Index

Abbe number, 356, 368Aberrations, 366–368Absolute error, 1101Absolute humidity, 739Absolute maximum error, 1101Absolute maximum ratings, 1025Absolute mean value, 515Absolute motion, 6Absolute sensitivity, 403Absolute zero, 633–634, 702Absorptance, 764–765Absorption

photon, 879radiation, 764

Absorption coefficient, 401, 870Absorption cross-section, 925Absorption edges, 870Absorption law, 401Absorption lines, 151Absorption spectrum, 853–854Acceleration, 17–19

curvature of, 27–28determination of velocity from,

18–19of gravity (g), 53–54, 131of rockets, 79–80

Acceleration vector, 25–28Accelerators, 898–899Acceptor, 1014Accommodation, optical, 371

Accumulators, 559Accuracy of measurement, 1100Achromat, 390Achromatic prism, 390Acid constant, 747Acids, density of, table, 237Acoustic phonons, 993Acoustic radiation resistance, 315Acoustical-attenuation coefficients for

building materials, 412Acoustics

musical, 331–334physiological, 329–331symbols used in formulae on,

407–408tables on, 409–414

Action function, 89Action line, 98Action principle, 41Activators, 1063Active region, 1025Active two-terminal network, 501Activity, 748, 939, 958Activity concentrations, 748Actual value, 1100A.D., 9Adaptation, optical, 371Addition of vectors, 1117Addition theorem of velocities,

142–143

1131

1132 Index

Additive correction term for pressuremeasurement, 800–801

Addressing, 308Adhesion, 185Adiabatic compression, 704–705Adiabatic expansion, 704Adiabatic index, 690–691, 695–696Adiabatic-isobaric states, 649Adiabatic-isochoric states, 649Adiabatic process, 695Adiabats, 695Adjustable resistor, 436Adsorbed surfaces, work function for,

1084AE (astronomical unit), 134Aerodynamic tunnels, 206Aerodynamics, 186–210Aerostatics, 171–186Affine coordinate system, 4Age-related far-sightedness, 371Aggregation states, 717–718

conversions of, 718–719Aging objects, 1112Air

sound field quantities in, 410sound velocity in, 409

Air pressure, altitude and, 798Alcohols, density of, table, 237Alfven waves, 584Alkali antimonides, photo cathodes

of, 1085Alkali atoms, 854All-round effects, 989Allowed transitions, 945–946Alloys, 988–990

electricity in, tables, 598low-melting, melting points of,

785magnetic, table on, 614metallic, density of, table, 232–233table of, 1092

Almost-free electrons, 1007α-decay, 941–943α-particles, table of ranges of, 1088Alternating current, 427Alternating-current circuits, 502,

514–544basic components in, 529–533capacitor in, 531–532inductor in, 532–533Kirchhoff’s laws for, 528

ohmic resistor in, 530power in, 526–527

Alternating-current engineering, basicsof, 522–529

Alternating-current source, 502Alternating quantities, 514–516Altitude, air pressure and, 798Aluminum, electrons in,

mass-attenuation coefficient for,1088

Aluminum alloys, density of, table, 232AM (amplitude modulation), 308Aminoplasts, electric properties of, 604Ammeters, 509Amorphous solids, 967, 983Amount of substance, 551, 638, 639Ampere (unit), 427, 471Ampere/meter, 469Ampere/weber, 471Ampere’s law, 428, 472–474Ampere’s magnetic moment, 475Amplification factor of vacuum tubes,

570Amplifier stage, 1028Amplitude, 256Amplitude dependence, 211Amplitude modulation (AM), 308Analyzer, 391Anastigmat, 366Anergy, 683Aneroid barometer, 173Angle, 11–12

definition of, 11Angle units, 11Anglo-American units, table of, 1130Angular acceleration, 33–34Angular frequency, 515Angular momentum, 48–49, 116–117Angular momentum conservation,

927–928Angular momentum conservation law,

85Angular velocity, 32–33Anharmonicity, 212Anions, 421, 552Anisotropic solid, 967Anisotropy coefficients, table of, 618Anode, 552, 1016Anode current, 567Anode potential, 567Anomalous dispersion, 305, 389

Index 1133

Anomalous Zeeman effect, 875–876Anti-Stokes lines, 874Antiderivative function, 1122Antiferroelectric phase transitions,

Curie temperature of, 786Antiferromagnetic phase transitions,

Neel temperature of, 786Antiferromagnetism, 483–484,

1054–1055Antiferromagnets, properties of,

619–620Antimatter, 935Antinode of standing wave, 297Antiparticles, 902–903Antiprotons, 902Antireflection coatings, 383Antisymmetric wave function, 844Aperture aberration, 344, 366Aperture diaphragm, 365Aperture ratio, 374Aphelion, 132Apochromat, 390Apparent power, 527Apparent resistance, 523Appendix, 1095–1130Applied forces, 3Apse line, rotation of, 149Aqueous solutions, temperature

correction for, 803Arc discharge, 564Archimedes, principle of, 181Architectural statics, 97Area, 10Arithmetic mean, 1102Arithmetic mean value, 515Armature, 545Artificial exposure, 965Artificial radioactivity, 937Artificial satellites, 135Artificially produced elements, 878Aspiration hygrometers, 739Assignment, 5Asteroids, 135Astigmatism, 366, 371Astronomical telescope, 374–375Astronomical unit (AE), 134Asymmetric unit, 969Asymmetry defect, 366Asymptotic freedom, 888Asynchronous machine, 549–550Atmospheric excess pressure, 636

Atmospheric humidity, 739Atmospheric pressure, 172Atomic coordinates, 973Atomic mass unit, 637–638, 912Atomic nucleus, 907

basic quantities of, 910–912constituents of, 907–910shape of, 910

Atomic number, 851, 907Atomic physics, 851–881Atomic radii of elements, 1078–1082Atomic radius, 851Atoms, 851

in external fields, 874–877interaction of photons with, 879–881vector model of, 864

Attack, angle of, 197Attenuation law, 961Attraction pool, 220Attractors, 220Audible sound, 314Auditory canal, 329Auditory ossicles, 329Auger effect, 870Autoclave, 173Automatic gears, 110Avalanche breakdown, 1017Average error, 1101Average velocity, 754, 769Avogadro constant, 551, 637Avogadro number, 551, 637Axial vector, 33

Backward diode, 1022Balance scale, 38Balance spring, 8Balancing calculation, 1100, 1103Ballistic galvanometer, 272, 422Balloon, 182Balmer series, 857Band model, 1007–1011Band spectrum, 853Bang, 332Bar (unit), 635Barkhausen discontinuities, 1054Barkhausen effect, 1053Barkhausen equation, 570Barn (unit), 659Barometer, 175Barometric equation, 177Barometric formula, 664–665

1134 Index

Barometric measurementswith brass scale, 802with glass scale, 802

Bartlett force, 913Baryon charge, 893Baryon number, 893Baryons, 894Base, 968Base-centered lattice, 970Base constant, 747Base resistor, 1025Basic quantities, 1098

table on, 1125Basic units, 1098Basilar membrane, ear, 329Battery, leakage of, 558B.C., 9BCS theory, 1044Bearing forces, 127Bearing moment, 121Bearing reactions, 104–105Bearings, 104Beat period, 279–280Beats, 279Beaufort degrees, 205Becquerel, 939, 958Belt drives, 109Bending, 155

definition of, 160–161lens, 363of rods, 160–164

Bending moment, 161–162Bending stress, 164Bennett equation, 587Bent levers, 106–107Bernoulli mapping, 220Bernoulli’s equation, 192, 203Bernoulli’s law, 191–193β-decay, 943–946β-stability, 944

line of, 917Bethe-Bloch equation, 954–955Bethe-Weizsacker cycle, 151Bethe-Weizsacker formula, 916Bicycle, 127Bidirectional thyristor, 1034Bifurcation diagram, 224Bifurcations, 221–225Big bang, 150Billiards, 212Bimetal thermometer, 672

Bimetals, 987Binary iron alloys, ferromagnetic

properties of, 615–616Binary nickel alloys, ferromagnetic

properties of, 616–617Binding energy, 911

per nucleon, 912Binomial distribution, 1109Bio-acoustic transducer, 323Biological half-life, 963Biot-Savart’s law, 474–475Bipolar transistors, 1023–1025Black body, 402

radiation constant of, 764Black body radiator, 765Black hole, 149, 152Black radiator, 818Blasius formula, 208Bloch theorem, 1007Bloch walls, 481, 728Body, human, effect of electric current

on, 609Body-centered lattice, 970Body cone, 125Body-fixed coordinate system, 96Bohr frequency condition, 855Bohr magneton, 847, 1051Bohr orbital radius, 855Bohr radius, 855Bohrium, 878, 935Bohr’s correspondence principle, 843Bohr’s postulates, 855–859Boiling, 718, 736Boiling-point elevation, 737Boiling points, 718

of elements, 777–778of oils, 784of organic compounds, 782–784

Boiling-water reactors, 950Bolometer, 396Boltzmann constant, 661Boltzmann distribution, 575, 880Boltzmann factor, 656Bomb calorimeter, 678Bond relations in crystals, 976–979Bose-Einstein condensation, 890–891Bose-Einstein distribution, 890, 996Bose-Einstein statistics, 890Boson-exchange potential, 915Bosons, 890Bottom quark, 893

Index 1135

Boundary-value problem, 190Bourdon’s tube, 173Boyle-Mariotte law, 651, 692Brackett series, 857Bragg condition, 974–975Bragg grating, 353Bragg maximum, 954Bragg peak, 954Bragg’s reflection condition, 378, 1007Braking distance, 21Branch, 503Branch point, 503Branch-point rule, 503

in complex domain, 528Brass scale, barometric measurements

with, 802Braun’s tube, 571Bravais lattices, 970–973Break point, 168, 169Breakdown voltage, 1017Breeder reactors, 950Breeding of nuclear fuel, 950Breeding ratio, 950Breit-Wigner formula, 930Bremsstrahlung, 869–870, 953Brewster’s angle, 348, 392Bricks, building

density of, table, 236thermal transmittance of, 796

Bridge rectifier, 1019Bridge scale, 107Bridgeman method, 968Brillouin zone, first, 992Brinell hardness, 170–171British Thermal Unit (BTU), 676Bubble chamber, 899Buckling, 169–170Buckminster fullerene, 730Buckybabies, 730Buckygiants, 730Buckyonions, 730Buckytubes, 730Building bricks, see Bricks, buildingBuilding materials

acoustical-attenuation coefficientsfor, 412

density of, table, 236sound absorptance of, 414thermal properties of, 791–792thermal transmittance of, 795

Bulk, 1030

Bulk goods, density of, table, 237Bulk modulus, 160Buoyancy, 180–183

in flow around bodies, 196–197Buoyant force, 180–181, 196–197Burgers vector, 981–982

Calculation rules for phasor quantities,519–522

Calendar, 9Calendar week, 9Calibration points

of temperature, 630–631of temperature scales, 775–776

Calorie, 676Calorimeters, 678Camera, 369–370Camera obscura, 369Candela, 404Canonical ensemble, 624Canonically conjugate quantities, 89Cantor set, 225Capacitance, 457–460

of galvanic cell, 557of simple arrangements of

conductors, 459–460Capacitance diode, 1022Capacitor plates, electric voltage

between, 446Capacitor voltage, 512Capacitors, 457

in alternating-current circuits,531–532

charging of, 511–512discharging of, 512–513parallel connection of, 458–459resistors and

parallel connection of, 535series connection of, 534

series connection of, 459voltage at, 511

Capillarity, 185–186Capillary ascension, 185Capillary cells of Corti’s organ, 330Capture cross-section, 925Carbon, structures of, 729Carbon arc lamp, 564Carbon dioxide, table of

compressibility of, 247Carbon-nitrogen (CN) cycle, 151,

951–952

1136 Index

Carnot cycle, 702–706efficiency of, 705stages of, 703–705

Cartesian coordinate system, 4Cartesian representation of complex

numbers, 517–518Catacaustic, 344Catalyst, 647Catapult, 107Cathode, 552, 1016Cathode rays, 571Cations, 421, 552Cauchy, theorem of, 1104Cavity radiation, 818Cavity radiator, 818Cellulose derivates, electric properties

of, 604Celsius (unit), 630Celsius scale, 633Center

of gravity, 13, 82, 94–95of mass, 82, 94–95of pressure, 197of rotation, 100

Center-of-mass energy, 148Center-of-mass law, 84–85Center-of-mass rule, 95Center-of-mass system, 924Centered system, 338Central collision, 74Central forces, 47, 50Central motion, 50Central value, 1103Central value limit theorem, 1111Centrifugal force, 44, 60, 61Centrifugal potential, 859Centrifugal pump, 179Centripetal acceleration, 28, 60Centripetal force, 47, 60–61Ceramics

density of, table, 234elastic properties of, table, 242electricity for, tables, 602high-temperature, melting points of,

784–785Cerenkov counter, 899Cerenkov radiation, 302Chain reaction, 947Chain rule, 1122Change of entropy, 720Changes of state, 691–698

Channel radius, 923Channel rays, 571–572Channel spin, 923Chaos, routes to, 224Chaotic phase-space trajectory, 217Chaotic system, 221Characteristic acoustic impedance, 315Characteristic curves, 1018Characteristic temperatures, tables on,

775–786Charge carriers, mobility of, 433–434Charge conjugation, 902–903Charge conservation, 422, 901–902Charge independence of nuclear forces,

908Charge operator, 908Charge separation, 422

by electrostatic induction, 453Charged hollow cylinder, field strength

and potential of, 450Charged hollow sphere, field strength

and potential of, 449Charged particles in magnetic fields,

582Charging current, 512Charging of capacitors, 511–512Charging process, 559Charm quark, 893Chemical dehydration, efficiency of,

805Chemical equilibrium, 626Chemical potential, 677–678, 890Chemical reactions, 648, 742–748

phase rule for, 744χ2-distribution, 1110–1111Chladni’s acoustic figures, 320Cholesteric phase, 990Chromatic aberration, 341, 366Chromatic scale, 333Ciliary muscle, 370Circular double refraction, 393Circular motion, 31, 59

in plane, 24–25vibrations and, 262–263

Circular orbit velocity, 135Circular polarization, 294Circularly polarized light, 391Clamps, 105Class, 1107Class center, 1107Classical optics, 336

Index 1137

Claude process, 716Clausius-Clapeyron equation, 735–736Clausius-Rankine cycle, 709–710Clocks, 8Closed channel, 923Closed isochoric states, 649Closed polygon, 103Closed system, 13, 623–624, 641, 710Closed universe, 149Clouds, 740Cluster decay, 947CN (carbon-nitrogen) cycle, 151,

951–952CNO cycles, 951Coast line, 226Coaxial conductor, 491Cochlea, 329Coercitive field strength, 482Coercive field strength, 1053Coexistence region, 722–723Coherence, 294–295Coherence condition, 380–381Coherence lengths, 295, 1047

of light sources, 416Coherent waves, 294Cohesion, 183Coil current, 513–514Coil voltage, 513–514Coinciding states, law of, 669Cold conductor, 435Cold welding, 989Collective model, 920–922Collector, 545Collector resistor, 1025Colliders, 898Collision frequency, 658Collision geometry, 74Collision normal, 74Collision plane, 74Collision processes, 72–79

in gases, 658Collisions, 72Colloids, 199Color, quark, 893–894Color centers, 980Colors, 336, 390Coma, 366Combustion calorimeter, 678Combustion energy converted into heat,

681Comets, 135

Common base circuit, 1029Common collector circuit, 1028Common emitter circuit, 1026, 1028Commutating poles, 546Commutation relations, 845Commutator, 545, 834Compact packing of spheres, 971Compensation method, resistance

measurement by, 510–511Complex amplitude, 388Complex conductance, 524–526Complex conductance plane, 525–526Complex-conjugate phasor, 521Complex domain

branch-point rule in, 528mesh rule in, 528

Complex exponential function, 518Complex numbers, Cartesian

representation of, 517–518Complex power, 527–528Complex resistances, 522–524

parallel connection of, 529series connection of, 528–529of two-terminal networks, 533

Component representation, 1115Component tolerance, 1038Composition of forces, 45–46Compound materials, 987–988Compound motor, 547Compound-nuclear reactions, 929–931Compound semiconductors, 1011

thermal, magnetic and electricproperties of, 1093

Compound units, 1098Compressibility, 160, 176, 671, 723

of fluids under normal conditions,table on, 247

of solids at 0◦ C, table on, 247tables on, 244–247temperature dependence of, table on,

