Müller I. A history of thermodynamics. The doctrine of energy and entropy (Müller I. A history of thermodynamics. The doctrine of energy and entropy.pdf), страница 8

a gasclose to condensation. That Joule and Kelvin could detect it in air at room temperaturedoes them credit as very careful experimenter. Gay-Lussac had missed the cooling whenhe made the expansion experiment earlier.40 J.P. Joule: “Heating during the electrolysis of water.” Memoirs of the literary andPhilosophical Society of Manchester. Series II, Vol. 7 (1864) p. 67.41 J.P. Joule: (1850) loc.cit.42 Helmholtz was ennobled by Kaiser Wilhelm I in 1883.

In 1891 he became a real privycouncillor with the right to be addressed as Your excellency. Such were the rewards forsuccessful scientists in 19th century Europe.Hermann Ludwig Ferdinand (von) Helmholtz (1821–1894)25turn a wheel (say) and still come back to the original position in order tobegin a new cycle. These attempts had always failed and people came to theconclusion that a perpetuum mobile was impossible. Therefore as early as1775 the Paris Academy decided not to review new propositions anymore.The conservation of mechanical energy – kinetic energy, gravitationalpotential energy, and elastic energy was firmly believed in, no matter howcomplex the arrangement of masses and springs and wheels was, cf.Fig. 2.5.

This could not be proved, of course, since not all possiblearrangements could be tried, nor could the equations of motion be solvedfor complex arrangements.Fig. 2.5. Design of a perpetuum mobile by Ulrich von Cranach, 1664A perpetuum mobile was a proposition of mechanics. To be sure,friction and inelastic collisions were recognized as counterproductive,because they absorb work and annihilate kinetic energy, – both produceheat. Helmholtz conceived the idea that…what has been called … heat is firstly the … life force [kinetic energy]of the thermal motion [of the atoms] and secondly the elastic forcesbetween the atoms.

The first is what was hitherto called free heat and thesecond is the latent heat.So far that idea had been expressed before – more or less clearly – butnow came Helmholtz’s stroke of insight: The bouncing of the atoms and theattractions between them just made a mechanical system more complexthan any macroscopic system had ever been.43 But the impossibility of a43And some of those machines were complicated, see Fig.

2.5.262 Energyperpetuum mobile should still prevail. Just like energy was conserved in acomplex macroscopic arrangement without friction and inelastic collisions,so energy is still conserved – even with friction and inelastic collisions – ifthe motion of the atoms, and the potential energy of their interaction forces,is taken into account. Friction and inelastic collisions only serve toredistribute the energy from its macroscopic embodiment to a microscopicone. And on the microscopic scale there is no friction, nor do inelasticcollisions occur between elementary particles.The idea was set forth by Helmholtz in 1847 in his first work onthermodynamics “Über die Erhaltung der Kraft”44 which he read to thePhysical Society in Berlin.

Note that thus all three of the early protagonistsof the first law of thermodynamics used the word force rather than energy.Helmholtz’s work begins with the sentence: We start from the assumptionthat it be impossible – by any combination of natural forces – to create lifeforce [kinetic energy] continually from nothing.While Helmholtz may have been unaware at first of Mayer’s work, hedid know Joule’s measurements of the mechanical equivalent of heat. Hecites them. When his work was reprinted in 1882,45 Helmholtz added anappendix in which he says that he learned of Joule’s work only just beforesending his paper to the printer.

On Mayer he says in the same appendixthat his style was so metaphysical that his works had to be re-invented afterthe thing was put in motion elsewhere, probably meaning by himself,Helmholtz. One thing is true though: Mayer, and to some extent even Joulehemmed and hawed and procrastinated over heat and force; they adducedthe theorem of logical cause and the commands of the Creator. Helmholtz’swork on the other hand is crystal clear, at least by comparison.We have previously reviewed Mayer’s and Joule’s frustrating attempts topublish their works. Helmholtz fared no better.

