The first law of thermodynamics is basically as follows: there are different types of energy, the energy of motion, the energy in a compressed spring, the energy of a rock lifted off the ground, the energy of heat, nuclear energy, etcetera.
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Emilie du Chatelet
Energy can by transferred from one type to another and from one object to another, but the grand total is always the same, where the work (the force times the distance) equals the change in energy of a single object.
This law didn’t, as Marie Slodowska Curie like to say, spring fully armed from Jupiter’s head like Minerva, but instead was the product of dozens of people debating the nature of force, heat and motion for over 150 years! Ready to learn the story? Let’s go!
I would like to start in the early 1700s with a remarkable woman named Emilie du Chatelet.
Emilie was born in 1706, and was the only daughter of a wealthy and connected French family. Emilie was brilliant at languages and mathematics from an early age. Her father lamented, “my youngest flaunts her mind and frightens away the suitors… we don’t know what to do with her.”
Her father was exaggerating, of course, because with wealth, beauty, and high social status there were plenty of men who were willing to look past her unusual intelligence.
When she was 18, Emilie decided that she didn’t want to be forced to live in a convent like most unmarried upper class women were at the time and agreed to an arranged marriage to a 34 year old marquis.
They had three children in quick succession and afterwards they then had what can be only described as an open marriage, which was not unusual at the time. In 1733, Emilie met the poet Voltaire and they immediately fell in love.
Emilie and Voltaire
Voltaire was always in trouble with the French government for pushing for freedom of religion and speech and satirizing the religious and secular leaders of the day.
In fact, when he met Emilie he had just returned from exile in England where he had learned about Newton’s scientific philosophies. (Voltaire just missed out on meeting Newton as Newton died just as Voltaire arrived in England). Soon, Emilie, her husband, and her lover Voltaire decided to hole up at her country home called Cirey.
Emilie wrote a friend, “There is heroism or perhaps madness in my shutting myself up at Cirey, with the three of us.” Emilie and Voltaire then built an academy of science with over 21,000 books, larger than most university libraries at the time. In 1738, Emilie du Chatelet and Voltaire created a book about Newton’s theories where Emilie did most of the math and Voltaire wrote most of the prose, or as he put it to a friend, “Madame du Chatelet had her part in the work… [in that she] dictated and I wrote.”
Of course, all of Emilie du Chatelet’s work did not induce Voltaire to include her name in the title although he did dedicate it to her and put her (topless) image inside the cover as an angel.
After that Voltair started work for a competition on the nature of light and fire and Emilie felt that Voltaire’s theories about the mass of fire were dead wrong. Frustrated with Voltaire ignoring her ideas, Emilie secretly wrote her own paper. She determined that if a ray of light had a mass that was even a tiny fraction of the mass of a cannon ball, the speed of light would mean that an “instant of light” would “destroy all the universe.”
Emilie du Chatelet also decided that fire (ie. heat) was “the cause of the internal motion of the particles of all bodies” and even predicted the 3rd law of thermodynamics almost 200 years before Walther Nernst writing that it was impossible to have a particle “that is in perfect repose,” and that “all in nature is in perpetual oscillations of dilation and contraction caused by the action of fire.” Emilie knew she would never win the contest writing a friend that, “the originality of my ideas would keep me from winning, aside from the other reason [i.e. being a woman]” but she just wanted an honorable mention, “I wanted to stand out from the crowd and to be taken seriously by the judges”.
Neither Voltaire nor Emilie du Chatelet won or even got honorable mention, however, Emilie’s reputation as a serious scientist was made, her friend Madame de Graffigny wrote, “I … read the dissertation on fire that Madame wrote… It is so clear! So precise! I apologize to Monsieur de Voltaire, but it’s much better than his… and when did she write this discourse? At night, because she was hiding from Voltaire!”
While researching how destructive sunlight could be if it had mass Emilie started to study what different scientists thought about the damaging effect of moving objects.
