/550/ ************************************************************************ * Edit v1.000 from 2022-09-26 to 2022-09-26 by MSc * ************************************************************************ Taschenbuch der Physik Professor Dr. Horst Stoecker Thun 1998, 3. Auflage ISBN=3-8171-1556-3 Seite Auszug ======================================================================== 1 1 Mechanik ------------------------------------------------------------------------ 1 1 Kinematik ------------------------------------------------------------------------ 1 1.1 Beschreibung von Bewegungen ------------------------------------------------------------------------ 1 1.1.1 Bezugssysteme ------------------------------------------------------------------------ 5 1.1.2 Zeit ------------------------------------------------------------------------ 7 1.1.3 Laenge, Flaeche, Volumen ------------------------------------------------------------------------ 8 1.1.4 Winkel ------------------------------------------------------------------------ 10 1.1.5 Mechanische Systeme ------------------------------------------------------------------------ 12 1.2 Bewegung in einer Dimension ------------------------------------------------------------------------ 12 1.2.1 Geschwindigkeit ------------------------------------------------------------------------ 14 1.2.2 Beschleunigung ------------------------------------------------------------------------ 16 1.2.3 Einfache Bewegungen in einer Dimension ------------------------------------------------------------------------ 19 1.3 Bewegung in mehreren Dimensionen ------------------------------------------------------------------------ 20 1.3.1 Geschwindigkeitsvektor ------------------------------------------------------------------------ 22 1.3.2 Beschleunigungsvektor ------------------------------------------------------------------------ 25 1.3.3 Freier Fall und Wurf ------------------------------------------------------------------------ 27 1.4 Drehbewegung ------------------------------------------------------------------------ 28 1.4.1 Winkelgeschwindigkeit ------------------------------------------------------------------------ 30 1.4.2 Winkelbeschleunigung ------------------------------------------------------------------------ 30 1.4.3 Bahngeschwindigkeit ------------------------------------------------------------------------ 32 2 Dynamik ------------------------------------------------------------------------ 32 2.1 Grundgesetze der Dynamik ------------------------------------------------------------------------ 32 2.1.1 Masse und Impuls ------------------------------------------------------------------------ 34 2.1.2 Newtonsche Gesetze ------------------------------------------------------------------------ 43 2.1.3 Bahndrehimpuls ------------------------------------------------------------------------ 44 2.1.4 Drehmoment ------------------------------------------------------------------------ 46 2.1.5 Dynamisches Grundgesetz fuer Drehbewegungen ------------------------------------------------------------------------ 47 2.2 Kraefte ------------------------------------------------------------------------ 47 2.2.1 Gewichtskraft ------------------------------------------------------------------------ 48 2.2.2 Federkraefte und Torsionskraefte ------------------------------------------------------------------------ 50 2.2.3 Reibungskraefte ------------------------------------------------------------------------ 53 2.3 Traegheitskraefte in rotierenden Bezugssystemen ------------------------------------------------------------------------ 53 2.3.1 Zentripetalkraft und Zentrifugalkraft ------------------------------------------------------------------------ 55 2.3.2 Corioliskraft ------------------------------------------------------------------------ 57 2.4 Arbeit und Energie ------------------------------------------------------------------------ 57 2.4.1 Arbeit ------------------------------------------------------------------------ 59 2.4.2 Energie ------------------------------------------------------------------------ 60 2.4.3 Kinetische Energie ------------------------------------------------------------------------ 61 2.4.4 Potentielle Energie ------------------------------------------------------------------------ 63 2.4.5 Reibungsarbeit ------------------------------------------------------------------------ 64 2.5 Leistung ------------------------------------------------------------------------ 64 2.5.1 Wirkungsgrad ------------------------------------------------------------------------ 65 2.6 Stoszprozesse ------------------------------------------------------------------------ 67 2.6.1 Elastische, gerade, zentrale Stoesze ------------------------------------------------------------------------ 68 2.6.2 Elastische, schiefe, zentrale Stoesze ------------------------------------------------------------------------ 69 2.6.3 Elastischer, schiefer Stosz mit einem ruhenden Koerper ------------------------------------------------------------------------ 71 2.6.4 Unelastische Stoesze ------------------------------------------------------------------------ 71 2.7 Raketen ------------------------------------------------------------------------ 72 2.7.1 Schubkraft ------------------------------------------------------------------------ 73 2.7.2 Raketengleichung ------------------------------------------------------------------------ 74 2.8 Massenpunktsysteme ------------------------------------------------------------------------ 74 2.8.1 Bewegungsgleichungen ------------------------------------------------------------------------ 76 2.8.2 Impulserhaltungssatz ------------------------------------------------------------------------ 77 2.8.3 Drehimpulserhaltungssatz ------------------------------------------------------------------------ 77 2.8.4 Energieerhaltungssatz ------------------------------------------------------------------------ 78 2.9 Lagrange- und Hamilton-Gleichungen ------------------------------------------------------------------------ 78 2.9.1 Lagrange-Gleichungen und Hamiltonsches Prinzip ------------------------------------------------------------------------ 81 2.9.2 Hamilton-Gleichungen ------------------------------------------------------------------------ 83 3 Starre Koerper ------------------------------------------------------------------------ 83 3.1 Kinematik ------------------------------------------------------------------------ 83 3.1.1 Dichte ------------------------------------------------------------------------ 83 3.1.2 Schwerpunkt ------------------------------------------------------------------------ 85 3.1.3 Kinematische Grundgroeszen ------------------------------------------------------------------------ 87 3.2 Statik ------------------------------------------------------------------------ 87 3.2.1 Kraftvektoren ------------------------------------------------------------------------ 89 3.2.2 Drehmoment ------------------------------------------------------------------------ 91 3.2.3 Kraeftepaar ------------------------------------------------------------------------ 92 3.2.4 Gleichgewichtsbedingungen der Statik ------------------------------------------------------------------------ 94 3.2.5 Technische Mechanik ------------------------------------------------------------------------ 95 3.2.6 Maschinen ------------------------------------------------------------------------ 100 3.3 Dynamik ------------------------------------------------------------------------ 100 3.4 Traegheitsmoment und Drehimpuls ------------------------------------------------------------------------ 100 3.4.1 Massentraegheitsmoment ------------------------------------------------------------------------ 105 3.4.2 Drehimpuls ------------------------------------------------------------------------ 106 3.5 Arbeit, Energie und Leistung ------------------------------------------------------------------------ 107 3.5.1 Kinetische Energie ------------------------------------------------------------------------ 109 3.5.2 Potentielle Energie der Torsion ------------------------------------------------------------------------ 109 3.6 Kreiseltheorie ------------------------------------------------------------------------ 110 3.6.1 Traegheitstensor ------------------------------------------------------------------------ 112 3.6.2 Nutation und Praezession ------------------------------------------------------------------------ 115 3.6.3 Anwendungen von Kreiseln ------------------------------------------------------------------------ 117 4 Mikromechanik ------------------------------------------------------------------------ 117 4.1 Duennschichttechnik ------------------------------------------------------------------------ 118 4.2 Belichtungs- und AEtzverfahren ------------------------------------------------------------------------ 119 4.3 Anwendungen ------------------------------------------------------------------------ 119 4.3.1 Sensoren ------------------------------------------------------------------------ 121 4.3.2 Aktoren ------------------------------------------------------------------------ 121 4.3.3 Technische Anwendungen ------------------------------------------------------------------------ 123 5 Gravitation und Relativitaetstheorie ------------------------------------------------------------------------ 123 5.1 Gravitationsfeld ------------------------------------------------------------------------ 123 5.1.1 Gravitationsgesetz ------------------------------------------------------------------------ 125 5.1.2 Planetenbewegung ------------------------------------------------------------------------ 126 5.1.3 Planetensystm ------------------------------------------------------------------------ 130 5.2 Spezielle Relativitaetstheorie ------------------------------------------------------------------------ 130 5.2.1 Relativitaetsprinzip ------------------------------------------------------------------------ 132 5.2.2 Lorentz-Transformation ------------------------------------------------------------------------ 136 5.2.3 Relativistische Effekte ------------------------------------------------------------------------ 137 5.2.4 Relativistische Dynamik ------------------------------------------------------------------------ 140 5.3 Allgemeine Relativitaetstheorie und Kosmologie ------------------------------------------------------------------------ 141 5.3.1 Sterne und Galaxien ------------------------------------------------------------------------ 144 6 Mechanik der deformierbaren Koerper ------------------------------------------------------------------------ 144 6.1 Elastizitaetslehre ------------------------------------------------------------------------ 144 6.1.1 'Spannung ------------------------------------------------------------------------ 147 6.1.2 Elastische Verformung ------------------------------------------------------------------------ 157 6.1.3 Plastische Verformung ------------------------------------------------------------------------ 161 6.2 Hydrostatik, Aerostatik ------------------------------------------------------------------------ 161 6.2.1 Fluessigkeiten und Gase ------------------------------------------------------------------------ 162 6.2.2 Druck ------------------------------------------------------------------------ 170 6.2.3 Auftrieb ------------------------------------------------------------------------ 172 6.2.4 Kohaesion, Adhaesion, Oberflaechenspannung ------------------------------------------------------------------------ 175 6.3 Hydrodynamik, Aerodynamik ------------------------------------------------------------------------ 175 6.3.1 Stroemungsfeld ------------------------------------------------------------------------ 177 6.3.2 Grundgleichungen idealer Stroemungen ------------------------------------------------------------------------ 186 6.3.3 Reale Stroemungen ------------------------------------------------------------------------ 