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On the Concept of Energy: How Understanding its History can Improve Physics Teaching

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Abstract

Some physicists have pointed out that we do not know what energy is. Many studies have shown that the concept of energy is a problem for teaching. A study of the history of the concept shows that the discoverers of energy did not find anything which is indestructible and transformable but rather that the concept of energy underwent a change of meaning and energy was considered a substance towards the end of the nineteenth century. In distinguishing between the treatment of phenomena and the theories carried out by Mayer and Joule, it can be concluded that they established equivalences between different domains, such as motion and heat, motion and electricity or position and motion. This complies with the interpretation presented in textbooks published about a century ago and enables us to overcome some difficulties with the concept of energy.

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Notes

  1. See, for instance, Breger (1982), Schirra (1989), Smith (1998), Guedj (2000) or Caneva (1993), Cardwell (1989), Dahl (1963) and Bevilacqua (1983).

  2. See, for instance, Preston (1919, p. 288), Müller and Pouillet (1926, p. 110), Hund (1956, p. 50), Allen and Maxwell (1962, p. 284), Tipler (2000, p. 554), Cassiday et al. (2002, p. 255), Young and Freedman (2004, p. 653).

  3. “Der Zweck folgender Zeile ist, die Beantwortung der Frage zu versuchen, was wir unter ‘Kräften’ zu verstehen haben, und wie sich solche untereinander verhalten” (p. 233).

  4. “Kräfte sind Ursachen, mithin findet auf dieselbe volle Anwendung der Grundsatz: causa aequat effectum” (p. 233).

  5. “In einer Kette von Ursachen und Wirkungen kann, wie aus der Natur einer Gleichung erhellt, nie ein Glied oder ein Theil eines Gliedes zu Null werden. Diese erste Eigenschaft aller Ursachen nennen wir ihre Unzerstörlichkeit” (p. 233).

  6. “Hat die gegebene Ursache c eine ihr gleiche Wirkung e hervorgebracht, so hat eben damit c zu seyn aufgehört; c ist zu e geworden” (p. 234).

  7. “Kräfte sind also: unzerstörliche, wandelbare, imponderable Objecte” (p. 234). “Ursachen sind (quantitativ) unzerstörlich und (qualitativ) wandelbare Objecte” (p. 234).

  8. Textbooks of that time are often divided into two parts, where the first one deals with matter which has weight and corresponds to mechanics; and the second one deals with optics, electricity, magnetism and heat and has ‘imponderables’ in the title, like ‘on the fundamental imponderable substances of bodies’ (Suckow 1813) or ‘on imponderable powers’ (Muncke 1829).

  9. “Um daß ein Körper fallen könne, dazu ist seine Erhebung nicht minder notwendig, als seine Schwere, man darf daher auch letzterer allein den Fall der Körper nicht zuschreiben” (p. 236).

  10. “Die Größe der Fallkraft v steht [...]—mit der Größe der Masse m und mit der ihrer Erhebung d, in geradem Verhältnisse; v = md” (p. 236).

  11. “Geht die Erhebung d = 1 der Masse m in Bewegung dieser Masse von der Endgeschwindigkeit c = 1 über, so wird auch v = mc; aus den bekannten zwischen d und c stattfindenden Relationen ergiebt sich aber für andere Werthe von d oder c, mc 2 als das Maß der Kraft v” (p. 236).

  12. “Wasser erfährt, wie der Verfasser fand, durch starkes Schütteln eine Temperaturerhöhung. Das erwärmte Wasser (von 12° und 13°C.) [..]” (p. 238).

  13. “umgekehrt dienen wieder die Dampfmaschinen zur Zerlegung der Wärme in Bewegung oder Lasterhebung” (p. 239).

  14. “Ist es nun ausgemacht, daß für die verschwindende Bewegung in vielen Fällen (exceptio confirmat regulam) keine andere Wirkung gefunden werden kann, als die Wärme, für die enstandene Wärme keine andere Ursache als die Bewegung, so ziehen wir die Annahme, Wärme entsteht aus Bewegung, der Annahme einer Ursache ohne Wirkung und einer Wirkung ohne Ursache vor” (p. 238).

