A History of Thermodynamics Julian Barbour Copyright c 2020 by Julian Barbour Contents 1 Preface 2 2 Sadi Carnot and the Steam Engine 3 3 The Mechanical Equivalent of Heat 15 4 The Conservation of Energy 20 5 The First Law of Thermodynamics 31 6 The Second Law of Thermodynamics 36 7 The Dissipation of Mechanical Energy 41 8 The Discovery of Entropy 47 9 Statistical Mechanics 56 10 Boltzmann and the Second Law. I 66 11 Maxwell's Demon and Thomson on Time 71 12 Boltzmann and the Second Law. II 75 13 Boltzmann's Tussle with Zermelo 83 1 1 Preface This `book' consists largely of text removed, on the very sensible recommendation of my editor TJ Kelleher, from a first draft of my The Janus Point published on 1st December 2020 by Basic Books in the United States and by Bodley Head on 3rd December in the United Kingdom. The history it contains would have taken up too much space in the book now published and tried the patience of readers wanting to get on to new ideas. However, colleagues urged me not to jettison the material and to seek to turn it into a separate book on the discovery of thermodynamics. In the preface to The Janus Point I announced my intention to do that and as an interim measure to put the material on my website, where you have now found it. In its present state, it is certainly not ready for publication, in part because it contains some material that is already included in The Janus Point and should be edited out and also because the present text needs the inclusion of more material. For those readers who have or intend to read The Janus Point, Sadi Carnot's work is here, in the first chapter, much more fully covered, and the same is true of the next seven chapters. The chapter on Maxwell's demon and William Thomson on time contains material that, except for a small part, is not in the published book at all. The three chapters here with Boltzmann in their title have significant overlap with material in The Janus Point. Julian Barbour, College Farm, South Newington. Note added 16/08/2021. Since I posted this `book' on my website in December 2020, Paul Sen's Einstein's Fridge: The science of fire, ice and the universe has been published. I recommend the book. It is very readable and contains much historical material that in part complements my own account. In particular Sen devotes much space to the outstanding work of J Willard Gibbs, who hardly appears below except for his critical comment about the need for confinement of a dynamical system if it is to be treated in thermodynamics and statistical mechanics. This issue, which I believe is critical if the system considered is the universe, is at the heart of my The Janus Point but is not considered by Sen. If I do manage to develop this text into a proper book, Gibbs must surely be given more prominence. I was recently able to acquire second-hand copies of his collected papers in two volumes originally published shortly after his death in 1903 and subsequently reprinted by Dover. Lucky the person who has them on their bookshelf. I have also taken the opportunity to rejig the text, which I had inadvertently right aligned for the original posting. I, and you if you read this `book', can, like me, be thankful to Kartik Tiwari, who is reading it and sent me an email yesterday asking \Why is the manuscript right-aligned? It seems like a very trivial and useless question but it was bugging me so much that I thought I should ask you." 2 2 Sadi Carnot and the Steam Engine It can be argued that thermodynamics as a science began with a strange observation made by Joseph Black (1728-1799). A professor at Edinburgh who discovered magnesium and advised whisky distillers, he happened during his work to leave two buckets of water in a room. The first contained ice and water, the second only water. The water temperature in both buckets was at the freezing point. When he came back a few hours later, the first bucket contained less ice and correspondingly more water but, to Black's surprise, it was still at the freezing point. The water in the second bucket was noticeably warmer. Only when all the ice had melted did the water in the first bucket begin to get warmer. Ambient heat in the room had obviously entered the contents of both buckets and brought about the changes. But why had it only melted some of the ice in the first bucket without heating the water as well? It seemed heat could disappear. Believing its amount should remain constant, Black suggested it had become latent, the Latin for hidden. He also showed that the addition of heat to boiling water did not raise its temperature, which also suggested it had become hidden. To this day, physics students learn about latent heat, but it now refers only to the phenomenon Black observed, not his interpretation of it. Latent heat is a measure of the amount of heat needed to bring about some transformation like the melting of ice. Black's observation was a factor in the development by Antoine Lavoisier (1743-1794)1 of the ice calorimeter, which he used to measure the heat released in chemical reactions. Together with Pierre-Simon Laplace (1749-1827) Lavoisier developed the theory of caloric. This was supposed to be an invisible, weighless and indestructible `heat fluid’ that could pass from one body to another, raising the latter's temperature and causing it to expand. Besides giving a simple explanation of Black's observations, caloric served as the foundation of Laplace's theory of the propagation of sound. Newton had argued this involved transfer of heat; Laplace's caloric-based theory assumed there was none and was a significant im- provement on Newton's theory; it continued to make improvements to the theory of sound for a century. I have recalled the theory of caloric for two reasons: first, it is a good example of a seemingly sound idea that, as we will see, remained unchallenged for a surprisingly long time. The turning points, when they do come, provide much of the fascination in the history of science. Second, caloric provides the background to this chapter on the work of Sadi Carnot. There were, in fact, two Sadi Carnots, the one who first understood the essence of steam 1Known as `the father of modern chemistry', Lavoisier is above all associated with its transformation, so decisive throughout the scientific revolution, from a qualitative to a quantitative science. He recognized and named oxygen and hydrogen and helped construct the metric system. There is a superb 1788 portrait of Lavoisier and his wife by the great painter Jacques-Louis David. The opulence of the setting gives a clue to Lavoisier's gruesome end. He was a tax-collecting administrator of the F´ermeg´en´eral, which in Revolutionary France was a greatly hated part of the Ancien R´egime, and from its profits he funded his scientific research and, no doubt, his private life. He was accused of selling adultered tobacco and guillotined. The appeal to spare his life so that he could continue his experiments is said to have been dismissed by the judge with the words \The Republic has no need of scientists (savants) or chemists." This may be apocryphal, but not the comment of the great mathematician Lagrange: \It took them only an instant to cut off this head, and one hundred years might not suffice to reproduce its like." 3 engines and the other his nephew, the president of France from 1887 until his assassination by an Italian anarchist 1894. The first Sadi's father was Lazare Carnot, a hugely significant historical figure on account of his role in revolutionary France. He appointed Napoleon to his first indepedent command and organized the fourteen French armies involved in the Napoleonic wars. He was the only one of Napoleon's generals to be undefeated. He was also a scientist of no mean ability. In 1803 he published a book on mechanical machines such as pulleys. This reveals an ability, inherited by his son, to see through details and grasp the essential. He saw clearly that the most important thing in machines is to maximize their efficiency. That seems obvious today but is in part due to Lazare and even more so his son. Sadi, who was born in 1796 and was named for a Persian poet then in vogue, seems to have had a very attractive personality: honourable, sober, modest and an excellent violinist. There are some brief biographical details about him in the introduction by the editor, E. Mendoza, to the translation of Sadi's justly famous Reflections on the Motive Power of Fire published in 1824 (the year after Lazare died). For those who want to go into these things a bit more deeply, I strongly recommend the Dover publication of this work, which also includes translations of two papers, one in 1834 by Emile´ Clapeyron and the other in 1850 by Rudolf Clausius. These papers transformed Carnot's ideas into the two fundamental laws of thermodynamics and were extremely important, since Carnot's book went completely unnoticed by contemporary scientists and was only saved from oblivion by Clapeyron, who usefully sharpened the mathematical formulation of Carnot's insights and made the later work of Clausius and others possible.