and, 19195

as state function, 153

summary, 199201

temperature and, 153

thermodynamic potentials, 19495

of universe, 168

of vaporization, 157, 158

Entropy, calculation of, 15363, 199

basic formula, 154

change at constant pressure, 155

change of bath, 15961

compressed liquids, 156

constant-pressure path, no phase change, 15354

constant-volume path, no phase change, 154

energy balances with phase change, using CP and ΔHvap, 15859

ideal-gas state, 16162, 161f

phase change, 15758, 157f

solids, 15556

steam, 163

tabulated values used for, 162

vaporization, 158

Entropy balance, 25866

heat exchange between streams, 26263

in open systems, 25866

processes with entropy generation, 262f

reversible adiabatic process, 26061

steady state, 260, 261

stream acting as a bath, 26465

Entropy generation

cooling system, choosing, 26971

in power plant, 267

processes with, 262f

Equations of state

appeal of, 453

binary VLE using Soave-Redlich-Kwong, 45253

BWR, 6771, 70f, 71t

in compressibility factor, 44

cubic, 5767

defined, 29

fugacity from, 44648

Henry’s law from, 57273

ideal-gas law and, 34, 54

interaction parameter, 45153

Lee-Kesler, 6870

mathematical representation of, 44

for mixtures, 41921

other, 6771

phase diagrams from, 35658

Pitzer, 71

properties from mixtures, 42127

saturation pressure from, 35356

summary, 77

in theory of VLE, 44853

in truncated virial equation, 54

Equilibrium, 1516, 54591. See also Liquid miscibility

chemical, 15

conditions at constant temperature and pressure, 19194

conditions fulfilled by, 15

constrained, 1516

entropy and, 19195

gas liquids, solubility of, 56174

liquid-liquid (LLE), 369

liquid-liquid-vapor (LLVE), 369

mechanical, 15

osmotic, 58086

phase splitting and Gibbs free energy, 54856

problems, 58691

schematic of, 546f

solids in liquids, solubility of, 57580

solids involved in, 62932

vs. steady state, 261

summary, 586

thermal, 15

thermodynamic potentials and, 19495

Equilibrium composition, 62224

with multiple reactions, 63435

pressure in, effect of, 62324

Equilibrium constant, 61420, 621

Ethylene, phase diagram of, 35658

Euler’s theorem, 406

Eutectic point, 57980

Exact differential, 21112

Excess properties, 48996

as mathematical operator, 490

molar, 49091, 492f

in nonideal solutions, 48996

Redlich-Kister expansion, 49596

volume, 49495, 495f

in volume of mixing, 49294

Exergy, 18991

Exothermic process, 410

Expansion, PV work in, 9293

Expansion and Compression of Liquids, 29294

Experimental activity coefficient, 51015

fitting, 51214

Pxy graph of, 515f

Extensive property, 1617

Fahrenheit, 2324

First law

Carnot cycle analyzed by, 170

for closed system, 98101

defined, 87

energy and, 87148

history of, 100101

Joule’s experiment, 100101

operator Δ used in, 99100

paths in, 1018

problems, 14048

schematic illustration of, 98f

summary, 13940

Fixed property, 17

Flash separation, 37576, 376f

Flash units, multiple, 37778

Flory-Huggins equation, 52122

Flow streams, 25253, 252f

Force, 25t

Fugacity, 34353

chemical potential and, 444

defined, 34343

from equations of state, 44648

from experimental data, 445

Gibbs free energy and, 34445

Henry’s law used to calculate, 57374, 574f

in ideal-gas state, 344

in ideal solution, 46465

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

in mixture using Soave-Redlich-Kwong, 44748

of solubility of gases in liquids, 564f

steam, 349

from steam tables, 347

in theory of VLE, 44348

Fugacity, calculation of, 34553

compressibility factor used in, 34849

from cubic equations of state, 35253

from generalized graphs, 34952, 350f, 351f

Poynting equation for compressed liquids, 34547

saturated liquid, 346

from Soave-Redlich-Kwong, 352, 353

tabulated properties used in, 34748

Function, differential and integral forms of, 20911

Fundamental relationships

calculating, 21417

change of variables, 217

summary of, 216t

Gas

activity of, 6078, 611

Linde process for liquefaction of, 310f

Gases in liquids, solubility of, 56374. See also Henry’s law

fugate of, 564f

Generalized correlations, calculating, 23536, 23738f

Generalized graphs, 77

fugacity calculated from, 34952, 350f, 351f

Gibbs, J. Willard, 45, 4f

Gibbs-Duhem equation, 4067, 43940

Gibbs free energy, 5, 19495, 195f

calculating, 215, 225, 242

chemical potential in, 44042

excess, activity coefficient and, 5057, 51014, 511f

fugacity and, 34445

