The first law of thermodynamics: 2. The Joule–Mayer ...

Chapter 8b

The first law of thermodynamics:

2. The Joule?Mayer Controversy

M.W. Collins College of Engineering, Design & Physical Sciences, Brunel University London, United Kingdom.

Abstract

Two pioneering scientists are associated with the formulation of the first law of thermo dynamics, James Prescott Joule and Julius Robert Mayer. There are two distinct aspects to their contributions: the actual statement of the equivalence of heat and work, and the experimental justification for that statement. In terms of the former, Mayer and Joule independently made that statement, Mayer a year or so earlier than Joule. In terms of the latter, Joule carried out a scientifically superb range of experiments allowing him to quantify accurately the mechanical equivalent of heat.

To begin with, both had very great problems in gaining acceptance from their peers. Joule was ultimately successful, in large measure due to the strong support of Kelvin. Mayer, on the other hand, had the bitter experience of never gaining that acceptance in his lifetime. The situation was exacerbated by the heated controversy initiated by John Tyndall and the biologically o riented X-Club. In strong opposition to the thermodynamic community, they not only maintained the historical precedence of Mayer over Joule but were derogatory to Joule's contributions.

In this chapter, it will be shown that at the time the controversy was unnecessary.

Moreover, scientific history, while fully crediting Joule, has been kind to Mayer, in the presentday use of the expression `the Mayer?Joule Principle'.

1Introduction

The scientific community's ethos includes correctly recognising the originality of researchers' work. The time-honoured way of doing this is by peer review of papers submitted to scientific journals. This achieves further protection for the researcher since the act of publishing is a defence against plagiarism. In the case of the First Law of Thermodynamics, there was the question, even at the time, of Julius Mayer's contribution to the debate, and as a consequence and more importantly whether he should be given precedence over Joule in the development of the First Law. This issue arose at the time and it had two quite separate aspects: peer assessment

WIT Transactions on State of the Art in Science and Engineering, Vol 89, ? 2015 WIT Press , ISSN 1755-8336 (on-line) doi:10.2495/978-1-84564-149-8/009

232 Kelvin, thermodynamics and the natural world

by scientific contemporaries and the way in which the matter was inflamed by John Tyndall of the X-Club (the group founded in 1864 by T.H. Huxley and eight associates) [1, p. 171]. These are addressed in this chapter.

2 Joule, Mayer and the First Law: their peer assessment problems

With reference to the first aspect, there was a nascent peer assessment in place in those times, from which both Joule and Mayer suffered. `...both ... Mayer ... and ... Joule had, in different ways, been largely ignored and even scorned by their respective German and British scientific peers' [1, p. 9].

Joule had a great struggle to achieve scientific credibility, epitomised by his striving after publication in the Royal Society's Proceedings. In 1844, `Once again, however, the Royal Society's Phil. Trans rejected the full paper ...' [1, p. 68], which was published instead in the Philosophical Magazine. Cardwell gives Joule's paper the highest praise: `This splendid paper was rejected by the Royal Society' [2, p. 234], but via Phil Mag `the scientific world learned not only of Joule's fundamental insights ... but also of his penetrating criticisms of Clapeyron and Carnot'. It was a scientific `first' ? `for the first time the fundamental ideas of thermodynamics were subject to the (constructive) criticism of a first-class scientific intellect'. Recounting the story as told by Cardwell, Joule achieved another `first' in 1847. In 1845, as fully described in Section 3 above, he presented at the Cambridge meeting of the BAAS his `new method of determining the mechanical equivalent of heat' using a paddle-wheel. Again, with the exception of Helmholtz, in `his important paper On the conservation of energy in 1847 `no one seemed very interested'. It was in that year, at the Oxford meeting of the BAAS that he presented `an improved paddlewheel apparatus' which aroused `the keen appreciation' of Kelvin. Again, more details of this meeting have been given in Section 3. Cardwell described Joule's second `first' as `an historic stage in the history of thermodynamics: the real beginning of the acceptance of the first law' (all quotes from [2, p. 235]. Returning to the question of Joule's publication endeavours, he was ultimately successful, with his definitive Royal Society paper of 1850 `On the mechanical equivalent of heat' [3, p. 312].