247Compression, 155Compression front, 311Compression modulus, 671Compression springs, 55Compressional work, 174, 676–677Compressor, 180Compton effect, 822, 957Compton mass-attenuation coefficient,

957Compton wavelength, 823

1138 Index

Computer-generated holograms,387–388

Concave mirror, 342–345Concentration, 732, 743Concentration differences, 768Concert pitch, 333Condensation, 719Condensation heat, 719Condensation nuclei, 740Condensation water, 739Condenser microphone, 322Conductance, 432Conducting elastomers, 987Conduction band, 1008Conductivity, 432–433Conductor loop, moving, in magnetic

field, 544–545Conductors, 1001

capacitance of simple arrangementsof, 459–460

inductances of geometricarrangements of, 490–491

Configuration mixing, 920Configuration space, 91, 214, 1002Confinement techniques, 590Confinement time, 589Connection-rod ratio, 110Connections between rigid bodies, 105Conservation laws, 903–904, see also

specific quantities beingconserved

in nuclear reactions, 926–928Conservative forces, 86Conservative systems, 212, 217–219Conserved quantity, 699Consonance, 332Constant current source, 1028Constant galvanic cells, 557Constant molar heat capacity, 691Constant rule, 1121, 1123Constants of motion, 219Constraint forces, 64Constraint reactions, 13, 47Construction materials

density of, table, 232–233sound velocity in, 412thermal properties of, 791–792

Constructive interference, 296, 382Contact materials

density of, table, 233table on, 607

Continuity equation, 188–190,766–767, 768–769

Continuous distributions, special,1110–1111

Continuous gears, 110Continuous measured quantities, 1097Continuous mechanical gears, 110Continuous spectrum, 853Continuous system, 213Continuum theories, 583Contraction, coefficient of, 195Control characteristic, 1025Control rods, 948Control voltage, 570Controlled chain reaction, 947Convection, 750Convergent rays, 338Converging lens, 362–363Conversion table of energy units,

1129Conversion temperatures of inorganic

compounds, 779–781Conversions of units, 1099Convex mirror, 345Coolants, 949Cooper pairs, 730, 1044Coordinate systems, 4–5, 96Coordinate transformation, 219Coordinates, 3Coordination number, 972Copper alloys, density of, table, 232Coriolis force, 60, 62–63Cork-screw rule, 465Cornea, 370Corona discharge, 564Corpuscular theory, 336Correction data, practical, tables on,

798–804Correction factors for pendulum period,

409Correction term, additive, for pressure

measurement, 800–801Correlation, 1105–1106Correlation coefficient, 1105Corresponding states, theorem of, 727Corti’s organ, capillary cells of, 330Cosmic radiation, 145, 964Cosmology, 137, 148–152Coulomb, 421Coulomb barrier, 932Coulomb energy, 917

Index 1139

Coulomb friction, 269Coulomb logarithm, 577Coulomb processes, 934Coulomb/square meter, 453Coulomb’s law, 423–424Coulomb’s magnetic moment, 475Counter-current principle, 716Coupled vibrations, 283–285Couples, 51, 101–102

torque of, 102Coupling coefficient, 285, 492Coupling constants, 888Coupling efficiency, 353–354Covalent bond, 978Covariance, 1105Crank mechanism, 110Creeping, 984Crest factor, 516Critical assembly, 947Critical current density, 1045Critical damping, 272Critical indices, 723Critical isotherm, 668, 723, 725Critical magnetic flux density, 1045Critical molar volume, 669Critical point, 669, 723, 725

gases at, table on, 787Critical pressure, 669Critical Reynolds number, 206–207Critical stresses, 168

table on, 240Critical temperature, 668, 725–726,

730Cross-product, 1118

two-fold, 1119Cross-section, 658–659, 925

for scattering of neutrons byelements, 1087

Crown glasses, 369Cryogenic fluids, viscosity of, table,

248Cryoscopic constant, 737

table on, 806Crystal axes, 969Crystal direction, 972Crystal lattice, 968

dipole field in, 1057Crystal structures, 969

change in, 729–730simple, 973

Crystal system, 970

Crystalline lens, 370Crystalline solid, 967Crystals, 967

bond relations in, 976–979optical properties of, 1060–1064structure of, 968–970

CsCl-structure, 973Cubic Bravais lattice, 970Cubic crystals

magnetic anisotropy of, 617magnetization in, 618

Cubic lattice types, 1057Cubic meter, 10Curie plot, 944–945Curie temperature, 727

of ferro- and antiferroelectric phasetransitions, 786

of ferromagnetic phase transitions,786

Curie-Weiss law, 482, 1053Curie’s law, 480, 1051Curl, 190Current, electric, see Electric current

entriesCurrent balance, 428Current conduction

in gases, 560–564in liquids, 551–560

Current connection, 510Current density, 188Current division rules, 505Current-gain characteristic, 1025Current limiter, 564Current measurement, 509Current reverser, 545Current-voltage characteristic, 432

of gaseous discharge, 564of gases, 562–563

Curvatureradius of, 27of space, 149of trajectory and acceleration, 27–28

Curved four-dimensional space-timecontinuum, 148

Cyclic coordinate, 91Cyclotron, 898Cyclotron frequency, 875Cylindrical capacitor, 459Cylindrical coordinate system, 5Cylindrical lens, 358Czochralski method, 968

1140 Index

d’Alembert’s principle, 44Dalton’s law, 732Dam, 195Damped electric oscillator circuit,

273–274Damped vibrations, 257, 268–274Damping coefficient, 270

for sound in gases, 410Damping constant, 270Damping factor

of parallel-resonant circuit, 541of series-resonant circuit, 539

Dark discharge, 561, 564Dark matter, 149–150Darlington transistor, 1029–1030Date, 9Daughter nuclides, 940dB (decibel), 317

loudness levels in, 413de Broglie wavelength, 826De-electrification field, 1056Dead time, 563Debye frequency, 314, 997Debye length, 579Debye model, 997–999Debye-Scherrer method, 975–976Debye temperature, 998Debye’s T3-law, 999Decay chains, 940–941Decay constant, 938Decay law, 938–941Deceleration, 17, 21–22Decibel, see dBDecimal prefixes, 1099, 1126Declination, 464Decomposition of forces, 46–48Deconfinement, 935Deep-inelastic reactions, 934Defect electrons, 1011Definite integral, 1123Deflection, 162Deflection angle, 355–356Deformable body, 14Deformation, work of, 68–69, 166–167Deformation speed, 986Deformed mean potential, 918Degeneracy, 831, 861Degenerated semiconductor, 1064Degree

of angles, 11of ionization, 573–574

of moisture, 739Degrees

of freedom, 7–8, 657number of, 657

as ratios, 317Dehydration, 738Dehydrators, 805Del operator, 189Delayed boiling, 727Delayed condensation, 727Delayed neutrons, 936, 948Delayed nucleon emission, 947Demodulation of waves, 308Density, 93–94

of gases, 787at critical point, 787

of inhomogeneous bodies, 38–39unit of, 38

Density difference, 723Density field, 186Density mean, 1108Density variation, flow with, 209–210Depletion layer, 1017Depletion mode, 1032Depletion-type FET, 1031Deposition of radiation, 764–766Derivative, 1121Derivatives of elementary functions,

1124Derived units, 1098Destructive interference, 296, 382Desublimation, 719, 740Detailed balance, principle of, 574Detectors, 899–900Deterministic chaos, 211, 221Deterministic system, 213Deuterium, 854Deuteron, 854Deuteron cycle, 951Dew-point, 739Dew-point hygrometers, 739Dewar flasks, 623DIAC (diode alternating current)

trigger diode, 1020Diamagnetic molar susceptibility,

1050Diamagnetic substances, 1049Diamagnetism, 480, 879, 1050Diamond, 729Diaphragm electricity, 560Diaphragm pump, 178

Index 1141

Diaphragms, 365lenses with, 365–366

Diatomic gases, 658Diatomic molecules, dissociation

energies of, 1078Diatomic particles, 657Diatonic tone scale, 332Dichroism, 394Dielectric losses, 1059Dielectric properties, 1055–1060Dielectrics, 456–457, 1009, 1055

tables on, 601–606Diesel cycle, 712–713Diesel engine, 713Difference amplifier, 1037Difference quotient, 1121Differential calculus, 1121–1122Differential cross-section, 925Differential gears, 110Differential quotient, 1121Differentiation of phasors, 521–522Differentiation rules, 1121–1122Differentiator, 1041Diffraction, 305–308

optical, 377–379Diffraction effects, 384Diffraction gratings, 384Diffractional disk, 378Diffractive optical elements, 384–388Diffuse rays, 338Diffuse scattering, 376Diffuser, 192Diffusion constant, 660, 768, 769Diffusion equation, 769

solution of, 769–770Diffusion pump, 179Diffusion voltage, 1016Dilatometer, 672Dimension(s)

onemotion in, 14–22simple motion in, 19–22

several, motion in, 22–31of spaces, 3–4three, trajectory in, 22of units, 1099

Dimensionless relative quantities,317

Diode alternating current (DIAC)trigger diode, 1020

Diodes, 1016

Diopters, 362Dipole, field strength and potential of,

449Dipole field, 1057Direct current, 427, 502Direct-current circuit, 502–514

energy in, 507Kirchhoff’s laws for, 503power in, 507resistors in, 503–505

Direct-current machine, 545–547Direct inelastic scattering, 932Direct reactions, 931–932Direct voltage, 502Direct-voltage source, 502Directional quantization, 832, 864Discharge, coefficient of, 195Discharge current, 512Discharging of capacitors, 512–513Discrete distributions, special, 1109Discrete measured quantities, 1097Discrete system, 213Dislocation, 981Dislocation density, 982Dislocation line, 981Dispersion, 199, 305, 389–390

of elastic waves, 992Dispersion hardening, 987Dispersion relations, 835Displacement, 258Displacement current, 497–498Displacement flux, 451Displacement polarization, 454, 1055Displacement work, 645Dissipated heat, 167Dissipation factor, 271Dissipative power, 508Dissipative systems, 212, 219–221Dissociation, 552Dissociation continuum, 873Dissociation energies of diatomic

molecules, 1078Dissolutions, surface tension of, table,

251Dissonance, 332Distinct visual range, 371Distortion factor, 516Distribution functions of plasmas,

574–576Divacancies, 979–980Divergent rays, 337

1142 Index

Diverging lens, 363Domains, 1060Donor, 1014Doping, 1036

in germanium, properties of, 1094of semiconductors, 1014–1016in silicon, properties of, 1094

Doppler effect, 15, 300–302Dosage measurements, methods of,

962–963Dose rate, 960Dosimetry, 958–965Double star, 151Doubly differential cross-section,

925Doubly-magic nuclei, 919Drag coefficient, 204–205Drag force, 197, 204Drag velocity, 581Drain, 1030Drift gain, 1028Drift motion in external electric

field, 582–583Drift velocity of ions, 553

in gases, 561Drive shaft, 108Droplet model, 916–917, 936Dry-cell battery, 557Dual-gate MOSFET, 1032Duffing oscillator, 216, 221Dulong-Petit law, 995–996Dulong-Petit rule, 691Duromers, 987Dutch telescope, 375–376Dynamic buoyant force, 196–197Dynamic pressure, 191Dynamic viscosity, 198, 660

of gases, tables on, 788–789of liquids, table on, 789

Dynamical equilibrium, 44Dynamical evolution, sensitive

dependence of, on initialconditions, 211, 220

Dynamical properties, tables on,243–251

Dynamical systems, 212–217Dynamics, 37–91

defined, 37fundamental law of, 41fundamental laws of, 37–53nonlinear, 211

relativistic, 145–148of rigid bodies, 111

Dynamometer, 55

Eardrum, 329Earth, 133

basic data for, 134Earth’s moon, 135Ebullioscopic constant, 737

table on, 806Eccles relation, 585Ecliptic, 132Eddy current, 487Eddy-current brake, 487Eddy-current losses, 488Eddy-current tachometer, 15Edge dislocation, 981Edge-tone generator, 320–321Educts, 742Effective-absorption coefficient, 580Effective concentrations, 748Effective mass, 1010–1011Effective potential, 860Effective power, 71, 508Effective sound pressure, 313Effective value, 515Efficiency

of Carnot cycle, 705of chemical dehydration, 805of energy conversion, 71–72, 675,

683of physical dehydration, 805

Effluent velocity, 193–195Eigenfunction, 830–831Eigenvalue, 830Einstein equation, 565–566Einstein model, 996–997Einstein sum convention, 122Elastic collision, 73Elastic constant, 991, 995Elastic deformation, 153, 156–167Elastic modulus, 156–157, 168Elastic non-central collision with body

at rest, 76–78Elastic off-center central collisions, 76Elastic properties, tables on, 239–242Elastic region, 168, 984Elastic scattering, 928–929Elastic scattering cross-section, 925Elastic straight-line central collisions,

74–75

Index 1143

Elastic waves, 991–995equation of motion for, 994

Elasticity, 54, 985theory of, 153–171

Elasticity modulus, 157, 995Elastomers, 986

density of, table, 235electric properties of, 605

Electrets, 1059–1060electric properties of, 605–606

Electric charge density, 424–426Electric charges, 421–424Electric circuit, 267–268, 501Electric conductance, 432

of electrolytes, 553–554of gases, 561

Electric conductor, 422, 440Electric current, 426–428, see also

Current entrieseffect of, on human body, 609switching on and off, in RL-circuit,

513–514Electric current density, 428–431Electric current flow field, 430–431Electric dipole, 442–443Electric displacement density, 1055Electric displacement in vacuum,

453–454Electric double layer, 555–556Electric energy converted into heat,

679–680Electric engineering

practical tables of, 606–609voltage ranges in, 608

Electric field, 439–440energy density of, 460–461energy of, 461external, drift motion in, 582–583at interfaces, 461–462

Electric field lines, 441–444Electric field strength, 440

of point charges, 444of various charge distributions,

448–451Electric flux, 451–452Electric line charge density, 425Electric machines, 544–550Electric materials, density of, table, 233Electric nonconductor, 422Electric permittivity of free space, 423Electric polarizability, 455, 877

Electric polarization, 454–457Electric potential, 447–454

of various charge distributions,448–451

Electric properties of insulatingmaterials, 604–605

Electric quadrupole moment, 921Electric quantities, analogy between

magnetic quantities and,495–496

Electric resistance, 431–432Electric space charge density, 424Electric surface charge density, 425Electric susceptibility, 456, 1055, 1058Electric tachometers, 15Electric voltage, 445–446, see also

Voltage entriesbetween capacitor plates, 446

Electric(al) conductivity, 1000of plasmas, 577–578

Electrical engineering, applications in,501–550

Electricity, 419–620applications of, 419symbols used in formulae on,

593–594tables on, 595–620

Electro-acoustic transducers, 321–324Electro-acoustic transmission factor,

322Electro-osmosis, 560Electrochemical electrode, 552Electrochemical equivalent, 555Electrochemical potential series,

556–557tables on, 598–600

Electrodes, 552Electrodynamic transducer, 323Electrodynamically driven emitter, 321Electrodynamics, energy law of,

499–500Electrokinetic effects, 560Electrokinetic potential, 557Electrolysis, 428, 551–560

defined, 554Electrolytes, 552–557

electric conductance of, 553–554ion motion in, 553

Electrolytic capacitor, 458Electrolytic polarization, 557–558Electromagnetic interaction, 885

1144 Index

Electromagnetic oscillations, 543Electromagnetic radiative losses, 543Electromagnetic waves, 290, 498–500

in plasmas, 585propagation and applications,

543–544subdivision of, 336

Electromagnetically driven emitter, 321Electromagnets, 463Electromotive force, 502, 556Electron capture, 869, 943Electron concentration, time variation

of, 1062Electron density, 862

in semiconductors, 1011–1012Electron diffraction, 826, 974Electron emission, 565–567

tables on, 1082–1086Electron exchange, 978Electron microscope, 826Electron number densities, 1003–1004Electron optics, 337Electron plasma waves, 583–584Electron shells, 862, 877Electron spin resonance, 876Electron states, filling of, 878Electron volt, 676, 825Electronegativity, 553Electronic band spectrum, 873Electronic heat conductivity in metals,

