ABOUT THE CHARACTERS
Ludwig Boltzmann (1844–1906)
Austrian physicist tormented by depression and mood swings. Uses statistical methods to show how agitations of swarms of tiny atoms give rise to bulk properties of matter. Famous for the Boltzmann equation, S = k log W. Deeply troubled by attacks on atomic theory, and thus his work, by prominent colleagues. In 1906, on vacation near Trieste, hangs himself while his wife and daughter are swimming. His equation is engraved on his tombstone in Vienna.
Lazare Carnot (1753–1823)
French military engineer specializing in the elimination of waste. Military duties interrupt his studies of inefficiency in water-powered machines. Does a jail spell when he seduces a woman betrothed to another man. Nicknamed ‘Organizer of Victory’ by French Revolutionaries thanks to his creative problem-solving for the cause. Fathers and homeschools two sons: Sadi and Hippolyte.
Sadi Carnot (1796–1832)
Son of Lazare, a quiet engineer who inherits from his father an apartment and an interest in reducing inefficiency in heat engines. Writes the most seminal work on the subject, Reflections on the Motive Power of Heat, which his brother Hippolyte edits. It contains the notion of conservation, reversibility, and the famous ‘Carnot cycle.’ But the book is ignored, Carnot stops publishing, catches scarlet fever, brain fever, cholera, and dies, age 36, in a madhouse.
Rudolf Clausius (1822–1888)
German physicist who settles the battle between the conversionists and the conservationists by declaring that two principles are in play, one involving the conservation of what is soon called energy in exchanges of heat and mechanical work, the other the conversion of heat into energy. Coins the word ‘entropy,’ which he refers to as S, and is another claimant as discoverer of the second law.
Hermann von Helmholtz (1821–1894)
German physicist who masters and contributes to an astounding variety of fields, including acoustics, aesthetics, anatomy, biology, magnetism, mathematics, mechanics, meteorology, ophthalmology, optics, phenomenology, philosophy, physics, physiology, and psychology. Invents the ophthalmoscope for examining the inner eye. Mentors many scientific stars, including Nobel Prize winners Albert Michelson, Max Planck, and Wilhelm Wien.
James Prescott Joule (1818–1889)
As a youth, James builds a home science lab in his parents’ brewery. A few years later, he manages highly accurate measurements of various conversions of heat and electrical, mechanical, and chemical energy into one another. He’s the first to measure the mechanical equivalent of heat. His work promotes the idea of the conversion of energy, and sets off a battle between proponents of conversion and of conservation.
James Clerk Maxwell (1831–1879)
An improbable prodigy taunted by cruel classmates who nickname him ‘Dafty’ for his plain clothes, country accent, and candid questions. Establishes the field of electromagnetism via one of the most brilliant uses of analogy in history, and lays the groundwork for the electronic age. Explains, among other things, the rings of Saturn, the behaviour of gases, and the nature of spinning tops, constructing ‘the fanciest top ever made.’ Dies at age 48.
Robert Mayer (1814–1878)
While a doctor on a boat in the East Indies, notices the unusual redness of his crew’s blood, meaning it is oxygen-rich. Deduces that human metabolism is slower in the tropics and that mechanical work and heat are interchangeable. His unintelligible paper on the subject is rejected by a journal, though he later revises and publishes it. Depressed by rejection of his claim to the second law, he flings himself from a third-floor window and is sent to an asylum in a straitjacket.
Max Planck (1858–1947)
Undeterred by his professor’s warning that everything in physics has been discovered already, while focusing on neatening up the old – tidying up thermodynamics – he invents the quantum and changes the world! His eldest son dies in World War I at Verdun; his second eldest is hanged in World War II for joining the plot to kill Hitler. Wins the Nobel Prize in 1919. A world-famous research organization is named for him. So is a 43-kilometer-long asteroid.
Count Rumford (1753–1814)
British soldier of fortune, amateur scientist, and spy, who conducts experiments on heat in between courtships of wealthy widows. Refutes the ‘caloric’ theory of heat proposed by the former husband of his latest conquest. Proclaims that heat is not a substance but comes from motion generated by friction, and uses this idea to quantitatively compare different kinds of work. Thinks he’s another Newton.