What of Mayer? While both Joule and Mayer struggled, Joule's success contrasted strongly with Mayer's unfortunate experience. Mayer, a German physician, was initially unsuited to scientific publication and Crosbie Smith tells how in a number of regards his submission to the `prestigious' Poggendorff's Journal was unacceptable. His paper was not just rejected ? it was not even returned to him. However, like Joule, Mayer did not give up and (like many successful researchers today?) `undertook a thorough revision of strategy'. In 1842, he achieved his sole success ? `his only paper submitted directly to, and accepted for publication by, a national and international journal'. It was `On the Forces of Inorganic Nature' in Liebig's Annalen der Chemie und Pharmazie' (all quotes from [1, p. 75]). Cardwell paints a vivid picture of Mayer's despair. Despite his sole success `he was almost entirely ignored' especially by his fellow-countrymen Helmholtz and Clausius who instead referenced Joule's work. The `tragic irony' of this epitomising `the evident scorn of his peers led to mental collapse' (quotes from [2, p. 231]).

In the late 1840s, Mayer became aware of Joule's papers and in 1848 `wrote to the French Academy of Sciences pointing out his claims to priority' [1, p. 73]. This was an extremely significant matter ? in effect Mayer was claiming precedence over Joule in being credited with the concept of the

WIT Transactions on State of the Art in Science and Engineering, Vol 89, ? 2015 WIT Press , ISSN 1755-8336 (on-line)

The first law of thermodynamics: The Joule?Mayer Controversy 233

mechanical equivalent of heat. Joule's approach, agreed with Kelvin, was to acknowledge the fact of Mayer's historical priority, but to claim that the scientific substance was his (Joule's). What Joule wrote is worth quoting in full `I shall be quite content to leave M. Meyer in the enjoyment of the credit of having predicted the law of the equivalency. But it would certainly be absurd to say that he has established it' [1, pp. 73, 74 from Smith's Reference 70, [1, p. 325]. The chronological order (the years are given) has considerable significance, because it was in 1850 that Clausius published the key paper (Section 4) re-expressing Carnot's theory in non-caloric terms [4, 5]. Sections 4 and 5 explain the significance of Clausius's paper for Kelvin's progress towards the `dynamical theory of heat'. Here, the focus is on the relevance to Joule and Mayer. Mayer's publication was indeed referenced by Clausius [5, p. 111] in a well-focused introductory discussion which needs some explanation.

Clausius identified the problem clearly: Did the `quantity of heat remain unchanged' (as promulgated by Carnot and Clapeyron) or could there be `an increase in the quantity of heat' as `the careful investigations of Joule ... have almost certainly proved'? He then cites Holtzmann who, using Mayer's method both agrees with Joule's equivalent but then in developing the equations `proceeds as Clapeyron' and `tacitly assumes that the quantity of heat is constant' (all quotes from [5, pp. 110, 111]). In contrast to identifying the ambiguity of Holtzmann (and, therefore, Mayer), Clausius, in the climactic conclusion of his paper, hugely complimented Joule. He quoted no less than three of Joule's experimental methods `The agreement of these three numbers, in spite of the difficulty of the experiments, leaves really no further doubt of the correctness of the fundamental principle of the equivalence of heat and work, and their agreement with the number 421 confirms in a similar way the correctness of Carnot's principle' [5, p. 152]. Such praise, by a peer of both Mayer and Joule, must be regarded as justifying Joule's words of the following year. There are two further points, though. First, Ref. [5] is part of the Dover publication edited by E. Mendoza, who also gives a thorough introduction in [6]. Referring to Mayer's paper, Mendoza comments `the famous paper by Mayer ... is almost unreadable today, the physical ideas being obscured by layers of philosophical verbiage' [6, p. xix]. Secondly, the story does not end there. In 1854, Rankine confirmed a prediction of Mayer in his (Rankine's) very masterly Royal Society publication [7]. It related to the possible deviation of high-density saturated steam from the perfect gas law. Rankine pointed out that Clausius's calculations showed either that `the supposition of Mayer is erroneous, or steam deviates very much .....' [7, p. 158]. Rankine then calculated a table of steam volumes concluding that it added to the evidence for such deviation. [7, pp. 159, 160].

