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 5

This observation should have disqualified the caloric, but itdid not, not for another 40 year.After England, Rumford went to Paris where, posthumously, he crossedthe path of Lavoisier, because he married the chemist’s widow. AsimovwritesThe marriage was unhappy. After four years they separated and Rumfordwas so ungallant as to hint that she was so hard to get along with thatLavoisier was lucky to have been guillotined13. However, it is quiteobvious that Rumford was no daisy himself.Rumford’s insight into the nature of heat was largely ignored and thecaloric theory of heat prevailed until the 1840s. At that time, however, inthe short span of less than a decade three men independently – as far as onecan tell14 – came up with the first law of thermodynamics in one way orother.

Basically this was the recognition that the gravitational potentialenergy of a mass at some height, or the kinetic energy of a moving mass,may be converted into heat by letting it hit the ground. The three men whorealized that fact in the 1840s were Mayer, Joule and Helmholtz. All threeof them are usually credited with the discovery. And although all threedevote part of their works to the discussion of the weightless caloric –actually to its refutation – it is clear that that theory had run its course. SaysMayer in his usual florid style: Let’s declare it, the great truth. There areno immaterial materials.Robert Julius Mayer (1814–1878)Mayer was first and he went further than either of his competitors, becausehe felt that energy generally was conserved. He included tidal waves in hisconsiderations and conceived of falling meteors as a possible source ofsolar heat- and light-radiation.

Nor did he stop at chemical energy, not evenchemical energy connected with life functions.Mayer was born and lived most of his life in Heilbronn, a town in thethen kingdom of Württemberg. Württemberg was one of the several dozenindependent states within the loose German federation, whose rulers13Lavoisier was executed on May 8, 1794 because of his involvement in tax collection underthe ancien régime.

On the eve of his execution he wrote a letter to his wife. The chemistwas being philosophical: “It is to be expected ” the letter reads ‘‘that the events in which Iam involved will spare me the inconvenience of old age.”14 This is what is usually said. It is not entirely true, though. To be sure, it is likely that Jouleand Helmholtz were unaware of Mayer’s ideas, but Helmholtz was fully aware of Joule’smeasurements, he cites them, see below.142 Energysuppressed all activity to promote German unity. Unity, however, wasvociferously clamoured for by the idealistic students in their fraternities;therefore fraternities were declared illegal.

But in Tübingen, where Mayerstudied medicine, he and some friends were indiscreet enough to found anew fraternity. He was arrested for that – and for attending a ball indecentlydressed – and relegated from the university for one year.Mayer made good use of the enforced inactivity by continuing hismedical education in Munich and Paris and then took hire as a ship’sphysician – a Scheeps Heelmeester – on a Dutch merchantman for a roundtrip to Java.

This left him a lot of free time since, in his words, on the highseas people tend to be healthy. He learned about two important phenomenawhich he lists in his diaries:x The navigator told him that during a storm the ocean water becomeswarmer,15 andx while bleeding patients he observed that in the tropics venous blood issimilar in colour to arterial blood.The first observation could be interpreted as motion of the water wavesbeing converted to heat and the second seemed to imply that the desoxidization of blood is slower when less heat must be produced to maintainthe body temperature.The flash of insight, a kind of ecstatic vision, came to Mayer when hisship rode at anchor off Surabaja taking on board a consignment of sugar.Henceforth he was a changed man, a fanatic in the effort of spreading hisgospel.

And he hurried back home in order to let the world know about hisdiscovery. 16The gospel, however, left something to be desired. At least nobodywanted to hear it. Right after his return from Java Mayer rushed out a paper:“Über die quantitative and qualitative Bestimmung der Kräfte.”17 Actuallythere was nothing quantitative in the paper and, moreover, it was totally andcompletely obscure. There was hapless talk in hapless mathematical andgeometrical language which could not possibly mean anything to anybody.The only saving grace is the sentence: Motion is converted to heat, whichRumford had said 40 years before.

The paper ends characteristically in oneof the hyperbolic statements which are so typical for Mayer’s style: In starsthe unsolvable task of explaining the continuous creation of force, i.e. the15This observation is also mentioned by J.P. Joule: ‘‘On the mechanical equivalent ofheat’’. Philosophical Transaction (1850) p. 61 ff.16 Later, in 1848, Mayer was involved in a political squabble and he was ridiculed publiclyas having travelled as far as East India without setting his foot on land. This, however,seems to be untrue, if Mayer’s diary is to be believed. He did leave the ship for a shortexcursion; cf. H. Schmolz, H.