in Margules equation, linearized form of excess, 518f

multicomponent equilibrium in, 43738, 437f

phase rule in, 43839

phase splitting and, 54856

in theory of VLE, 43539

Gibbs’s phase rule, 43839

Heat, 9697

capacities, 10919

of combustion in reacting systems, 6035

direction of flow, second law to determine, 18485

entropy used to calculate, 166

as path function, 1056

sensible, 109

sign convention for, 97

specific, 111

transfer, in entropy generation, 188

transfer, irreversible processes in, 133

of vaporization, 11924, 120f

of vaporization using Soave-Redlich-Kwong, 338

work and, shared characteristics with, 97

work value of, Carnot cycle and, 18283, 182f

Heat bath (or heat reservoir), 19

Heat capacity, 10919

constant-pressure heat capacity, 11112, 112f

constant-volume heat capacity, 109, 11112, 112f

defined, 11213

effect of pressure and temperature on, 11319, 113f

excess, 499500

Heat effects of mixing, 496504

enthalpies, excess, 496, 497f

enthalpy charts, 500504

excess heat capacity, 499500

isothermal, 49799

Heat exchanger, 27881, 279f

in ideal solution, 47980

Heat of vaporization (ΔHvap), 11924, 120f

CP and ΔHvap, energy balances with phase change using, 12224

latent, 119

Pitzer correlation for, 12122

tables, energy balances with phase change using, 12122

Helmholtz free energy, 194, 216, 225, 242

Henry’s law, 56474

alternative forms of, 56667

carbonated soda and, 57172

from equation of state, 57273

formal thermodynamics and, 56970, 571f

fugacity calculated with, 57374, 574f

vs. Lewis-Randall rule, 57374

other units for, 56566

in simultaneous dissolution of two gases, 56769

temperature and pressure effects on, 569

VLE using, 56465

Household refrigerator, 304

Humidification, 48183

dew point, 483

relative humidity, 482, 483

Hypothetical states, 47677

Ideal gas

filling a tank with, 31818

throttling of, 288

venting, 32223

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, 1011, 12432

calculating, 21920

Carnot cycle using, 17375

chemical potential in, 440

equations, summary of, 219t

fugacity in, 344

hypothetical, 223

irreversible expansion of, 137

in isothermal compression of steam, 12627

log-x mean, 130

mixtures in, 41319

paths in, 132f

residual properties of, 22526

reversible adiabatic compression of nitrogen, 13132

reversible adiabatic process, 12730, 13132, 132f

reversible adiabatic process in, 16466

triple-product rule in, 207

Ideal solution, 46188

defined, 462

energy balances in, 47580

entropy of mixing in, 46364

fugacity in, 46465

ideality in, 46163

noncondensable gases in, 48083

practical significance of, 463

problems, 48488

in separation of work, 464

summary, 484

VLE in, Raoult’s law, 46674

Ideal work, 18388

for heat transfer, 26869

in open systems, 26671

Incompressible phases, 22021

Inexact differential, 212

Integral form of a function, 20911

Integrals with functions of multiple variables, 110

Integration of differentials, 21314, 214f

Integration paths, 10910

Intensive property, 1617

Interaction parameter, 45153

Intermolecular potential, 67, 7f

Internal energy, 96, 215, 219, 22425, 24142

Interpolations, 4043, 41f

accuracy in, 40

example of, using steam tables, 4143

types of, 41f

Irreversible processes, energy balances and

adiabatic mixing, 13436

heat transfer, 133

of ideal gas, 137

against pressure, 138

against vacuum, 13637

Isentropic step in Carnot cycle, 170

Isolated system, 13

Isothermal compression of steam

in first law paths, 108

in ideal-gas state, 12627

in PV work, 9495, 96f

Isothermal mixing, heat effects of, 49799

Isothermal step in Carnot cycle, 16970

Isotherms

critical point and, 33

of Lee-Kesler method, 68

of modified BWR equation, 67, 70f

pressure-volume, of acetone, 7475, 76f

on PV graph, 31, 33

of Soave-Redlich-Kwong equation, 6162, 62f

at zero pressure, 44

on ZP graph, 53, 57f

Joule, James Prescott, 100101

Kelvin (K), 23

Kelvin-Plank statement, 178

K-factors, 382, 449, 468

Kinetic energy, 90

Latent heat of vaporization, 119

Laws of classical thermodynamics, 1112

Lee-Kesler method

compressibility factor in, 56, 68

in phase diagrams of pure fluids, 4849, 48f, 49f, 50f

for residual enthalpy, 237f

for residual entropy, 238f

Length, 25t

Lever rule, 3436, 35f

defined, 35

for enthalpy, 11920

partially miscible liquids and, 388

in phase behavior of mixtures, 37273

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, 57374

Linde process, 310f