  15. “Angenommen, ein Kubikzoll Luft von 0° und 27 Zoll Quecksilber Druck, sey durch die Wärmemenge x bei constantem Volumen um 274°C. erwärmt worden [...] Ein andermal aber werde unser Cubikzoll Luft nicht unter constantem Volumen, sondern unter constantem Drucke der 27zölligen Quecksilbersäule von 0 auf 274° erwärmt. Diessmal ist eine grössere Wärmemenge erforderlich als zuvor; es sey dieselbe = x + y” (p. 12).

  16. “Ein Kubikcentimeter atmosphärische Luft bei 0° und 0 m, 76 Barometer, wiegt 0.0013 Gramme; bei constantem Drucke um 1°C. erwärmt, dehnt sich die Luft um 1/274 ihres Volumens aus und hebt somit eine Quecksilbersäule von einem Quadratcentimeter Grundfläche und 76 Centimeter Höhe um 1/274 Centimeter. Das Gewicht dieser Säule beträgt 1033 Gramme. Die specifische Wärme der atomsphärischen Luft ist bei constantem Drucke, die des Wassers = 1 gesetzt, nach Delaroche und Bérard = 0.267; die Wärmemenge, die unser Kubikcentimeter Luft aufnimmt, um bei constantem Drucke von 0 auf 1° zu kommen, ist also der Wärme gleich, durch welche 0.0013 × 0.267 oder 0.000347 Gramme Wasser um 1° erhöht werden. Nach Dulong [...] verhält sich die Wärmemenge, welche die Luft bei constantem Volumen aufnimmt, zu der bei constantem Drucke, wie 1:1,421; hiernach gerechnet ist die Wärmemenge, die unseren Kubikcentimeter Luft bei constantem Volumen um 1° erhöht, = 0.000347/1,421 = 0.000244 Grad. Es ist folglich die Differenz y = 0.000347 − 0.000244 = 0.000103 Grad Wärme, durch deren Aufwand das Gewicht P = 1033 Gramme auf h = 1/274 Centimeter, gehoben wurde. Durch Reduktion dieser Zahlen findet man 1° Wärme = 1 Grm. auf 367 m [...] Höhe” (pp. 14–15).

  17. “Aus Nichts wird Nichts. Die Elektrizität des Harzkuchens kann, da sie sich unvermindert erhalten hat, die fortlaufende Summe el. Effekte nicht hervorgebracht haben; der bei jedem Turnus verschwundene mechanische Effekt kann nicht zu Null geworden seyn. Was bleibt übrig, wenn man sich nicht in einem doppelten Paradoxon gefällt? nichts, als auszusprechen: der mechanische Effekt ist in Elektrizität verwandelt worden” (p. 24).

  18. “Während wir also jedesmal einen mechanischen Effekt = x aufwenden, gewinnen wir den el. Effekt z + z′. So ist folglich: x = z + z′” (pp. 23–24).

  19. “Wenn hier eine Verwandlung der Wärme in mechanischen Effekt statuirt wird, so soll damit nur eine Thatsache ausgesprochen, die Verwandlung selbst aber keineswegs erklärt werden. Ein gegebenes Quantum Eis lässt sich in eine entsprechende Menge Wassers verwandeln; diese Thatsache steht fest da und unabhängig von unfruchtbaren Fragen über Wie und Warum und von gehaltlosen Speculationen über den letzten Grund der Aggregats-Zustände. Die ächte Wissenschaft begnügt sich mit positiver Erkenntniss und überlässt es willig dem Poëten und Naturphilosophen, die Auflösung ewiger Räthsel mit Hülfe der Phantasie zu versuchen” (p. 10).

  20. “Näheres über die Art und Weise, wie das Organ, der Muskel, die Metamorphose einer chemischen Differenz in mechanischen Effekt vollbringt, wissen wir nicht zu sagen. [...] Die scharfe Bezeichnung der natürlichen Grenzen menschlicher Forschung ist für die Wissenschaft eine Aufgabe von praktischem Werthe, während die Versuche, in die Tiefen der Weltordnung durch Hypothesen einzudringen, ein Seitenstück bilden zu dem Streben des Adepten” (p. 88).