Of course, having just co-written a book on Newton, she was aware of Newton’s view on matter and force. However, despite what I was told in school, Newton never wrote that force equals mass times acceleration. In fact, the closest he came to it was, “a change in motion is proportional to the motive force impressed.”
Instead, Newton was focused on mass times speed as if two objects collided with identical mass times speed and stuck they would stop moving (for this reason, some people started called mass times speed the “dead force”).
However, unlike most French and English scientists at the time Emilie du Chatelet wasn’t limited to Newton. See, at the time, science was almost a nationalist pastime. If you were English, you needed to support Newton, if you were German, Leibnitz, if French, Descartes often to the exclusion of the others.
Emilie thought that was ridiculous and wrote, “About a book of physics one must ask if it is good, not if the author is English, German, or French.” Or as Voltaire put it, “in the kingdom of Madame du Chatelet, there is absolute freedom of conscience.” In 1738 or so Emilie learned that a few years before Newton, Newton’s rival Gottfried Leibniz proposed something he called the living force that was dependent on the mass times the velocity squared which was conserved when objects bounced off each other (living because this “force” was only conserved for moving objects).
Newton and Leibniz were enemies and had long arguments on who discovered Calculus so that almost everyone in Europe was firmly in one camp or the other. However, Emilie felt differently telling her son, “do not carry respect for the greatest men to the point of idolatry… no book is so good that one might not improve it.” One of the definitive experiments that convinced Emilie du Chatelet that the damage from stopping a moving object is related to the mass times the speed squared (or the “living force”) is dramatized in the 2005 documentary “Einstein’s Big Idea”:
Emilie du Chatelet’s Book: Lessons in Physics
Anyway, in 1740, Emilie du Chatelet published a book called “Lessons in Physics” which was the first to champion Newton’s theories and the idea of living force and helped promote both Newton’s and Liebniz’s theories in France, Germany and even England. One reviewer gushed, “there appeared at the beginning of this year a work that would give honor to our century if it were by one of the principal members of the Academies of Europe.
This work, however, is by a woman, [who] has had for a teacher only her genius and her application to self-instruction.” Du Chatelet continued to research science and by 1747, du Chatelet started to work on her magnum opus, the first French translation of Newton’s Principia with footnotes about the living force.
Tragically, she died just before its publication at age 42 from complications from childbirth. After her death, Emilie du Chatelet’s ideas about Newton, Leibniz, fire, light, philosophy, and living forces, were all reproduced (sometimes plagiarized word for word) by her friend Diderot in the very influential French Encyclopedia. Her influence was obscured by her death, but her scientific theories flourished.
Fast forward to England in 1807. That was when a doctor and scientist named Thomas Young, who was famous for his double-slit experiment from a few years earlier that demonstrated that light acts like a wave, was asked to give a series of talks on the current state of science.
Young decided to make his talks as simple as possible as his lectures were devoted to the women in the audience as he thought “the acquisition of knowledge” was superior to “the insipid consumption of superfluous time”. Anyway, in his fifth lecture (out of 60) Young decided that rename the living force (the mass times the speed squared) saying that, “the living force … is somewhat more concisely expressed by the term energy”.
Young’s lectures were published as a book and his simplified physics “for the ladies” became a popular science textbook in the 1800s. Soon, the term “energy” for mass times speed squared started to gain popularity although only in England.
Ideas of Conserving “Living Force”
Now we go back to France (again) and two ex-soldiers, Sadi Carnot and Gasbard-Gustave Coriolis, who were interested in the efficiency of machines. As Carnot put it, “the study of engines is of the greatest interest, [as] their importance is enormous… and they seem destined to produce a great revolution in the civilized world.”
Both men were children of soldiers who went to the same school to become engineers for the military in the very early 1800s. However, Carnot started in a far better position in French society as he was the son of one of Napoleon’s top captains and Coriolis was the son of one of the former King’s top captains and King Louis the 16th had been decapitated when Coriolis was just an infant.
