Conservation and Innovation : Helmholtz's Struggle with Energy ...

More documents

Recommendations

Info

Clausius' approach is in fact different: starting from the same work-vis viva equation as Helmholtz does, he recognizes that in certain cases the work done is a complete differential. Thus the vis viva can be equated to a difference of potential. But Clausius does not mention at this stage the potential energy, nor does he think that it should be a positional term. Even much later, the principle of conservation of energy for Clausius was meant to be the requirement that the work be expressed as a total differential. Clausius believed in the kinetic theory of heat, but he did not apply to it the dichotomy of vis viva and tension forces as Helmholtz had done in the fourth chapter of the Erhaltung . Clausius asserted in 1852 that "heat consists in a motion of the ultimate particles of bodies and is a measure of the vis viva of this motion" 277. Thus the work done, or the difference of potential between the initial and final conditions, includes this effect too: " The sum of all the effects produced by an electric discharge is equal to the increase of the potential of the entire electricity upon itself" 278. Mechanical work, electricity and heat are unified here but "potential energy" and "energy" do not appear. Even farther away from Clausius' perspective is the idea of a conservation of the sum of sharply separated kinetic and positional terms. In the paper mentioned, Clausius too relies on the model of central Newtonian forces depending only on distance, but introduces it only as a case which is mathematicallly simple, often occurring in physical situations: "The determination of the work may be much simplified in particular cases which very often present themselves" 279. Clausius does not believe central Newtonian forces to be a conceptual model necessary for the intelligibility of nature. This criticism of Helmholtz's approach does not appear in the 1852 paper, but after Helmholtz's remarks of 1853, Clausius in the same year expressed his views on this point rather clearly. The central issue is immediately faced, "not for personal reasons, but because it is connected with problems of general scientific interest" 280. The problem is clearly defined: Helmholtz asserted that the vis viva principle holds only when the acting forces can be decomposed in forces acting on material points, in the 277 Clausius "Electrical Discharge" p.5 278 Clausius "Electrical Discharge" p.6 279 Clausius "Electrical Discharge" p.4. 280 Clausius "Einige Stellen" p.574.
directions that join them and whose intensity depends only on the distance, that is only for central forces. But Clausius claims that the demonstration given by Helmholtz does not justify the assertion. In fact, during the demonstration, one of the very statements to be derived, that the intensity of the force is a function of the distance, is presupposed 281. This presupposition is part of Helmholtz's model as expressed in the Einleitung. Thus the principle of vis viva is either unnecessary to derive the central forces (if we already presuppose that the intensity is a function of the distance) or is insufficient (if we do not make that assumption). Moreover, Clausius asserted that from the vis viva theorem, assuming that the vis viva is a function only of the space coordinates, we can derive that the work too is a total differential and also that the force acting is a function of the space coordinates. But this does not imply that the force be central. The only possible implication for Clausius is that, if one of the two conditions hold (direction or intensity) the other does too. Finally Clausius, while not questioning the "physical probability", denies the "mathematical necessity" of central forces 282. Helmholtz, apart from deriving them from the vis viva principle in the second chapter, had assumed in the Introduction that a point acts in different directions with the same force. Clausius does not consider this as evident: the contrary is not "unthinkable". Moreover in Helmholtz's first chapter of the Erhaltung, when the principle of virtual velocities is derived from the vis viva principle it is also asserted that the result is that the forces of two points act on the direction joining them. But for Clausius this, again, was part of the assumptions and cannot be considered a deduction. Helmholtz's whole attempt to demonstrate the mathematical need for central forces is, for Clausius, a flaw. The core of Helmholtz's program was seriously shaken. No doubt he was deeply worried by the criticisms for he dedicated a great effort to preparing a twenty page paper, to be published in 1854 and reprinted in 1882 in the energy section of the WA 1, after the Erhaltung. Replying to Clausius in this paper, Helmholtz asserted that he could derive from the vis viva principle the need for the forces to be central, without further hypotheses, because he expressed the principle only with reference to the relative positions of the points and not to the absolute ones. In Helmholtz's view this 281 Clausius "Einige Stellen" p.575. 282 Clausius "Einige Stellen" p.577.