  21. “Der Zusammenhang, in welchem, wie wir gesehen haben, die Wärme mit der Bewegung steht, bezieht sich auf die Quantität, nicht auf die Qualität, denn es sind—um mit Euklid zu reden—Gegenstände, die einander gleich sind, sich desshalb noch nicht ähnlich” (p. 43).

  22. “Diese, zwischen der Fallkraft und der Bewegung bestehende constante Proportion, welche in der höheren Mechanik unter dem Namen ‘Princip der Erhaltung lebendiger Kräfte’ aufgeführt wird, kann kurz und passend mit dem Ausdrucke ‘Umwandlung’ bezeichnet werden. [...] Etwas anderes, als eine constante numerische Beziehung soll und kann hier das Wort ‘Umwandeln’ nicht ausdrücken” (pp. 41–42).

  23. The five kinds of forces are: 1. force of falling, 2. motion, 3. heat, 4. magnetism and electricity, and 5. chemical separation and combination (1845, p. 33).

  24. “The various experiments of this section prove, I think, most completely the production of electricity from ordinary magnetism” (p. 138). “I propose to call the agency thus exerted by ordinary magnets, magneto-electric or magnelectric induction” (p. 139).

  25. “We have therefore in magneto-electricity an agent capable by simple mechanical means of destroying or generating heat” (p. 146).

  26. “The axle b [...] was wound with a double strand of fine twine, and the strings [...] were carried over very easily-working pulleys, placed on opposite sides of the axle [...] By means of weights placed in the scales attached to the ends of the strings, I could easily ascertain the force necessary to move the apparatus at any given velocity” (p. 150).

  27. “when the battery was thrown out of communication with the electro-magnet, and the motion was opposed solely by friction and the resistance of the air, only 2 lb 13 oz were required for the same purpose” (pp. 150–151).

  28. “2°.46 × 1.114 = 2°.74; and this has been obtained by the power which can raise 4 lb 12 oz to the perpendicular height of 517 feet” (p. 151).

  29. “1° of heat per lb of water is therefore equivalent to a mechanical force capable of raising a weight of 896 lb to the perpendicular height of one foot” (p. 151).

  30. “Two other experiments, conducted precisely in the same manner, gave a degree of heat to mechanical forces represented respectively by 1001 lb and 1040 lb.” (p. 151).

  31. “Hence 4°.54 were evolved in the experiment over and above the heat due to the chemical changes taking place in the battery, by the agency of a mechanical power capable of raising 7 lb 8 oz to the height of 551 feet” (p. 152).

  32. “In other words, one degree is equivalent to 910 lb raised to the height of one foot” (pp. 152–153).

  33. “An experiment was now made, using the same apparatus as an electro-magnetic engine” (p. 153).

  34. “Hence 0°.603 has been converted into a mechanical power equal to raise 2 lb 4 oz to the height of 275 feet […] one degree per lb of water may be converted into the mechanical power which can raise 1026 lb to the height of one foot” (p. 153).

  35. “At present we shall adopt the mean result of the thirteen experiments given in this paper, and state generally that, The quantity of heat capable of increasing the temperature of a pound of water by one degree of Fahrenheit's scale is equal to, and may be converted into, a mechanical force capable of raising 838 lb to the perpendicular height of one foot” (p. 156). Greenslade (2002) indicates some values of the mechanical equivalent of heat in modern units.

  36. “it must be admitted that hitherto no experiments have been made decisive of this very interesting question; for all of them refer to a particular part of the circuit only, leaving it a matter of doubt whether the heat observed was generated, or merely transferred from the coils in which the magneto-electricity was induced, the coils themselves becoming cold” (p. 123).

  37. “It is pretty generally, I believe, taken for granted that the electric forces which are put into play by the magneto-electrical machine possess, throughout the whole circuit, the same calorific properties as currents arising from other sources. And indeed when we consider heat not as a substance, but as a state of vibration, there appears to be no reason why it should not be induced by an action of a simply mechanical character, such, for instance, as is presented in the revolution of a coil of wire before the poles of a permanent magnet” (p. 123).