191 6.3.4 Turbulente Stroemungen ------------------------------------------------------------------------ 194 6.3.5 AEhnlichkeitsgesetze ------------------------------------------------------------------------ 197 6.3.6 Stroemungen mit Dichteaenderungen ------------------------------------------------------------------------ 199 7 Nichtlineare Dynamik, Chaos und Fraktale ------------------------------------------------------------------------ 199 7.1 Dynamische Systeme und Chaos ------------------------------------------------------------------------ 200 7.1.1 Dynamische Systeme ------------------------------------------------------------------------ 205 7.1.2 Konservative Systeme ------------------------------------------------------------------------ 207 7.1.3 Dissipative Systeme ------------------------------------------------------------------------ 209 7.2 Bifurkationen ------------------------------------------------------------------------ 209 7.2.1 Logistische Abbildung ------------------------------------------------------------------------ 212 7.2.2 Universalitaet ------------------------------------------------------------------------ 212 7.3 Fraktale ------------------------------------------------------------------------ 215 Formelzeichen Mechanik ------------------------------------------------------------------------ 216 8 Tabellen zur Mechanik ------------------------------------------------------------------------ 216 8.1 Dichte ------------------------------------------------------------------------ 216 8.1.1 Festkoerper ------------------------------------------------------------------------ 221 8.1.2 Fluessigkeiten ------------------------------------------------------------------------ 222 8.1.3 Gase ------------------------------------------------------------------------ 223 8.2 Elastische Eigenschaften ------------------------------------------------------------------------ 226 8.3 Dynamische Eigenschaften ------------------------------------------------------------------------ 226 8.3.1 Reibungszahlen ------------------------------------------------------------------------ 228 8.3.2 Kompressibilitaet ------------------------------------------------------------------------ 231 8.3.3 Viskositaet ------------------------------------------------------------------------ 234 8.3.4 Stroemungswiderstand ------------------------------------------------------------------------ 235 8.3.5 Oberflaechenspannung ------------------------------------------------------------------------ 236 II Schwingungen und Wellen ------------------------------------------------------------------------ 236 9 Schwingungen ------------------------------------------------------------------------ 239 9.1 Freie ungedaempfte Schwingungen ------------------------------------------------------------------------ 239 9.1.1 Federpendel ------------------------------------------------------------------------ 241 9.1.2 Fadenpendel ------------------------------------------------------------------------ 244 9.1.3 Physisches Pendel ------------------------------------------------------------------------ 246 9.1.4 Torsionsschwingung ------------------------------------------------------------------------ 247 9.1.5 Fluessigkeitspendel ------------------------------------------------------------------------ 248 9.1.6 Elektrischer Schwingkreis ------------------------------------------------------------------------ 249 9.2 Gedaempfte Schwingungen ------------------------------------------------------------------------ 250 9.2.1 Reibung ------------------------------------------------------------------------ 254 9.2.2 Gedaempfter elektrischer Schwingkreis ------------------------------------------------------------------------ 255 9.3 Erzwungene Schwingungen ------------------------------------------------------------------------ 257 9.4 UEberlagerung von Schwingungen ------------------------------------------------------------------------ 257 9.4.1 UEberlagerung von Schwingungen gleicher Frequenz ------------------------------------------------------------------------ 259 9.4.2 UEberlagerung von Schwingungen ungleicher Frequenz ------------------------------------------------------------------------ 260 9.4.3 UEberlagerung von Schwingungen in ungleicher Richtung und mit verschiedener Frequenz ------------------------------------------------------------------------ 261 9.4.4 Fourier-Analyse, Zerlegung nach Schwingungen ------------------------------------------------------------------------ 263 9.5 Gekoppelte Schwingungen ------------------------------------------------------------------------ 266 10 Wellen ------------------------------------------------------------------------ 266 10.1 Grundlegende Eigenschaften von Wellen ------------------------------------------------------------------------ 272 10.2 Polarisation ------------------------------------------------------------------------ 272 10.3 Interferenz ------------------------------------------------------------------------ 272 10.3.1 Kohaerenz ------------------------------------------------------------------------ 273 10.3.2 Interferenz ------------------------------------------------------------------------ 274 10.3.3 Stehende Wellen ------------------------------------------------------------------------ 277 10.3.4 Wellen mit unterschiedlichen Frequenzen ------------------------------------------------------------------------ 278 10.4 Doppler-Effekt ------------------------------------------------------------------------ 279 10.4.1 Mach-Welleu und Mach-Stoszwellen ------------------------------------------------------------------------ 280 10.5 Brechung ------------------------------------------------------------------------ 281 10.6 Reflexion ------------------------------------------------------------------------ 281 10.6.1 Phasenbeziehungen ------------------------------------------------------------------------ 282 10.7 Dispersion ------------------------------------------------------------------------ 283 10.8 Beugung ------------------------------------------------------------------------ 283 10.8.1 Beugung am Spalt ------------------------------------------------------------------------ 284 10.8.2 Beugung am Gitter ------------------------------------------------------------------------ 285 10.9 Modulation von Wellen ------------------------------------------------------------------------ 287 10.10 Oberflaechenwellen und Schwerewellen ------------------------------------------------------------------------ 288 11 Akustik ------------------------------------------------------------------------ 288 11.1 Schallwellen ------------------------------------------------------------------------ 288 11.1.1 Schallgeschwindigkeit ------------------------------------------------------------------------ 289 11.1.2 Schallkenngroeszen ------------------------------------------------------------------------ 293 11.1.3 Verhaeltnisgroeszen ------------------------------------------------------------------------ 295 11.2 Schallquellen und Schallempfaenger ------------------------------------------------------------------------ 295 11.2.1 Mechanische Schallsender ------------------------------------------------------------------------ 297 11.2.2 Elektroakustische Schallwandler ------------------------------------------------------------------------ 300 11.2.3 Schallabsorption ------------------------------------------------------------------------ 302 11.2.4 Schalldaemmung ------------------------------------------------------------------------ 303 11.2.5 Stroemungsgeraeusch ------------------------------------------------------------------------ 304 11.3 Ultraschall ------------------------------------------------------------------------ 305 11.4 Physiologische Akustik und das Gehoer ------------------------------------------------------------------------ 305 11.4.1 Schallempfindung ------------------------------------------------------------------------ 306 11.4.2 Bewertete Schallpegel ------------------------------------------------------------------------ 307 11.5 Musikalische Akustik ------------------------------------------------------------------------ 310 12 Optik ------------------------------------------------------------------------ 311 12.1 Geometrische Optik ------------------------------------------------------------------------ 313 12.1.1 Optische Abbildung - Grundbegriffe ------------------------------------------------------------------------ 316 12.1.2 Reflexion ------------------------------------------------------------------------ 320 12.1.3 Brechung ------------------------------------------------------------------------ 333 12.2 Linsen ------------------------------------------------------------------------ 333 12.2.1 Dicke Linsen ------------------------------------------------------------------------ 339 12.2.2 Duenne Linsen ------------------------------------------------------------------------ 339 12.3 Linsensysteme ------------------------------------------------------------------------ 340 12.3.1 Linsen mit Blenden ------------------------------------------------------------------------ 340 12.3.2 Abbildungsfehler ------------------------------------------------------------------------ 343 12.4 Optische Instrumente ------------------------------------------------------------------------ 343 12.4.1 Lochkamera ------------------------------------------------------------------------ 344 12.4.2 Fotokamera ------------------------------------------------------------------------ 344 12.4.3 Auge ------------------------------------------------------------------------ 346 12.4.4 Auge und optische Instrumente ------------------------------------------------------------------------ 351 12.5 Wellenoptik ------------------------------------------------------------------------ 351 12.5.1 Streuung ------------------------------------------------------------------------ 351 12.5.2 Beugung und Aufloesungsbegrenzung ------------------------------------------------------------------------ 354 12.5.3 Brechung im Wellenbild ------------------------------------------------------------------------ 354 12.5.4 Interferenz ------------------------------------------------------------------------ 358 12.5.5 Diffraktive optische Elemente ------------------------------------------------------------------------ 363 12.5.6 Dispersion ------------------------------------------------------------------------ 364 12.5.7 Spektralapparate ------------------------------------------------------------------------ 365 12.5.8 Polarisation des Lichts ------------------------------------------------------------------------ 370 12.6 Photometrie ------------------------------------------------------------------------ 370 12.6.1 Photometrische Groeszen ------------------------------------------------------------------------ 376 12.6.2 Lichttechnische Groeszen ------------------------------------------------------------------------ 380 Formelzeichen Schwingungen und Wellen ------------------------------------------------------------------------ 382 13 Tabellen zu Akustik und Optik ------------------------------------------------------------------------ 382 13.1 Tabellen zur Akustik ------------------------------------------------------------------------ 386 13.2 Tabellen zur Optik ------------------------------------------------------------------------ 390 III Elektrizitaetslehre ------------------------------------------------------------------------ 390 14 Ladungen und Stroeme ------------------------------------------------------------------------ 390 14.1 Elektrische Ladung ------------------------------------------------------------------------ 392 14.1.1 Coulombsches Gesetz ------------------------------------------------------------------------ 393 14.2 Elektrische Ladungsdichte ------------------------------------------------------------------------ 395 14.3 Elektrischer