William Thomson (1824–1907)
A polymathic, trilingual, and farsighted son of a mathematics professor, the future Lord Kelvin. He’s torn by the conflict between the conversionists and the conservationists, and is determined to make peace. Developer of the new science of heat-mechanics, which he names thermodynamics. Co-author of thermodynamics’ Principia, the Treatise on Natural Philosophy, and one of several claimants as discoverer of the second law.
Wilhelm Wien (1864–1928)
A farmer at heart, takes on physics as a second career. Authors Wien’s law, which uses the second law of thermodynamics to map radiation’s dependence on temperature, thereby leading us ‘to the very gates of quantum physics.’ Discovers a positively charged particle which, when further explored by others, becomes the proton. Wins the Nobel Prize in 1911. A crater on Mars, 120 kilometers in diameter, is named after him.
My thoughts on this subject are even more radical. I think that the second law of thermodynamics is actually Shakespearean. Its story involves powerful and finely drawn characters. It has fundamental implications for human life. And it unfolded in somewhat the way Shakespearean dramas do.
Here’s a plot summary of how one version might go.
PROLOGUE
Europe, end of the eighteenth century
A new mechanics is on the horizon. The steam engine and other technologies have drawn attention to phenomena relating to heat. Driven by practical necessity and curiosity, legions of inventors are attempting to develop better steam engines. But their work is mostly tinkering, because as yet little is known about heat. Heat seems to be a force – we can put it to work! – but not one whose operations are explained by Newtonian pushes and pulls. A theory of heat is clearly needed, and a crude one, called ‘caloric theory’, appears. Developed in the second half of the eighteenth century by French scientist Antoine Lavoisier – the ‘father of modern chemistry’ – caloric theory conceives of heat as an invisible and weightless fluid that flows from place to place, which provides the beginning point for understanding heat as a force. Several scientists, whose motives range from curiosity and professional duty to pride and ambition, turn their attention to this heat-force. They are soon embroiled in a conflict about whether utilizing this heat-force involves conservation or conversion of heat: is the total amount of heat always the same, or does it get converted to something else? The resolution of this conflict will turn out to be the key to the new mechanics.
ACT ONE
Paris and Munich, end of the eighteenth century
Scene 1. Paris, 1803
Lazare Carnot (1753–1823), a military engineer whose talent is uncovering and eliminating administrative and mechanical inefficiency, publishes a treatise on water-powered machines, General Principles of Equilibrium and Motion. Follow the water, he writes: the maximum power depends on how great a distance it falls. Track down and eradicate sources of waste, he also counsels, to make your machine work better. But Lazare can’t pursue these insights. He’s forced back to military duties; later he seduces a woman betrothed to another and ends up in jail. He’s released as the French Revolution begins and joins the revolutionaries, who nickname him ‘Organizer of Victory’ for the innovative way he mobilizes, trains, and supplies troops. He has two sons, whom he homeschools and who will carry on his legacy: Sadi, a military engineer (named after a Persian poet), and Hippolyte, a journalist and politician.
Scene 2. Munich, 1797–98
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sp; Count Rumford (1753–1814), soldier of fortune and amateur scientist, is in Munich, momentarily between courtships of wealthy widows. Keen to reveal the mysteries of heat, he puts a 6-pound brass cannon barrel in a vat of water, inserts a drill bit driven by a winch, hitches up a horse to the winch, and finds that this generates enough heat through the drilling to boil the water in 2½ hours. The caloric theory formulated by Lavoisier (the former husband of one of Rumford’s mistresses) is wrong, Rumford proclaims, for the seemingly inexhaustible amount of heat generated in the process is not coming from either the brass or the water, but is clearly a form of motion coming from the friction between the bit and the cannon. He counts the candles it takes to boil the same amount of water, to compare the amount of heat and mechanical force. Reporting to the Royal Society, he implicitly likens himself to Newton, saying the laws of heat are as important as those of gravity. But Rumford is no Newton. His arguments are not entirely convincing and he has no overall theory of heat, just a very suggestive set of observations. Yet his idea that one can quantitatively compare various kinds of work that create the same amount of heat (candles, horses), and the work that heat does in different forms, helps to set up the looming conflict between conservation and conversion.