1000Electronic hygrometers, 739Electronic polarization, 1058Electronic work function, 565Electrons, 421, 851, 854

in aluminum, mass-attenuationcoefficient for, 1088

equation of motion of, 1010in magnetic fields, 874–875mobility of, 434in solids, 1000–1011stopping power for, 955

Electrophoresis, 560Electrostatic energy, 268Electrostatic induction, 422, 440–444

charge separation by, 453Electrostatic transducer, 323Electroweak interaction, 887–888Electroweak theory, 883Elemental semiconductors, 1093,

1011

Elementary cell, 969packing density of, 971–972

Elementary charge, 422Elementary functions

derivatives of, 1124integrals of, 1124

Elementary volume, 1003Elementary waves, 292Elements

atomic radii of, 1078–1082boiling points of, 777–778cross-section for scattering of

neutrons by, 1087ionic radii of, 1078–1082ionization energies of, 1071–1075magnetic susceptibility of, table on,

609–610melting points of, 777–778Periodic Table of, 877–879work function for, 1082–1083x-ray spectrum of, main lines of

characteristic, 1086Elliptic polarization, 294Elliptically polarized light, 391Emission bands, 151Emission coefficient, 580Emission spectrum, 852–853Emittance, 764Emitter follower, 1028Emitter resistor, 1025Empirical expectation value, 1102Empirical variance, 1105Endoergic reactions, 648Endothermal collision, 73Endothermal reactions, 924Endothermic reaction, 647Energy, 65–66, 119–121

in direct-current circuit, 507of electric field, 461equivalence of mass and, 147–148of magnetic field, 495of mass and spring system,

259–260of motion, 66zero of, 66

Energy band, 1008Energy change, 924Energy conservation, 66, 72Energy conservation law, 86, 120

in plastic deformations, 167Energy conversion, 679

Index 1145

Energy density, 396of electric field, 460–461of magnetic field, 494–495pressure and, 635of sound wave, 316

Energy difference, 66Energy dose, 958–959Energy eigenfunctions, 837Energy eigenvalues, 837Energy flux, 961Energy flux density, 961Energy forms, 675–679Energy function, 217Energy gaps, 1007, 1008Energy law of electrodynamics,

499–500Energy level(s), 851

of Mott-Wannier exciton, 1061Energy loss, 78Energy-momentum relation for

relativistic particles, 148Energy production with plasmas,

588–592Energy-range relation, 954Energy spectrum, 837Energy splitting in magnetic fields, 876Energy-transfer coefficient, 961Energy units, 675–676

conversion table of, 1129Enhancement mode, 1031Enhancement-type FET, 1031Enriched uranium, 949Enrichment mode, 1031Enthalpy, 644–647

of ideal gas, 646phase transitions and, 646

Entrance channel, 923Entrance pupil, 365Entropy, 640–641, 642

change of, 720of ideal gas, 643as thermodynamic potential, 642–643

Entropy jump, 720Environment, radionuclides in, 939–940Environmental radioactivity, 964–965Epitaxial HTSC films, 1048Equality of upper and lower boundary,

1123Equalization of temperature, 748–750Equation of motion

for elastic waves, 994

of electron, 1010Equation of state, 627, 661–673

of ideal gas, 652–653, 661–662for liquids, 671of real gas, 665–670for solids, 671

Equator, 135Equatorial moments of inertia, 113Equidirectional or equal-phase

vibration, 284–285Equilibrium, 625–627

for rotational motion, 117state variables and, 623–673

Equilibrium conditions of statics,103–104

Equilibrium constant, 746Equilibrium position, 255, 258Equilibrium state(s), 255, 625, 641,

649, 691, 697–698Equipartition law, 657–658Equipotential surfaces, 448Equivalent dose, 959Erg, 676Ergodicity, 220Ericsson cycle, 713–714Error estimation, 1097Error propagation, 1102Error theory, statistics and, 1100–1113Errors, types of, 1100–1102Escape velocity, 81, 134, 136Ether hypothesis, 139Ethylene derivates, electric properties

of, 604Euler equation, 190–191, 733Euler’s Formula (Buckling), 169Euler’s formula, 518Evaluation curve, 331Evaluation factor, 959Evaporation enthalpy, 646Evaporation heat, 718

temperature dependence of, 811Evaporation spectrum, 930–931Evaporative cooling, 891Event, 137Exchange calorimeter, 678Exchange force, 913Exchange integral, 1052Exchange interaction, 978Excited state, 851Excitons, 1061–1062Exergy, 683

1146 Index

Exit channel, 923Exit pupil, 365Exoergic reactions, 648Exothermal collision, 73Exothermal reactions, 924Exothermic reaction, 647Expectation value, 833, 1097Exponential distribution, 1110–1111Exponential representation, 518Exposure meter, 1063Extensive thermodynamic properties,

628Extensive variables, 641External ear, 329External fields, atoms in, 874–877External forces, 13, 83External parameter, 221External photo effect, 566Extrapolated range, 954Extrinsic conduction, 1014–1016Eye, 370–371Eye lens, 373

F-center, 980–981Face-centered compact packing of

spheres, 971Face-centered lattice, 970Factor rule, 1121Factors, 317Fahrenheit scale, 630Failure density, 1112Failure probability, 1112Failure rates, 1112, 1113Fall-out, 964Fall time, 29Far-sightedness, 371Farad, 457Faraday cage, 441Faraday constant, 554Faraday effect, 392Faraday’s first law, 554Faraday’s law of induction,

486–487Faraday’s laws, 554–555Faraday’s second law, 555Fast breeders, 950Fast-fission factor, 948Fast reactors, 949Feigenbaum constant, 225Feigenbaum law, 225Fermat’s principle, 337

Fermi-Dirac distribution, 575Fermi-Dirac distribution function,

1005–1006Fermi-Dirac statistics, 889Fermi distribution, 889Fermi energy, 915, 1002Fermi function, 945Fermi gas, 1001

characteristics of, 1002Fermi-gas model, 915Fermi level, 1002

of metals, 1005Fermi momentum, 915, 1002Fermi plot, 944–945Fermi sphere, 1002, 1003Fermi systems, state density in, 1005Fermi temperature, heat capacity and,

1006Fermi velocity, 1002Fermions, 843, 889–890Ferrimagnetism, 484, 1054–1055Ferrites, 484

density of, table, 234magnetic properties of, 619

Ferroelectric crystals, 1059Ferroelectric Curie temperature, 1059Ferroelectric phase transitions, Curie

temperature of, 786Ferroelectrics, 1059–1060

with oxygen octahedron structure,606

Ferromagnetic Curie temperature, 482Ferromagnetic elements, ferromagnetic

properties of, 615Ferromagnetic phase transitions, Curie

temperature of, 786Ferromagnetic properties, tables on,

614–618Ferromagnetism, 481–483, 1052–1054

Langevin equation of, 1052–1053Ferromagnets, 727, 1049, 1052FET (field effect transistor), 1030Fiber materials, table of elastic

properties of, 242Fiber-optical sensors, 352–353Fiber-reinforced compound materials,

988Fiber types for optical

telecommunication, 414Fibonacci sequence, 214Fick’s law, 768

Index 1147

Field curvature, 366–367Field diaphragm, 366Field effect transistor (FET),

1030Field emission, 566Field emission microscope, 566Field energy of coil, 495Field lens, 373Field lines, 441Field quanta, 887–889Field rheostat, 547Film dosimeters, 963Final temperature, 748Fine structure, 858Fine-structure constant, 859Finite elements, method of, 156First critical velocity, 135Fission, see also Nuclear fissionFission barrier, 936Fission isomerism, 936Fission neutrons, 935Fission probability, 948Fission products, 935Fissionable material, 949Fixed axis, 97Fixed point, 219

attractive, 223Fixed pulley, 108Fizeau fringes, 383Flavors, quark, 893Flint glasses, 369Flip-flop circuit, 1042Floating floor, 327Flow

around sphere, 202–203with density variation, 209–210

Flow bi-refringence, 393Flow field, 186–187Flow limit, 169Flow noise, 328Flow nozzle, 192Flow potential, 189Flow resistance, tables on, 250–251Fluid mechanics, 186Fluidity, 199Fluids

density of, tables, 237–238surface tension of, table, 251viscosity of, table, 248

Fluorescence, 1063Fluorescence radiation, 868

Fluorescent lamps, 563–564Fluorocarbones, electric properties of,

605Flux quantum, 1047Flux tubes, 1045FM (frequency modulation), 309Focal length, 342Focal ratio, 370Focal ray, 343Focus-image distance, 340Focus-object distance, 340Fog, 740Footstep sound, 327Forbidden transitions, 945–946Force, 41–43

electric test charge, 445impulse of, 42moment of, 101relativistic, 146

Force diagram, 45Force parallelogram, 45Force polygon, 45Force vectors, 98–100Forced damped vibration, 257Forced vibration, 257, 275–277Forces, 53–59

composition of, 45–46decomposition of, 46–48

Form factor, 516Formula symbols used in mechanics,

229Forward blocking region, 1033Forward breakover ignition, 1033Forward conduction region, 1033Forward direction, 1018Forward leakage current, 1033Four-layer diode, 1032Four-quadrant family of characteristics,

1024Fourier analysis, 282–283Fourier decomposition, 282Fourier optics, 388Fourier spectrum, 282Fourier synthesis, 282Fourier’s law, 766Fractal dimension, 225Fractals, 225–227Fractional change in thickness, 158Francis turbine, 180Franck-Hertz experiment, 856Fraunhofer diffraction, 377

1148 Index

Fraunhofer lines, 356table on, 417

Free axis, 97Free-electron gas, 1001–1006Free energy, 643–644Free enthalpy, 647–648Free fall, 28–29Free particles, 828Free-phonon gas, 999Free point mass, 13Free pulley, 108Free space

electric permittivity of, 423permeability of, 469–470permittivity of, 454

Free undamped vibrations, 257–268Free vector, 102Free vibrations, 257Free waves, 287Freedom, degrees of, 7–8Freezing mixtures, 714Freezing-point depression, 737Frenkel defect, 980Frenkel exciton, 1061–1062Frequency, 255, 335Frequency dependence, 764Frequency modulation (FM), 309Frequency range of hearing, 330Fresnel diffraction, 377Fresnel lens, 358Fresnel-zone lens, 385–386Fresnel-zone plate, 384–385Fresnel’s formulas, 347–348Friction, 269–273

coefficients of, tables on, 243–244oscillation equation with, 269for screws, 107

Frictional forces, 56–59Frictional work, 70Froude number, 207f t-value, 945–946Fuel cell, 558Fuel elements, 558–559Fuel pellet, 591Fullerene(s), 729, 730Fullerene-like structures, 730Fundamental functional principle,

544–545Fundamental law

of dynamics, 41of rotational dynamics, 52–53

Fundamental particles, 883Fundamental quantities, 1098Fundamental tone, 333Fundamental translation vector, 969,

1007Fundamental vibration, 284, 320Fusion, see also Nuclear fusion

with inertial confinement, 591–592with magnetic confinement, 590–591

Fusion reactions, 935Fusion reactor, 952

g (acceleration of gravity), 53–54, 131Galaxy, 151Galilean transformation, 137–138Galileo’s principle of inertia, 40Galileo’s telescope, 375–376Galton whistle, 314Galvanic cells, 557–559

parallel connection of, 559series connection of, 559

γ -decay, 946γ -radiation, 956–958Gap, 995Gas amplification, 962Gas constants, 661–662Gas discharge, 560Gas law, calculation of quantities from,

663–664Gas liquefaction, 714–716Gas mixtures, 663

heat conductivity of, 755Gas nebulae, 151Gas theory, principal equation of, 653Gas thermometer, 631Gas transmittance of quartz glasses, 608Gas turbine, 180, 713–714Gaseous discharge, current-voltage

characteristic of, 564Gases, 172, 718

collision processes in, 658at critical point, table on, 787current conduction in, 560–564current-voltage characteristic of,

562–563damping coefficient for sound in, 410density of, 787

table, 238drift velocity of ions in, 561dynamic viscosity of, tables on,

788–789

Index 1149

electric conductance of, 561ideal, see Ideal gasmolar mass of, 787pressure due to gravity in, 176–178real, see Real gassound velocity in, 409specific calorific values of, 809specific gas constant of, 787specific heat capacity of, 689tables of compressibility of, 245–247thermal properties of, 792velocity of sound in, 312viscosity of, table, 249

Gate, 1030Gate turn-off thyristor (GTO), 1034Gauge bosons, 887Gauge theory, 888Gauss’ distribution, 1110–1111Gauss’ law of error propagation, 1102Gauss’ minimum principle, 1106Gauss’ normal distribution, 1110–1111Gaussian optics, 340Gaussian pattern, 398Gay-Lussac, law of, 651–652, 694,

695Gear pump, 178Gearboxes, 109Gears, 108–109Geiger-Muller counter, 563, 963Geiger-Nutall relation, 941General gas constant, 661General theory of relativity, 137,

148–152Generalized coordinates, 86–87Generalized forces, 87Generalized momentum, 89Generalized Pauli principle, 908Generalized velocities, 87Generator, 544Geodesic pressure, 191Geomagnetic field, 464Geometric mean, 1104Geometric optics, 337–358Geometric similarity, 206Geometrical bodies, moments of inertia

of, 114–115Germanium, doping in, properties of,

1094Getter pump, 179Giant resonances, 931Gibbs-Duhem relation, 733

Gibbs phase rule, 734–735extended, 744

Gibbs potential, 647Ginsburg-Landau parameter, 1047Glan-Thompson prism, 395Glass(es), 967

density of, table, 234electricity for, tables, 603sound velocity in, 412

Glass constant volume thermometer,temperature correction for, 804

Glass scale, barometric measurementswith, 802

Glide plane, 981Global equilibrium, 625Glow cathode, 565Glow discharge, 563–564Glueballs, 888Gluons, 886, 888Glycerol, water dissolutions in,

viscosity of, table, 248Golden rule of mechanics, 106Gon (unit), 11Gradient, 189Gradient-B drift, 582Gradient-index fibers, 352Gradient-index lenses, 367–368Grain, 968Grain boundaries, 968, 982Grand canonical ensemble, 624Grand Unified Theory (GUT), 904Graphical data processing, 376Graphite, 729Grating constant, 307Grating spectroscope, 391Gravitation, 129–152

law of, 129–131Gravitational constant, 130Gravitational field, 129–136Gravitational field strength, 130Gravitational force

lifting against, 67–68properties of, 129–130

Gravitational interaction, 884–885Gravitational mass, 37, 54Gravitational pendulum, 263–265Gravitational potential, 130–131Graviton, 884, 887Gravity

acceleration of (g), 53–54, 131center of, 82, 94–95

1150 Index

Gravity (cont.)pressure due to

in gases, 176–178in liquids, 174–175

Gravity gyroscope, 125Gravity waves, 309Gray (unit), 959Grazing angle, 378Green functions, 388Gregorian calendar, 8, 9Grid transparency, 569Grid voltage, 568GRIN rod, 368Gross caloric value, 681Ground state, 851, 916, 1002Group velocity, 300, 994Growth velocity, 1104GTO (gate turn-off thyristor), 1034Guide values

table of, 797of voltages, 608

Guiding force, 47GUT (Grand Unified Theory), 904Gyration, 581Gyrocompass, 127–128Gyromagnetic factor, 848Gyroscope horizon, 128Gyroscope moments, 127Gyroscope pendulum, 128Gyroscopes, 121–128

applications of, 127–128

H , x-diagram, 741Hadron jets, 888Hadrons, 892, 894–898Hagen-Poiseuille law, 201Hail, 740Hair hygrometers, 739Half-life, 939Half-tones, 333Half-value depth, 961Half-width, 1110Hall coefficient, 1004

for metals, 1089–1090Hall effect, 465, 1003–1004

table for, 1089–1090Hall probes, 466Hall voltage, 465, 1004Halley’s comet, 135Halogen compounds, ionization

energies of, 1077

Hamiltonian, 89–90, 835, 874Hamilton’s equations, 89–90Hamilton’s principle, 89Hard-core potential, 914Hard magnets, 1053Hardness, 170–171Harmonic, of standing wave, 297Harmonic mean, 1104Harmonic oscillator, 841–843

two-dimensional, 281–282Harmonic sound pressure, 313Harmonic vibration, 255–256, 258,