Strom ------------------------------------------------------------------------ 396 14.3.1 Amperesches Gesetz ------------------------------------------------------------------------ 397 14.4 Elektrische Stromdichte ------------------------------------------------------------------------ 398 14.4.1 Elektrisches Stroemungsfeld ------------------------------------------------------------------------ 399 14.5 Elektrischer Widerstand und elektrischer Leitwert ------------------------------------------------------------------------ 399 14.5.1 Elektrischer Widerstand ------------------------------------------------------------------------ 400 14.5.2 Elektrischer Leitwert ------------------------------------------------------------------------ 400 14.5.3 Spezifischer Widerstand und elektrische Leitfaehigkeit ------------------------------------------------------------------------ 401 14.5.4 Beweglichkeit von Ladungstraegern ------------------------------------------------------------------------ 402 14.5.5 Temperaturabhaengigkeit des Widerstandes ------------------------------------------------------------------------ 403 14.5.6 Veraenderliche Widerstaende ------------------------------------------------------------------------ 404 14.5.7 Schaltung von Widerstaenden ------------------------------------------------------------------------ 406 15 Elektrisches und magnetisches Feld ------------------------------------------------------------------------ 406 15.1 Elektrisches Feld ------------------------------------------------------------------------ 407 15.2 Influenz ------------------------------------------------------------------------ 407 15.2.1 Elektrische Feldlinien ------------------------------------------------------------------------ 411 15.2.2 Elektrische Feldstaerke von Punktladungen ------------------------------------------------------------------------ 411 15.3 Kraft ------------------------------------------------------------------------ 412 15.4 Elektrische Spannung ------------------------------------------------------------------------ 413 15.5 Elektrisches Potential ------------------------------------------------------------------------ 414 15.5.1 AEquipotentialflaechen ------------------------------------------------------------------------ 414 15.5.2 Feldstaerke und Potential einiger Ladungsverteilungen ------------------------------------------------------------------------ 417 15.5.3 Elektrischer Fluss ------------------------------------------------------------------------ 419 15.5.4 Verschiebungsdichte im Vakuum ------------------------------------------------------------------------ 420 15.6 Elektrische Polarisation ------------------------------------------------------------------------ 421 15.6.1 Dielektriit ------------------------------------------------------------------------ 423 15.7 Kapazitaet ------------------------------------------------------------------------ 423 15.7.1 Plattenkondensator ------------------------------------------------------------------------ 424 15.7.2 Parallelschaltung von Kondensatoren ------------------------------------------------------------------------ 424 15.7.3 Reihenschaltung von Kondensatoren ------------------------------------------------------------------------ 425 15.7.4 Kapazitaeten einfacher Leiteranordnungen ------------------------------------------------------------------------ 426 15.8 Energie und Energiedichte des elektrischen Feldes ------------------------------------------------------------------------ 427 15.9 Elektrisches Feld an Grenzflaechen ------------------------------------------------------------------------ 428 15.10 Magnetisches Feld ------------------------------------------------------------------------ 428 15.11 Magnetismus ------------------------------------------------------------------------ 429 15.11.1 Magnetische Feldlinien ------------------------------------------------------------------------ 430 15.12 Magnetische Flussdichte ------------------------------------------------------------------------ 432 15.13 Magnetischer Fluss ------------------------------------------------------------------------ 434 15.14 Magnetische Feldstaerke ------------------------------------------------------------------------ 435 15.15 Magnetische Sparnung und magnetischer Kreis ------------------------------------------------------------------------ 437 15.15.1 Durchflutungssatz ------------------------------------------------------------------------ 438 15.15.2 Biot-Savartsches Gesetz ------------------------------------------------------------------------ 440 15.15.3 Magnetfeld eines geraden Leiters ------------------------------------------------------------------------ 441 15.15.4 Magnetische Felder einiger Stromverteilungen ------------------------------------------------------------------------ 442 15.16 Materie im Magnetfeld ------------------------------------------------------------------------ 443 15.16.1 Diamagnetismus ------------------------------------------------------------------------ 444 15.16.2 Paramagnetismus ------------------------------------------------------------------------ 444 15.16.3 Ferromagnetismus ------------------------------------------------------------------------ 447 15.16.4 Antiferromagnetismus ------------------------------------------------------------------------ 448 15.16.5 Ferrimagnetismus ------------------------------------------------------------------------ 448 15.17 Magnetische Felder an Grenzflaechen ------------------------------------------------------------------------ 449 15.18 Induktion ------------------------------------------------------------------------ 449 15.18.1 Bewegungsinduktion ------------------------------------------------------------------------ 450 15.18.2 Transformatorische Induktion ------------------------------------------------------------------------ 450 15.19 Selbstinduktion ------------------------------------------------------------------------ 452 15.19.1 Induktivitaeten geometrischer Leiteranordnungen ------------------------------------------------------------------------ 454 15.19.2 Magnetischer Leitwert ------------------------------------------------------------------------ 454 15.20 Gegeninduktion ------------------------------------------------------------------------ 455 15.20.1 Transformator ------------------------------------------------------------------------ 456 15.21 Energie und Energiedichte des Magnetfeldes ------------------------------------------------------------------------ 459 15.22 Maxwellsche Gleichungen ------------------------------------------------------------------------ 459 15.22.1 Verschiebungsstrom ------------------------------------------------------------------------ 460 15.22.2 Elektromagnetische Wellen ------------------------------------------------------------------------ 462 15.22.3 Poynting-Vektor ------------------------------------------------------------------------ 463 16 Anwendungen in der Elektrotechnik ------------------------------------------------------------------------ 464 16.1 Gleichstromkreis ------------------------------------------------------------------------ 465 16.1.1 Kirchhoffsche Gesetze im Gleichstromkreis ------------------------------------------------------------------------ 465 16.1.2 Widerstaende im Gleichstromkreis ------------------------------------------------------------------------ 467 16.1.3 Reale Spannungsquelle ------------------------------------------------------------------------ 468 16.1.4 Leistung und Energie im Gleichstromkreis ------------------------------------------------------------------------ 470 16.1.5 Leistungsanpassung ------------------------------------------------------------------------ 470 16.1.6 Strom- und Spannungsmessung ------------------------------------------------------------------------ 471 16.1.7 Widerstandsbestimmung mittels Kompensationsmethode ------------------------------------------------------------------------ 472 16.1.8 Auf- und Entladung von Kondensatoren ------------------------------------------------------------------------ 474 16.1.9 Ein- und Ausschalten des Stroms im RL-Kreis ------------------------------------------------------------------------ 475 16.2 Wechselstromkreis ------------------------------------------------------------------------ 475 16.2.1 Wechselgroeszen ------------------------------------------------------------------------ 477 16.2.2 Darstellung von Sinusgroeszen im Zeigerdiagramm ------------------------------------------------------------------------ 479 16.2.3 Rechenregeln fuer Zeigergroeszen ------------------------------------------------------------------------ 481 16.2.4 Grundbegriffe der Wechselstromtechnik ------------------------------------------------------------------------ 488 16.2.5 Grundbauelemente im Wechselstromkreis ------------------------------------------------------------------------ 491 16.2.6 Reihenschaltung von Widerstand und Kapazitaet ------------------------------------------------------------------------ 492 16.2.7 Parallelschaltung von Widerstand und Kapazitaet ------------------------------------------------------------------------ 493 16.2.8 Parallelschaltung von Widerstand und Induktivitaet ------------------------------------------------------------------------ 494 16.2.9 Reihenschaltung von Widerstand und Induktivitaet ------------------------------------------------------------------------ 495 16.2.10 Reihenschwingkreis ------------------------------------------------------------------------ 496 16.2.11 Parallelschwingkreis ------------------------------------------------------------------------ 498 16.2.12 AEquivalenz von Reihenschaltung und Parallelschaltung ------------------------------------------------------------------------ 499 16.2.13 Radiowellen ------------------------------------------------------------------------ 501 16.3 Elektrische Maschinen ------------------------------------------------------------------------ 501 16.3.1 Prinzipielle Funktionsweise ------------------------------------------------------------------------ 502 16.3.2 Gleichstrommaschine ------------------------------------------------------------------------ 504 16.3.3 Drehstrommaschine ------------------------------------------------------------------------ ------------------------------------------------------------------------ 508 17 Stromleitung in Fluessigkeiten, in Gasen und im Vakuum ------------------------------------------------------------------------ 508 17.1 Elektrolyse ------------------------------------------------------------------------ 508 17.1.1 Stoffmenge ------------------------------------------------------------------------ 508 17.1.2 Ionen ------------------------------------------------------------------------ 509 17.1.3 Elektroden ------------------------------------------------------------------------ 509 17.1.4 Elektrolyte ------------------------------------------------------------------------ 513 17.1.5 Galvanische Elemente ------------------------------------------------------------------------ 516 17.1.6 Elektrokinetische Effekte ------------------------------------------------------------------------ 517 17.2 Stromleitung in Gasen ------------------------------------------------------------------------ 517 17.2.1 Unselbstaendige Gasentladung ------------------------------------------------------------------------ 520 17.2.2 Selbstaendige Gasentladung ------------------------------------------------------------------------ 521 17.3 Elektronenemission ------------------------------------------------------------------------ 522 17.3.1 Gluehemission ------------------------------------------------------------------------ 522 17.3.2 Photoemission ------------------------------------------------------------------------ 523 17.3.3 Feldemission ------------------------------------------------------------------------ 523 17.3.4 Sekundaerelektronenemission ------------------------------------------------------------------------ 524 17.4 Elektronenroehren ------------------------------------------------------------------------ 524 17.4.1 Roehrendiode ------------------------------------------------------------------------ 525 17.4.2 Roehrentriode ------------------------------------------------------------------------ 527 17.4.3 Tetrode ------------------------------------------------------------------------ 527 17.4.4 Katodenstrahlen ------------------------------------------------------------------------ 528 17.4.5 Kanalstrahlen ------------------------------------------------------------------------ ------------------------------------------------------------------------ 529 18 Plasmaphysik ------------------------------------------------------------------------ 529 18.1 Eigenschafteneines Plasmas ------------------------------------------------------------------------ 529 18.1.1 Plasmakenngroeszen ------------------------------------------------------------------------ 535 18.1.2 Plasrnastrahhhg ------------------------------------------------------------------------ 536 18.1.3 Plasmen in Magnetfeldern ------------------------------------------------------------------------ 538 18.1.4 Plasnkiwellen ------------------------------------------------------------------------ 540 18.2 Erzeugung von Plasmen ------------------------------------------------------------------------ 541 18.2.1 Thermische Plasmaerzeugung ------------------------------------------------------------------------ 541 18.2.2 Plasmaerzeugng durch Kompression ------------------------------------------------------------------------ 543 18.3 Energieerzeugung mit Plasmen ------------------------------------------------------------------------ 543 18.3.1 MHD-Generator ------------------------------------------------------------------------ 544 18.3.2 Kernfusionsreaktoren ------------------------------------------------------------------------ 545 18.3.3 Fuesion unter magnetischer Halterung ------------------------------------------------------------------------ 546 18.3.4 Fusion unter Traegheitseinschluss ------------------------------------------------------------------------ 548 Formelzeichen Elektrizitaetslehre ------------------------------------------------------------------------ ------------------------------------------------------------------------ 550 19 Tabellen zur Elektrizitaetslehre ------------------------------------------------------------------------ 550 19.1 Metalle und Legierungen ------------------------------------------------------------------------ 550 19.1.1 Spezifischer elektrischer Widerstand ------------------------------------------------------------------------ 552 19.1.2 Spannungsreihen ------------------------------------------------------------------------ 554 19.2 Dielektrika ------------------------------------------------------------------------ 560 19.3 Praktische Tabellen der Elektrotechnik ------------------------------------------------------------------------ 562 19.4 Magnetische Eigenschaften ------------------------------------------------------------------------ 564 19.5 Ferromagnetische Eigenschaften ------------------------------------------------------------------------ 566 19.5.1 Magnetische Anisotropie ------------------------------------------------------------------------ 567 19.6 Ferrite ------------------------------------------------------------------------ 568 19.7 Antiferromagnete ------------------------------------------------------------------------ 568 19.8 lonenbeweglichkeit ------------------------------------------------------------------------ ------------------------------------------------------------------------ 569 IV Waermelehre ------------------------------------------------------------------------ ------------------------------------------------------------------------ 569 20 Gleichgewicht und Zustandsgroeszen ------------------------------------------------------------------------ 569 20.1 Systeme, Phasen und Gleichgewicht ------------------------------------------------------------------------ 569 20.1.1 Systeme ------------------------------------------------------------------------ 570 20.1.2 Phasen ------------------------------------------------------------------------ 571 20.1.3 Gleichgewicht ------------------------------------------------------------------------ 573 20.2 Zustandsgroeszen ------------------------------------------------------------------------ 573 20.2.1 Zustandsgroesze: Begriffsbestimmung ------------------------------------------------------------------------ 575 20.2.2 Temperatur ------------------------------------------------------------------------ 580 20.2.3 Druck ------------------------------------------------------------------------ 584 20.2.4 Teilchenzahl, Stoffmenge und Avogadrozahl ------------------------------------------------------------------------ 587 20.2.5 Entropie ------------------------------------------------------------------------ 588 20.3 Thermodynamische Potentiale ------------------------------------------------------------------------ 588 20.3.1 Prinzip der maximalen Entropie - Prinzip der minimalen Energie ------------------------------------------------------------------------ 588 20.3.2 Innere Energie als Potential ------------------------------------------------------------------------ 589 20.3.3 Entropie als thermodynamisches Potential ------------------------------------------------------------------------ 590 20.3.4 Freie Energie ------------------------------------------------------------------------ 591 20.3.5 Enthalpie ------------------------------------------------------------------------ 593 20.3.6 Freie Enthalpie ------------------------------------------------------------------------ 594 20.3.7 Maxwell-Relationen ------------------------------------------------------------------------ 595 20.3.8 Thermodynamische Stabilitaet ------------------------------------------------------------------------ 596 20.4 Ideales Gas ------------------------------------------------------------------------ 596 20.4.1 Boyle-Mariottesches Gesetz ------------------------------------------------------------------------ 597 20.4.2 Gesetz von Gay-Lussac ------------------------------------------------------------------------ 598 20.4.3 Zustandsgleichung ------------------------------------------------------------------------ 599 20.5 Kinetische Theorie des idealen Gases ------------------------------------------------------------------------ 599 20.5.1 Druck und Temperatur ------------------------------------------------------------------------ 601 20.5.2 Maxwell-Boltzmann-Verteilung ------------------------------------------------------------------------ 602 20.5.3 Freiheitsgrade ------------------------------------------------------------------------ 603 20.5.4 Gleichverteilungssatz ------------------------------------------------------------------------ 603 20.5.5 Transportvorgaenge ------------------------------------------------------------------------ 606 20.6 Zustandsgleichungen ------------------------------------------------------------------------ 606 20.6.1 Zustandsgleichung des idealen Gases ------------------------------------------------------------------------ 610 20.6.2 Zustandsgleichung realer Gase ------------------------------------------------------------------------ 615 20.6.3 Zustandsgleichungen fuer Fluessigkeiten und Festkoerper ------------------------------------------------------------------------ 618 21 Waerme, Energieumwandlung und Zustandsaenderungen ------------------------------------------------------------------------ 618 21.1 Energieformen ------------------------------------------------------------------------ 618 21.1.1 Energieeinheiten ------------------------------------------------------------------------ 619 21.1.2 Arbeit ------------------------------------------------------------------------ 620 21.1.3 Chemisches Potential ------------------------------------------------------------------------ 620 21.1.4 Waerme ------------------------------------------------------------------------ 622 21.2 Energieumwandlung ------------------------------------------------------------------------ 622 21.2.1 Umwandlung von aequivalenten Enaergien in Waerme ------------------------------------------------------------------------ 625 21.2.2 Umwandlung von Waerme in andere Energieformen ------------------------------------------------------------------------ 625 21.2.3 Exergie und Anergie ------------------------------------------------------------------------ 626 21.3 Waermekapazitaet ------------------------------------------------------------------------ 626 21.3.1 Totale Waermekapazitaet ------------------------------------------------------------------------ 628 21.3.2 Molare Waermekapazitaet ------------------------------------------------------------------------ 629 21.3.3 Spezifische Waermekapazitaet ------------------------------------------------------------------------ 633 21.4 Zustandsaenderungen ------------------------------------------------------------------------ 633 21.4.1 Reversible und irreversible Prozesse ------------------------------------------------------------------------ 634 21.4.2 Isothermer Prozess ------------------------------------------------------------------------ 635 21.4.3 Isobarer Proiess ------------------------------------------------------------------------ 636 21.4.4 Isochorer Prozess ------------------------------------------------------------------------ 636 21.4.5 Adiabatischer (isentroper) Prozess ------------------------------------------------------------------------ 639 21.4.6 Gleichgewichtszustaende ------------------------------------------------------------------------ 639 21.5 Thermodynamischet.iiptsaetze ------------------------------------------------------------------------ 639 21.5.1 Nullter Hauptsatz ------------------------------------------------------------------------ 640 21.5.2 Erster Hauptsatz ------------------------------------------------------------------------ 642 21.5.3 Zweiter Hauptsatz ------------------------------------------------------------------------ 643 21.5.4 Dritter Hauptsatz ------------------------------------------------------------------------ 643 21.6 Carnotscher Kreisprozuess ------------------------------------------------------------------------ 646 21.6.2 Reduzierte Waerme ------------------------------------------------------------------------ 647 21.7 Thermodynamische Maschinen ------------------------------------------------------------------------ 647 21.7.1 Rechts- und linkslaufende Prozesse ------------------------------------------------------------------------ 648 21.7.2 Waermepumpe und Kaeltemaschine ------------------------------------------------------------------------ 649 21.7.3 Stirling-Prozeis ------------------------------------------------------------------------ 650 21.7.4 Dampfmaschine ------------------------------------------------------------------------ 651 21.7.5 Offene Systeme ------------------------------------------------------------------------ 652 21.7.6 Otto- und Diesel-Motor ------------------------------------------------------------------------ 654 21.7.7 Gasturbinen ------------------------------------------------------------------------ 655 21.8 Gasverfluessigung ------------------------------------------------------------------------ 655 21.8.1 Herstellung tiefer Temperaturen ------------------------------------------------------------------------ 656 21.8.2 Joule-Thomson-Effekt ------------------------------------------------------------------------ 659 22 Phasenumwandlungen, Reaktionen und Waermeausgleich ------------------------------------------------------------------------ 659 22.1 Phase und Aggregatzustand ------------------------------------------------------------------------ 659 22.1.1 Phase ------------------------------------------------------------------------ 659 22.1.2 Aggregatzustaende ------------------------------------------------------------------------ 660 22.1.3 Aggregatumwandlungen ------------------------------------------------------------------------ 661 22.1.4 Dampf ------------------------------------------------------------------------ 662 22.2 Ordnung von Phasenuebergaengen ------------------------------------------------------------------------ 662 22.2.1 Phasenuebergang erster Ordnung ------------------------------------------------------------------------ 663 22.2.2 Phasenuebergang zweiter Ordnung ------------------------------------------------------------------------ 664 22.2.3 Lambda-UEbergaenge ------------------------------------------------------------------------ 664 22.2.4 Phasenkoexistenzgebiet ------------------------------------------------------------------------ 665 22.2.5 Kritische Indizes ------------------------------------------------------------------------ 665 22.3 Phasenuebergang und Van-der-Waals-Gas ------------------------------------------------------------------------ 665 22.3.1 Phasengleichgewicht ------------------------------------------------------------------------ 666 22.3.2 Maxwell-Konstruktion ------------------------------------------------------------------------ 668 22.3.3 Siedeverzug und Kondensationsverzug ------------------------------------------------------------------------ 669 22.3.4 Gesetz der uebereinstimmenden Zustaende ------------------------------------------------------------------------ 669 22.4 Beispiele fuer Phasenuebergaenge ------------------------------------------------------------------------ 669 22.4.1 Magnetische Phasenumwandlungen ------------------------------------------------------------------------ 670 22.4.2 Ordnungs-Unordnungs-Phasenuebergaenge ------------------------------------------------------------------------ 670 22.4.3 Umwandlungen der Kristallstruktur ------------------------------------------------------------------------ 672 22.4.4 Fluessige Kristalle ------------------------------------------------------------------------ 672 22.4.5 Supraleitung ------------------------------------------------------------------------ 672 22.4.6 Suprafluiditat ------------------------------------------------------------------------ 673 22.5 Mehrkomponentige Gase ------------------------------------------------------------------------ 674 22.5.1 Partialdruck und Daltonsches Gesetz ------------------------------------------------------------------------ 674 22.5.2 Euler-Gleichung und Gibbs-Duhem-Relation ------------------------------------------------------------------------ 675 22.6 Mehrphasensysteme ------------------------------------------------------------------------ 675 22.6.1 Phasengleichgewicht ------------------------------------------------------------------------ 676 22.6.2 Gibbssche Phasenregel ------------------------------------------------------------------------ 676 22.6.3 Clausius-Clapeyron-Gleichung ------------------------------------------------------------------------ 677 22.7 Dampfdruck von Loesungen ------------------------------------------------------------------------ 677 22.7.1 Raoultsches Gesetz ------------------------------------------------------------------------ 678 22.7.2 Siedepunktserhoehung und Gefrierpunktserniedrigung ------------------------------------------------------------------------ 679 22.7.3 Henry-Dalton-Gesetz ------------------------------------------------------------------------ 679 22.7.4 Dampf-Luft-Gemische (feuchte Luft) ------------------------------------------------------------------------ 683 22.8 Chemische Reaktionen ------------------------------------------------------------------------ 684 22.8.1 Stoechiometrie ------------------------------------------------------------------------ 685 22.8.2 Phasenregel bei chemischen Reaktionen ------------------------------------------------------------------------ 685 22.8.3 Massenwirkungsgesetz ------------------------------------------------------------------------ 687 22.8.4 pH-Wert und Loeslichkeitsprodukt ------------------------------------------------------------------------ 688 22.9 Temperaturausgleich ------------------------------------------------------------------------ 688 22.9.1 Mischungstemperatur zweier Systeme ------------------------------------------------------------------------ 689 22.9.2 Reversible und irreversible Prozessfuehrung ------------------------------------------------------------------------ 690 22.10 Waermeuebertragung ------------------------------------------------------------------------ 690 22.10.1 Waermestrom ------------------------------------------------------------------------ 691 22.10.2 Waermeuebergang ------------------------------------------------------------------------ 692 22.10.3 Waermeleitung ------------------------------------------------------------------------ 696 22.10.4 Waermewiderstand ------------------------------------------------------------------------ 698 22.10.5 Waermedurchgang ------------------------------------------------------------------------ 702 22.10.6 Waermestrahlung ------------------------------------------------------------------------ 702 22.10.7 Strahlungsaufnahme ------------------------------------------------------------------------ 704 22.11 Waerme- und Massentransport ------------------------------------------------------------------------ 704 22.11.1 Fouriersches Gesetz ------------------------------------------------------------------------ 704 22.11.2 Kontinuitaetsgleichung ------------------------------------------------------------------------ 705 22.11.3 Waermeleitungsgleichung ------------------------------------------------------------------------ 706 22.11.4 Ficksches Gesetz und Diffusionsgleichung ------------------------------------------------------------------------ 707 22.11.5 Loesung von Waermeleitungs- und Diffusionsgleichung ------------------------------------------------------------------------ 708 Formelzeichen Waermelehre ------------------------------------------------------------------------ 711 23 Tabellen zur Thermodynamik ------------------------------------------------------------------------ 711 23.1 Charakteristische Temperaturen ------------------------------------------------------------------------ 711 23.1.1 Einheiten und Eichpunkte ------------------------------------------------------------------------ 712 23.1.2 Schmelz- und Siedepunkte ------------------------------------------------------------------------ 719 23.1.3 Curie- und Neel-Temperaturen ------------------------------------------------------------------------ 720 23.2 Kenngroeszen realer Gase ------------------------------------------------------------------------ 721 23.3 Thermische Eigenschaften der Stoffe ------------------------------------------------------------------------ 721 23.3.1 Viskositaet ------------------------------------------------------------------------ 721 23.3.2 Ausdehnung, Waermekapazitaet und thermische Leitfaehigkeit ------------------------------------------------------------------------ 727 23.4 Waermeuebertragung ------------------------------------------------------------------------ 729 23.5 Praktische Korrekturdaten ------------------------------------------------------------------------ 729 23.5.1 Druckmessung ------------------------------------------------------------------------ 733 23.5.2 Volumenmessungen - Umrechnung auf Standardtemperatur ------------------------------------------------------------------------ 734 23.6 Erzeugung fiuissigerTieftemperaturbaeder ------------------------------------------------------------------------ 734 23.7 Trockenmittel ------------------------------------------------------------------------ 735 23.8 Dampfdruck ------------------------------------------------------------------------ 735 23.8.1 Loesungen ------------------------------------------------------------------------ 735 23.8.2 Relative Feuchte ------------------------------------------------------------------------ 736 23.8.3 Dampfdruck von Wasser ------------------------------------------------------------------------ 738 23.9 Spezifische Enthalpien ------------------------------------------------------------------------ V Quantenphysik ------------------------------------------------------------------------ 741 24 Photonen - Elektromagnetische Strahlung und Lichtquanten ------------------------------------------------------------------------ 741 24.1 Plancksches Strahlungsgesetz ------------------------------------------------------------------------ 744 24.2 Photoelektrischer Effekt ------------------------------------------------------------------------ 745 24.3 Compton-Effekt ------------------------------------------------------------------------ 748 25 Materiewellen - Wellenmechanik der Teilchen ------------------------------------------------------------------------ 748 25.1 Wellennatur der Teilchen ------------------------------------------------------------------------ 749 25.2 Heisenbergsche Unschaerferelation ------------------------------------------------------------------------ 750 25.3 Wellenfunktion und Observable ------------------------------------------------------------------------ 757 25.4 Schrodingergleichung ------------------------------------------------------------------------ 758 25.4.1 Stueckweise konstante Potentiale ------------------------------------------------------------------------ 762 25.4.2 Harmonischer Osziliator ------------------------------------------------------------------------ 765 25.4.3 Pauli-Prinzip ------------------------------------------------------------------------ 765 25.5 Spin und magnetische Momente ------------------------------------------------------------------------ 765 25.5.1 Spin ------------------------------------------------------------------------ 768 25.5.2 Magnetische Momente ------------------------------------------------------------------------ 771 26 Atom- und Molekuelphysik ------------------------------------------------------------------------ 772 26.1 Grundbegriffe der Spektroskopie ------------------------------------------------------------------------ 774 26.2 Wasserstoffatom ------------------------------------------------------------------------ 775 26.2.1 Bohrsche Postulate ------------------------------------------------------------------------ 775 26.2.1 Bohrsche Postulate ------------------------------------------------------------------------ 779 26.3 Stationaere Zustaende und Quantenzahlen im Zentralfeld ------------------------------------------------------------------------ 783 26.4 Vielelektronenatoeme ------------------------------------------------------------------------ 788 26.5 Roentgenstrahlen ------------------------------------------------------------------------ 789 26.5.1 Anwendung von Roentgenstrahlen ------------------------------------------------------------------------ 791 26.6 Molekuelspektren ------------------------------------------------------------------------ 794 26.7 Atome in aeuszeren Feldern ------------------------------------------------------------------------ 796 26.8 Periodensystem der Elemente ------------------------------------------------------------------------ 798 26.9 Wechselwirkung von Photonen mit Atomen und Molekuelen ------------------------------------------------------------------------ 798 26.9.1 Spontane und induzierte Emission ------------------------------------------------------------------------ 801 27 Elementarteilchenphysik das Standard Modell ------------------------------------------------------------------------ 801 27.1 Vereinheitlichung der Wechselwirkungen ------------------------------------------------------------------------ 801 27.1.1 Standard-Modell ------------------------------------------------------------------------ 804 27.1.2 Feldquanten oder