Linear interpolations, 41f, 71, 79

Liquefaction, 30915

of gas, Linde process for, 310f

of nitrogen, 310f, 31114

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

Liquid-liquid-vapor equilibrium (LLVE), 369

Liquid miscibility

complete, 55861

partial, equilibrium between, 54548

temperature and, 55658

Liquids. See also Compressed liquids; Vapor-liquid mixture

activity of, 6089, 611

CO2, density of, 10

constant-pressure cooling of, 11517

of enthalpy and entropy, pressure and temperature’s effect on, 22022

entropy of, 156, 157

expansion of, 29294

fugacity of saturated, 346

gases in, solubility of, 56374

heat capacities, 114

hypothetical state of, 472

properties, compressed, 11719, 118f

pump, calculating, 294

solids in, solubility of, 57580

Log-x mean, 130

Lost work in open systems, 26671

Magdeburg hemispheres, 2728

Margules equation, 51519

Gibbs free energy in, 518f

Pxy graph reconstructed from limited data, 517, 51819

Mass, 25t

Mass balance, 25355, 254f

Mathematical conditions for stability, 552

Maxwell-Boltzmann distribution, 8, 9f

Maxwell relationships, 214, 216

Measurable quantities relating to entropy, 15153

Mechanical equilibrium, 15

Mechanically reversible process, 9192, 92f

Methane, virial coefficient used for residual properties of, 22728

Mixing, 41113. See also Mixtures

athermal process of, 410

endothermic process of, 410

enthalpy of, 425

exothermic process of, 410

heat effects of, 496504

molecular view of, 412f

non-isothermal, 41618

properties of, 40911

rules, 419

separation and, 41113

separation of air, 41891

volume of, 40910

volume of, excess properties in, 49295

Mixtures, 40133. See also Mixing

binary, 42021

composition of, 4024

equations of state for, 41921

formation of, at constant pressure and temperature, 410f

fugacity in, using Soave-Redlich-Kwong, 44748

homogeneous properties of, 4034

in ideal-gas state, 41319

mathematical treatment of, 4049

phase behavior of, 369400

problems, 42833

properties from equations of state, 42127

real, compression of, 427

real, properties of, 42425

residual properties of, 420, 421

subscripts, 411

summary, 428

VLE of, using equations of state, 44853

Mixtures, mathematical treatment of, 4049

Euler’s theorem, 406

Gibbs-Duhem equation, 4067

partial molar property, 405, 4088

systems of constant composition, 4078

Molar mass, 23

Molar property, 1617

excess, in nonideal solutions, 49091, 492f

partial, 405, 4089

residual, 4089

residual partial, 4089

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, 7273

mean intermolecular distance and, 29

proper, selecting, 63

in PT graph of pure fluid, 37, 37f

in PV graph of pure fluid, 30f, 3135

in PVT behavior of pure fluid, 2930

in Soave-Redlich-Kwong equation, 62

in van der Waals equation, 59

in virial equation, 55, 56

Mole, 24

Molecular basis of thermodynamics, 511

condensed phases, 9

density of liquid CO2, 10

ideal-gas state, 1011

intermolecular potential, 67, 7f

Maxwell-Boltzmann distribution, 8, 9f

phase transitions, 89

temperature and pressure, 78

Molecular collisions, 78, 97

Molecular view of entropy, 19599, 197f

equally probable microstates, 199

probabilities and, 19899

Mollier chart. See Enthalpy-entropy (Mollier) chart

Multicomponent mixture, state of, 18

Multiple reactions, 63235

equilibrium compositions with, 63435

number of, determining, 63334

Naphthalene, solubility of, 57778, 578f

Newton, 23

Nitrogen

liquefaction of, 310f, 31114

reversible adiabatic compression of, 13132

Nomenclature, 17

Noncondensable gases. See also Humidification

in ideal solution, 48083

Nonideal solutions, 489543. See also Activity coefficient

excess properties, 48996

heat effects of mixing, 496504

molecular view of, 507, 507f

problems, 53343

summary, 53133

Nonrandom two liquid model (NRTL). See NRTL equation

NRTL equation, 52021

Open systems. See also Balances in open systems

defined, 13

ideal and lost work in, 26671

Operator Δ, 99100, 255

Osmotic equilibrium, 58086, 580f

desalination and, 58586

diffusion in, chemical potential and, 58283

pressure in, 58485

reverse osmosis, 58384, 584f

Osmotic pressure, 58485

P°, working with, 608

Partially miscible liquids, 38489

equilibrium between, 54548

lever rule and, 388

Pxy graph of, 387f, 55254, 553f

qualitative-phase diagram of, 38889, 389f

Txy graph of, 385f, 55456, 554f, 557f

Partial molar, 405, 4089

Pascal, 23

Path, 1819, 18f

defined, 18