333Hassium, 878, 935Health, noise injurious to, 413Hearing, 329–331

frequency range of, 330Hearing impressions, classification of,

332Hearing threshold, 315, 331Heat, 66, 678–679

conversion of, into other forms ofenergy, 683

conversion of equivalent energiesinto, 679–683

of dissolution, 714–715transport of, 766–770

Heat bath, 749Heat capacity, 678, 684–691, 995

Fermi temperature and, 1006Heat conduction, 750, 753–757,

999–1000in metals, 1000solution of equation of, 769–770at temperatures, 795of thermal insulators, 794through several walls with same

surface, 756Heat conduction equation, 767–768Heat conductivity, 659–660, 754, 766

of gas mixtures, 755in insulators, 999of plasmas, 578of solids, 793–794

Heat conductivity coefficient, 754Heat engine, 703Heat exchange, 748Heat flow, 751, 752

thermal resistance and, 760–761through single layer tube wall,

756–757

Index 1151

through tube wall consisting ofseveral layers, 757

Heat flow density, 766, 999–1000Heat flow density vector, 766Heat flux, 751Heat interchangers, 716Heat pump, 703, 707–708, 715Heat radiation, 750, 764Heat transfer, 750–766Heat transfer coefficient, 751, 761Heat transition, 751–753Heat transmission, 759–764

through encased tube, 762–764Heat transmission coefficients, 751

table of, 797Heat transport, 750Heating power boiler, 682Heavy-ion reactions, 932–935Heisenberg force, 913Heisenberg picture, 835Heisenberg’s uncertainty principle, 827Helium, table of compressibility of, 245Helium burning, 951Helium II, 731Helium-neon laser, 881Helmholtz condition, 190Helmholtz equation, 388Helmholtz potential, 643Henry (unit), 488, 491Henry-Dalton law, 738Hermitean matrices, 833Hermitean polynomials, 842Herpolhode, 125Hertz (unit), 255Hertz dipole, 542Hertz oscillator, 542Hess, theorem of, 647Heterogeneous mixture, 988Heterogeneous system, 624–625, 717,

734Heterogeneous total systems, 628Hexagonal Bravais lattice, 971Hexagonal compact packing of spheres,

971Hexagonal crystals, magnetic

anisotropy of, 617Higgs particle, 888High-spin states, 928High-temperature superconductor

(HTSC), 730, 1047–1049Hinges, 105

Holding current, 1033Holes, 1011Holograms, 386–387Homocentric rays, 338Homogeneity

of space, 900of time, 900

Homogeneous rod pendulum, 265Homogeneous system, 624, 717Hooke’s law, 54–55, 120, 156, 258, 984Hoppler’s sphere viscosimeter, 202Horns, 321Horsepower, 71Hot-air engine, 709Hot-wire amperemeter, 428HTSC (high-temperature

superconductor), 730,1047–1049

Hubble constant, 149Hubble effect, 149Huffman-Kraetschmer method, 729Human body, effect of electric current

on, 609Humid air, 738–742Humidification, 738Hund rules, 867Huygens’ principle, 292, 387Huygens’ telescope, 375–376Hydratization, 552Hydraulic press, 173Hydraulics, 110, 173–174Hydroacoustics, 329Hydrocarbon compounds, ionization

energies of, 1076Hydrodynamic paradox, 196Hydrodynamic similarity, 206Hydrodynamics, 171, 186–210Hydrogen, table of compressibility of,

245Hydrogen atom, 854–859

accidental degeneracy in, 857, 861Hydrogen burning, 951Hydrogen cycle, 951Hydrogen-like systems, 854Hydrogen spectrum, 856

degeneracy in, 857–858fine structure of, 858–859

Hydrostatic paradox, 175Hydrostatic pressure, 155Hydrostatics, 171–186Hygrometers, 739

1152 Index

Hypergeometric distribution, 1109Hypernuclei, 935Hyperons, 894–895Hypersound, 314, 328Hysteresis, 1053Hysteresis curve, 167, 481Hysteresis losses, 494

IC (integrated circuits), 1034–1037Ideal current source, 502Ideal flow, 187

basic equations of, 187–197Ideal gas, 187, 650–653

enthalpy of, 646entropy of, 643equation of state of, 652–653,

661–662internal energy in, 642kinetic theory of, 653–655specific heat capacity of, 689–690

Ideal liquid, 187Ideal operational amplifier, 1038Ideal plasma, 579Ideal transformer, 493Ideal voltage source, 501, 503IGBT (insulated-gate bipolar thyristor),

1034IGFET (insulated gate FET),

1031–1032Ignition voltage, 564Illuminances, 405

table on, 416Image distance, 340Image focal length, 339Image focus, 339Image point, 338Image principal point, 339Image-side focal length, 339Image size, 340Imaginary unit, 517Imaging equation, 340Impact parameter, 927Impact velocity, 29Impedance, 523Impedance converter, 1029, 1042Impulse

of force, 42of torque, 53

Impurity atoms, 1014Incidence, plane of, 304Inclination, 464

Inclined plane, 47–48Indefinite integral, 1123Indirectly driven pellet, 592Individual gas constant, 662, 690Induced emission, 879Induced voltage, 545Inductance(s), 488

of geometric arrangements ofconductors, 490–491

parallel connection of, 489series connection of, 489

Induction, 485–488Induction flux, 489Inductor(s)

in alternating-current circuits,532–533

resistors andparallel connection of, 536series connection of, 536–537

Inelastic collision, 73–74, 78–79Inelastic neutron scattering, 993Inelastic scattering cross-section, 925Inert-gas atoms, 878Inertia, 40

moments of, see Moments of inertiaproducts of, 122tensor of, 121–124

Inertial confinement, 590, 952fusion with, 591–592

Inertial forces, 43–44in rotating reference systems, 59–63

Inertial mass, 37Inertial system, 40, 137Infinitely extended plate, field strength

and potential of, 451Infinitely high potential well, 840Infinitely thin lens, 364Infrasound, 314Inhomogeneous bodies, density of,

38–39Initial conditions

sensitive dependence of dynamicalevolution on, 211, 220

sensitive dependence on, 220Initial magnetization curve, 1053Initial phase, 256Inorganic compounds

conversion temperatures of, 779–781magnetic susceptibility of, table on,

611–613Input characteristic, 1024

Index 1153

Input resistance, 1028Instantaneous acceleration, 17–18Instantaneous-rotation axis, 124Instantaneous value, 514Instantaneous velocity, 16–17, 23–24Instruments, tonal ranges of, 334Insulated-gate bipolar thyristor (IGBT),

1034Insulated gate FET (IGFET),

1031–1032Insulating materials

electric properties of, 604–605specific electric resistance of, 603

Insulator(s), 422, 999–1000, 1001,1009

heat conductivity in, 999Integrability, 218–219Integral calculus, 1122–1124Integral function, 1122Integrals

of elementary functions, 1124of motion, 219

Integrated circuits (IC), 1034–1037Integrated optics, 354Integration, 1122

of phasors, 522Integration constant, 1122Integration rules, 1123–1124Integrator, 1040–1041Intensity of waves, 296Intensive thermodynamic properties,

628Interaction region, 923Interactions

fundamental, 883–884unification of, 883–891

Intercalary day, 9Intercept distances, 340Interface tension, 625Interference

optical, 380–384wave, 294–300

Interference term, 296Interferometer, 9Interferometry, 383–384Intermediate processes, 932Intermetallic compounds, 988Internal ear, 329Internal energy, 174, 641, 699

of crystal, 996in Debye model, 998

in ideal gas, 642as potential, 641–642

Internal forces, 13, 82Internal friction, 197–199Internal photo effect, 566, 821Internal pressure, 666Internal resistance, 569Internal volume, 666International barometric equation, 178International Practical Temperature

Scale, 631International Standardization

Organization, see ISO entriesInternational Union of Pure and

Applied Physics (IUPAP), 1098Intersection distances, 358Interstitial atoms, 980Interval center, 1107Interval notations, table of, 332Interval rule, 1124Intrinsic charge-carrier density,

1012–1013Intrinsic conduction, 1011Inverse magnetostriction, 483Inverse reactions, 903Inverse vector, 1116Inversion, 33, 880

of phasor quantity, 521Inversion curve, 715Inversion rule, 1123Inversion temperature, 715Inverting amplifier, 1039Inverting input terminal, 1037Ion beams, 592Ion lifetime, 562Ion mobility, table on, 620Ion motion in electrolytes, 553Ion optics, 337Ion plasma waves, 584Ion sound velocity, 584Ionic bond, 977Ionic crystals, 995Ionic polarization, 1058Ionic radii of elements, 1078–1082Ionic valence, 552Ionization, 552, 953

degree of, 573–574Ionization chamber, 563, 899, 962Ionization energies, 851

of elements, 1071–1075of halogen compounds, 1077

1154 Index

Ionization energies (cont.)of hydrocarbon compounds, 1076of nitrogen compounds, 1076of oxygen compounds, 1077

Ionization losses, 953Ionization potentials, tables on,

1071–1078Ionization work, 851Ionizing particles, 953–956Ionizing radiation, effect of, on

semiconducting materials, 1094Ions, 552, 851

drift velocity of, 553IPTS-90 fixed points, 631Iris diaphragm, 370Iron alloys

binary, ferromagnetic properties of,615–616

density of, table, 233Irradiance, 399Irradiation, 399Irreversible process, 691, 750Irrotational flow, 190Isentropic index, 691Isentropic process, 695Isentrops, 695Islands of stability, 935ISO (International Standardization

Organization), 1098ISO standard atmosphere, 178Isobaric adiabatic system, 645Isobaric processes, 694Isobars, 694, 908Isochoric cooling, 709Isochoric heating, 709Isochoric processes, 694–695Isochors, 695Isoclines, 464Isogons, 464Isolated system, 623Isospin, 908Isotherm, 667Isothermal compression, 704, 709Isothermal expansion, 703, 709Isothermal-isobaric states, 649Isothermal-isochoric states, 649Isothermal processes, 644, 692–693Isotherms, 692Isotones, 908Isotope effect, 908, 1044–1045Isotopes, 907–908

Isotopic shift, 868Isotropic compression, 159–160Isotropic pressure, 155, 172Isotropic solid, 967Isotropy of space, 900IUPAP (International Union of Pure and

Applied Physics), 1098

Jar model, 1107, 1108, 1111Jet engine, 79, 180JET Tokamak, 591JFET (junction field effect transistor),

1030–1031jj-coupling, 866Joints, 105Josephson effect, 1045Joule, 64, 65, 675Joule cycle, 713Joule magnetostriction, 483Joule-Thomson coefficient, 715Joule-Thomson effect, 715–716Journal bearings, 105Julian calendar, 9Junction field effect transistor (JFET),

1030–1031Jupiter, 133

K-capture, 944K-meson, 894–895K-series, 869, 1086k-space, 1002k-value, 761Kaon, 894–895Kaplan turbine, 180Kelvin (unit), 6303–Kelvin-background radiation, 150Kelvin scale, 633Kepler’s laws, 131–132Kepler’s telescope, 374Kerma, 962Kerr cells, 395Kerr effect, 395Kilogram, 37

per cubic meter, 38times meters squared, 112

per second, 49, 116Kilogram meter per second, 39Kilopond, 636Kinematic quantities, basic, 96–97Kinematic viscosity, 199Kinematics, 93–97

Index 1155

Kinetic energy, 66–67, 119–120mean, 654relativistic, 147–148

Kinetic theory, 186, 213of ideal gas, 653–655

Kirchhoff’s first law, 430, 503Kirchhoff’s laws, 402, 765

for alternating-current circuits, 528for direct-current circuit, 503

Kirchhoff’s second law, 503Kirschmer-Prandtl-Karman formula,

208Koch curve, 226Koch’s snowflake, 226Kronig-Penny model, 1007Kundt’s tube, 298–299

Laboratory system, 148, 924Lagrange equations, 87Lagrange function, 87Lamb shift, 859Lambda transitions, 722Lambert law, 398Lambertian source, 398Laminar boundary layer, 206Laminar flow, 197–198

in tube, 200–202Landau damping, 585Lande factor, 849, 876Langevin equation, 582, 1051

of ferromagnetism, 1052–1053Langmuir frequency, 579–580Langmuir waves, 583–584Laplace operator, 189

angular component of, 830Laplace’s equation, 189Larmor frequency, 849Larmor precession, 849Laser beams, 591Laser diode, 1064Lasers, 380, 880

longitudinal vibrational modes of,1064

types of, 416Lateral magnification, 344Lattice constants, 969Lattice defects, 968, 979–983

one-dimensional, 981–982two-dimensional, 982–983

Lattice energy, 976Lattice impurities, 980

Lattice plane, 972Lattice types, 970Lattice vectors, 969Lattice vibrations, 991Laue method, 975Lawson criterion, 589–590, 953Layer-compound materials, 987LCD (liquid-crystal display), 392,

991LDR (light-dependent resistor), 436Le Chatelier, principle of, 648Lead-acid accumulator, 559Leakage of battery, 558Leakage rate, 948Least squares, principle of, 1106LED (light-emitting diode), 1023,

1063–1064Left-handed processes, 707–714Legendre transformation, 90Length, 9–10Length contraction, 144Lennard-Jones potential, 871, 979Lens eye, 370Lens systems, 364–368Lenses, 358–364

with diaphragms, 365–366Lenz’s law, 488Lepton charge, 892Lepton number, 892Leptons, 883, 891–892Level-measuring sensor, 352–353Level scheme, 852Levels, 317Lever arm, 100, 106Levers, 106–107Lifetime, 1111, 1112

of protons, 904Lifting against gravitational force,

67–68Light

main characteristics of, 335speed of, see Speed of lighttheoretical models of, 336

Light deflection, 149Light-dependent resistor (LDR), 436Light-emitting diode (LED), 1023,

1063–1064Light measurement, 403–405Light path, 337Light pressure, 823Light rays, 337

1156 Index

Light second, 141Light sources, coherence lengths of,

416Light wave guide, 349–355Light year, 134Limit cycle, 219Linde process, 716–716Line broadening, 853Line shape, 853Line spectrum, 853Linear accelerator, 898Linear-attenuation coefficient, 870,

958Linear collider, 899Linear double refraction, 393Linear energy-transfer coefficient, 961Linear energy-transfer power, 954Linear expansion coefficient, 672Linear extension, coefficient of, 157Linear force law, 258Linear oscillator, 542

resonance frequency of, 543Linear polarization, 294Linear region, 1038Linear regression, 1106Linear resistance, 432Linear Stark effect, 877Linear system, 213–214Linear variance, 1101Linearly polarized light, 391Liouville’s theorem, 218Liquid calorimeter, 678Liquid-crystal display (LCD), 392, 991Liquid crystals, 730, 990–991Liquid gears, 110Liquid layers, detachment of, 203Liquid low-temperature baths,

generation of, 804–805Liquid manometers, 636Liquid pendulum, 266–267Liquid plastics, 199Liquid state, metals in, density of, table,

238Liquid thermometer, 631Liquids, 172, 718

current conduction in, 551–560dynamic viscosity of, table on, 789equation of state for, 671pressure due to gravity in, 174–175sound-damping coefficients for, 411sound velocity in, 410

specific calorific values of, 809specific heat capacity of, 691tables of compressibility of, 247thermal properties of, 793velocity of sound in, 312volume expansion of, 795

Lissajous patterns, 280–281Ljapunov exponent, 220Load current, 544Load current definition, 502Load power, 508Loading speed, 986Local dose, 963Local field, 1056Local pressure, 637Local thermal equilibrium, 576, 625Localized levels, 1014Locus, 529Logarithmic decrement, 273Logarithmic derivative, 1122Logarithmic integration, 1124Logistic mapping, 222–224London penetration depth, 1046, 1047Longitudinal phonons, 993Longitudinal polarization, 294Longitudinal vibrational modes of

lasers, 1064Longitudinal wave, 293, 311Longitudinal Zeeman effect, 875Lorentz field, 1057Lorentz force, 466, 587

properties of, 467Lorentz transformation, 140–143Loschmidt number, 551Lost head, 203Loudness, 331Loudness levels, 330

in dB, 413Loudspeaker sensitivity, 322Loudspeakers, 321

range of, 323Lower heating value, 682LS-coupling, 865–866Lumen, 404Luminance, 404Luminescence, 1063Luminescence layer, 1063Luminophors, 1063Luminosity, 374, 899

relative, table on, 417Luminous dials, 1063

Index 1157

Luminous fluxes, 404table on, 417

Luminous intensity, 404Luneburg lens, 368Lux (unit), 405Lyman series, 857

Mach angle, 209, 302Mach cone, 209, 302Mach formula, 302Mach number, 302Mach shock waves, 302Mach wave, 302Machines, 106–110Macrocanonical ensemble, 624Macromolecular solids, 984–987Macrostate, 640Madelung constant, 977Magnetic alloys, table on, 614Magnetic anisotropy, tables on,