  38. “Heat is a very brisk agitation of the insensible parts of the object, which produces in us that sensation from whence we denominate the object hot; so what in our sensation is heat, in the object is nothing but motion”—Locke. “The force of a moving body is proportional to the square of its velocity, or to the height to which it would rise against gravity”—Leibnitz (p. 298).

  39. “For a long time it had been a favourite hypothesis that heat consists of ‘a force or power belonging to bodies’, but it was reserved for Count Rumford to make the first experiments decidedly in favour of that view [...] ‘It appears to me’, he remarks, ‘extremely difficult, if not quite impossible, to form any distinct idea of anything capable of being excited and communicated in the manner the heat was excited and communicated in these experiments, except it be motion’ [...]” (pp. 298–299).

  40. “By rubbing two pieces of ice against one another in the vacuum of an air-pump [...]” This experiment was the more decisively in favour of the doctrine of the immateriality of heat, inasmuch as the capacity of ice for heat is much less than that of water. It was therefore with good reason that Davy drew the inference that “the immediate cause of the phenomena of heat is motion, and the laws of its communication [...]” (p. 300).

  41. “A third proposition, suppressed in accordance with the wish of the Committee to whom the paper was referred, stated that friction consisted in the conversion of mechanical power into heat” (p. 328).

  42. There were two main theses concerning the nature of heat. According to Rumford (1798, p. 99) or Davy (1799, pp. 13–14), heat was motion. According to Carnot (1824, pp. 10–11, 28) or William Thomson (1849, p. 315), heat was a substance. Some authors had posed the question, “what is heat?”, in connection with their experimental works during the first part of the nineteenth century. This was the case of Haldat (1807, p. 214), Berthollet, in cooperation with Pictet and Biot (1809, p. 447) or Colladon and Sturm (1828, p. 161). Joule’s research concerns this question: heat is either a substance or motion.

  43. “The term energy may be applied, with great propriety, to the product of the mass or weight of a body, into the square of the number expressing its velocity. […] This product has been denominated the living or ascending force, since the height of the body’s vertical ascent is in proportion to it; and some have considered it as the true measure of the quantity of motion; but although this opinion has been very universally rejected, yet the force thus estimated well deserves a distinct denomination” (pp. 78–79).

  44. “Aus meinen Untersuchungen [...] hatte sich ergeben, daß die Intensität des Magnetismus dieser Ketten in geradem Verhältniß zu der Energie der durch den feuchten Leiter begründeten chemischen Action stehe” (p. 265).

  45. “[...] ce qu’il est mis en action par une pile de Volta, dont on peut augmenter l’énergie à volonté en augmentant le nombre et l’étendue des plaques” (p. 60).

  46. “It possessed also the power of making magnets with more energy, apparently, than when no iron cylinder was present” (p. 133, § 34).

  47. “Wenn für die kleine Raumabstände und Geschwindigkeiten die Energie der mechanischen Effekte, den ausgezeichneteren chemischen Kräften gegenüber, sehr in den Hintergrund treten [...]” (1845, p. 28); “[...] einen Einfluss, durch den im allgemeinen die Energie des Oxydationsprocesses erhöht” (1845, p. 79); “die einzelnen Blutkörperchen nehmen mit verstärkter Energie den Sauerstoff auf” (1845, p. 82); “L’éxtrême énergie avec laquelle la chaleur des rayons solaires pénètre des corps transparents, fait voir […]” ((1846) 1893, p. 265).

  48. “When ‘thermal agency’ is thus spent in conducting heat through a solid, what becomes of the mechanical effect which it might produce? Nothing can be lost in the operations of nature—no energy can be destroyed” (p. 545).

  49. “The total mechanical energy of a body might be defined as the mechanical value of all the effect it would produce, in heat emitted and in resistances overcome, if it were cooled to the utmost, and allowed to contract indefinitely or to expand indefinitely according as the forces between its particles are attractive or repulsive, when the thermal motions within it are all stopped” (p. 475).

  50. “in our present state of ignorance regarding perfect cold, and the nature of molecular forces, we cannot determine this ‘total mechanical energy’ for any portion of matter” (p. 475).