They switched social positions in 1815 when Napoleon was defeated (again) and Carnot’s father was exiled. Sadi Carnot was allowed to remain but was generally found military life frustrating with no family power. By 1818 Carnot left the military and holed up in his brother’s apartment in Paris secretively studying science (Carnot wouldn’t even tell his brother what he was working on).
Meanwhile, Coriolis’s father died and Coriolis dropped out of the army to make a little more money as a scientist studying mechanical systems. Because of his engineering background, Coriolis had far more technical expertise in machines than the typical academic and in 1829 Coriolis published a book on the physics of machines.
In this book, Coriolis defined a new term that he called work that he defined as the Force times the distance in the direction of motion. Surprisingly, this is still the modern definition of Work.
Moreover, with this new definition of Work, Coriolis used calculus and found that if an object was pushed on a flat surface the object would have a change in ½ the mass times the speed squared. He therefore decided to make a “slight modification” to the definition of the “living force” and define it as ½ mv^2 (instead of mv^2) to add “simplicity to the principles”.
He then found that if you had a machine that pushed an object up a hill then the Work minus the weight times the height equaled the change in “living force”. In other words, the work equals the change in the potential energy due to gravity (mgh) plus the change in kinetic energy (1/2mv^2). If this sounds like what you learned in High School Physics you are right! The only thing missing was heat.
Now we go back to Carnot hiding out in his brother’s apartment. In 1824, Carnot decided to publish his theories on heat and heat engines. In this pamphlet, Carnot assumed that heat came from hot objects and went to cold objects and the bigger the temperature difference, the more efficient the engine (all things we consider true today).
Carnot then came up with the form of an idealized engine that would be the most efficient (the Carnot engine). He then declared that, “the production of … power is not …[due] to an actual consumption of [heat], but to its transportation from a warm body to a cold body.” In other words, Carnot thought that heat-engines absorb same amount of heat that they discharge and it is the movement of heat that allows the engine to perform work.
(The theory that heat is a fluid that is always conserved was called the caloric theory and was very popular in France at the time.) Over the years, Carnot privately started to rethink the idea of heat as an indestructible fluid. He wrote in his notebook, “When a hypothesis no longer suffices to explain phenomena, it should be abandoned.
This is that case with regards [to the imperishable] caloric.” In around 1830 or so Carnot prophetically wrote, “Heat is simply… a movement among the particles of bodies. Wherever there is destruction of motive power there is, at the same time, production of heat in quantity exactly proportional to the quantity of motive power destroyed.
Reciprocally, wherever there is destruction of heat, there is production of motive power.” Tragically, before he could publish these thoughts Carnot died of Cholera (at the age of 36) and his private words were only published in 1890, many years after others gained fame for its discovery. Very few people read Carnot’s work while he was alive, but 2 years after his death another Frenchman and engineer named Paul Clapeyron used it for his book on heat engines which slowly gained popularity around the world.
Whew! That is a lot of people, let’s do a little recap. In 1747 Emilie du Chatelet combined the ideas of conserving “living force” (mv^2) with Newton’s ideas and her theories were plagiarized/ ahem memorialized in the French Encyclopedia of 1751. In 1807, Robert Young gave a series of lectures “for the ladies” where he renamed the “living force” the “energy”. In 1824, Carnot wrote his book on heat. In 1827 Coriolis defined Work as Force times distance and redefined the “living force” (ie. kinetic energy) as ½ mv2. In 1834 Clapeyron published his thoughts on Carnot’s work including the ideas that heat flows from hot to cold and the erroneous idea that heat is indestructible.
Now we move back to England and a young brewer named James Joule. In 1840, 22-year-old Joule decided to systematically study if an electric motor would be more efficient then a steam engine in his bottling factory. Joule then found an equation for the amount of heat that a resistor would produce and created an equation we still use today (P = I^2R).
He also studied how much chemical energy was used in the battery and was surprised to find them equivalent. Joule became fascinated with the science and started building elaborate (and astonishingly precise) devices where falling weights would drive a spinning paddle, which would then increase the temperature of the water to demonstrate the relationship between work and heat.