ACT TWO
Paris, Manchester, and Oxford, 1820s–40s
Scene 1. Paris, 1823
Sadi Carnot (1796–1832), a quiet engineer, returns from his father Lazare’s deathbed to the apartment he has just inherited. Determined to carry on his father’s work, Sadi sets to work composing a treatise, Reflections on the Motive Power of Heat, on ways to make steam engines more practical and efficient. Fearing that his prose is too convoluted to appeal to the general audience that he covets, he has his brother Hippolyte edit his manuscript and steady his prose. Steam engines, he begins, ‘seem destined to produce a great revolution in the civilized world.’ Nevertheless, he continues, ‘their theory is very little understood.’ Such a theory must begin by considering the general question of what the most efficient way is to use steam. One key thing to consider in a machine, Carnot realizes, is its maximum duty, or maximum output; for instance, how high a given amount of coal in the machine can raise a given amount of water. Follow the heat, he writes. Caloric in a heat engine, like water in a water engine, is conserved as it flows from the hot to the cold places, and the maximum power depends on the magnitude of the temperature drop. The most efficient machine is modeled by an ideal cycle of expansion and compression in which the engine works reversibly, the caloric being conserved in going back and forth between the two temperature endpoints with no heat diverted (wasted) to friction or dissipation. This is a key insight, but Reflections is almost totally ignored. Carnot publishes nothing more, catches scarlet fever, brain fever, cholera, and dies, aged thirty-six, in a madhouse.
Scene 2. Manchester, 1840s
James Prescott Joule (1818–1889), who as a youth built a home lab in his parents’ brewery, manages to get highly accurate measurements of various conversions of heat and electrical, mechanical, and chemical energy into each other; for instance, the temperature increase that rotating paddles, stirring up water, produce in the water thanks to friction. He determines the mechanical equivalent of heat: 772 foot-pounds of work make a 1-degree F rise in 29 cubic inches of water.
Scene 3. Oxford, 1847
The conflict between conservation (Carnot’s approach) and conversion (Joule’s) begins to come to a head. Young William Thomson (later Lord Kelvin, 1824–1907), the polymathic, trilingual, and farsighted son of a mathematics professor, travels to Paris, where he reads the only published comment on Sadi Carnot’s work and is so impressed he tries in vain to find a copy of the original. Then he attends a conference in Oxford, where he hears Joule. Joule is treated badly by the conference organizers, who instruct him to be brief. But Joule’s words jolt Thomson. How can heat be converted to something else when Carnot’s spectacular work relies on the fact that the amount of caloric in an engine is constant? Joule’s work must have ‘great flaws’, Thomson decides, and he resolves to find them.
ACT THREE
Great Britain and Germany, 1840s–60s
Scene 1. Glasgow
Thomson, still convinced that Carnot’s conservation theory is right and that something must be wrong with Joule’s work, gets another jolt. He reads a paper by German physicist Rudolf Clausius (1822–1888), who has also noticed the conflict between the approaches of Carnot and Joule. Clausius has been examining the kinetic theory according to which heat and gases consist of tiny particles in constant motion. And Clausius says that the conflict between Carnot and Joule is only apparent, and is not a conflict in reality because two principles are in play. One involves the conservation of something (not heat, and soon called energy) in exchanges of heat and mechanical work; the other the conversion of heat into energy, and the property that heat cannot flow spontaneously from colder to warmer bodies. Thomson, inspired, begins to leapfrog works with Clausius on the new heat-mechanics. In 1854 Thomson names it thermodynamics, after the Greek for heat and force. Some heat in every engine, Thomson writes, ‘is irrevocably lost to man, and therefore ‘wasted’ although not annihilated’ – his version of the second of Clausius’s two principles. Clausius embarks on a series of papers that culminate in 1865, when he names the tendency of the energy transfer process to occur spontaneously (disorder, we now say) ‘entropy’, after the Greek for ‘transformation’; he referred to entropy as S, a function of the state of a system, and uses the formula ∫dQ/T ≤ 0. In 1867, Thomson and his collaborator Tait compose thermodynamics’ Principia, the Treatise on Natural Philosophy. In 1872, Clausius formulates what becomes known as the two laws of thermodynamics this way: ‘The energy of the world is constant; the entropy of the world strives toward a maximum.’