  51. “the ‘mechanical energy of a body in a given state,’ will denote the mechanical value of the effects the body would produce in passing from the state in which it is given, to the standard state, or the mechanical value of the whole agency that would be required to bring the body from the standard state to the state in which it is given” (p. 475).

  52. “The following general conclusions are drawn from the propositions stated above [...] 1. There is at present in the material world a universal tendency to the dissipation of mechanical energy” (p. 141).

  53. “The object of the present communication is to call attention to the remarkable consequences which follow from Carnot’s proposition, established as it is on a new foundation, in the dynamical theory of heat; that there is an absolute waste of mechanical energy available to man” (p. 139).

  54. “As it is most certain that Creative Power alone can either call into existence or annihilate mechanical energy, the ‘waste’ referred to cannot be annihilation, but must be some transformation of energy” (p. 139).

  55. “To explain the nature of this transformation, it is convenient, in the first place, to divide stores of mechanical energy into two classes—statical and dynamical. A quantity of weights at a height, ready to descend and do work when wanted, an electrified body, a quantity of fuel, contain stores of mechanical energy of the statical kind. Masses of matter in motion, a volume of space through which undulations of light or radiant heat are passing, a body having thermal motions among its particles (that is, not infinitely cold), contain stores of mechanical energy of the dynamical kind” (p. 139).

  56. “All conceivable forms of energy may be distinguished into two kinds; actual or sensible, and potential or latent. Actual energy is a measurable, transferable, and transformable affection of a substance, the presence of which causes the substance to tend to change its state in one or more respects […] by the occurrence of which changes, actual energy disappears, and is replaced by Potential energy” (p. 106).

  57. “The energy of motion may be called either ‘dynamical energy’ or ‘actual energy’. The energy of a material system at rest, in virtue of which it can get into motion, is called ‘potential energy.’” (p. 34).

  58. “[...] It had kinetic or (as it has sometimes been called) actual energy. We prefer the first term, which indicates motion as the form in which the energy is displayed” (p. 602).

  59. “A few years later, in advocating a restoration of the original and natural nomenclature—‘mechanics the science of machines,’—‘dynamics the science of force,’ I suggested (instead of statics and dynamics the two divisions of mechanics according to the then usual nomenclature) that statics and kinetics should be adopted to designate the two divisions of dynamics. At the same time I gave, instead of ‘dynamical energy,’ or ‘actual energy,’ the name ‘kinetic energy’ which is now in general use to designate the energy of motion” (1884, Vol. II, p. 34).

  60. “the energy of a body may be defined as the capacity which it has of doing work” (p. 90).

  61. “we cannot determine experimentally the whole energy of the body. It is sufficient, however, for all practical purposes to know how much the energy exceeds or falls short of the energy of the body in a certain definite condition—for instance, at a standard temperature and a standard pressure” (pp. 183–184).

  62. “If the body in its actual state has less energy than when it is in the standard state, the expression for the relative energy will be negative. This, however, does not imply that the energy of a body can ever be really negative, for this is impossible. It only shows that in the standard state it has more energy than in the actual state” (p. 184).

  63. “The reason for believing heat to be a form of energy is that heat may be generated by the application of work, and that for every unit of heat which is generated a certain quantity of mechanical energy disappears” (p. 93).

  64. “The reason for believing heat not to be a substance is that it can be generated, so that the quantity of it may be increased to any extent, and it can also be destroyed, though this operation requires certain conditions to be fulfilled” (p. 93).

  65. “This definition of energy, as the effect produced in a body by an act of work, is not so simple as the usual one—‘the power of doing work’ but this latter definition seems a little unhappy” (p. 279).

  66. “energy is power of doing work in precisely the same sense as capital is the power of buying goods. […] money is a power of buying goods. It does not, however, necessarily confer upon its owner any buying-power, because there may not be any accessible person to buy from; and if there be, he may have nothing to sell. Just so with energy: it usually […] confers upon the body possessing it a certain power of doing work, which power it loses when it has transferred it” (p. 279).

  67. “Whenever work is done upon a body, an effect is produced in it which is found to increase the working-power of that body (by an amount not greater than the work done); hence this effect is called energy” (pp. 278–279).

