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On the Concept of Energy: Eclecticism and Rationality

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Abstract

In the theory of heat of the first half of the nineteenth century, heat was a substance. Mayer and Joule contradicted this thesis but developed different concepts of heat. Heat was a force for Mayer and a motion for Joule. Both Mayer and Joule determined the mechanical equivalent of heat. This result was, however, justified in accordance with those concepts of heat. Mayer’s characterisation of force reappears in the very common textbook definition ‘energy cannot be created or destroyed but only transformed’ and his theory led to a phenomenological approach to energy. Joule and Thomson’s concept of heat led to a mechanistic approach to energy and to the common definition ‘energy is the capacity of doing work’. One and the same term ‘energy’ subsumed these two approaches. The problematic concept of energy, energy as a substance, appears then as a result of an eclectic development of the concept. Another approach, which appeared in the 1860s, is directly based on the mechanical equivalent of heat and can be characterized by the use of ‘principle of equivalence’ instead of ‘principle of energy conservation’. Unlike the others, this approach, which has been lost, poses no problems with the concept of energy. The problems with the energy concept as to the kind of phenomena dealt with in the present paper can, however, be overcome, as we shall see, in distinguishing between that which comes from experiments and that which is an interpretation of the experimental results within a conceptual framework.

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Notes

  1. See, for instance, Chalmers (1963, p. 43), Bueche (1972, p. 95), Hudson and Nelson (1982, p. 95), Hänsel and Neumann (1993, p. 222), Cutnell and Johnson (1997, p. 177), Dransfeld, Kienle and Kalvius (2001, p. 109), Young and Freedman (2004, p. 264).

  2. The need of supporting students’ logical and critical thinking has been pointed out by several authors (Bailin 2002; Kalman 2002, 2011; Doménech et al. 2007; Matthews 2009; Galili 2009; Malamitsa, Kasoutas and Kokkotas 2009).

  3. Atkins (1986, p. 233), Hänsel and Neumann (1993, p. 222), Böge and Eichler (2002, p. 83), Nolting (2002, p. 148).

  4. See, for instance, Sexl (1981), Duit (1981, 1987), Hicks (1983), Bauman (1992), Chrisholm (1992), Arons (1999), Galili and Lehavi (2006), Doménech et al. (2007), Rizaki and Kokkotas (2009), Papadouris and Constantinou (2011).

  5. See, for instance, Breithaupt (1999, p. 157), Tipler (2000, p. 129), Serway and Beichner (2000, p. 183).

  6. See, for example, Lehrman (1973), Sexl (1981, p. 287), Duit (1981, p. 293), Hicks (1983), Kemp (1984, p. 234), Doménech et al. (2007, p. 49).

  7. If we do not know what energy is, then it is not to be expected that students will grasp it. Empirical research has shown their difficulties with the concept (Watts 1983, Duit 1986, Nicholls and Ogborn 1993, Trumper 1990, 1991, Cotignola et al. 2002, Barbosa and Borges 2006, de Berg 2008, Svedholm and Lindeman 2012, among others).

  8. According to Bunge (2000), the general concept of energy belongs in metaphysics (Bunge 2000, p. 461).

  9. Planck (1921 [1887]), Mach (1896), Helm (1898), Haas (1909), Kuhn (1959), Theobald (1966), Breger (1982), Schirra (1989), Smith (1998), Guedj (2000), Coelho (2006), Coopersmith (2010). On Mayer: Weyrauch (1890), Riehl (1900), Hell (1914), Timerding (1925), Lindsay (1973), Mittasch (1940), Heimann (1976), Caneva (1993); On Joule: Fox (1969), Forrester (1975), Cardwell (1989); on Colding: Dahl (1963); on Helmholtz: Elkana (1974), Heimann (1974), Bevilacqua (1983, 1993), Ordónez (1996).

  10. Indeed, ‘mass’ was not the term used by Descartes and ‘velocity’ is not a vector in his theory of motion.

  11. This contradicted the science of that time, according to which ‘weight’ alone was the cause of falling. Mayer argues however that weight is not enough for falling because without height there is no fall. Thus, he justified that weight · height is ‘fall force’ (Mayer 1842, p. 236).

  12. Mayer did not distinguish between weight and mass.

  13. Mayer quoted this proposition in Latin, “causa aequat effectum” (Mayer 1842, p. 233).

  14. Helmholtz proposed to take ½ mv 2 as vis viva, instead of mv 2, which he did throughout his paper.

  15. Rumford (1799) had experimentally shown that heat has no effect on the weight of bodies (Rumford 1799, p. 194).

  16. Equations of this form support the calculation of the mechanical equivalent of heat (see Joule 1884 [1843, 1845], 1850).

  17. Beyond these results, there are three more that the author does not consider capable of being valuable (Colding 1972, p. 12).

  18. Helmholtz’s approach to electrical and magnetic phenomena will not be considered in the present paper (see Bevilacqua 1983, 1993).

  19. Boltzmann (1896a, b), Planck (1896), see also Ostwald (1896) and Helm (1896).

  20. It is true that the meaning of energy has changed and energy has become a substance, which Mayer’s force was not, but this alteration was not a consequence of a discovery of a substance with those properties. If it were, energy would belong to the primary level.

  21. If the question is not well-posed, then there is no reason for keeping it. Hertz presented a similar solution for a similar question. Concerning the question of what force is, he wrote: “the answer which we want is not really an answer to this question. It is not by finding out more and fresh relations and connections that it can be answered; but by removing the contradictions existing between those already known, and thus perhaps by reducing their number. When these painful contradictions are removed, the question as to the nature of force will not have been answered; but our minds, no longer vexed, will cease to ask illegitimate questions” (Hertz 1899, p. 8).

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    Ricardo Lopes Coelho

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Correspondence to Ricardo Lopes Coelho.

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Coelho, R.L. On the Concept of Energy: Eclecticism and Rationality. Sci & Educ 23, 1361–1380 (2014). https://doi.org/10.1007/s11191-013-9634-1

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