617–628Magnetic circuits, 471

calculation of, 472Magnetic conductance, 491Magnetic confinement, 590, 952

fusion with, 590–591Magnetic coupling, 492Magnetic dipole moment, 649Magnetic dipoles, 463Magnetic energy, 268Magnetic field(s), 462–463

charged particles in, 582electrons in, 874–875energy density of, 494–495energy of, 495energy splitting in, 876at interfaces, 484–485matter in, 478–484moving conductor loop in, 544–545plasmas in, 581–583of rectilinear conductor, 476of various current distributions,

477–478Magnetic field lines, 463–465Magnetic field strength, 469–470Magnetic flux, 467–469Magnetic flux density, 465–467Magnetic hysteresis, 1053–1054Magnetic induction, 465Magnetic materials, density of, table,

233

Magnetic moment, 847–849of neutrons, 910of nucleons, 909–910of protons, 910

Magnetic monopole, 905Magnetic phase transitions, 727–728Magnetic polarization, 479Magnetic potential difference, 470–471Magnetic pressure, 583Magnetic properties, 1049–1055

of ferrites, 619tables on, 609–614

Magnetic quantities, analogy betweenelectric quantities and, 495–496

Magnetic quantum number, 832, 861Magnetic reluctances, 471, 491

parallel connection of, 472series connection of, 472

Magnetic scattering, 974Magnetic self-compression, 586Magnetic spin moment, 847Magnetic susceptibility, 479, 1049

of elements, table on, 609–610of inorganic compounds, table on,

611–613Magnetism, 463, 1049Magnetization, 479, 1049

in cubic crystals, 618virgin curve of, 482

Magnetization curves, 480Magnetohydrodynamic waves, 584Magnetohydrodynamics, 583Magnetorotation, 392Magnetostatics, 462Magnetostriction, 483Magnetostriction emitter, 322Magnetostrictive transducer, 323Magnification, 344, 371Magnifying glass, 362, 372Magnus effect, 196Majorana force, 913Majorana neutrinos, 905Majority-charge carriers, 1015Man-made exposure, 965Mandelbrot set, 227Manometer, 173, 175Many-electron atoms, 864–868Mapping, 213Mars, 133Martensitic phase transition, 988Masers, 880

1158 Index

Mass, 37–39, 42center of, 82, 94–95equivalence of energy and, 147–148measurement of, 38relativistic increase of, 145–146on spring, 258–260transport of, 766–770

Mass action, law of, 574, 648, 744–746Mass-attenuation coefficient, 956

for electrons in aluminum, 1088for pair production, 957for photons, 957for x-rays, 1088

Mass current density, 188Mass defect, 911–912Mass-density distribution, 911Mass deposition, 555Mass distribution in fission, 937Mass energy, 147Mass fraction, 640, 732, 743Mass number, 907Mass percentage, 743Mass spectrometer, 38Mass stopping power, 956Mass transport, 555Massive neutrinos, 905Matching for power transfer, 508–509Material constants, 1100Material dispersion, 352Materials, mechanical properties of,

984–991Mathematical pendulum, 212, 260Matrix representation of operators, 833Matter

interaction of radiation with,953–958

tables on, 1088in magnetic fields, 478–484speed of light in, 499

Matter waves, 826Maximum bending stress, 162Maximum energy, principle of, 641Maximum load power, 508Maxwell-Boltzmann distribution,

655–656Maxwell construction, 668, 724–726Maxwell equations, 139, 496–500Maxwell model, 986Maxwell relations, 648–649Maxwellian velocity distribution, 575Maxwell’s fish eye, 368

McLeod pressure gauge, 634–635, 651Mean absolute deviation, 1105Mean acceleration, 17Mean charge density, 426Mean collision time, 658Mean error

of individual measurement, 1101of mean value, 1102

Mean fission-neutron number, 948Mean free path, 658, 754, 769

of phonons, 999Mean kinetic energy, 654Mean lifetime, 853, 939Mean line charge density, 426Mean nuclear potential, 917Mean range, 401, 953Mean relative molecular mass, 985Mean space charge density, 426Mean square deviation, 1104Mean surface charge density, 426Mean time between failures (MTBF),

1112Mean value(s), 515, 1100

mean error of, 1102of runs, 1102–1104

Mean velocity, 14–15, 23, 654, 656,754, 769

Mean-velocity vector, 655Measured quantity, 1097Measured result, 1100Measured value, 1100Measured variable, 1097Measurement(s), 1097

accuracy of, 1100description of, 1097–1100

Measurement error, 1100–1102Measures, 317Measuring equipment, 1097Measuring prescription, 1097Mechanical energy converted into heat,

680Mechanical equilibrium, 626Mechanical properties of materials,

984–991Mechanical sound emitters, 319–321Mechanical stress, 984Mechanical systems, 12–14Mechanics, 3–251

formula symbols used in, 229golden rule of, 106tables on, 231–251

Index 1159

Median, 1103Meissner effect, 1043Meissner-Ochsenfeld effect, 731,

1043Meitnerium, 879, 935Melt-spinning, 983Melting, 719

relative volume change in, 811Melting enthalpy, 646Melting heat, 719Melting point(s), 719

of elements, 777–778of high-temperature ceramics,

784–785of low-melting alloys, 785metals at, relative change at, 597of oils, 784of organic compounds, 782–784

Membranes as sources of sound, 320Memory alloy, 988Mercury (planet), 133Mercury barometer, 173Mercury barometer measurements,

temperature correction for,802

Mercury diffusion pump, 179Mercury gauge, 175Mercury-vapor blast pumps, 195Mercury-vapor lamp, 564Meridional section, 359Mesh, 503Mesh rule, 503

in complex domain, 528in magnetic circuit, 471

Meson exchange, 914Meson exchange potentials, 914–915Mesons, 894Metal-oxide-silicon (MOS) technology,

1031, 1037Metallic alloys, density of, table,

232–233Metallic bond, 977–978Metallic calorimeter, 678Metallic glasses, 983Metallic phase, 729Metals, 1009

electricity in, tables, 595–600electronic heat conductivity in, 1000Fermi level of, 1005Hall coefficient for, 1089–1090heat conduction in, 1000

in liquid state, density of, table, 238at melting point, relative change at,

597Peltier coefficient for, 600pure

specific evaporation enthalpy of,810–811

specific melting enthalpy of,810–811

thermal properties of, 789–791at room temperature, electricity in,

table, 595–596simple, density of, table, 231–232sound velocity in, 411

Meteorites, 135Meter, 9Meter/second, 311Methane, table of compressibility of,

246MHD generator, 588–589Michelson interferometer, 139,

383–384Michelson-Morley experiment, 139Microcanonical ensemble, 623Micromechanics, 555Microphone sensitivity, 324Microphones, 323–324Microscope, 372–373Microstate, 640Milky Way, 151Miller indices, 972Millikan’s oil-droplet experiment, 423Millimeters of water, 636Mineral-oil products, sound velocity in,

410Minimum action, principle of, 89Minimum energy, principle of, 641Minimum hearing threshold, 315Minimum surface, 184Minkowski diagram, 140, 141–142Minkowski space, 3Mirror effect, 582Mirror machine, 590Mirror symmetry of world, 900Mirror telescope, 375Mirrors, 341Mixed crystals, 988Mixing temperature of two systems,

748–749Mixture calorimeter, 678Modal value, 1108

1160 Index

Mode dispersion, 352Moderators, 948, 949Modulation of waves, 308–309Mohr’s balance, 38, 182Moist air, density of, 740–741Mol (unit), 638Molar fraction, 736Molar heat capacity, 686–687, 995Molar mass, 638–639

of gases, 787Molar quantity, 629Molar volume, 638Molarity, 743Mole, 551Mole fraction, 639–640, 663, 731Molecular field, 1052Molecular mass distribution, 985Molecular physics, 851–881Molecular pump, 179Molecular spectra, 871–874Molecules, interaction of photons with,

879–881Mollier diagram, 646, 741–742Moment, 50–52

of force, 101Momentary value, 514Moments of inertia, 111–115, 122,

657of point mass, 49principal, 123

Momentum, 39relativistic, 146

Momentum conservation, 72Momentum conservation law, 84–85Momentum operators, 874Momentum space, 1002Momentum sphere, 76Monatomic gases, 658Monatomic particles, 657Monochromator, 390Monoclinic Bravais lattice, 970Monocrystal, 967Monocrystal growing, 967–968Monomers, 984Moon, 135MOS (metal-oxide-silicon) technology,

1031, 1037Moseley’s law, 869MOSFET, 1031–1032Mossbauer effect, 946Most-probable velocity, 656

Motion, 3description of, 3–14energy of, 66equation(s) of, 60, 82–84of mass on spring, 259in one dimension, 14–22rotational, 31–35in several dimensions, 22–31simple, in one dimension, 19–22

Motional induction, 486Motor, 544Mott scattering, 928–929Mott-Wannier exciton, energy level of,

1061MTBF (mean time between failures),

1112Multi-hyperon matter, 935Multicomponent gases, 731–733Multifragmentation, 935Multiphase systems, 734–736Multiplet, 866Multiplication

by scalar, 1116of vectors, 1117–1119

Multiplication factor, 947Multiplicity, 866Multistage gears, 109–110Musical acoustics, 331–334Mutual inductance, 492–493Mutual induction, 492–494

n-conducting semiconductor, 1015n-doping, 1015Nabla operator, 189NaCl-structure, 973Nanocrystalline materials, 983Natural constants, 1100Natural exposure, 964Natural frequency, 257Natural line width, 853Natural materials, modified, electric

properties of, 605Natural radioactivity, 937Natural stones, density of, table, 236Natural vibrations, 298, 319Navier-Stokes equation, 200Near field, 373Near-field microscope, 373Near point, 371Near-sightedness, 371Nebula clusters, 151

Index 1161

Neel temperature, 484, 1054of antiferromagnetic phase

transitions, 786Neel’s law, 483Negative charges, 421Negative correlation, 1106Negative current feedback, 1028Negative feedback, 1027Negative-feedback operational

amplifier, 1038–1039Negative focal length, 342Negative temperature coefficient

(NTC), 435Negative voltage feedback, 1027Negatively uniaxial crystals, 394Nematic phases, 990Neptune, 133Nernst equation, 556–557Network elements, 501Network theory, 501Neutral axis, 161Neutrinos, 943Neutron balance, 948Neutron diffraction, 974Neutron number, 907Neutron scattering

kinematics of, 993methods of, 975–976

Neutron spectrum, 948–949Neutron star, 152Neutrons, 907

magnetic moment of, 910New degree, 11Newton (unit), 42Newton friction, 273Newton meter, 50, 675Newton per meter squared, 154Newtonian viscosity, 198Newtonmeter, 100Newton’s first law, 40Newton’s imaging equation, 361Newton’s law for materials, 984Newton’s laws, 40–48Newton’s rings, 383Newton’s second law, 41Newton’s third law, 43Nickel alloys

binary, ferromagnetic properties of,616–617

density of, table, 233Nicol prism, 395

Nikuradse formula, 208Nitrogen, table of compressibility of,

245Nitrogen compounds, ionization

energies of, 1076Nitrogen monoxide, table of

compressibility of, 246Nodding motion, 124Node of standing wave, 297Noether theorem, 900Noise, 332

injurious to health, 413Nominal power, 71Non-aging objects, 1111Non-central collision, 74Non-equilibrium states, 691Non-ideal plasma, 579Non-inverting input terminal, 1037Non-metals, density of, tables,

234–237Non-Newtonian materials, 199Non-self-sustained discharge, 560–563Non-SI units, 676

accepted, 1128–1129Non-uniform motion, 3Nondimensional units, 1099Nonlinear dynamics, 211Nonlinear resistance, 432Nonlinear system, 214Nonsaturated vapor, 719Norm pressure, 636Normal acceleration, 26, 47Normal dispersion, 305, 389Normal distribution, 1110–1111Normal force, 47Normal plane, 22–23Normal stress, 153, 155Normal surface, 288Normal to curve, 22Normal Zeeman effect, 875Normality, 744Normalization, 828

of wave function, 836–837Normalized rate distribution, 1107Novae, 151Nozzle device, 192–193npn-transistor, 1023NTC (negative temperature coefficient),

435Nuclear charge number, 851Nuclear decay, 937–947

1162 Index

Nuclear fission, 935–937, see alsoFission entries

Nuclear forcescharge independence of, 908saturation of, 912

Nuclear fusion, 950–953, see alsoFusion entries

nuclear reactions for, 589Nuclear-fusion process, 150Nuclear-fusion reactions, table of, 1087Nuclear-fusion reactors, 589–590Nuclear isomerism, 946Nuclear magnetic spin, 849Nuclear magneton, 909Nuclear matter, 915–916Nuclear models, 915–922Nuclear plates, 899Nuclear radius, 910Nuclear reactions, 922–937

conservation laws in, 926–928for nuclear fusion, 589tables on, 1087

Nuclear reactors, 947–950types of, 949–950

Nuclear resonance fluorescence, 946Nuclear spin resonance, 909Nuclear spin resonance technique, 910Nucleon configuration, 918–919Nucleon-nucleon interaction, 912–915Nucleon-number density, 910Nucleons, 907

binding energy per, 912emission of, 947fundamental properties of, 909magnetic moment of, 909–910

Numerical aperture, 350Numerical value, 1098Nutation, 124–125Nutation cone, 125Nutcracker, 107

Object distance, 340Object focal length, 339Object focus, 339Object point, 338Object principal point, 339Object-side focal length, 339Object size, 340Objective lens, 372Objective photometry, 396Observables, 829–830

Occupation inversion, 880Occupation number, 880, 1010Occupation number ratio, 880Octave, 333Ocular lens, 373Off-center collision, 74Ohm (unit), 431Ohm-meter, 433Ohmic components, thermal load of,

516Ohmic resistance, 431Ohmic resistor in alternating-current

circuits, 530Ohm’s law, 431

in complex domain, 524of thermodynamics, 758

Oil(s)boiling points of, 784density of, table, 237melting points of, 784sound velocity in, 410

One-pion-exchange potential (OPEP),914

One-way effects, 988Open channel, 923Open-circuit voltage, 502, 506Open system, 624, 711Open universe, 149OPEP (one-pion-exchange potential),

914Operating point, 1025Operation work, 711Operational amplifiers, 1037–1042Operators, matrix representation of, 833Opposite-directional or opposite-phase

vibration, 284–285Opposite forces, 99–100Opposite vector, 1116Optical activity, 392Optical axis, 338, 393Optical birefringence, 990Optical communication, 352Optical crystals, 393Optical density, 345Optical depth, 580Optical elements, 338Optical glass, 368Optical grating, 390Optical image, 338Optical imaging, 338–341Optical instruments, 368–376, 372–376

Index 1163

Optical model, 931Optical path differences, 352Optical path length, 337Optical phonons, 994Optical potential, 931Optical properties

of crystals, 1060–1064of solids, 1009

Optical resonators, 881Optical telecommunication, fiber types

for, 414Optical tube length, 373Optics, 335–408

subfields of, 336–337symbols used in formulae on,

407–408tables on, 414–417wave, 376–395

Opto-electronics, 1063Opto-electronic properties, 1063–1064Orbital, 878Orbital angular momentum, 48–49Orbital angular momentum quantum

number, 861Orbital velocity, 34–35Order-disorder phase transitions, 728Organic compounds

boiling points of, 782–784melting points of, 782–784

Orientation elasticity, 990Orientation polarizability, 1059Orientation polarization, 455, 1055Orientational order, 728Orthohelium, 867Orthorhombic Bravais lattice, 971Oscillation equation, 268

with friction, 269Oscillator, 255, 258Oscillator circuit, 267–268Oscillator parameter, 842Oscillator potential, 918Osculating plane, 22–23Otto cycle, 711–712Otto engine, 712Output characteristic, 1024Output resistance, 1028Oval window, ear, 329Overdamped case, 272Overexcitation, 549Overhead projector, 362Overtones, 320, 333