Scene 2. Heilbronn, Germany
Priority battles erupt. In 1847, German physician Robert Mayer (1814–1878) reads a paper by Joule on the conversion of heat into mechanical energy and says he discovered it first. Seven years previously, as a doctor on a Dutch ship in the East Indies, Mayer had realized that the unusual redness of the blood of the crew – meaning it was oxygen-rich – was due to the fact that human metabolism is slower in the tropics. This had inspired him to write a paper on the interchangeability of mechanical work and heat to Annalen der Physik und Chemie, the leading German science journal, but the poorly written paper had been treated as a crackpot letter by the editor and Mayer didn’t receive a reply, though he later revised it and published it elsewhere. Depressed when Joule disputes his priority, Mayer flings himself out a third-floor window, and is committed to an asylum in a straitjacket. Meanwhile, another German physicist, Hermann von Helmholtz (1821–1894), is also a contender for discovering the first law of thermodynamics thanks to an 1847 paper on ‘the conservation of force.’ Tait and Clausius battle over who discovered various principles of thermodynamics, slinging mud at each other in journals and books.
ACT FOUR
London, Graz, and Vienna, 1870s
Scene 1. London and Graz
Another battle breaks out, this time over which of the two laws of thermodynamics is more important. For they seem to conflict. The first law (conservation of heat/energy) implies that processes are reversible – that the ‘before’ and ‘after’ states of a physical process cannot be distinguished, for each can turn into the other. The second law (heat cannot be completely turned back into work) implies irreversibility, or what is later known as the ‘arrow of time’, that change tends to go in one direction only. The problem comes to a head in Clausius’s specialty, the kinetic theory of gases. A gas is a ‘big thing’ governed by irreversible processes and the second law, but is composed of ‘little things’ – atoms and molecules – each of which obeys reversible Newtonian principles governed by the first law. In 1859, James Clerk Maxwell (1831–1879) comes across Clausius’s paper on the kinetic theory of gases, and decides that the statistical methods he had just used for studying Saturn’s rings as a coll
ection of small bodies might also apply to gases. Maxwell realizes that a gas’s jostling molecules do not end up, or reach equilibrium, with all of them having exactly the same speed; rather, they have a range of speeds clustered about one value. Imagine a dense crowd of people randomly milling about in a train station: the people are not all moving at exactly the same speed, but most are moving at about the same speed, with only a handful dead-still or going very fast. To understand the behaviour of the gas, furthermore – or of a crowd – it is not necessary to track the positions and velocities of each and every individual in it, but suffices to know the distribution of positions and velocities. Using only statistical methods and assumptions of Newtonian mechanics, Maxwell comes up with an equation to describe the spectrum of velocities of the gas molecules. The plot describes a bell-shaped curve: few lie at the extremes, moving almost not at all or very fast, but most cluster about an average velocity with the numbers tapering off at higher and lower velocities. But Clausius’s 1865 paper, and Maxwell’s own experimental work, force him to modify the theory, and he publishes a revision in 1867. Maxwell concludes that the second law is merely statistical, true only when vast quantities of particles are involved and not true of individual motions. The second law, he writes, is true for the same reason as is the statement that ‘if you throw a tumblerful of water into the sea, you cannot get the same tumblerful out again (i.e., exactly the same molecules as before).’1 At the atomic level, reversibility is possible and the second law does not hold, he thought. But why can’t reversibility be possible for large bodies in principle; why cannot heat flow sometimes from a cold to a hot body? In 1867, writing to Tait, Maxwell demonstrates this imaginatively and theatrically by a thought experiment involving a little ‘being’ that can detect faster-moving molecules in a gas, and by opening and shutting a door at the right time gets the faster ones on one side of a barrier, thus causing heat to flow to one side of the box. In this way the creature seems to refute Thomson’s idea of dissipation by getting heat to flow from a colder to a hotter place. Maxwell publishes this idea in 1871, in a short section entitled ‘Limitations of the Second Law of Thermodynamics’ in his Theory of Heat. That seems to end the matter; it is all a question of statistics.
A Brief Guide to the Great Equations Page 11