illustration of, 18f

Paths in first law, 1018

alternate, 1067, 107f

constant-pressure cooling, 1045

constant-pressure heating, 1023

constant-temperature process, 107, 108

constant-volume cooling, 102

constant-volume heating, 1012

enthalpy of steam, 1035

heat as path function, 1056

integration, 10910

in isothermal compression of steam, 108

work as path function, 1056

Peng-Robinson equation

compressibility factor in, 67

fugacity calculated from, 352, 353

fugacity from, 44647

residual properties from, 232t

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

Phase behavior of mixtures, 369400

azeotropes, 38081

compositions at bubble and dew point, 374f

distillation, 378, 379f

flash separation, 37576, 376f

flash units, multiple, 37778

lever rule in, 37273

partially miscible liquids, 38489

problems, 394400

Pxy graph, 37379

summary, 393

ternary systems, 39093

Txy graph, 37073

VLE at elevated pressures and temperatures, 38384, 384f

xy graph, 38183, 382f

Phase change, entropy and, 15358, 157f

constant-pressure path, no phase change, 15354

constant-volume path, no phase change, 154

energy balances with, using CP and ΔHvap, 15859

Phase diagrams. See also Pure fluids, phase diagrams of

of acetic acid/water/methylisobutyl ketone, 390f

from equations of state, 35658

of ethylene, 35658

in Raoult’s law, 47374, 474f

Phase equilibrium

chemical equilibrium and VLE, 62528

as chemical reaction, 62829

reactions and, 62429

Phases, calculating incompressible, 22021

Phase splitting Gibbs free energy and, 54856, 550f

equilibrium and stability in, 55152, 551f

Phase transitions, 89

Pipe, flow through, 27276

energy losses in, schematic for calculating, 273f

pressure drop, 27576

Pitzer method

compressibility factor in, 48, 71

for heat of vaporization, 12122

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, 295300

Poynting equation, 34547

PR equation. See Peng-Robinson equation

Pressure, 78, 2223, 25t

in equilibrium composition, effect of, 62324

Henry’s law and, 569

irreversible expansion against, 138

Pressure, effect on heat capacities, 11319, 113f

compressed liquid properties, 11719, 118f

constant-pressure cooling of liquid, 11517

heat capacity of steam, 11415

ideal-gas heat capacity, 114

liquid heat capacities, 114

Pressure-enthalpy chart, 24243, 243f

Pressure-explicit relations, 22830

enthalpy, 229

entropy, 22930

Pressurizing, 321

Processes, 1819, 18f

defined, 18

energy requirements of, calculating, 5

entropy and, 17677

Properties, 1617

defined, 1617

extensive and intensive properties, 1617

fixed, 17

molar, 1617

nomenclature and, 17

of pure component, 17

specific, 1617

tabulated values of, 4043

Properties, calculating, 205

cubic equations, application to, 23034

differentials, integration of, 21314

enthalpy, 21719

entropy, 21719

fundamental relationships, 21417

generalized correlations, 23536, 23738f

ideal-gas state, 21920

in compressible phases, 22021

pressure-explicit relations, 22830

problems, 24650

of reference states, 236, 23942

residual properties, 22228

summary, 24546

thermodynamic charts, 24245

thermodynamics, 20512

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

PT graph of pure fluid, 3640, 37f

Pure component

multicomponent mixture, state of, 18

property of, 17

state of, 1718

Pure fluid, 33766

fugacity, 34353

phase diagrams from equations of state, 35658

problems, 36066

saturation pressure from equations of state, 35356

summary, 35860

two-phase systems, 33740

VPE of, 34043

Pure fluids, phase diagrams of, 2985

compressibility factor, 4345, 45f

corresponding states, 45, 46f

empirical equations, 57

PVT behavior of, 2940

tabulated values of properties, 4043

virial equation, 53

PV graph of pure fluid, 3136, 31f

critical point, 33

ideal-gas state, 3334

two-phase region and lever rule, 3436, 35f

PVT behavior

boiling in open air, 32

PT graph of pure fluid, 3640, 37f

of pure fluids, phase diagrams of, 2940

PV graph of pure fluid, 3136, 31f

PVT surface of pure fluid, 30f

PVT surface of pure fluid, 30f

PV work, 9096, 91f

equation for, obtaining, 9091

in expansion, 9293

in isothermal compression of steam, 9495, 96f

reversible, 9192, 92f

Soave-Redlich-Kwong equation used for, 9394

Pxy graph, 37379

of CO2/n-pentane calculated using Soave-Redlich-Kwong, 451f, 45253

of completely immiscible liquids, 56162, 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, 55254, 553f

