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

More documents

Recommendations

Info

conformity with Gauss in his magnetical researches" 262 as the sum of tensions consumed by the motion from infinity to r, and, equivalently, as the sum of the vis viva produced. Thus : "the increase of vis viva in any movement must be considered equal to the difference of the potential at the end of the trajectory with respect to the potential at the beginning" 263. That is, the sum of tension forces is equivalent to the difference of potentials: − ∫ r R φ dr = e1e2 R − e1e2 r and, of course, also to the gain in vis viva caused by passing from the distance R to r. Helmholtz then introduces the concept of the potential of a body in itself and of the potential of a body on another. In a specific case given as an example, he calculates the difference of potentials before and after the movement of a quantity of electricity. This difference is defined as equivalent to the quantity of work done: -(V + (Wa +Wb)/2) 264 As already seen Clausius in 1852 criticised Helmholtz assertion that in the above expression the potential W of a body on itself is not equal to the corresponding work done, but twice as much (the corresponding work is in fact W/2). The accusation of not having understood the deep relations between potential and work was a serious one from Clausius' point of view. Clausius in the same1852 paper had established a relation between vis viva and potential different from that of Helmholtz's Erhaltung. He started from the vis viva theorem and equated the increase of vis viva to the quantity of mechanical work produced during the same time in the system 265. Clausius did not accept Helmholtz's "sum of tension forces" (potential energy) and the corresponding interpretation of the conservation principle. For Clausius, work, being in most cases a total differential and thus its integral depending only on the initial and final positions, can be identified with a difference of potentials. The potential of an exterior system of masses on a given system is introduced as the function: 262 Helmholtz Erhaltung p. 38. 263 Helmholtz Erhaltung p. 38. 264 Helmholtz Erhaltung Pp.42-3. 265 Clausius "Electric Discharge" p.3.
where μ are immovable masses, m the masses of the system and ρ the distance of the two masses from each other. In a similar way: is the potential of the given system of masses upon itself. "The work consists simply in the increase of these potentials" 266. Thus in 1852 Clausius explicitly asserted that the potential is work stored in the system. Work as total differential and difference of potential are identical concepts. This is a statement of the greatest relevance, but very different from Helmholtz's. In the Gauss-Clausius tradition energy would never become a physical quantity. The principle of conservation was often to be called, following the old tradition, the vis viva conservation 267 and the only really important requirement was that work be a total differential. This interpretation left open the possibility that forces other than the central Newtonian ones could satisfy the conservation principle, if the work done by these forces satisfies the mentioned requirement. An answer to Clausius was thus due. In 1853 Helmholtz clarifies his own use of the term "free tension" in the fifth paragraph of the Erhaltung asserting that its definition "is identical to what Gauss defined as potential and Green as potential function" 268. Thus in 1853 Helmholtz explicitly acknowledges a result of the unifying power of the mathematical potential theory: the concept of electrical tension, formerly with Volta and Ohm density of the elastic fluid called electricity, had been redefined by Kirchhoff in 1849, both for static electricity and for currents, as difference of electrical potential 269. Electrostatics and galvanism had thus been unified. In a note in the same page 270, Helmholtz replied to Clausius' criticisms of 1852 asserting that the problem of the definition of the potential does not imply any 266 Clausius "Electric Discharge" in the note of p.5, quotes both Gauss and Green. 267 See for instance: Riemann Schwere Elektricität Magnetismus ; Sturm, M. Cours de Mécanique , M.Prohuet ed. Vols. 2. Paris: Mallet-Bachelier, 1861. 268 Helmholtz "Einige Gesetz" p.224. 269 Kirchhoff, Gustav. "On a Deduction of Ohm's Law, in Connection with the Theory of Electrostatics" Phil Mag s3 37 (1850): 463-8; translated from Pogg Ann 78 (1849) p.506. 270 Helmholtz "Einige Gesetz" p.224.
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: The controversy started with some r
Page 77 and 78: demonstration criticised by Clausiu
Page 79 and 80: directions that join them and whose
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 ...

Create successful ePaper yourself

Delete template?

Save as template?