Eichbosonen ------------------------------------------------------------------------ 806 27.1.3 Fermionen und Bosonen ------------------------------------------------------------------------ 808 27.2 Leptonen, Quarks und Vektorbosonen ------------------------------------------------------------------------ 808 27.2.1 Leptonen ------------------------------------------------------------------------ 809 27.2.2 Quarks ------------------------------------------------------------------------ 811 27.2.3 Hadronen ------------------------------------------------------------------------ 816 27.2.4 Beschleuniger und Detektoren ------------------------------------------------------------------------ 817 27.3 Symmetrien und Erhaltungssaetze ------------------------------------------------------------------------ 818 27.3.1 Paritaetserhaltung und schwache Wechselwirkung ------------------------------------------------------------------------ 819 27.3.2 Ladungserhaltung und Paarbildung ------------------------------------------------------------------------ 820 27.3.3 Ladungskonjugation und Antiteilchen ------------------------------------------------------------------------ 820 27.3.4 Zeitumkehr Invarianz und Umkehrreaktionen ------------------------------------------------------------------------ 821 27.3.5 Erhaltungssaetze ------------------------------------------------------------------------ 822 27.3.6 Jenseits des Standard-Modells ------------------------------------------------------------------------ 824 28 Kernphysik ------------------------------------------------------------------------ 824 28.1 Bausteine des Atomkerns ------------------------------------------------------------------------ 827 28.2 Grundgroeszen des Atomkerns ------------------------------------------------------------------------ 829 28.3 Nukleon-Nukleon-Wechselwirkung ------------------------------------------------------------------------ 829 28.3.1 Phaenomenologische Nukleon-Nukleon-Potentiale ------------------------------------------------------------------------ 830 28.3.2 Mesonenaustauschpotentiale ------------------------------------------------------------------------ 831 28.4 Kernmodelle ------------------------------------------------------------------------ 831 28.4.1 Fermigas-Modell ------------------------------------------------------------------------ 831 28.4.2 Kernmaterie ------------------------------------------------------------------------ 832 28.4.3 Troepfchen-Modell ------------------------------------------------------------------------ 833 28.4.4 Schalenmodell ------------------------------------------------------------------------ 836 28.4.5 Kollektivmodell ------------------------------------------------------------------------ 838 28.5 Kernreaktionen ------------------------------------------------------------------------ 838 28.5.1 Reaktionskanaele und Wirkungsquerschnitte ------------------------------------------------------------------------ 841 28.5.2 Erhaltungssaetze in Kernreaktionen ------------------------------------------------------------------------ 844 28.5.3 Elastische Streuung ------------------------------------------------------------------------ 845 28.5.4 Compoundkernreaktion ------------------------------------------------------------------------ 847 28.5.5 Optisches Modell ------------------------------------------------------------------------ 848 28.5.6 Direkte Reaktion ------------------------------------------------------------------------ 849 28.5.7 Schwerionenreaktionen ------------------------------------------------------------------------ 851 28.5.8 Kernspaltung ------------------------------------------------------------------------ 853 28.6 Kernzerfall ------------------------------------------------------------------------ 854 28.6.1 Zerfallsgesetz ------------------------------------------------------------------------ 858 28.6.2 Alpha-Zerfall ------------------------------------------------------------------------ 859 28.6.3 Beta-Zerfall ------------------------------------------------------------------------ 862 28.6.4 Gamma-Zerfall ------------------------------------------------------------------------ 862 28.6.5 Emission von Nukleonen und Nukleonenclustern ------------------------------------------------------------------------ 863 28.7 Kernreaktor ------------------------------------------------------------------------ 865 28.7.1 Reaktortpen ------------------------------------------------------------------------ 866 28.8 Kernfusion ------------------------------------------------------------------------ 869 28.9 Wechselwirkung von Strahlung mit Materie ------------------------------------------------------------------------ 869 28.9.1 Ionisierende Teilchen ------------------------------------------------------------------------ 872 28.9.2 Gamma-Strahlung ------------------------------------------------------------------------ 874 28.10 Dosimetrie ------------------------------------------------------------------------ 877 28.10.1 Dosismessverfahren ------------------------------------------------------------------------ 879 28.10.2 Umweltradioaktivitaet ------------------------------------------------------------------------ 882 29 Festkirperphysik ------------------------------------------------------------------------ 882 29.1 Struktur fester Koerper ------------------------------------------------------------------------ 882 29.1.1 Einige Grundbegriffe der Festkoerperphysik ------------------------------------------------------------------------ 883 29.1.2 Struktur der Kristalle ------------------------------------------------------------------------ 885 29.1.3 Bravais Gitter ------------------------------------------------------------------------ 889 29.1.4 Methoden der Strukturuntersuchung ------------------------------------------------------------------------ 891 29.1.5 Bindungsverhaeltnisse in Kristallen ------------------------------------------------------------------------ 894 29.2 Gitterfehler ------------------------------------------------------------------------ 894 29.2.1 Punktfehler ------------------------------------------------------------------------ 896 29.2.2 Eindimensionale Defekte ------------------------------------------------------------------------ 898 29.2.3 Zweidimensionale Gitterfehler ------------------------------------------------------------------------ 898 29.2.4 Amorphe Festkoerper ------------------------------------------------------------------------ 899 29.3 Mechanische Eigenschaften von Werkstoffen ------------------------------------------------------------------------ 900 29.3.1 Makromolekulare Festkoerper ------------------------------------------------------------------------ 903 29.3.2 Verbundwerkstoffe ------------------------------------------------------------------------ 904 29.3.3 Legierungen ------------------------------------------------------------------------ 906 29.3.4 Fluessigkristalle ------------------------------------------------------------------------ 907 29.4 Phononen und Gitterschwingungen ------------------------------------------------------------------------ 907 29.4.1 Elastische Wellen ------------------------------------------------------------------------ 911 29.4.2 Phononen und spezifische Waermekapazitaet ------------------------------------------------------------------------ 912 29.4.3 Einstein-Modell ------------------------------------------------------------------------ 913 29.4.4 Debye-Modell ------------------------------------------------------------------------ 915 29.4.5 Waermeleitung ------------------------------------------------------------------------ 917 29.5 Elektronen im Festkoerper ------------------------------------------------------------------------ 917 29.5.1 Freies Elektronengas ------------------------------------------------------------------------ 922 29.5.2 Baendermodell ------------------------------------------------------------------------ 927 29.6 Halbleiter ------------------------------------------------------------------------ 929 29.6.1 Stoerstellenleitung ------------------------------------------------------------------------ 932 29.6.2 Halbleiterdiode ------------------------------------------------------------------------ 939 29.6.3 Transistor ------------------------------------------------------------------------ 946 29.6.4 Unipolare (Feldeffekt-)Transistoren ------------------------------------------------------------------------ 949 29.6.5 Thyristor ------------------------------------------------------------------------ 951 29.6.6 Integrierte Schaltkreise (IC) ------------------------------------------------------------------------ 954 29.6.7 Operationsverstaerker ------------------------------------------------------------------------ 960 29.7 Supraleitung ------------------------------------------------------------------------ 960 29.7.1 Grundlegende Eigenschaften der Supraleitung ------------------------------------------------------------------------ 964 29.7.2 Hochtemperatur-Supraleiter ------------------------------------------------------------------------ 966 29.8 Magnetische Eigenschaften ------------------------------------------------------------------------ 968 29.8.1 Ferromagnetismus ------------------------------------------------------------------------ 971 29.8.2 Antiferromagnetismus und Ferrimagnetismus ------------------------------------------------------------------------ 972 29.9 Dielektrische Eigenschaften ------------------------------------------------------------------------ 975 29.9.1 Paraelektrika ------------------------------------------------------------------------ 976 29.9.2 Ferroelektrika ------------------------------------------------------------------------ 977 29.10 Optische Eigenschaften von Kristallen ------------------------------------------------------------------------ 977 29.10.1 Exzitonen und ihre Eigenschaften ------------------------------------------------------------------------ 979 29.10.2 Photoleitfaehigkeit ------------------------------------------------------------------------ 980 29.10.3 Lumineszenz ------------------------------------------------------------------------ 980 29.10.4 Optoelektronische Eigenschaften ------------------------------------------------------------------------ 982 Formelzeichentabelle Mikrophysik ------------------------------------------------------------------------ 987 30 Tabellen zur Quantenphysik ------------------------------------------------------------------------ 987 30.1 lonisationspotentiale ------------------------------------------------------------------------ 992 30.2 Atom- und lonenradien der Elemente ------------------------------------------------------------------------ 994 30.3 Elektronenemission ------------------------------------------------------------------------ 998 30.4 Roentgenstrahlung ------------------------------------------------------------------------ 998 30.5 Kernreaktionen ------------------------------------------------------------------------ 999 30.6 Wechselwirkung der Strahlung mit Materie ------------------------------------------------------------------------ 1000 30.7 Halleffekt ------------------------------------------------------------------------ 1001 30.8 Supraleiter ------------------------------------------------------------------------ 1003 30.9 Halbleiter ------------------------------------------------------------------------ 1003 30.9.1 Thermische, magnetische und elektrische Eigenschaften von Halbleitern ------------------------------------------------------------------------ VI Anhang ------------------------------------------------------------------------ 1005 31 Messungen und Messfehler ------------------------------------------------------------------------ 1005 31.1 Beschreibung von Messungen ------------------------------------------------------------------------ 1005 31.1.1 Groeszen und SI-Einheiten ------------------------------------------------------------------------ 1008 31.2 Fehlerrechnung und Statistik ------------------------------------------------------------------------ 1008 31.2.1 Fehlerarten ------------------------------------------------------------------------ 1009 31.2.2 Mittelwerte von Messreihen ------------------------------------------------------------------------ 1011 31.2.3 Streuung ------------------------------------------------------------------------ 1012 31.2.4 Korrelation ------------------------------------------------------------------------ 1012 31.2.5 Ausgleichsrechnung, Regression ------------------------------------------------------------------------ 1013 31.2.6 Haeufigkeitsverteilungen ------------------------------------------------------------------------ 1018 31.2.7 Zuverlaessigkeit ------------------------------------------------------------------------ 1020 32 Vektorrechnung ------------------------------------------------------------------------ 1020 32.1 Vektoren ------------------------------------------------------------------------ 1021 32.2 Multiplikation mit einem Skalar ------------------------------------------------------------------------ 1021 32.3 Addition und Subtraktion von Vektoren ------------------------------------------------------------------------ 1022 32.4 Multiplikation von ------------------------------------------------------------------------ 1025 33 Differential- und Integralrechnung ------------------------------------------------------------------------ 1025 33.1 Differentialrechnung ------------------------------------------------------------------------ 1025 33.1.1 Differentiationsregeln ------------------------------------------------------------------------ 1026 33.2 Integralrechnung ------------------------------------------------------------------------ 1027 33.2.1 Integrationsregeln ------------------------------------------------------------------------ 1028 33.3 Ableitungen und Integrale elementarer Funktionen ------------------------------------------------------------------------ 1029 34 Tabellen zum SI-System ------------------------------------------------------------------------ Tabellenverzeichnis ------------------------------------------------------------------------ 216 8.1/1 Einfache Metalle ------------------------------------------------------------------------ 217 8.1/2 Konstruktionswerkstoffe ------------------------------------------------------------------------ 217 8.1/3 Elektrische Funktionswerkstoffe ------------------------------------------------------------------------ 218 8.1/4 Magnetische Funktionswerkstoffe ------------------------------------------------------------------------ 218 8.1/5 Ferrite ------------------------------------------------------------------------ 218 8.1/6 Glas ------------------------------------------------------------------------ 218 8.1/7 Keramik ------------------------------------------------------------------------ 219 8.1/8 Kunststoffe ------------------------------------------------------------------------ 220 8.1/9 Halbleiter ------------------------------------------------------------------------ 220 8.1/10 Baustoffe ------------------------------------------------------------------------ 221 8.1/11 Schuettgueter ------------------------------------------------------------------------ 221 8.1/12 Fluessigkeiten unter Normalbedingungen ------------------------------------------------------------------------ 222 8.1/13 Dichte einiger Metalle im fluessigen Zustand ------------------------------------------------------------------------ 223 8.2/1 Elastische Eigenschaften ------------------------------------------------------------------------ 224 8.2/2 Kritische Spannungen ------------------------------------------------------------------------ 224 8.2/3 Draehte ------------------------------------------------------------------------ 224 8.2/4 Whisker ------------------------------------------------------------------------ 225 8.2/5 Stahl ------------------------------------------------------------------------ 225 8.2/6 Keramische Werkstoffe ------------------------------------------------------------------------ 226 8.2/7 Kunststoffe ------------------------------------------------------------------------ 226 8.2/8 Faser ------------------------------------------------------------------------ 226 8.3/1 Rollreibung ------------------------------------------------------------------------ 227 8.3/2 Gleitreibungszahl ------------------------------------------------------------------------ 227 8.3/3 Haftreibung ------------------------------------------------------------------------ 228 8.3/4 Helium ------------------------------------------------------------------------ 228 8.3/5 Stickstoff ------------------------------------------------------------------------ 229 8.3/6 Wasserstoff ------------------------------------------------------------------------ 229 8.3/7 Methan ------------------------------------------------------------------------ 230 8.3/8 Stickstoffmonoxid ------------------------------------------------------------------------ 230 8.3/9 Kohlendioxid ------------------------------------------------------------------------ 230 8.3/10 Temperaturabhaengigkeit der Kompressibilitaet ------------------------------------------------------------------------ 231 8.3/11 Kompressibilitaet von Fluessigkeiten ------------------------------------------------------------------------ 231 8.3/12 Kompressibilitaet von Festkoerpern ------------------------------------------------------------------------ 231 8.3/13 Viskositaet von Fluessigkeiten ------------------------------------------------------------------------ 231 8.3/14 Viskositaet kryogener Fluessigkeiten ------------------------------------------------------------------------ 231 8.3/15 Viskositaet waessriger Loesungen ------------------------------------------------------------------------ 232 8.3/16 Viskositaet von Wasser ------------------------------------------------------------------------ 232 8.3/17 Viskositaet als Funktion der Temperatur ------------------------------------------------------------------------ 232 8.3/18 Viskositaet von Gasen ------------------------------------------------------------------------ 233 8.3/19 Viskositaet von Gasen ------------------------------------------------------------------------ 233 8.3/20 Temperaturkorrekturfaktor ------------------------------------------------------------------------ 234 8.3/21 Widerstandsbeiwerte ------------------------------------------------------------------------ 235 8.3/22 Oberflaechenspannung von Fluessigkeiten und Loesungen ------------------------------------------------------------------------ 382 13.1/1 Korrekturfaktoren harmonische Schwingung ------------------------------------------------------------------------ 382 13.1/2 Schallgeschwindigkefr jR,Gasen ------------------------------------------------------------------------ 382 13.1/3 SchallgeschwindigkIt in Luft ------------------------------------------------------------------------ 382 13.1/4 Schalldaempfungskoeffizient in Gasen ------------------------------------------------------------------------ 382 13.1/5 Schallfeldgroeszen in Luft ------------------------------------------------------------------------ 383 13.1/6 Schallgeschwindigkeiten in Erdoelprodukten ------------------------------------------------------------------------ 383 13.1/7 Schallgeschwindigkeiten in Fluessigkeiten ------------------------------------------------------------------------ 383 13.1/8 Schalldaempfungskoeffizienten in Fluessigkeiten ------------------------------------------------------------------------ 384 13.1/12 Daemmzahlen fuer Baustoffe ------------------------------------------------------------------------ 385 13.1/13 Schallschwaechung in Luft ------------------------------------------------------------------------ 385 13.1/14 Lautstaerken ------------------------------------------------------------------------ 385 13.1/15 Gesundheitsschaedlicher Laerm ------------------------------------------------------------------------ 386 13.1/16 Schallabsorptionsgrade ------------------------------------------------------------------------ 386 13.2/1 Fasertypen der optischen Signaluebertragung ------------------------------------------------------------------------ 387 13.2/2 Brechzahlen ------------------------------------------------------------------------ 387 13.2/3 Wichtige Lasertyp en ------------------------------------------------------------------------ 388 13.2/4 Kohaerenzlaengen einiger Lichtquellen ------------------------------------------------------------------------ 388 13.2/5 Beleuchtungsstaerken ------------------------------------------------------------------------ 388 13.2/6 Lichtstroeme ------------------------------------------------------------------------ 388 13.2/7 Hellempfindlichkeitsgrad ------------------------------------------------------------------------ 389 13.2/8 Ultraviolettes Spektralgebiet ------------------------------------------------------------------------ 389 13.2/9 Fraunhoferlinien ------------------------------------------------------------------------ 550 19.1/1 Metalle bei Raumtemperatur ------------------------------------------------------------------------ 550 19.1/2 Druckabhaengigkeit ------------------------------------------------------------------------ 551 19.1/3 Relative AEnderung am Schmelzpunkt ------------------------------------------------------------------------ 551 19.1/4 Legierungen ------------------------------------------------------------------------ 552 19.1/5 Elektrochemische Spannungsreihe ------------------------------------------------------------------------ 552 19.1/6 Thermoelektrische Spannungsreihe ------------------------------------------------------------------------ 553 19.1/7 Thermospannung gebraeuchlicher Thermoelemente ------------------------------------------------------------------------ 553 19.1/8 Gebraeuchliche Thermopaare ------------------------------------------------------------------------ 554 19.1/9 Peltier-Koeffizient fuer verschiedene Metalle ------------------------------------------------------------------------ 554 19.2/1 Dielektrizitaetszahl ------------------------------------------------------------------------ 556 19.2/2 Keramiken ------------------------------------------------------------------------ 556 19.2/3 Glaeser ------------------------------------------------------------------------ 556 19.2/4 Elektrische Eigenschaften von Polymeren ------------------------------------------------------------------------ 557 19.2/5 Spezifischer Widerstand von Isolierstoffen ------------------------------------------------------------------------ 557 19.2/6 Elektrische Eigenschaften von Isolierstoffen ------------------------------------------------------------------------ 559 19.2/7 Elektrische Eigenschaften von Transformatoroel ------------------------------------------------------------------------ 559 19.2/8 Einige Eigenschaften von Elektreten ------------------------------------------------------------------------ 559 19.2/9 Ferroelektrika mit Sauerstoff-Oktaederstruktur ------------------------------------------------------------------------ 560 19.3/1 Widerstandslegierungen ------------------------------------------------------------------------ 560 19.3/2 Spannung Weston-Normalelemente ------------------------------------------------------------------------ 560 19.3/3 Kontaktwerkstoffe ------------------------------------------------------------------------ 560 19.3/4 Spannungsbereiche in der Elektrotechnik ------------------------------------------------------------------------ 561 19.3/5 Richtwerte einiger Spannungen ------------------------------------------------------------------------ 561 19.3/6 Gasdurchlaessigkeit einiger Quarzglaeser ------------------------------------------------------------------------ 