reconstructing from limited data, 517, 51819

for UNIFAC equation, 530f, 531f

UNIQUAC equation used to calculate, 52425, 526f

Quantities relating to entropy, measurable, 15153

Quasi-static process, 1922, 20f

example of, 2122

explained, 21

reversible, 2021

Rackett equation, 73

Rankine (R), 23

Rankine power plant, 295300, 295f

Raoult’s law, 46674

bubble and dew pressure in, 46970

bubble T calculation in, 467

deviations from, 50810, 509f

dew P calculation in, 46768

dew T calculation in, 468

flash calculation in, 46869

fugacity and, 47071

hypothetical liquid state in, 472

phase diagram in, 47374, 474f

Reactions, 593645

activity, 60613

energy balances in, 6016

equilibrium composition, 62224

equilibrium constant, 61420

equilibrium involving solids, 62932

multiple, 63235

phase equilibrium and, 62429

problems, 63745

standard enthalpy of, 596601, 599f

stoichiometry, 59396

summary, 63637

Real mixtures

chemical potential in, 440

compression of, 427

properties of, 42425

Redlich-Kister expansion, 49596

Reference states

calculating, 236, 23942

using, 24041

Refrigerants, 3079

ASHRAE designation of, 307t

environment and, 3089

saturation pressure of, 308f

Refrigeration, 3019

ammonia refrigerator, 3046

cycle on PH graph, 303f

household refrigerator, 304

refrigerants, 3079

thermodynamic analysis of, 3026

vapor-compression refrigeration cycle, 301f

Relative humidity (RH), 482, 483

Relative volatility, 382

Residual molar, 4089

Residual molecular interactions, 507

Residual partial molar, 4089

Residual properties, 22228

applications, 22528

from corresponding states, 23536

from cubic equations of state, 23234, 232t

defined, 22

enthalpy, 223

entropy, 224

in ideal-gas state, 22526

of methane, using virial coefficient, 22728

of mixtures, 420, 421

other, 22425

from truncated virial equation, 22627

volume, 224

Reverse osmosis, 58384, 584f

Reversible PV work, 9192, 92f

Reversibility, entropy and, 17677

Reversible adiabatic processes, 12730, 13132, 132f

in entropy balance, 26061

in ideal-gas state, 16466

in mixing, 13436

in nitrogen compression, 13132

in steam compression, 165

Reversible quasi-static process, 2021

Roots

in compressibility factor, acceptable, 63, 66, 67

of cubic equation of state, 6365

Saturated liquid, fugacity of, 346

Saturation pressure from equations of state, 35356, 354f, 355f

Second law

alternative statements of, 17782

Carnot cycle analyzed by, 171

in closed system, 15053

consequences of, 180, 200201

defined, 149

direction of heat flow determined by, 18485

entropy and, 149204

in feasibility of process, 18587

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, 2223

temperature measured in, 23

Soave-Redlich-Kwong equation

binary mixture properties using, 423t

binary VLE using, 45253

calculation of Henry’s law constant, 56970, 571f

CO2/n-pentane calculated using, 451f, 45253

coefficient of thermal expansion using, 2079

compressibility factor in, 61

fugacity from, 352, 353, 44648

heat of vaporization using, 338

for PV work, 9394

residual properties from, 23234, 232t

vapor-liquid mixture calculated by, 33940

Solids

activity of, 60910, 612

entropy of, 15556, 157

in liquids, solubility of, 57580

Solubility

of benzene, 57778, 578f

eutectic point, 57980

of gases in liquids, 56374