By 1843, Joule was trying to convince anyone and everyone that, “wherever mechanical force is expended, an exact equivalent of heat is always obtained.” But Mr. Joule was not a professor, just a lowly brewer, so he was mostly ignored, but he kept on speaking wherever anyone would listen.
In 1847, Joule was allowed to give a speech at Oxford where he greatly impressed the audience including a 23-year-old Scottish math and physics phenomenon named William Thomson.
Thomson was impressed with Joule’s experiments but he didn’t initialy agree with his conclusions as he had just read Clapeyron’s paper on Carnot and was a huge fan and was deeply reluctant to accept anything that was contrary to Carnot’s writings (he didn’t know about Carnot’s unpublished ideas of course).
In fact, in 1848, Thomson decided that Carnot’s theories were a good theoretical basis for creating an absolute temperature scale, and became the first person to correctly get that absolute zero is 273 degrees Celsius below freezing.
[Thomson was knighted some 44 years later to be Lord Kelvin, which is why the absolute temperature scale is measured in Kelvins in his honor].
Anyway, in this paper of 1848, Thomson mirrored what he thought was Carnot’s feeling about heat (or the caloric) that it that “the source of power [is] not in any absorption and conversion [of heat], but merely in a transmission of heat.” (Although Thomson did admit in a footnote that “Mr. Joule of Manchester” made “some very remarkable discoveries” which led to a contrary opinion on heat).
This paper made Carnot’s theories instantly and internationally famous. In addition, Joule was delighted to have a “real” scientist mentioning him even in a footnote and they started a correspondence, which led to a fruitful collaboration.
Eventually, Joule became a famous professor and the units of energy are called Joules in his honor. Meanwhile, back in January of 1849, Thomson wrote another paper that was only about Carnot.
In this paper, Thomson declared that the idea that heat was indestructible was “the fundamental principle” of Carnot’s theories: “to deny it would be to overturn the whole theory of heat”. It was this paper that led to the last scientist on our list, a quiet German named Rudolf Clausius.
Clausius was born in 1822 and was the youngest of 18 children! Yep, I said that right 18. When Clausius was 21, his family ran into financial difficulties and he ended up working as a high school teacher while he got his Ph.D. (Clausius remained a devoted teacher his entire life and even gave lessons on his deathbed).
When 26 year old Clausius read Thomson’s papers he was intrigued and felt that it might be a way to make his name and get out of teaching high school.
Like Emilie du Chatelet over 100 years before, Clausius took what seemed like desperate and conflicting ideas and elegantly meshed them together. In 1850, Clausius then came up with a new theory that was “opposed, not to the real fundamental principle of Carnot, but to the addition ‘no heat is lost’”. Clausius wrote that Carnot’s theories and heat being a form of energy, “may not only exist together, but that they mutually support each other”.
Clausius included the idea of what he called “interior work” (as compared to “exterior work”). This interior work, which he gave the letter U, represented how the heat affected the internal heat of the gas or changed its properties.
We know call the “interior work” the internal energy although we still use the letter U. In fact, one of the modern forms of the first law, that the change in internal energy equals the heat added minus the work done by an object is exactly how Clausius put it, with the same sign conventions, AND the same letters used! With this paper, Clausius made his mark in the scientific world and finally got a job as a professor.
Meanwhile, Thomson said that he independently realized that Clausius was right in that Heat is not conserved but energy is. Thomson then published a series of five papers “On the Dynamical Theory of Heat” between 1851 and 1855 where he lay out new mathematics and theories on the conservation of energy. In these papers, Thomson used the term energy instead of “living force”. In 1852, Thomson divided energy into two types, “statical and dynamical” which was a very good entomology in my humble opinion.
However, another Scottish scientist, William Rankine, named it “potential and actual” in 1853, and then Thomson changed it to “potential and kinetic” in 1855, the names we are stuck with today. Although Clausius had innumerable petty arguments with Thomson, he decided that the term “energy” was appropriate as “an abbreviated mode of expression,” and by 1865 Clausius had formed the first law to be that: “the energy of the universe is constant”.