  68. “But in every action taking place between two bodies the work is equal to the antiwork (§ 3); hence the energy gained by the first body is equal to the energy lost by the second; or, on the whole, energy is neither produced nor destroyed, but is simply transferred from the second body to the first” (p. 279).

  69. “Let r be the radius of the wire, i the current along it, α the magnetic intensity at the surface, P the electromotive intensity at any point within the wire, and V the difference of potential between the two ends. Then the area of a length l of the wire is 2πrl, and the energy entering from the outside per second is \( \frac{{{\text{area}}\times{\text{EMI}}\times{\text{MI}}}} {{4\pi }} = \frac{{2\pi rlP\alpha }} {{4\pi }} = \frac{{2\pi r\alpha Pl}} {{4\pi }} = \frac{{4\pi iV}} {{4\pi }} = iV \) for the line integral of the magnetic intensity 2πrα round the wire is 4π × current through it, and Pl = V. But by Ohm’s law V = iR and iV = i 2 R, or the heat developed according to Joule’s law” (pp. 350–351).

  70. “In this case very near the wire, and within it, the lines of magnetic force are circles round the axis of the wire. The lines of electric force are along the wire [...] energy is therefore flowing in perpendicularly through the surface, that is, along the radius towards the axis” (p. 350).

  71. “In that paper he introduces the idea of continuity in the existence of energy [...] whenever energy is transferred from one place to another at a distance, it is not to be regarded as destroyed at one place and recreated at another, but it is to be regarded as transferred, just as so much matter would have to be transferred; and accordingly we may seek for it in the intervening space, and may study the paths by which it travels” (p. 482).

  72. “The energy may be watched at every instant. Its existence is continuous; it possesses identity” (p. 483).

  73. “In the older and more hazy view of conservation of energy the idea of ‘potential energy’ has always been felt to be a difficulty [...] it was not easy or possible always to form a clear and consistent mental image of what was physically meant by it [...] The usual ideas and language current about potential energy are proper to notions of action at a distance” (p. 484).

  74. “diese Auffassung ist für die unmittelbare Anschauung überaus bequem durch ihre Analogie mit dem Verhalten der Materie, die auch in verschiedene Formen überführbar, aber nach ihrer Quantität (Masse) unveränderlich ist. Ebenso wie die Gesamtmasse eines Körpers sich als die Summe der Massen der einzelnen in demselben enthaltenen chemischen Substanzen darstellt, so setzt sich die Energie eines Systems zusammen aus der Summation der einzelnen Energiearten” (p. 116).

  75. “die Unbestimmtheit liegt dann im Begriff der Energie, man kennt den Platz nicht, den man ihr anweisen soll, und hat auch kein Mittel, ihn zu finden” (p. 117).

  76. “Gewiß ist zuzugeben, daß diese (sozusagen materielle) Auffassung der Energie als eines Vorrats von Wirkungen, dessen Menge durch den augenblicklichen Zustand des materiellen Systems bestimmt ist, möglicherweise später einmal ihre Dienste getan haben und einer anderen, allgemeineren und höheren, Vorstellung Platz machen wird: gegenwärtig ist es jedenfalls Sache der physikalischen Forschung, diese Auffassung als die anschaulichste und fruchtbarste überall bis ins einzelne durchzubilden und ihre Konsequenzen an der Hand der Erfahrung zu prüfen” (p. 118).

  77. “Mehrere ausgezeichnete Physiker versuchen heutzutage, der Energie so sehr die Eigenschaften der Substanz zu leihen, daß sie annehmen, jede kleinste Menge derselben sei zu jeder Zeit an einen bestimmten Ort des Raumes geknüpft und bewahre bei allem Wechsel desselben und bei aller Verwandlung der Energie in neue Formen dennoch ihre Identität” (pp. 25–26).

  78. “[...] kann der Inhalt eines physikalischen Systems an einer Substanz nur abhängen von dem Zustande des Systems selbst; der Inhalt gegebener Materie an potentieller Energie aber hängt ab von dem Vorhandensein entfernter Massen, welche vielleicht niemals Einfluß auf das System hatten” (p. 26).