limits using activity coefficients, 54748

of naphthalene, 57778, 578f

of solids in liquids, 57580

Solute, activity of, 609, 61112

Specific energy, 25t

Specific heat, 111

Specific property, 1617

SRK equation. See Soave-Redlich-Kwong equation

Stability, 35556

entropy and, 19195

equilibrium and, in phase splitting, 55152, 551f

mathematical conditions for, 552

Standard state, activity and, 610, 613

State function, 17

constant-volume heat capacity as, 109, 113

enthalpy as, 103, 12526

entropy as, 153

heat capacity as, 109

internal energy as, 89, 96, 107

Statistical thermodynamics, 1113

Steady state

energy balance, 258

entropy balance, 260, 261

vs. equilibrium, 261

Steam

in Carnot cycle, 17576

Carnot cycle using, 17576

compression of, 29192

entropy of, 163

filling a tank with, 31718

fugacity of, 349

tables, 66375

tables, fugacity from, 347

venting, 322

Steam turbine, 28287

actual operation, 283

ideal and lost work in, 28687

Mollier graph used in, 28586, 285f

reversible operation, 283

steam tables used in, 28384

Stoichiometry, 59396

Storable energy, 89

Subscripts, 411

Successive interpolations, 42

Summary, 26

Surroundings, in system, 13

System, 1314

adiabatic, 13

classifying, 1314

closed, 13

composite, 13

diathermal, 13

equilibriumin, 1516

examples of, 14f

isolated, 13

open, 13

simple, 13

surroundings in, 13

universe in, 13

Tabulated properties

entropy calculated using, 162

fugacity calculated using, 34748

interpolations, 4043, 41f

Temperature

adiabatic flame, 6056

defined, 8

entropy and, 153

in heat transfer, 20f

Henry’s law and, 569

liquid miscibility and, 55658

measuring, 2324

in molecular collision, 78

upper consolute, 557

Temperature, effect on heat capacities, 11319, 113f

compressed liquid properties, 11719, 118f

constant-pressure cooling of liquid, 11517

heat capacity of steam, 11415

ideal-gas heat capacity, 114

liquid heat capacities, 114

Temperature-enthalpy chart, 24344, 244f

Ternary systems, 39093

Thermal equilibrium, 15

Thermal expansion coefficient using Soave-Redlich-Kwong, 2079

Thermodynamic analysis

of processes, 31415

of refrigeration, 3026

Thermodynamic charts, 24245

enthalpy-entropy (Mollier chart), 24445, 245f

pressure-enthalpy, 24243, 243f

temperature-enthalpy, 24344, 244f

Thermodynamic cycle, notion of, 169

Thermodynamic potential function, 195

Thermodynamic potentials, 19495, 195f

Thermodynamics

chemical, 35, 4f

definitions, 1317

development of, 1213

how and why in, 1213

introduction, 35

molecular basis of, 511

multicomponent mixture, state of, 18

problems, 2628

process and path, 1819, 18f

pure component, state of, 1718

quasi-static process, 1922, 20f

statistical vs. classical, 1113

summary, 26

units, 2225

Thermodynamics, calculus of, 20512

differential and integral forms of a function, 20912

thermal expansion coefficient using Soave-Redlich-Kwong, 2079

triple-product rule in ideal-gas state, 207

Thermodynamics of steady-state processes, 27294

adiabatic mixing, 27678, 277f

expansion and compression of liquids, 29294

flow through pipe, 27276

gas compression, 29092

heat exchanger, 27881, 279f

power generation, 295300

steam turbine, 28287

throttling, 28790

Thomson, William, 100, 178

Throttling, 28790

of compressed liquid, 28889, 290f

of ideal gas, 288

Time, 25t