It would have been great comfort to Mayer who had been able to foresee that history would treat him kindly, in fact very kindly, reflecting the `famous' compliment of Mendoza rather than his `unreadability'. Today, this kindness goes hand-in-hand with due regard to the genius of Joule. Two examples are given. In the text, Modern Thermodynamics of 1999, co-authored by the thermodynamics Nobel Laureate Ilya Prigogine [8], we first read of Joule's `series of experiments that established the equivalence between mechanical energy and heat' [8, p. 13], and then `the most important contributions to the idea of conservation of energy as a universal law of Nature came from Julius Robert von Mayer ... James Prescott Joule and Hermann von Helmhotz. Two landmarks ... are a paper by Robert Mayer ... published in 1842 ...' [8, p. 36]. Overall, the relative credits to Joule and Mayer could barely be clearer, and virtually coincident with the assessment of Joule himself ? Kondepudi and Prigogine using Joule's own word ?`established'.

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234 Kelvin, thermodynamics and the natural world

An even more recent publication is that by Newburgh and Leff [9] ? The Mayer?Joule Principle: The Foundation of the First Law of Thermodynamics. In the summary we read: `Independently, Julius Robert Mayer and James Prescott Joule found the connection between heat and work, the Mayer?Joule principle'.

This unexpectedly long treatment represents an attempt to assess objectively the contribution of Mayer. We will now examine how, one decade after the original historical events, the wellconnected researcher John Tyndall `unleashed a massive extension of hostilities to North Britain ... .ostensibly over the historical claims of Joule and Mayer' [1, p. 171].

3 Joule, Mayer and the First Law: the X-club controversy

The whole story is told by Crosbie Smith in Chapter 9 of [1] from the point of view of the `North British' thermodynamicists. The controversy involved John Tyndall on the one side and P.G. Tait on the other. The latter was yet another ex-Cambridge Wrangler thermodynamicist to add to Kelvin and Maxwell. (To digress, the mathematical abilities of these three were bewildering: Kelvin in 1845 (senior wrangler and first Smith's prizeman [1, p. 80]), Tait in 1852 (senior wrangler and first Smith's prizeman [3, p. 174]) and Maxwell in 1854 (second wrangler and first-equal Smith's prizeman [1, p. 214]). To cap it all, Tait was credited with the remark `I could coach a coal scuttle to be Senior Wrangler' [1, p. 174]. The complexities take Crosbie Smith over 20 pages (170?191) to describe. The X-club was the group founded in 1864 by T.H. Huxley and eight associates to promote a gospel of `scientific naturalism'. It used Darwin's evolutionary theory as a principal weapon. Crosbie Smith has two main themes of interpretation ? scientific authority morphing into Christian belief. `I argue that the Tait?Tyndall controversy should be construed as a contest for scientific authority' and `some of the fundamental differences between scientific naturalism (united by a stand against Christian doctrine) and the science of energy (promoted as a natural philosophy in harmony with, though not subservient to, Christian belief)' [1, pp. 171, 172]. The arguments need not be repeated as the key facts about Joule and Mayer have already been discussed. Both Tyndall and Tait tended to downplay the achievements of Joule and Mayer, respectively: and, so Smith concludes, `Tait sought to secure not only the reputation of Joule but the ...basis of a North British science of energy against ... its appropriation by the scientific naturalists' [1, p. 191].

Cardwell [2] addresses this matter, too, in two sections in pages 229?238 and page 282 onwards. In the first section, Tyndall is interpreted as someone whom today we would call a white knight. `Mayer was eventually rescued from his undeserved oblivion through the good offices and by the generous impulses of John Tyndall [2, p. 231]. It is in the second section that the interchanges are more fully addressed and Cardwell does this personally, that is without mention of the X-club. Using the source [1] in addition, the events may be summarised as follows: (i) in 1862, Tyndall gave an address to the Royal Institution in which he suggested `it had all been the work of a comparatively unknown ... doctor' [2, p. 283); (ii) Joule then wrote to the Philosophical Magazine `to set the history ... right' [1, p. 181, 283]); (iii) still in 1862, Tyndall replies that `to Mr Joule ... we are almost wholly indebted for the experimental treatment of this subject' ([1, p. 182, Smith's Reference 42 of Chapter 9, p. 337]). Cardwell describes (ii) and (iii) in terms of quite complimentary to Tyndall: `Joule ... felt his particular claim to have established, independently and scientifically, the doctrine of energy conversion could not be denied'. `With this Tyndall entirely agreed' (both quotes [2, p 283]).