Oxidation, 1035Oxygen compounds, ionization

energies of, 1077Oxygen octahedron structure,

ferroelectrics with, 606Oxyhydrogen reaction, 647

p-conducting semiconductor, 1015p-doping, 1015p-wave scattering, 927Packing density, 971

of elementary cell, 971–972Pain threshold of hearing, 331Pair annihilation, 148, 902Pair production, 902, 957

mass-attenuation coefficient for, 957Pairing energy, 917Paper electrophoresis, 560Para-electric materials, 1059Parabola, 30Parabolic mirror, 342, 344Parabolic orbit velocity, 136Parabolic velocity, 134Parahelium, 867Parallax, 10, 134Parallax range finding, 134Parallel connection

of capacitors, 458–459of complex resistances, 529equivalence of series connection and,

541–542of galvanic cells, 559of inductances, 489of magnetic reluctances, 472of resistor and inductor, 536of resistors, 436–437, 504–505of resistors and capacitors, 535of springs, 55

Parallel forces, 99Parallel-plate capacitor, 442, 458Parallel ray, 338, 343Parallel resonance, 541Parallel-resonant circuit, 539–541Parallel shift, 102Parallelogram of forces, 98Paramagnetic electron resonance, 876Paramagnetic nuclear spin resonance,

909Paramagnetic substances, 1049Paramagnetism, 480, 879, 1050Paramagnets, 727

1164 Index

Paraxial approximation, 388Paraxial region, 340Parent nuclides, 940Parity, 831, 861Parity conservation, 900Parity operator, 901Parity violation, 901Parsec, 134Partial decay constant, 939Partial integration, 1124Partial pressure, 732Particle-compound materials, 987Particle flux, 960Particle flux density, 960

vector of, 768Particle-hole excitation, 920Particle number, 637Particles

fundamental, 883wave character of, 825–827

Partly inelastic collisions, 78Pascal (unit), 172, 635Pascal second, 198Paschen series, 857Passive two-terminal network, 501Path, 6Path difference, 295, 381Pathlines, 187Pauli principle, 843–844, 864, 877

generalized, 908Pauli spin matrices, 845–846Peak value, 515Peltier coefficient for metals, 600Pendulum, 8, 128, 216–217

gravitational, 263–265homogeneous rod, 265liquid, 266–267mathematical, 212, 260physical, 263–265standard, 260–263

Pendulum period, correction factors for,409

Penetrability of potential wall, 943Penning tubes, 636Percentage error, 1101Percentile, 1103Perception of sound, 330–331Perfect wetting, 185Perihelion, 132Period, 33, 255Period doubling, 223

Periodic functions, time average of,515–516

Periodic phase-space trajectory, 217Periodic processes, 255Periodic Table of elements, 877–879Permanent magnets, 463Permeability, 479

of free space, 469–470Permittivity of free space, 454Perpetuum mobile

of first kind, 700of second kind, 702

Personal dosimetry, 962Perturbation, 258Pfund series, 857pH-value, 746Phase(s), 256, 624–625, 717, 734

of wave, 288Phase angle, 256, 523Phase angle control, 1033Phase boundary, 717, 734Phase-coexistence region, 668, 722–723Phase constant, 256Phase difference, 295Phase equilibrium, 724, 734Phase interface, 625Phase modulation, 309Phase rule for chemical reactions, 744Phase shift, 276Phase-shift analysis, 912–913Phase space, 91, 215Phase-space projection, 216Phase transitions, 717

enthalpy and, 646examples of, 727–731first-order, 720–721order of, 720–723second-order, 721Van der Waals gas and, 724–727

Phase velocity, 289Phasor, 517Phasor addition, 519Phasor diagram, 518

representation of sinusoidalquantities in, 517–519

Phasor division, 520Phasor multiplication, 520Phasor quantities, calculation rules for,

519–522Phasor subtraction, 520Phenoplasts, electric properties of, 604

Index 1165

Phon (unit), 330Phonon spectrum, 993Phonon velocity, 994–995Phonons, 843, 992–994

specific heat capacity and, 995–996Phosphorescence, 1063Photo cathodes of alkali antimonides,

1085Photo diode, 396, 1020–1021Photo emission, 565–566Photo emulsion, 396Photo multiplier, 567Photoconductivity, 1062–1063Photocurrent, 820Photoeffect, 820Photoelasticity, 395Photoelectric cell, 566Photoelectric current, 820Photoelectric effect, 820–821, 957Photoelectric Einstein equation, 820Photoelectrons, 820Photolithography, 1035Photometric inverse-square law, 399Photometric limiting distance, 397Photometric quantities, 396–402Photometry, 395–405Photon energy, 817Photon momentum, 817, 825Photons, 817, 885, 887

energy of, 855interaction of, with atoms and

molecules, 879–881mass-attenuation coefficient for, 957

Photoresistor, 436Photovoltaic cell, 566Physical dehydration, efficiency of,

805Physical pendulum, 263–265Physical quantity, 1097Physiological acoustics, 329–331Pick-up reaction, 932Piecewise constant potential, 837–841Piezoelectric crystals, 321Piezoelectric elements, 173Piezoelectric sound emitter, 321Piezoelectric transducer, 323Piezoelectricity, 1060Piezoresistive transducer, 323PIN diode, 1021Pinch effect, 586–588Pinhole camera, 369

Pinning, 1045Pinning centers, 1046Piston manometer, 636Piston pressure, 173–174Piston pump, 178Pitch, 333

lens, 368Pitot tube, 192Planck mass, 905Planck’s quantum hypothesis, 825Planck’s quantum of action, 817Planck’s radiation law, 402, 575, 764,

818–819Plane, circular motion in, 24–25Plane area moment of inertia, 161–162Plane mirror, 342Plane parallel glasses, refraction by,

356–357Plane system of forces, 98Plane truss, 105Plane wave, 290–291Planet rotation, 135Planetary gears, 110Planetary motion, 131–132Planetary system, 133–136Planets, 133

forces between, 211Plasma-acoustic waves in plasmas,

583–584Plasma dynamics, 583Plasma oscillation frequency, 579–580Plasma oven, 586Plasma parameters, 573–580Plasma physics, 573–594

symbols used in formulae on,593–594

Plasma radiation, 580Plasma waves, 583–585Plasmas, 573, 718

distribution functions of, 574–576electric conductivity of, 577–578electromagnetic waves in, 585energy content of, 576–577energy production with, 588–592generation of, 586–588

by compression, 586–588heat conductivity of, 578in magnetic fields, 581–583plasma-acoustic waves in, 583–584properties of, 573–585thermal generation of, 586

1166 Index

Plastic deformation(s), 153, 167–171energy conservation law in, 167

Plastic-elastic region, 168Plastic materials, thermal properties of,

793Plastic region, 168Plasticity, 982, 985Plate resistance, 567Platinum resistance thermometer, 632Pliers, 107Plumbline, 128Pluto, 133Pneumatics, 174pnp-transistor, 1023Pockels effect, 395pOH-value, 747Poincare cut, 216Poincare mapping, 217Point charge(s), 441

electric field strength of, 444field strength and potential of, 448

Point defects, 979–981Point dipole, 1057Point lattice, 968Point mass(es), 12–13, 37

moment of inertia of, 49system of, 82–86

Point of application, 98Poisson coefficient, 158Poisson distribution, 1109, 1111Poisson’s equation, 189, 448Polar coordinate system, 4Polar moments of inertia, 113Polar vector, 33Polarizability, 1056Polarization, 293–294, 391–395, 422,

441, 1055Polarization angle, 392Polarization direction, 391Polarization vector, 455Polarizer, 391–392Polhode, 125Polyatomic molecules, 657, 658Polycarbonate, electric properties of,

604Polycrystalline solids, 968Polygon of forces, 99Polymerization, 985Polymers, 967, 984–986

electric properties of, 603Polytropic index, 697

Polytropic processes, 696–697Population inversion, 1064Porro prism, 349, 375Position energy, 68Position function, 6Position space, 1002Position-time graph, 14Position vector, 6, 22Positional order, 728Positive acceleration, 17Positive charges, 421Positive correlation, 1106Positive-feedback operational amplifier,

1042Positive temperature coefficient (PTC),

435Positively uniaxial crystals, 394Positron annihilation spectroscopy, 980Positron-emission tomography, 871Positrons, 421, 892Potential, internal energy as, 641–642Potential difference, 447Potential energy, 67–70

electron, 859torsional, 120–121

Potential equation, 448Potential jump, 556Potential wall, penetrability of, 943Potential well, 839–840Potentiometer, 436Potentiometer circuit, 437Power, 70–72, 118

in alternating-current circuits,526–527

in direct-current circuit, 507Power balance, 508Power density, 589Power factor, 527, 528Power measurement, 509–510Power rule, 1121, 1123Power transfer, matching for, 508–509Poynting vector, 500Practical correction data, tables on,

798–804Prandtl’s impact tube, 192Precession, 125–127Precession rate, 126Prefixes, 1099Pressure, 172–180, 634–637

center of, 197decrease of, 202

Index 1167

due to gravity in gases, 176–178due to gravity in liquids, 174–175energy density and, 635of gases at critical point, 787microscopic interpretation of, 653at triple point, 788

Pressure balance, 636Pressure dependence, electricity with,

table, 596–597Pressure drag, 204Pressure energy, 191Pressure field, 186Pressure gauges, 636–637Pressure lever, 107Pressure measurement(s)

additive correction term for, 800–801tables on, 798–802

Pressure pumps, 180Pressure valve, 178Pressurized-water reactors, 949Primary cells, 557Primary kilogram, 37Primary list of data, 1100, 1106, 1107Primary radiation, 868Primitive elementary cell, 969–970Primitive lattice, 970Principal axes, 123Principal dispersion, 369Principal moments of inertia, 123Principal planes, 339Principal points, 339Principal quantum numbers, 856, 861Principal refractive index, 369Prism, 355

refraction by, 355–356Prism spectroscope, 390Probability density, 828, 1109Product rule, 1122Products, 742

of inertia, 122Projectile motion, 28–31Prompt neutrons, 936Propagation vector, 288Propagation velocity, 335Propeller noise, 321Proportional chamber, 900Proportional counter, 962Proportional range, 563Proteins, electric properties of, 605Proton number, 907Protons, 421, 854, 907

lifetime of, 904magnetic moment of, 910

Pseudoscalar mesons, 895Psychrometry, 739

table on, 806PTC (positive temperature coefficient),

435Pulleys, 108–110Pulsar, 152Pulse modulation, 309Pumping capacity, 179Pumping flow, 179Pumping height, 179Pumps, 178–180Pupil, 370Pyrometer, 632

Q-machine, 586Q-value, 924Quadratic mean, 1103Quadratic Stark effect, 877Quadrupole moment, 444Quality

of parallel-resonant circuit, 541of series-resonant circuit, 539

Quality factor, 271, 959Quanta, 825Quantile, 1103Quantities, SI units and, 1097–1100Quantization axis, 864Quantization of orbits, postulate of, 855Quantum chromodynamics, 883, 888Quantum generators, 880Quantum Hall effect, 1004Quantum-mechanical rotator, 872Quantum mechanics, 825

basic assumptions of, 825–826Quantum numbers, 918Quantum optics, 337Quantum physics, 815–1094

formula symbols used in, 1065–1069tables on, 1071–1094

Quark confinement, 889Quark-gluon plasma, 935Quarkonium, 896Quarks, 883, 892–894Quartz glasses, gas transmittance of,

608Quasi-elastic reactions, 934Quasi-momentum, 993Quasi-neutrality, 573

1168 Index

Quasi-periodic motion, 218Quasi-periodic phase-space trajectory,

217Quasi-reversible process, 692Quotient rule, 1122

Rabi experiment, 845Radar, 10Radar speed measurement, 302Radial momentum, 48Radial quantum number, 860Radian, 11

per second, 32per square second, 34

Radiant energy, 396Radiant flux, 396–397Radiant intensity, 397Radiant power, 396–397Radiation

deposition of, 764–766interaction of, with matter,

953–958tables on, 1088

Radiation constant of black body, 764Radiation losses, 953Radiation pattern, 398Radiation pressure, 823Radiation source, 398–399Radio, stereo, 324Radio waves, 542–544Radioactive decay, 937–938Radioactive equilibrium, 940Radioactive isotopes, 937Radioactivity, 937

environmental, 964–965Radionuclides, 937

in environment, 939–940Radiosity approach, 376Radiotoxicity, 963Radius of curvature, 27Rainbow, 348Raman spectra, 873–874Random errors, 1100Random surfaces, 625Rankine scale, 630Raoult’s law, 736Rarefaction front, 311Rate, 1107

of increase, 1104Rate distributions, 1106–1111Rate gyroscope, 128

Rate histogram, 1107Rate table, 1107Ray optics, 337Ray tracing, 377Rayleigh criterion, 379Rayleigh-Jeans law, 819Rayleigh lines, 874Rayleigh scattering, 376Reactance, 523Reaction channel, 923Reaction characteristic, 1025Reaction cross-section, 925Reaction enthalpy, 646–647Reaction equation, 742Reaction force, 13, 47Reaction heat conduction, 578Reaction mass, 79Reaction principle, 43Reactive impedance, 523Reactive power, 527Reactive power factor, 527Reactivity excess, 948Reader’s lens, 372Real gas

equation of state of, 665–670virial expansion of, 665

Real image, 338Real power, 527Real voltage source, 505–506Reaumur scale, 630Recoil, 80Recoil principle, 79Recombination, 562, 1061Recombination coefficient, 562Recombination range, 562Rectified alternating voltage, 502Rectified value, 515Rectifier diode, 1019Rectilinear conductor, magnetic field

of, 476Red giant star, 151Red limit, 821Red shift of star light, 149Reduced heat, 705–706Reduced variable, 669, 727Reference frames, 924Reference-sound intensity, 318, 330Reference-sound power, 318Reference-sound pressure, 315, 318Reference system, 5–6Reference visual range, 371

Index 1169

Reflectance, 765Reflection

optical, 341–345total, 349

radiation, 764wave, 304–305

Reflection coefficient, 838Reflection grating, 391Reflection law

collision, 77–78optical, 341wave, 304

Reflection polarizers, 392Refracting edge, 355Refraction

double, 393optical, 345–348, 379–380by plane parallel glasses, 356–357by prism, 355–356by spherical surfaces, 357–358wave, 302–303

Refraction lawoptical, 346–347wave, 303

Refractive index gradients, 367Refractive indices, 345–346

table on, 415Refractive optical elements, 384Refractive power, 361Refrigerating machine, 708Refrigerator, 703Regenerators, 709Regression, 1100, 1106Regression analysis, 1106Relative aperture, 370Relative atmospheric humidity, 739Relative biological efficiency, 962Relative error, 1101Relative humidity, table on, 806Relative maximum error, 1101Relative moisture, 739Relative permeability, 478Relative permittivity, 456, 1058

table on, 601–602Relative rate, 1107Relative rate distribution, 1106, 1107Relative refractive index, 347Relative roughness, 208Relative sensitivity, 403Relative variance measure, 1105Relative velocity, 301

Relative volume change in melting,811

Relativistic dynamics, 145–148Relativistic effects, 137, 144–145Relativistic factor, 141Relativistic force, 146Relativistic heavy-ion collisions, 935Relativistic increase of mass, 145–146Relativistic kinetic energy, 147–148Relativistic momentum, 146Relativistic particles, energy-

momentum relation for, 148Relativistic work, 147Relativity

general theory of, 137, 148–152principle of, 137–139of simultaneity, 142special theory of, 137–148

Relaxation, 986Reliability, 1111–1113Remanence, 482, 1053Remanence flux density, 482Repulsive interaction, 977Residual compression, 167Residual current, 568Residual magnetism, 1053Residual strain, 167Resistance, temperature dependence of,