As Richard Feynman said, “conservation of energy… is a most abstract idea, because… it is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.” But as a mathematical trick it sure is powerful. In 1881, Thomson wrote, “the very name energy, … first used in its present sense by Dr. Thomas Young [is now] a principle pervading all nature and guiding the investigator in every field of science.”
Clausius wasn’t done yet and in 1854 Clausius came up with a new, second law. This law was about the heat over the temperature. Clausius stated that for a perfect reversible cycle the heat divided by the temperature for the full cycle would add to zero and for anything else this quantity would be positive.
By 1865, Clausius renamed this function the “entropy” of a system and wrote the second law to be “the entropy of the universe is increasing”. But what is entropy, why did he name it that, what does it mean and what does it mean about the universe? That is next time on the Lightning tamers!
Clausius began to study different processes for a heat engine and determined that if two processes were equivalent, then the heat over the temperature had to be the same.
Clausius started to review Carnot’s other claims, specifically that “heat cannot by itself pass from a colder body to a warmer body” and Carnot’s idea about a “perfect” engine (currently called a Carnot cycle) where an object does work in 4 steps: two steps at constant temperature, and two where no heat is absorbed or emitted.
Clausius declared that he wanted a formulation of this law that was in equation form. While playing with the different variables, Clausius realized that the heat over the temperature
Three different men had different idea about heat. Ludwig Colding experimented in Denmark, “just as it is true that the human soul is immortal, so it must also surely be a general law of nature that the forces of nature are imperishable”. Julius von Mayer, in Germany, June 1841.
Joule didn’t know but the previous year in Germany, a chemist and medical student named Julius von Mayer had decided the same thing, “falling force and motion are equivalent to heat [and] heat must also be equivalent to motion or falling force.” However, Mayer’s understanding of basic physics was iffy and didn’t really convince much of anyone about his theory.
1 Emilie du Chatelet to the Duke de Richelelieu (June 15, 1735) translated by Bour, I and Zinsser, J Selected Philosophical and Scientific Writings of Emilie du Chatelet (2009) p. 16
2Voltaire (1737) translated and found in Hagengruber, R Emilie du Chatelet between Leibniz and Newton p. 5
3Emilie du Chatelet “History of Fire” translated by Bour, I and Zinsser, J Selected Philosophical and Scientific Writings of Emilie du Chatelet (2009) p. 53
4Isaac Newton translation found in Smith, George, “Newton’s Philosophiae Naturalis Principia Mathematica“, The Stanford Encyclopedia of Philosophy (Winter 2008 Edition), Edward N. Zalta (ed.)
5Voltaire to ‘s Gravesande (February 1740) translated and found in Arianrhod, R Seduced By Logic p. ?
6Carnot, S Motive Power of Heat (1924) p. 38
7Coriolis, J Du Calulation de L’effet des Machines (1829) p. 17
8Coriolis, J Du Calulation de L’effet des Machines (1829) p. 17
9Carnot, S Motive Power of Heat (English translation 1890) p. 46
10Carnot, S Motive Power of Heat (English translation 1890) p. 225
11Carnot, S Motive Power of Heat (English translation 1890) p. 225
12Thomson, W “On an Absolute Thermometric Scale” (1848) Mathematical and Physical Papers, Vol. 1 (1882) p. 103
13Thomson, W “Carnot’s theory of the motive power of heat” (1849) Mathematical and Physical Papers, Vol. 1 (1882) p. 116
14Thomson, W “Carnot’s theory of the motive power of heat” (1849) Mathematical and Physical Papers, Vol. 1 (1882) p. 116
15Thomson, W “On the Sources of Energy in Nature…” (Sept, 1881)
16Mayer, M “On the forces of Inorganic Nature” (May 1842) translated in The London, Edinburgh and Dublin Phil. Magazine Vol. XXIV – Fourth Series (1862)p. 376