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The first law of thermodynamics: The Joule?Mayer Controversy 235

From the above, Cardwell concludes:`. ... the whole matter could ? and certainly should ? have ended amicably with Joule's credit unimpaired and justice at last done to the unhappy Mayer'. He lays the blame for `this unnecessary and harmful squabble' (both quotes from [2, p 283]) largely with P.G. Tait, the professor of natural philosophy at Edinburgh. In the more diffuse discussion which follows Cardwell paints Tait rather unattractively. However, in 1875 Tyndall wrote a rather intriguing letter to Tait, which includes `I would rather see you and Clausius friends than Zollner and myself. Trust me, C. is through and through an honest high-minded man' [2, p. 288]. Public conflict and personal good relations are not unknown today in British political life!

4 Conclusion: honour satisfied

The realisation that heat and work were equivalent formed a crucial watershed in the history of thermodynamics and led to the first law. Our appreciation of this may have dulled with time and familiarity, but two of the references remind us the strongest terms. Cardwell describes the situation thus: `... after 1850 a developed, established science ... had to be re-established on a new basis: that of the axiom of the conservation of energy'. This was the first time in history that such a thing had happened ([2, p. 291], Cardwell's italics). Newburgh and Leff have very recently given the same message: `The path-breaking work of Mayer and Joule fusing heat and work is as fundamental to physics as the ideas of James Clerk Maxwell and Albert Einstein fusing electricity and magnetism' [9, p. 484].

Identification of the relative contributions of Mayer and Joule is therefore a matter of corres pondingly high scientific import. Broadly speaking, there was no disagreement, even at the time from Joule himself, that Mayer had historical priority in predicting the law. What Joule claimed was that he had established it, and again, at the time this was accepted by his peers and led ultimately to the SI Joule unit of energy. For Mayer, if the expression `the Mayer?Joule Principle' becomes generally accepted honour will be more than satisfied.

References

[1] Smith, C., The Science of Energy, Athlone Press: London, 1998. [2] Cardwell, D.S.L., From Watt to Clausius, Heinemann: London, 1971. [3] Smith, C. & Wise, M.N., Energy & Empire, Cambridge University Press: Cambridge, UK,

1989. [4] Clausius, R., ?ber die bewegende Kraft der W?rme, und die Gesetze, welche sich

daraus f?r die W?rmelehre selbst ableiten lassen. Annalen der Physik, 79, pp. 368?397, 500?524, 1850; English translation published in Phil. Mag. Series 4, 2, pp. 1?21, 102?119, 1851. [5] Clausius, R., On the motive power of heat, and on the laws which can be deduced from it for the theory of heat, translated by W.F. Magie, from Poggendorff's Annalen der Physik, LXXIX, p. 368, 500, 1850. Carnot, S., Reflections on the Motive Power of Fire, and Other Papers on the Second Law of Thermodynamics by E. Clapeyron and R. Clausius, with Introduction by E. Mendoza, (ed.), New Edition Dover: New York, pp. 107?152, 1988. [6] Mendoza, E., Introduction, in Carnot, S., Reflections on the Motive Power of Fire, and Other Papers on the Second Law of Thermodynamics by E. Clapeyron and R. Clausius, with Introduction by E. Mendoza, (ed.), New Edition Dover: New York, 1988.

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236 Kelvin, thermodynamics and the natural world

[7] Rankine, W.J., Mac, Q., On the geometrical representation of the expansive action of heat, and the theory of thermo-dynamic engines. Phil. Trans. R. Soc. Lond., 144, pp. 115?175, 1854.

[8] Kondepudi, D. & Prigogine, I., Modern Thermodynamics, John Wiley: Chichester, UK, 1999. [9] Newburgh, R. & Leff, H.S., The Mayer?Joule principle: the foundation of the first law of

thermodynamics. The Physics Teacher, 49(8), p. 484, 2011.

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