434–435Resistance alloys

density of, table, 233table on, 606

Resistance coefficient, table on,250–251

Resistance load line, 1025Resistance measurement by

compensation method, 510–511Resistance phasor, 523–524Resistance plane, 523–524Resistance thermometer, 632Resistive moment, 162Resistivity, 432–433Resistors

and capacitorsparallel connection of, 535series connection of, 534

connection of, 436–437in direct-current circuit, 503–505and inductors

parallel connection of, 536series connection of, 536–537

1170 Index

Resistors (cont.)parallel connection of, 436–437,

504–505series connection of, 436, 504

Resolving power, 379Resonance amplitude, 276Resonance catastrophe, 277Resonance-escape probability, 948Resonance factor, 948Resonance frequency, 276, 539, 541

of linear oscillator, 543Resonance matter, 935Resonance selectivity, 277Resonance spectroscopy, 854Resonances, broad spectrum of, 211Resonator, 257Resonator mirrors, 1064Rest energy, 147Rest friction, 56Restoring force, 68, 258, 261Resulting force, 45, 98Resulting spring constant, 55Retina, 370Reverberation, 327–328Reverberation time, 327–328Reverse blocking current, 1033Reverse blocking region, 1033Reverse breakdown voltage, 1033Reverse current, 1018Reverse direction, 1018Reverse recovery time, 1018Reverse voltage, 1016Reversible process, 692, 750Revolutions per second, 33Revolving-field machines, 545Reynolds number, 203–204, 206Rhodium/platinum thermocouple, 632Rhombohedral Bravais lattice, 971Richardson constant, 565Richardson equation, 565Richmann’s mixing rule, 748Right-hand rule, 33, 465Right-handed processes, 706Right-handed system, 4, 1119Rigid bodies, 13, 37, 93–128

connections between, 105dynamics of, 111general motion of, 97motion of, 14

Rigid connections, 105Rigid rotator, 872

Rim angle, 185Ring conductors, 490Rings of Saturn, 135RL-circuit, switching current on and off

in, 513–514Rocket equation, 81–82Rocket thrust, 79–81Rockets, 79–82

acceleration of, 79–80Rockwell hardness, 171Rod lenses, 368Rogowski coil, 471Roller bearings, 104Rolling friction, 57–58, 269

coefficients of, table on, 243Room temperature, 739

metals at, electricity in, table,595–596

Root-mean-square deviation, 1105Root-mean-square value, 515Root-mean-square velocity, 654–655Rope friction, 58–59Rotary pump, 179Rotary vibration, 265Rotating-coil instrument, 428Rotating-crystal method, 975–976Rotating-field speed, 550Rotating reference systems, inertial

forces in, 59–63Rotation, 14, 31, 97

of apse line, 149center of, 100

Rotation energy, 120Rotational dynamics, fundamental law

of, 52–53Rotational excitations, 921–922Rotational frequency, 32Rotational motion, 31–35, 100, 111

comparison of translational and, 53equilibrium for, 117

Rotational spectra, 872–873Rotational-vibrational band, 873Rotor, 545Roughness, 208Round window, ear, 329Rule of levers, 38Run(s), 1100

mean values of, 1102–1104Rupture stress, 169Rutherford scattering, 911, 928Rutherford scattering formula, 928

Index 1171

Rydberg atoms, 854Rydberg constant, 857

s-electrons, 862s-wave scattering, 927Sabine’s law, 328Safety factor, 170Sagittal section, 359Saha equation, 576Satellites, 135–136Saturated steam, 739Saturated vapor, 719Saturated vapor pressure, 719

table on, 806Saturation induction, 482Saturation line, 741Saturation magnetization, 727, 728,

1053Saturation range, 562Saturation region, 1024, 1038Saturn, 133Scalar, multiplication by, 1116Scalar field, 439Scalar product, 46, 1117–1118Scales, 107Scaling laws, 206–208Scanning tunneling microscope, 566Scattering, 376–377Scattering angle, 77Scattering center, 376Scattering conservation laws, 822Scattering states, 862Schmidt mirror, 375Schmitt trigger, 1042Schottky diode, 1019Schrodinger equation, 835–844Schrodinger picture, 835Scintillation counter, 899Scissors, 107Sclera, 370Screen-grid vacuum tube, 571Screened electric potential, 579Screening constant, 869Screw dislocation, 981Screws, 107Sea level, conversion to, 798–801Second, 8Second critical velocity, 136Secondary cells, 559Secondary-electron emission, 567

basic properties of, 1085–1086

Secondary electron multiplier, 567Secondary rainbow, 348Seger cone, 631Selection rules, 862, 867Selective total reflection, 990Self-excitation, 211Self-inductance, 488Self-induction, 488–491Self-radiation, 964Self-similarity, 227Self-sustained gaseous discharge,

563–564SELFOC lenses, 368Semi-metals, 1009Semiconducting materials, effect of

ionizing radiation on, 1094Semiconductor detectors, 899Semiconductor diode, 1016–1023Semiconductors, 396, 1001, 1009,

1011–1042density of, table, 236doping of, 1014–1016electric properties of, 1093–1094electron density in, 1011–1012magnetic properties of, 1093–1094tables on, 1093–1094thermal properties of, 1093–1094

Sensitive dependenceof dynamical evolution on initial

conditions, 211, 220on initial conditions, 220

Sensitivity, 1063Separate-excited motor, 546Separation of charge, 1055Series connection

of capacitors, 459of complex resistances, 528–529equivalence of parallel connection

and, 541–542of galvanic cells, 559of inductances, 489of magnetic reluctances, 472of resistor and capacitor, 534of resistors, 436, 504of resistors and inductors, 536–537of springs, 55of thermal resistors, 758–759

Series limit, 857Series motor, 547Series resonance, 539Series-resonant circuit, 538–539

1172 Index

Shadow, 306Shape-memory alloy, 988Shear, 155, 156, 164–165Shear angle, 164Shear modulus, 164–165Shear stress, 153, 155Shell model, 917–920, 936Shift moment, 102Shock tube, 586Shock wave, 209–210, 287Shockley diode formula, 1017Short-circuit current, 506Short-circuit power, 508Shunt motor, 546Shunt resistor, 509SI units, 1098

derived, 1126–1128quantities and, 1097–1100tables on, 1125–1130

Siemens (unit), 432Siemens/meter, 433Sierpinski triangle, 226Sievert, 959Signal dispersion, 352Silicon(s)

doping in, properties of, 1094electric properties of, 605

Silicon-strip detector, 899Similarity laws, 206Simple gas, 669, 727Simultaneity, relativity of, 142Simultaneous eigenfunction, 831–832Single-mode wave guide, 351Single-particle energies, 918Single-particle excitation, 920Single-phase alternating current motor,

547Single probability, 1108Singlet systems, 875Singularity, 215Sinks, 190Sinusoidal alternating quantities, 515Sinusoidal quantities, representation of,

in phasor diagram, 517–519Siphon, 183Siren, 320Skin effect, 487Sky maps, 150Slide projector, 362Sliding friction, 57, 70, 269

coefficients of, table on, 243–244

Slippage, 550Slope, 48Slope conductance, 568Small-angle grain boundaries,

982–983Smectic phases, 990Snell’s law, 303, 346Sockets, 105Soft magnets, 1053Soft superconductors, 1046Solar constant, 682, 764Solar energy converted into heat, 682Solar system, 133Solid angle, 12Solid bodies, structure of, 967–979Solid friction, 269Solid-state physics, 967–1069

basic concepts of, 967–968Solidification, 719, 736Solidification enthalpy, 646Solidification heat, 719Solids, 718, 967

density of, tables, 231–237electrons in, 1000–1011equation of state for, 671heat conductivity of, 793–794optical properties of, 1009specific calorific values of, 809specific heat capacity of, 691,

793–794tables of compressibility of, 247velocity of sound in, 312–313

Solubility product, 747–748Solutions, 743–744, 967

aqueous, temperature correction for,803

tables on, 806vapor pressure of, 736–742

table, 806Sonar, 10Sone (unit), 331Sound

damping coefficient for, in gases, 410parameters of, 313–317perception of, 330–331relative quantities, 317–319timbre of, 333wavelength of, 314

Sound-absorbing material, 325Sound absorptance of building

materials, 414

Index 1173

Sound absorption, 324–326degree of, 325–326

Sound attenuation, 327–328for standard pressure, 413

Sound damping, 325Sound-damping coefficients for liquids,

411Sound displacement, 314–315Sound dissipation, degree of, 326Sound emitter, 321Sound field quantities in air, 410Sound frequencies, 314Sound intensity, 316, 333Sound intensity level, 318Sound level difference, 319Sound level excess, 319Sound levels, evaluated, 331Sound particle velocity, 315Sound power, 317Sound power level, 318Sound pressure, 313–314Sound receivers, 323–324Sound reflection, degree of, 325Sound-reflection factor, 327Sound-relative quantities, 318Sound transducer, 321Sound-transmission degree, 326Sound velocity, 209, 311–313

in air, 409in construction materials, 412in gases, 409in liquids, 410in metals, 411in oil and mineral-oil products, 410in synthetic materials and glasses,

412Sound wave(s), 311–319

energy density of, 316Source point, 338Sources, 190, 1030

of sound, 319–323Space(s)

curvature of, 149dimension of, 3–4homogeneity of, 900isotropy of, 900of states, 215

Space charge regions, 1015Space cone, 125Space-fixed coordinate system, 96Space-grid vacuum tube, 571

Space lattice, 968Space-time continuum, 137

curved four-dimensional, 148Span, 1104Spark discharge, 564Spatial statics, 104Special continuous distributions,

1110–1111Special discrete distributions, 1109Special names, 1099Special theory of relativity, 137–148Specific activity, 939Specific caloric value, 681, 809Specific electric resistance

of insulating materials, 603tables on, 595–598

Specific energy, 933Specific enthalpy

of steam, 808tables on, 809–813of water, 807

Specific evaporation enthalpyof pure metals, 810–811of substances, 812–813

Specific evaporation heat, 718Specific gas constant, 662, 690

of gases, 787Specific heat, 679Specific heat capacity, 687–691, 723

phonons and, 995–996of solids, 793–794

Specific ionization, 956Specific melting enthalpy

of pure metals, 810–811of substances, 812–813

Specific melting heat, 719Specific quantity, 628–629

of heat per volume, 767Specific radiant emittance, 399Specific volume of steam, 808Spectral absorbance, 400–401Spectral class, 151Spectral colors, 336, 390Spectral decomposition, 390Spectral degree of brightness, 404Spectral energy flux density, 961Spectral filters, 400Spectral particle radiance, 960Spectral pure absorptance, 401Spectral pure transmittance, 402Spectral pyrometer, 632

1174 Index

Spectral quantities, 400Spectral radiance, 400Spectral-radiation density, 580Spectral reflectance, 400Spectral relative luminosity, 404Spectral resolving power, 379Spectral transmittance, 401Spectrograph, 390Spectrometer, 390Spectroscope, 390Spectroscopic apparatus, 390–391Spectroscopic photometer, 390Spectroscopy, 852

fundamentals of, 851–854Spectrum, 390, 852Spectrum analysis, 390Speed of light

in matter, 499in vacuum, 335, 499

Spent-fuel elements, 949Sphere, flow around, 202–203Spherical aberration, 344, 366Spherical capacitor, 460Spherical coordinate system, 4Spherical lens, 358Spherical mirror, 342Spherical surfaces, refraction by,

357–358Spherical wave, 291Spin, 844–847Spin eigenfunction, 846Spin operator, 845Spin-orbit coupling, 858, 864–865, 913,

918Spiral springs, 120Spitzer formula, 577–578Spontaneous emission, 879, 1064Spontaneous fission, 936Spontaneous magnetization, 728Spontaneous nucleon emission, 947Sprayer, 195Spring

mass on, 258–260vibration of, 69–70

Spring balance, 38Spring constant, 54Spring torsion forces, 54–55Square meter, 10Square-wave signals, 1042SQUID (superconducting quantum

interferometer device), 1045

Squirrel-cage winding, 549Stacking disorder, 982Stadium billiards, 212Standard acceleration of gravity, 54Standard atmosphere, 178, 636

in relative units, 798Standard conditions, 631, 636Standard density, 178Standard deviation, 1104, 1105Standard hydrogen electrode, 552, 556Standard model, 883–887

advances beyond, 904–905Standard normal distribution,

1110–1111Standard pendulum, 260–263Standard pressure, 178, 636

sound attenuation for, 413Standard resistance, 1004Standard temperature, 631

volume measurement conversion to,803

Standing electron waves, 1007–1008Standing waves, 296–299Star catalogs, 150Star evolution, 151–152Star light, red shift of, 149Stark effect, 876–877Stars, 150–152State density, 996

in Fermi systems, 1005State property, 627State property definitions, 627–629State variables, 623, 627–641

equilibrium and, 623–673Static friction, 56–57

coefficients of, table on, 244Static pressure, 191Static-pressure tube, 192Static stability, 103–104Statics, 97–110

equilibrium conditions of, 103–104Stationary Schrodinger equation, 837Stationary state(s), 837

postulate of, 855Statistical errors, 1100Statistics, error theory and, 1100–1113Stator, 545Steady state, 625–626Steam

specific enthalpy of, 808specific volume of, 808

Index 1175

Steam-air mixtures, 738–742Steam content, 740Steam engine, 709–710Steam turbine, 180Steel

density of, table, 233table of elastic properties of, 241

Steel girder, 163–164Stefan-Boltzmann constant, 764Stefan-Boltzmann law, 764, 820Steiner’s rule, 113–114Stellar brightness, 150Stellar clusters, 151Stellarator, 591Step-recovery diode, 1021Steradian, 12Stereo radio, 324Stern-Gerlach experiment, 844Stirling cycle, 708–709Stirling engine, 709Stoichiometric coefficients, 742Stoichiometry, 743–744Stokes (unit), 199Stokes’ friction, 270–273Stokes’ law of friction, 202Stokes lines, 874Stones, natural, density of, table, 236Stopping power, 954

for electrons, 955Stopwatch, 8Straight lever, 106Straight-line collision, 74Strain, 155, 156–157Strain tensor, 159Strange attractor, 221Strangeness, 894Stray flux, 492Stray light, 367Stream lines, 187Stream lines, electric current,

430–431Stream tube, 187Streamer chamber, 899Streamlined body, 205Stress, 153–156Stress-strain diagram, 167Stress tensor, 154Strings as sources of sound, 319–320Stripping reaction, 932Stroboscope, 216Strong interaction, 886–887

Structure investigation, methods for,974–976

Student’s distribution, 1110–1111Subatomic structures, 898Subcritical assembly, 947Subjective photometry, 396Sublimation, 719Sublimation enthalpy, 646Sublimation heat, 719Submersion depth, 183Subshell, 877Substances

specific evaporation enthalpy of,812–813

specific melting enthalpy of, 812–813thermal properties of, tables on,

788–795Substitution rule, 1124Substrate, 1030Subtraction of vectors, 1117Subtractor, 1040Suction effects, 195–196Suction pumps, 180Suction valve, 178Sum of error squares, 1106Sum rule, 1122, 1123Summing amplifiers, 1039–1040Summing integrator, 1041Sun, 133Superconducting compounds, table of,

1092Superconducting elements, selected

properties of, 1091Superconducting quantum

interferometer device (SQUID),1045

Superconductivity, 730–731,1042–1049

fundamental properties of,1043–1047

theory of, 1044Superconductors, 730

tables on, 1091–1092Supercooled vapor, 727Supercritical assembly, 947Superdeformed nuclei, 934Superelasticity, 989–990Superfluidity, 731Superheated liquid, 727Superheated steam, 740Superheavy elements, 879, 935

1176 Index

Supernovae, 151Superposition law, 277Superposition of vibrations, 277–283

in different directions and withdifferent frequencies, 280–282

of different frequencies, 279–280of equal frequency, 277–278

Superposition principle, 213–214, 292Supersaturated steam, 739Supersonic velocity, 209Supersymmetry model, 905Support force, 103Surface energy, 184, 917Surface-friction drag, 204Surface tension, 183–184Surface waves, 309–310Suspensions, 199Switching diode, 1018Switching hysteresis, 1042Symmetric axis, 124Symmetries, 900–905Symmetry energy, 917Synchronous machine, 548–549Synchrotron, 898Synthetic materials

sound velocity in, 412table of elastic properties of, 242

Synthetics, density of, table, 235System(s), 623–624

of principal axes, 123of units, 1098

Systematic errors, 1100Systeme International d’Unites, 1098,

see also SI units

t-distribution, 1110–1111Tachometer, 15Tachyons, 142Tangent to curve, 22Tangent unit vector, 24Tangential acceleration, 26, 47Tangential force, 47Tangential stresses, 155Tangential velocity, 34–35Technical atmosphere, 635Technical mechanics, 104–105Technical work, 645, 711Telescope, 363, 373–376Temperature(s), 629–634

calibration points of, 630–631equalization of, 748–750

of gases at critical point, 787heat conduction at, 795low, generation of, 714measurement of, 631–632at triple point, 788versus viscosity at normal pressure,