Torr, 23

Triple-product rule in ideal-gas state, 207

Truncated virial equation, residual properties from, 22627

Turbines, gas/steam, 28287

Two-phase systems, pure fluid in, 33740

condensing a vapor-liquid mixture, 340

heat of vaporization using Soave-Redlich-Kwong, 338

vapor-liquid mixture calculated by Soave-Redlich-Kwong, 33940

Txy graph, 37073, 379f

of completely immiscible liquids, 55961, 559f

of ethanol/water at elevated temperatures, 384f

of heptane and decane, 370f

of partially miscible liquids, 385f, 55456, 554f, 557f

UNIFAC equation, 52531

detailed calculation using, 52830

Pxy graph for, 530f, 531f

terms calculated by, 52728

using, 530, 532

UNIQUAC equation, 52225

group contribution method in, 52324

Pxy graph calculated from, 52425, 526f

Units, 2225

constants, 22t

conversions, 25t

energy, 2425, 25t

mole, 24

pressure, 2223, 25t

temperature, 2324

Universal Functional Activity Coefficient (UNIFAC). See UNIFAC equation

Universe

entropy of, 168

in system, 13

Unsteady-state balances, 31523

filling a tank with ideal gas, 31818

filling a tank with steam, 31718

pressurizing a tank, 31519, 315f

venting a tank, 31923

venting ideal gas, 32223

venting steam, 322

Upper consolute temperature (UCT), 557

Vacuum, irreversible expansion against, 13637

Van der Waals equation

compressibility factor in, 5860

residual properties from, 232t

Van der Waals forces, 6

Van Laar equation, 519

Vaporization. See also Vapor-liquid mixture

enthalpy of, 47879

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, 45253

chemical equilibrium and, 62528

chemical potential, 341

Clausius-Clapeyron equation, 34143

elevated pressures and temperatures, 38384, 384f

at elevated pressures and temperatures, 38384, 384f

equations in, solving, 44950, 451f

in ideal solution, 46674 (See also Raoult’s law)

problems in, classification of, 44849

of pure fluid, 34043

Vapor-liquid equilibrium, theory of, 43559

chemical potential in, 43942

fugacity in, 44348

Gibbs free energy in, 43539

using equations of state, 44853

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

Vapor-liquid mixture

condensing, 340

Soave-Redlich-Kwong equation used to calculate, 33940

Vapor-liquid separator, 4f, 5

Variables

change of, in fundamental relationships, 217

derivatives and integrals with functions of multiple, 110

Venting, 321

ideal gas, 32223

steam, 322

a tank, 31923

Virial equation

Benedict-Webb-Rubin equation and, 68

calculated isotherms using, 57f

compressibility factor in, 53, 54, 56

molar volume calculated with, example of, 5556

residual properties of methane using, 22728

second virial coefficient, 5354, 55

summary, 78

truncated, 54, 22627

Volume, 25t

excess properties in, 49495, 495f

residual, 224

Volume of mixing, 40910

Von Guericke, Otto, 2728

Wilson equation, 51920

Work, 8889, 88f

adiabatic production of, 261, 262

heat and, shared characteristics with, 97

ideal, 18388

lost, in entropy, 18388, 191

maximum, in feasibility design, 18687

as path function, 1056

PV, 9096, 91f

separation of, ideal solution in, 464

shaft, 90, 91f

sign convention for, 89

value of heat, Carnot cycle and, 18283, 182f

x, y, z, convention for, 372

xy graph, 38183, 382f

ZP graph of pure fluids, 4345, 45f, 56

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