  79. “Die Menge einer Substanz ist eine notwendig positive Größe; die in einem System enthaltene potentielle Energie scheuen wir uns nicht, als negativ anzunehmen” (p. 26).

  80. “Bedeutet ein analytischer Ausdruck die Menge einer Substanz, so hat eine additive Konstante in dem Ausdruck dieselbe Wichtigkeit wie der Rest; in dem Ausdruck für die potentielle Energie eines Systems hat die additive Konstante niemals eine Bedeutung” (p. 26).

  81. “Die Energie ist daher in allen realen oder konkreten Dingen als wesentlicher Bestandteil enthalten, der niemals fehlt, und insofern können wir sagen, daß in der Energie sich das eigentlich Reale verkörpert. Und zwar ist die Energie das Wirkliche in zweierlei Sinn. Sie ist das Wirkliche insofern, als sie das Wirkende ist; wo irgend etwas geschieht, kann man auch den Grund dieses Geschehens durch Kennzeichnung der beteiligten Energien angeben. Und zweitens ist sie das Wirkliche insofern, als sie den Inhalt des Geschehens anzugeben gestattet” (p. 5).

  82. “Es besteht [...] gar nicht mehr die Aufgabe, zu ermitteln, wie Geist und Materie in Wechselwirkung treten können, sondern es entsteht die Frage, wie sich der Begriff der Energie, der viel weiter als der der Materie ist, zu dem Begriff des Geistes stellt” (p. 144).

  83. See, for instance, Chalmers (1963, p. 43), Bueche (1972, p. 95), Hänsel and Neumann (1993, p. 222), Cutnell and Johnson (1997, p. 177), Young and Freedman (2004, p. 264).

  84. “The modern science of thermodynamics is based on two fundamental principles, both of which relate to the conversion of heat into work. The first of these is the principle of equivalence established by Joule, and is represented algebraically by the equation W = JH. This principle, which is known as the first law of thermodynamics, asserts than when work is spent in producing heat, the quantity of work spent is directly proportional to the quantity of heat generated […] This conception is derived from the dynamical theory, according to which heat is regarded as a form of energy” (p. 667).

  85. “Die am engsten an die unmittelbare Erfahrung sich anschließende Formulierung des ersten Hauptsatzes, die von jeder Hypothese, etwa über die Natur der Wärme frei ist, besagt daher einfach: Wärme und mechanische Arbeit sind äquivalent” (p. 109).

  86. “Energie (beliebiger Form) kann weder erzeugt, noch vernichtet werden. Die einfachste Gestalt nimmt das Energieprinzip wohl in der Form an: Die Summe aller einem abgeschlossenen System innewohnenden Energieformen bleibt bei sämtlichen Umwandlungen desselben konstant. Bei noch etwas schärferer Fassung nimmt der vorangehende Gedankengang folgende Gestalt an: Energie wird als unzerstörbar angesehen. Das Energieprinzip ist somit zunächst kein empirisches Gesetz, sondern ein Postulat, das sich allerdings mit den Erfahrungstatsachen (Äquivalenzgesetz) durchaus im Einklang befindet” (p. 126).

  87. “Es entsteht keine Wirkung ohne Ursache; keine Ursache vergeht ohne entsprechende Wirkung Ex nihilo nil fit. Nil fit ad nihilum” (p. 5).

  88. “A stone at a height [...] has potential energy. If the stone be let fall, its potential energy is converted into actual energy during its descent, exists entirely as the actual energy of its own motion at the instant before it strikes, and is transformed into heat at the moment of coming to rest on the ground” (p. 34).

  89. “Young persons who have grown up in scientific work within the last fifteen or twenty years seem to have forgotten that energy is not an absolute existence. Even the Germans laugh at the ‚Energetikers’. I do not know if even Ostwald knows that energy is a capacity for doing work” (Letter to Joseph Larmor, 1906, quoted by Smith 1998, p. 289).

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    Ricardo Lopes Coelho

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Lopes Coelho, R. On the Concept of Energy: How Understanding its History can Improve Physics Teaching. Sci & Educ 18, 961–983 (2009). https://doi.org/10.1007/s11191-007-9128-0

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