Weckbach: “Robert Mayer, sein Leben und Werk inDokumenten’’. Veröffentlichungen des Archivs der Stadt Heilbronn. Bd. 12. Verlag H.Konrad (1964) p. 86.17 “On the quantitative and qualitative determination of forces’’.Robert Julius Mayer (1814–1878)15differentiation of 0 to MC – MC, is solved by nature; the fruit of this is themost marvellous phenomenon of the material world, the eternal source oflight. And in unshared enthusiasm Mayer finishes the paper with thehopeful wordsFortsetzung folgt = to be continued.XWell, Poggendorff, to whose “Annalen der Physik and Chemie” Mayerhad sent the paper on June 16th 1841, was unimpressed.

Certainly andunderstandably he did not want to encourage the author. Despite severalurgent reminders by Mayer – the first one on July 3rd 1841 (!) –Poggendorff never acknowledged receipt, nor did he publish the paper.18He must have thought of Mayer as of some queer physician in Heilbronnwith an unrequited love of physics.Mayer had started a practice in Heilbronn, and in May 1841 he wasappointed town surgeon which gained him a regular salary of 150 florin.Later he changed to Stadtarzt, at the same salary, and in that capacity hehad to treat the poor, – free of charge – and also the lower employees of thetown, like the prison ward or the night watchman.19Mayer’s problem in physics was that he did not know mechanics. Hetook private instruction from his friend Carl Baur who was a professor ofmathematics at the Technical High-School Stuttgart, but Mayer nevergraduated to the knowledge that the gravitational potential energy mgH of amass m at height H is converted to the kinetic energy m2 2 when the massfalls and acquires the velocity ; specifically the factor ½ remained amystery for him.

To be sure, he never used the word energy in the abovesense: gravitational potential energy was falling force for him and kineticenergy was life force.20All he knew was, that motion, or the life force of motion could beconverted into heat and he even came up with a reasonable number: themechanical equivalent of heat, cf.

Insert 2.1.X365 mÎÞ1’ heat 1 gram at Ïß height .Ð 1130 Parisian feet à18The manuscript did survive and, when Mayer’s work was eventually recognized, the paperwas published in journals and books on the history of science, e.g. P. Buck (ed):“Robert Mayer – Dokumente zur Begriffsbildung des Mechanischen Äquivalents derWärme’’. [Robert Mayer – documents on the emergence of concepts concerning themechanical equivalent of heat] Reprinta historica didactica. Verlag B. Franzbecker, BadSalzdetfurth (1980) Bd. 1, p.

20–26.19 H. Schmolz, H. Weckbach: “Robert Mayer ...” loc.cit p. 66, p. 78.20 The life force must not be confused with the vis viva of the vitalists. In German the kineticenergy was called lebendige Kraft at that time, while the vis viva was called Lebenskraft.In English the distinction is not so clear and sometimes not strictly maintained, althoughusually the context clarifies the meaning.162 EnergyMayer’s calculation of the mechanical equivalent of heatcalMayer knew – or thought he knew – that the specific heats of air are 0.267 gKand0.267 cal1.421 gK3at constant pressure and volume respectively.

To heat 1 cm air at a-33density of 1.3 10 g/cm by 1°C it should therefore take–30.347 10 cal at fixed pressure, and–30.244 10 cal at fixed volume.-4At constant pressure the volume expands. The difference in heat is 1.03 10 cal andthat difference can lift a 76 cm tube of mercury of mass 1033g which exerts a1pressure of 1 atm. At 1°C the lift amounts to 274cm according to Mariotte’s law,which nowadays we call the thermal equation of state of ideal gases, like air.

Thusnow it is a simple problem of the rule of three:-41033 g at 1/274cm corresponds to 1.03 10 cal1 g at H = ? corresponds to 1cal.It follows that H = 365 m and so Mayer wrote:1° heat = 1 g at 365 m heightNote that Mayer did not measure anything. He took his specific heat from someFrench experimentalists whom he quotes as Delaroche and Bérard. And the ratio ofspecific heats he took from Dulong.

Both numbers are slightly off and thereforeMayer’s mechanical equivalent of heat was low.Insert 2.1In words: The fall of a weight from a height of ca. 365 m corresponds tothe heating of the same weight of water from 0°C to 1°C. Later, withreference to Joule’s better measurements, he changed to 425 m or 1308Parisian feet. The old value – but not its calculation – is included inMayer’s second paper, see Fig. 2.2, which otherwise is not much clearerthan the first one.