561 19.3/7 Wirkung des elektrischen Stromes ------------------------------------------------------------------------ 562 19.4/1 Magnetische Suszeptibilitaet ------------------------------------------------------------------------ 562 19.4/2 Magnetische Suszeptibilitaet anorganischer Verbindungen ------------------------------------------------------------------------ 564 19.4/3 Technisch relevante magnetische Legierungen ------------------------------------------------------------------------ 564 19.5/1 Ferromagnetische Elemente ------------------------------------------------------------------------ 565 19.5/2 Binaere Eisenlegierungen ------------------------------------------------------------------------ 565 19.5/3 Binare Nickellegierungen ------------------------------------------------------------------------ 566 19.5/4 Anisotropie-Koeffizienten ------------------------------------------------------------------------ 567 19.5/5 Magnetisierungsrichtungen in kubischen Kristallen ------------------------------------------------------------------------ 567 19.6/1 Magnetische Eigenschaften ------------------------------------------------------------------------ 568 19.7/1 Eigenschaften einiger Antiferromagnete ------------------------------------------------------------------------ 568 19.8/1 lonenbeweglichkeit p in Luft bei 18°C und Normaldruck ------------------------------------------------------------------------ 577 20.1 IPTS-90-Fixpunkte ------------------------------------------------------------------------ 737 23.8/6 Spez. Volumen und spez. Enthalpie von Wasserdampf ------------------------------------------------------------------------ 711 23.1/1 Eichpunkte ------------------------------------------------------------------------ 712 23.1/2 Schmelz- und Siedepunkte - Elemente ------------------------------------------------------------------------ 713 23.1/3 Schmelz- und Siedepunkte - anorgVerbindungen ------------------------------------------------------------------------ 715 23.1/4 Schmelz- und Siedepunkte - orgVerbindungen ------------------------------------------------------------------------ 717 23.1/5 Schmelz- und Siedepunkte - OElen ------------------------------------------------------------------------ 718 23.1/6 Schmelz- und Siedepunkte - Hochtemperaturkeramiken ------------------------------------------------------------------------ 718 23.1/7 Schmelz- und Siedepunkte - Legierungen ------------------------------------------------------------------------ 719 23.1/8 Curie-Temperatur ferromagnetischer Stoffe ------------------------------------------------------------------------ 719 23.1/9 Neel-Temperaturen ------------------------------------------------------------------------ 719 23.1/10 Curie-Temperatur ferroelektrischer Stoffe ------------------------------------------------------------------------ 720 23.2/1 Temperatur, Druck und Dichte am kritischen Punkt ------------------------------------------------------------------------ 720 23.2/2 Molmasse, spezifische Gaskonstante und Dichte von Gasen ------------------------------------------------------------------------ 720 23.2/3 Van-der-Waals Konstanten ------------------------------------------------------------------------ 721 23.2/4 Druck und Temperatur am Tripelpunkt ------------------------------------------------------------------------ 721 23.3/1 Dynamische Viskositaet von Gasen ------------------------------------------------------------------------ 721 23.3/2 Dynamische Viskositaet von Fluessigkeiten ------------------------------------------------------------------------ 722 23.3/3 ThermEigenschaften reiner Metalle ------------------------------------------------------------------------ 723 23.3/4 ThermEigenschaften von Baustoffen ------------------------------------------------------------------------ 724 23.3/5 ThermEigenschaften von Gasen ------------------------------------------------------------------------ 725 23.3/6 ThermEigenschaften von Fluessigkeiten ------------------------------------------------------------------------ 725 23.3/7 ThermEigenschaften von Kunststoffen ------------------------------------------------------------------------ 726 23.3/8 ThermEigenschaften anderer fester Stoffe ------------------------------------------------------------------------ 726 23.3/9 Waermeleitfaehigkeit von Waermedaemmstoffen ------------------------------------------------------------------------ 726 23.3/10 Waermeleitung bei verschiedenen Temperaturen ------------------------------------------------------------------------ 727 23.3/11 Ausdehnung von Wasser bei verschiedenen Temperaturen ------------------------------------------------------------------------ 727 23.3/12 Volumenausdehnung von Fluessigkeiten ------------------------------------------------------------------------ 727 23.4/1 Waermedurchgangskoeffizient verschiedener Materialien ------------------------------------------------------------------------ 728 23.4/2 Waermedurchgangskoeffizient verschiedener Bausteinarten ------------------------------------------------------------------------ 729 23.5/1 Normatmosphaere in relativen Einheiten ------------------------------------------------------------------------ 730 23.5/2 Luftdruck in absoluten Einheiten ------------------------------------------------------------------------ 730 23.5/3 Druckmessung: Temperatur-Hoehen- Korrektur ------------------------------------------------------------------------ 731 23.5/4 Druckmessung: Add4!rKorrekturfaktor ------------------------------------------------------------------------ 732 23.5/5 Druckmessung: Materialausdehnung Messingskala ------------------------------------------------------------------------ 732 23.5/6 Druckmessung: Materialausdehnung Glasskala ------------------------------------------------------------------------ 733 23.5/7 Volumenmessung: Temperaturkorrektur ------------------------------------------------------------------------ 733 23.5/8 Volumenmessung: Ausdehnung eines Glasbehaelters ------------------------------------------------------------------------ 734 23.6/1 Tieftemperaturbaeder ------------------------------------------------------------------------ 734 23.7/1 Trockenmittel chemische Trocknung ------------------------------------------------------------------------ 734 23.7/2 Trockenmittel: physikalische Trocknung ------------------------------------------------------------------------ 735 23.8/1 Saettigungsdampfdruck bei20 °C ------------------------------------------------------------------------ 735 23.8/2 Kryoskopische und ebullioskopische Konstante ------------------------------------------------------------------------ 735 23.8/3 Psychrometrie ------------------------------------------------------------------------ 736 23.8/4 Dampfdruck von Wasser bei niedrigen Temperaturen ------------------------------------------------------------------------ 736 23.8/5 Dampfdruck und spez. Enthalpie von Wasser ------------------------------------------------------------------------ 737 23.8/6 Spez. Volumen und spez. Enthalpie von Wasserdampf ------------------------------------------------------------------------ 738 23.9/1 Spezifischer Heizwert ------------------------------------------------------------------------ 738 23.9/2 Spez. Schmelz- und Verdampfungsenthalpien reiner Metalle ------------------------------------------------------------------------ 739 23.9/3 Relative Volumenaenderung beim Schmelzen ------------------------------------------------------------------------ 739 23.9/4 Temperaturabhaengigkeit der Verdampfungswaerme ------------------------------------------------------------------------ 740 23.9/5 SpezSchmelz- und Verdampfungsenthalpien anderer Stoffe ------------------------------------------------------------------------ 987 30.1/1 lonisationsenergien der Elemente ------------------------------------------------------------------------ 989 30.1/2 Ionisationsenergie von Stickstoffverbindungen ------------------------------------------------------------------------ 989 30.1/3 lonisationsenergien von Kohlenwasserstoffverbindungen ------------------------------------------------------------------------ 990 30.1/4 lonisationsenergien von Halogenverbindungen ------------------------------------------------------------------------ 990 30.1/5 lonisationsenergien von Sauerstoffverbindungen ------------------------------------------------------------------------ 991 30.1/6 Dissoziationsenergie zweiatomiger Molekuele ------------------------------------------------------------------------ 992 30.2/1 Atom- und Ioaeenradien der Elemente ------------------------------------------------------------------------ 994 30.3/1 Austrittsarbeit der Elektronen aus den reinen Elementen ------------------------------------------------------------------------ 996 30.3/2 Austrittsarbeit fuer adsorbierte Oberflaechen ------------------------------------------------------------------------ 996 30.3/3 Thermoemissionseigenschaften einer Wolframkathode ------------------------------------------------------------------------ 997 30.3/4 Photokatoden aus Alkaliantimoniden ------------------------------------------------------------------------ 997 30.3/5 Grundlegende Eigenschaften der Sekundaer-Elektronen-Emission ------------------------------------------------------------------------ 998 30.4/1 Hauptlinien des charakteristischen Roentgenspektrums einiger Elemente ------------------------------------------------------------------------ 998 30.5/1 Wirkungsquerschnitt fuer die Streuung von Neutronen an verschiedenen Elementen ------------------------------------------------------------------------ 999 30.5/2 Kernfusionsreaktionen ------------------------------------------------------------------------ 999 30.6/1 Massenschwaechungskoeffizient fuer Roentgenstrahlung ------------------------------------------------------------------------ 999 30.6/2 Massenschwaechungskoeffizient fuer Elektronen in Aluminium ------------------------------------------------------------------------ 999 30.6/3 Reichweite von u-Teilchen in Luft, biologischem Gewebe und Aluminium ------------------------------------------------------------------------ 1000 30.7/1 Hallkoeffizient fuer Metalle ------------------------------------------------------------------------ 1001 30.8/1 Supraleitende Elemente ------------------------------------------------------------------------ 1002 30.8/2 Supraleitende Verbindungen und Legierungen ------------------------------------------------------------------------ 1003 30.9/1 Elementhalbleiter ------------------------------------------------------------------------ 1003 30.9/2 Verbindungshalbleiter ------------------------------------------------------------------------ 1003 30.9/3 Dotierungen von Si ------------------------------------------------------------------------ 1004 30.9/4 Dotierungen in Ge ------------------------------------------------------------------------ 1004 30.9/5 Wirkung ionisierender Strahlung auf Halbleiter ------------------------------------------------------------------------ 1029 34.0/1 Basisgroeszen des ST ------------------------------------------------------------------------ 1029 34.0/2 Dezimalvorsaetze ------------------------------------------------------------------------ 1030 34.0/3 Abgeleitete ST-Einheiten ------------------------------------------------------------------------ 1032 34.0/4 ST-fremde gesetzliche Einheiten ------------------------------------------------------------------------ 1033 34.0/5 Umrechnungstabelle von Energieeinheiten ------------------------------------------------------------------------ 1033 34.0/6 Windstaerken ------------------------------------------------------------------------ 1034 34.0/7 Anglo-amerikanische Einheiten ------------------------------------------------------------------------ ******* EOF ************************************************************