249Temperature/altitude factors, 799–801Temperature coefficient, 434–435Temperature correction

for aqueous solutions, 803for glass constant volume

thermometer, 804for mercury barometer

measurements, 802Temperature correction factor,

249–250Temperature dependence

of evaporation heat, 811of resistance, 434–435

Temperature field, 186Temperature radiation, 818Temperature scales, calibration points

of, 775–776Temperature units, 629–630Tempering, 989Tensile load, regions in, 167–169Tensile strength, 169Tension, 155Tension energy, 69Tension springs, 55Tensor force, 913Tensor of inertia, 121–124Terminal voltage, 503Terrestrial radiation, 964Terrestrial telescope, 375Tesla (unit), 465Test charge, 440Tetragonal Bravais lattice, 970Tetragonal crystals, magnetic

anisotropy of, 617Tetrode, 571Texture, 968Texturization, 1048Theodolite, 10, 12Thermal conductivity, 754Thermal diffusivity, 768Thermal equilibrium, 626Thermal generation of plasmas, 586Thermal insulators, heat conduction of,

794

Index 1177

Thermal load of ohmic components,516

Thermal neutrons, 949Thermal noise, 629Thermal properties

of building materials, 791–792of construction materials,

791–792of gases, 792of liquids, 793of plastic materials, 793of pure metals, 789–791of substances, tables on, 788–795

Thermal radiation, 818Thermal reactors, 949Thermal resistance, 757–759

heat flow and, 760–761Thermal resistors, series connection

of, 758–759Thermal sound generation, 321Thermal transmittance

of building bricks, 796of building materials, 795

Thermistor, 435Thermo-ionic emission, 565Thermocouples, 396, 632

common, 599thermoelectric voltage of, 599

Thermodynamic machines,706–714

Thermodynamic potential(s), 627,641–650

entropy as, 642–643Thermodynamic quadrangle, 649Thermodynamic stability, 649–650Thermodynamic systems, 623

work in, 676–677Thermodynamic temperature, 633Thermodynamical equilibrium, 213Thermodynamics, 619–813

first law of, 675, 699–701formula symbols used in,

771–773laws of, 698–702Ohm’s law of, 758second law of, 679, 701–702tables on, 775–813third law of, 702zeroth law of, 626, 698–699

Thermoelectric emission properties oftungsten cathode, 1084

Thermoelectric potential series, tableson, 599

Thermoelectric voltage ofthermocouples, 599

Thermoluminescence dosimeter, 963Thermometers, 631

operation ranges of, 633Thermopane windows, 759Thermoplasts, 986

density of, table, 235Thermosets, density of, table, 235Thermovac tubes, 636Theta-pinch, 588Thick lenses, 358–364Thick spherical lens, 360Thin lenses, 364Thinness ratio, 170Third critical velocity, 136Three-fingers rule, 466Three-level laser, 880Three-phase machine, 547–550Threshold current, 1064Threshold energy, 926Threshold voltage, 1018Thrust, 79–81Thrust bearings, 105Thyristor, 1032–1034Tilting moment, 104Timbre of sound, 333Time, 8–9

homogeneity of, 900Time average of periodic functions,

515–516Time constant, 511, 1063Time dilatation, 144–145Time evolution of systems, 212Time evolution operator, 835Time interval, 8Time projection chamber (TPC), 900Time-reversal invariance, 903Time units, 8Time variation of electron

concentration, 1062Titius-Bode relation, 134Tokamak, 591Tonal ranges, 333–334Tone, 332Tone scale, 332Toothed gears, 109Top quark, 893Toroidal plasma confinement, 590–591

1178 Index

Torque, 50–52, 100–101, 156, 545of couples, 102impulse of, 53

Torr, 636Torricelli’s effluent formula, 193–195Torsion, 156, 165–166, 265Torsion springs, 55Torsion stress, 165–166Torsional constant, 120, 265Torsional oscillator, 265Torsional potential energy, 120–121Torsional vibration, 265–266Total-attenuation coefficient, 958Total cross-section, 925Total efficiency, 72Total heat capacity, 684–686Total polarization, 1058Total pressure, 732Total sound level, 318Totally inelastic collision, 74, 78–79TPC (time projection chamber),

900Trajectory, 6–7, 138

curvature of, 27–28in phase space, 215in three dimensions, 22

Transfer characteristic, 1025Transformer, 493–494Transformer induction, 487–488Transformer oil, electric properties

of, 605Transient oscillations, 219Transistor circuits

basic, 1026–1029notations for, 1024

Transistors, 1023–1030Transition elements, 878Transition metals, 977Translation, 14, 97, 969Translation energy, 120Translational motion, comparison of

rotational and, 53Transmission, radiation, 764Transmission coefficient, 838Transmission grating, 391Transmission ratio, 493Transmissions, 109–110Transmittance, 765Transport processes, 658–660Transport theory, 186Transuranic elements, 878, 935

Transverse drag, 581Transverse phonons, 993, 994Transverse polarization, 294Transverse strain, 155, 158–159Transverse wave, 293, 311, 542Transverse Zeeman effect, 875Traps, 1063TRIAC (triode alternating current)

switch, 1034Triangulation, 10Triatomic molecules, 658Triclinic Bravais lattice, 971Trigger pulse, 1033Trigger time, 1033Triggering current, 1033Trimmer capacitors, 458Triode alternating current (TRIAC)

switch, 1034Triple point, 719, 735

pressure at, 788temperature at, 788

Triple scalar product, 1119True error, 1101True value, 1100Trusses, 105Tube friction, 207–208Tunable capacitors, 458Tungsten cathode, thermoelectric

emission properties of, 1084Tunnel diode, 1021–1022Tunnel effect, 839, 941, 1021Tunnel microscope, 839Turbine, 179, 180Turboprop engine, 180Turbulences, 211Turbulent flow, 197–198, 203–205TV screens, 1063Twilight number, 374Twisted nematic structures, 990, 991Twisting, 165Two-body collisions, 72Two-dimensional harmonic oscillator,

281–282Two-port equations, 1026Two-port network, 501, 1026Two-terminal networks, 501, 529

complex resistances of, 533Two-way effects, 988–989Two-wire lines, 460Type-I and type-II superconductors,

1046

Index 1179

Ultrasonic diagnostics, 329Ultrasound, 314, 328–329Ultraviolet spectral range, table on, 417Uncertainty principle, Heisenberg’s,

827Underdamped case, 271Underexcitation, 549Unification of interactions, 883–891Uniform electric field, 440Uniform motion, 3, 19Uniformly accelerated motion, 19–21Uniformly charged cylinder, field

strength and potential of,450–451

Uniformly charged sphere, fieldstrength and potential of,449–450

Unipolar bond, 978Unipolar transistors, 1030–1032Unit vector, 1117Units, 1098

conversions of, 1099Universal constants, table of values of,

773Universal diodes, 1018Universal gas constant, 639, 661, 690Universal motor, 547Universality, 225, 883Universe, properties of, 149–150Upper heating value, 682Uranus, 133Urn model, 1108Useful flux, 492

Vacancies, 979–980Vacancy concentrations, measurement

of, 980Vacancy-formation energy, 980Vacuum

electric displacement in, 453–454speed of light in, 335, 499

Vacuum pump, 173Vacuum-tube diode, 568Vacuum-tube parameters, 568–570Vacuum-tube triode, 568Vacuum tubes, 567–572

amplification factor of, 570Valence band, 1008Valence electrons, 878Van der Waals bond, 978–979Van der Waals constants, table of, 788

Van der Waals equation, 666–668, 724in reduced variables, 727as virial expansion, 669–670

Van der Waals forces, 183Van der Waals gas, phase transitions

and, 724–727Vane pump, 178Vapor-ejector pump, 179Vapor-phase epitaxy, 1035Vapor pressure

of solutions, 736–742tables on, 806–808of water, tables on, 807

Vapor-pressure curve, 719, 724, 735,736

Varactor, 1022Variable-disk capacitors, 458Variable-resistor units, 435–436Variable stars, 151Variance, 1097, 1104–1105Variation coefficient, 1105Variation width, 1104Varistor, 436VDR (voltage-dependent resistor), 436Vector addition, 1117Vector calculus, 1115–1119Vector field, 439Vector mesons, 895Vector model of atom, 864Vector multiplication, 1117–1119Vector potential, 470Vector product, 1118–1119Vector subtraction, 1117Vector waves, 292–293Vectors, 1115–1116Velocity(ies), 14–17

addition theorem of, 142–143determination of, from acceleration,

18–19Velocity coefficient, 195Velocity-dependent mass, 147Velocity distribution, 653Velocity field, 186Velocity gradient, 198Velocity potential, 189Velocity profile, 198Velocity vector, 23

properties of, 24Venturi principle, 195Venturi tube, 192–193Venus, 133

1180 Index

Verdet constant, 392Vertex, 11Vertex rule in magnetic circuit, 471Vibration air columns, 320–321Vibration modes, 284Vibrational excitations, 871, 921Vibrational spectra, 871–872Vibrations, 253, 255–285

circular motion and, 262–263coupled, 283–285of spring, 69–70superposition of, see Superposition

of vibrationssymbols used in formulae on,

407–408tables on, 409–414waves and, 253–417

Vice, 105Vickers hardness, 171Video camera, 369Virgin curve of magnetization, 482Virial coefficient, 665Virial expansion

of real gas, 665Van der Waals equation as, 669–670

Virtual displacement, 88Virtual image, 338Virtual image focus, 363Virtual image point, 338Virtual particle, 886Virtual photons, 887Virtual trajectory, 88–89Visco-elasticity, 985–986Viscosity, 198

tables on, 248–250, 788–789versus temperature at normal

pressure, 249Viscous friction, 270–273Vision, defects in, 371Visual angle, 371Visual field, 374Voices, tonal ranges of, 334Voigt-Kelvin model of relaxation, 987Volt (unit), 446Volt-meter, 452Volt/meter, 440Voltage(s)

across coil, 513at capacitor, 511electric, see Electric voltageguide values of, 608

of Weston standard elements,607–609

Voltage amplifier, 1038Voltage connection, 510Voltage-dependent resistor (VDR), 436Voltage divider rules, 504Voltage followers, 1041–1042Voltage gain, 1028Voltage measurement, 509Voltage ranges in electric engineering,

608Voltampere, 528Voltampere-reactance, 528Voltmeters, 509Volume, 10Volume energy, 916Volume expansion

of liquids, 795of water, 795

Volume-expansion coefficient, 38, 176,652, 671

Volume flux, 188Volume magnetostriction, 483Volume measurement conversion to

standard temperature, 803Volume percentage, 743Vortex-free flow, 190Vortices, 1046

formation of, 203Vulcanization, 986

Waterspecific enthalpy of, 807vapor pressure of, tables on, 807viscosity of, table, 248volume expansion of, 795

Water anomaly, 673Water content, 739, 740Water dissolutions in glycerol, viscosity

of, table, 248Water droplets, 740Water equivalent, 685–686Water-jet pump, 179, 195Water jet turbine, 180Water turbine, 180Water waves, kinds of, 310Water wheel, 180Watt (unit), 71, 317Watt second, 675Watt/square meter, 316, 500Wave character of particles, 825–827

Index 1181

Wave equations, 287, 498Wave front, 288Wave function, 827

normalization of, 836–837Wave number, 288Wave-number vector, 825Wave-optical boundary condition, 351Wave optics, 337, 376–395Wave packet, 300, 828–829Wave-particle duality, 336, 826–827Wave propagation, direction of, 288Wave theory, 336Wave train, 294Wave vector, 288Wavelength, 289, 335Waves, 253, 287–310

basic features of, 287–293modulation of, 308–309symbols used in formulae on,

407–408vibrations and, 253–417

Weak coupling, 283Weak interaction, 885–886Weakons, 885, 887Weber (unit), 468, 489Weber-Fechner law, 330Wedges, 107Weibull distribution, 1110–1111, 1112Weight, 53–54, 131Weiss domains, 481, 728Well-tempered scale, 333Wendelstein Stellarator, 591Weston standard elements, voltage of,

607–609Wet steam, 719, 740Wetting energy, 186Wheatstone’s bridge, 510Wheelbarrow, 107Whiskers, 988

table of elastic properties of, 240Whole tone, 333Widemann-Franz law, 1000Widths, 1015–1016Wien’s displacement law, 819Wien’s law, 819Wigner force, 913

Wind forces, table of, 1129Wind load, 205Wires, table of elastic properties of, 240Wood, density of, table, 236Woods-Saxon potential, 931Woodwind instruments, 321Work, 63–65, 118

of deformation, 68–69, 166–167relativistic, 147in thermodynamic systems, 676–677

Work function, 565, 821for adsorbed surfaces, 1084for elements, 1082–1083

World, mirror symmetry of, 900World line, 141World point, 141

X-ray computer tomography, 871X-ray diffraction, 974X-ray scattering, methods of, 975–976X-ray sources, dose rate of, 965X-ray spectrum of elements,

characteristic, main lines of,1086

X-rays, 868–871applications of, 870–871mass-attenuation coefficient for, 1088

Year, 8Yield strength, 168, 169Young’s modulus, 156–157Yukawa potential, 887, 914Yukawa term, 131, 884

Z-diode, 1019–1020z-pinch, 587Zeeman effect, 875–876Zener effect, 1017Zener voltage, 1017Zero balancing, 510Zero of energy, 66Zero phase angle, 515Zero-point energy, 842Zinc-carbon battery, 558Zone melting method, 968Zoom objective, 369

Natural constants in SI units

The numerical values are taken from CODATA.

ErrorQuantity Symbol Value (ppm)

speed of light in vacuum c 2.99792458 · 108 m/s exactgravitational constant G 6.67259 · 10−11 m3/(kgs2) 128electron charge, e, e0 1.60217733 · 10−19 C 0.30

elementary chargePlanck’s quantum h 6.6260755 · 10−34 J · s 0.60

of actionPlanck’s constant � = (2π)−1h 1.05457266 · 10−34 J · s 0.60Avogadro’s number NA 6.0221367 · 1023 mol−1 0.59Faraday constant F = NAe0 9.6485309 · 104 C/mol 0.30electron mass me 9.1093897 · 10−31 kg 0.59

0.51099906 MeV 0.30Rydbeg constant R∞ = (2h)−1mecα2 1.0973731534 · 107 m−1 0.0012fine-structure constant α = e2

0(2ε0hc)−1 7.29735308 · 10−3 0.045α−1 137.0359895 0.045

electron radius re = �(mec)−1α 2.81794092 · 10−15 m 0.13e−-Compton λC = h(mec)−1 2.42631058 · 10−12 m 0.089

wavelengthBohr radius a0 = reα

−2 5.29177249 · 10−11 m 0.045atomic mass unit u = 1

12 m(12C) 1.6605402 · 10−27 kg 0.59proton mass mp 1.6726231 · 10−27 kg 0.59

938.27231 MeV 0.30neutron mass mn 1.6749286 · 10−27 kg 0.59

939.56563 MeV 0.30magnetic flux quantum �0 = h(2e0)

−1 2.06783461 · 10−15 Wb 0.30specific electron charge −e0m−1

e −1.75881962 · 1011 C/kg 0.30Bohr magneton µB = e0�(2me)

−1 9.2740154 · 10−24 J/T 0.34magnetic moment µe 9.2847701 · 10−24 J/T 0.34

of electronnuclear magneton µN = e0�(2mp)

−1 5.0507866 · 10−27 J/T 0.34magnetic moment µp 1.41060761 · 10−26 J/T 0.34

of protongyromagnetic ratio γp 2.67522128 · 108 rad/sT 0.30quantum Hall resistance RH 25812.8056 0.045universal gas constant R 8.314510 J/(mol K) 8.4Boltzmann constant k, kB = R NA

−1 1.380658 · 10−23 J/K 8.5Stefan-Boltzmann σ = π2k4

B(60�3c2)−1 5.67051 · 10−8 W/m2K4 34constant

Wien’s constant b = λmaxT 2.897756 · 10−3 m · K 8.4permeability of free space µ0 4π · 10−7 Vs/(Am) exactpermittivity constant ε0 = (µ0c2)−1 8.85418781762 · 10−12 As/(Vm) exact

of free space

1183

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p 1 p 2=

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p 1 p 2=( V

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ntn=

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U=

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Q=

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CV(T

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W=

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tech

nica

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k

Wt=∫ V

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S=

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( V2

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1184

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Otto

S Pr→

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Die

sel

S Pr→

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Joul

eS P

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csso

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S=−∂

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∣ ∣ ∣ ∣ V,N=−∂

G

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∣ ∣ ∣ ∣ p,N

S=

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gyF=

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H=

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free

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1185