Page 1 and 2:
Fabio Bevilacqua Conservation and I
Page 3 and 4:
different formulations 4 and priori
Page 5 and 6:
and interesting results, despite th
Page 7 and 8:
principle of correlation is express
Page 9 and 10:
principle to the existing empirical
Page 11 and 12:
the origin and meaning of the princ
Page 13 and 14:
Whether physiological research, apa
Page 15 and 16:
In a discussion on the origins of a
Page 17 and 18:
his "Wärme" that one of the differ
Page 19 and 20:
generate a determined equivalent of
Page 21 and 22:
"Bericht", despite the application
Page 23 and 24:
experiments in the most disparate b
Page 25 and 26:
The premise reveals that the struct
Page 27 and 28: intelligible if it can be referred
Page 29 and 30: elevant consequence of the deductio
Page 31 and 32: Needless to say the plan was to be
Page 33 and 34: and from here that the direction an
Page 35 and 36: since Leonardo 113; the "ad nihilum
Page 37 and 38: But unfortunately for the whole str
Page 39 and 40: The principle of conservation of vi
Page 41 and 42: different from the one joining the
Page 43 and 44: "The equality that exists between e
Page 45 and 46: In virtue of its limitations to New
Page 47 and 48: Helmholtz, while asserting that lig
Page 49 and 50: the temperature of 1 Kg of water ca
Page 51 and 52: In his search for a mechanical equi
Page 53 and 54: had already been achieved in the Be
Page 55 and 56: approach is discussed at length and
Page 57 and 58: and unaware of Green's results190,
Page 59 and 60: potential function 201. It is worth
Page 61 and 62: and judged unreliable, despite prov
Page 63 and 64: The relevance of the first question
Page 65 and 66: principle taking this potential int
Page 67 and 68: Finally we get to the real conclusi
Page 69 and 70: conservation 234, on the theory of
Page 71 and 72: for the mechanical equivalent of he
Page 73 and 74: The controversy started with some r
Page 75 and 76: where μ are immovable masses, m th
Page 77: demonstration criticised by Clausiu
Page 81 and 82: quotes 288 and criticises a proposi
Page 83 and 84: motion to all natural forces, the k
Page 85 and 86: measure this expenditure and compar
Page 87 and 88: " ...the quantity of force in natur
Page 89 and 90: forces is constant: but it relates
Page 91 and 92: experiences in general laws of unli
Page 93 and 94: "a series of important and difficul
Page 95 and 96: the Discontinuous Movements of Flui
Page 97 and 98: methodology. Dühring claimed the c
Page 99 and 100: The first history of the conservati
Page 101 and 102: while in Britain for the above talk
Page 103 and 104: apply it to acoustics (1859), hydro
Page 105 and 106: magnetic intensity. Maxwell realize
Page 107 and 108: and the electrostatic In modern not
Page 109 and 110: of conservation of energy: it is re
Page 111 and 112: efuted. But again in 1881 Helmholtz
Page 113 and 114: But was important here is that desp
Page 115 and 116: The second (1892-94), follows the i
Page 117 and 118: while the electromagnetic and the s
Page 119 and 120: can modify its specific theoric for
Page 121 and 122: considered relevant. In Poincarè
Page 123 and 124: meaning left is: "There is somethin
Page 125 and 126: interpretations at the beginning of
Page 127 and 128: while fighting metaphisicians, he w
Page 129 and 130:
literature 456. There is an intrins
Page 131 and 132:
assertion is surprising: it has lon
Page 133 and 134:
Kant was a Naturphilosophe 480. The
Page 135 and 136:
condition that work done by the for
Page 137 and 138:
histories cites these (Hirn's) arti
Page 139 and 140:
) the experimental determinations o
Page 141 and 142:
force principle 522. Elkana tried t
Page 143 and 144:
Blüh, Otto. "The Value of Inspirat
Page 145 and 146:
Graetz, L. "Das Mechanische Wärme
Page 147 and 148:
Helmholtz, Hermann. "Bericht über
Page 149 and 150:
Helmholtz, Hermann. Wissenschaftlic
Page 151 and 152:
Madison: Wisconsin U.P., 1959. Pp.
Page 153 and 154:
Poincarè, Henry. Electricité et O
Page 155:
Yagi, Eri."Clausius's Mathematical
show all

Conservation and Innovation : Helmholtz's Struggle with Energy ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?