His paper was dismissed byPoggendorff as mere philosophy.46 Therefore Helmholtz had to publish thework privately as a brochure, see Fig. 2.6.Helmholtz was not much younger than the other two men, and yet hewas a man of the new age. While the others had reached the limit oftheir capacities – and ambitions – with the discovery of the first law,Helmholtz was keen enough and knew enough mathematics to exploit thenew field.44[On the conservation of force].H. Helmholtz: “Über die Erhaltung der Kraft” [On the conservation of force]Wissenschaftliche Abhandlungen, Bd. I (1882).46 According to C. Kirsten, K. Zeisler (eds.): “Dokumente der Wissenschaftsgeschichte”[Documents of the history of science] Akademie Verlag, Berlin (1982) p.

6.45Hermann Ludwig Ferdinand (von) Helmholtz (1821–1894)27Fig. 2.6. Title page of Helmholtz’ brochure. [The dedication to “dear Olga” was scratchedout before printing.47]Thus Helmholtz put numbers to Mayer’s speculation about the source ofenergy of solar radiation. First of all he dismissed the idea that the energycomes from the impact of meteors. Rather he assumes that the sun contractsso that its potential energy drops and is converted into heat which is thenradiated off.

Taking it for granted that the solar energy output is constantthroughout the process – and therefore equal to the current value which is3.6·10 26 W – Helmholtz calculates that the sun must have filled the entireorbit of the earth only 25 million years ago, cf.

Insert 2.2. The earth wouldtherefore have to be younger than that. Geologists complained; they insistedthat the earth had to be much older than a billion years in order toaccommodate the perceived geological evolutionary processes, and theywere right. It is true that Helmholtz’s calculations were faultless, but hecould not have known the true source of energy of the sun, which is notgravitational but nuclear.Helmholtz, on his mother’s side a descendant of William Penn, thefounder of Pennsylvania, studied medicine and for a while he served as asurgeon in the Prussian army. When he entered academic life it was as aprofessor of physiology in Königsberg, where he did important work on thefunctions of the eye and the ear.

Without having a formal education inmathematics Helmholtz was an accomplished mathematician, see Fig. 2.7.He worked on Riemannian geometry, and students of fluid mechanics knowthe Helmholtz vortex theorems which are non-trivial consequences of themomentum balance, – certainly non-trivial for the time. Late in his life hebecame the first president of the Physikalisch-Technische Reichsanstalt, theGerman standardizing laboratory.484748Olga von Velten (1826–1859) became Helmholtz’s first wife in 1849.Now: Physikalisch Technische Bundesanstalt.282 EnergyHelmholtz was yet another physician turned scientists.He studied the working of the eye and the ear andformulated the “Helmholtz vortex theorems”,mathematically non-trivial results for his time.Lenard 49 says: … that Helmholtz, who had no formalmathematical education was able to do this, shows theabsolute uselessness of the extensive mathematicalinstruction in our universities, where the students aretortured with the most outlandish ideas, … when only afew are capable of getting results with mathematics,and those few do not even need this endless torment.

50Fig. 2.7. Hermann Ludwig Ferdinand von Helmholtz. Also a quote from Lenard, muchappreciated by students of thermodynamicsDespite the insight which Helmholtz had into the nature of heat anddespite the mathematical acumen which he exhibited in other fields, he didnot succeed to write the first law of thermodynamics in a mathematicalform, – not at the early stage of his professional career. The last importantstep was still missing; it concerned the concept of the internal energy andits relation to heat and work. That step was left for Clausius to do and itoccurred in close connection with the formulation of the second law ofthermodynamics.

The cardinal point of that development was the search forthe optimal efficiency of heat engines. We shall consider this in Chap. 3.Helmholtz’s hypothesis on the origin of the solar energyAlthough Helmholtz’s hypothesis on the gravitational origin of the solar energy isoften mentioned when his work is discussed, I have not succeeded to find theargument; it is not included in the 2500 pages of his collected works.51 Given this –and given the time – one must assume that the calculation was a rough-and-readyestimation rather than a serious contribution to stellar physics.