Another post inspired by my research into my Falling Felines and Fundamental Physics book!
Energy cannot be created or destroyed, but merely converted from one form to another.
Such is a typical statement of the law of conservation of energy, one of the most important unifying principles of physics. We constantly experience its effects in our day to day lives, whether we recognize it or not. When we accelerate our car, for instance, chemical energy in the fuel is converted into rotational energy in the wheels (with some lost as heat), which is in turn converted into kinetic energy — energy of motion — which carries us from place to place. When we step on the brakes to stop the car, that kinetic energy is converted into heat and some sound energy.
The conservation of energy proves the non-existence of perpetual motion machines: in order for a machine to provide unending motion, it must have an inexhaustible source of energy to power it. Or, in other words: you can’t get more energy out of a machine than you put into it.
The conservation of energy has even led to important new discoveries. In the 1920s, physicists realized that energy (and momentum) was seemingly not conserved in the process of beta decay, in which an electron or positron is emitted from an unstable atomic nucleus. Though some physicists (looking at you, Niels Bohr) were tempted to throw out the principle of energy conservation altogether, Wolfgang Pauli suggested in 1930 that there must in fact be another particle released in the decay — chargeless, nearly massless, and hardly interacting with ordinary matter. Experimental searches confirmed the existence of the neutrino, which is a key component in the current “theory of everything,” the Standard Model of Physics.
Though the conservation of energy is of fundamental importance in physics, it is a relative newcomer in the history of the subject. Isaac Newton’s Principia was published in 1687, marking the start of quantitative theoretical physics, but conservation of energy was not established until the 1840s, over 150 years later.
Even more curious is the manner in which the three key discoveries were made. The earliest major breakthrough was made via cannon-boring, the next work was done by a doctor, and the conclusive research was done by a brewer! Hence, a simplified history of the discovery of the conservation of energy can be described as booms, blood, and beer!
In this post, I’ll summarize the early history of the subject, and talk at length about the “booms” part of the history. In the next two posts, we’ll cover “blood” and “beer.”
Hints of the conservation of energy, in fact, stretch back to the time of Newton, and even earlier. In the 1600s, physics greats such as Christiaan Huygens and Gottfried Wilhelm Leibniz (co-discoverer of calculus and consequently Newton’s bitter rival) recognized that something besides momentum seemed to be conserved in the collisions of moving bodies; Leibniz called it the “vis viva” (living force) of the system. This vis viva was defined for a single object as
VIS VIVA = MASS × VELOCITY × VELOCITY
For multiple masses in motion, one determined the total vis viva by adding together all the individual values, and this quantity would remain constant in certain types of collisions. In hindsight, we recognize that Huygens and Leibniz had roughly identified the kinetic energy of moving masses.
However, these early researchers noted that the vis viva was not conserved in all circumstances. In modern terms, we recognize that kinetic energy can convert to other forms when objects collide; therefore vis viva is only conserved when there is no conversion. The most common situation, though, is that some kinetic energy in a collision turns into heat, and historically there was much disagreement as to what heat actually is. Today, we recognize heat as the measurable manifestation of the random motion of atoms and molecules; but in the era in which the physics of matter was not understood at all, and even the atomic theory was not widely accepted, this was by no means obvious and was difficult to prove.
By the late 1700s, the view held by most physicists was that heat was a form of fluid, named “caloric” by its initial proponent, Antoine Lavoisier, a chemist who made foundational discoveries in both chemistry and biology. Lavoisier argued that caloric is a fluid which is self-repelling, which explained why heat seems to spread away from its source, and which is conserved — heat doesn’t “disappear,” but simply spreads out and transfers to other objects. It was thought that caloric is attracted to matter, which was how the heat seemed to be drawn into solid objects.
Equal weights of different substances can absorb more or less heat in order to reach the same temperature; in this, the calorists argued that different materials have a different “capacity” for heat, and that some materials basically have more room, and attraction, for caloric than others. The term “heat capacity,” which is still used in physics today, comes originally from the caloric theory.
The known phenomenon in which bodies expand when heated could be explained through caloric: as caloric is self-repelling, then adding caloric to a material, i.e. heating it, would mean more repulsive force in the material, causing it to stretch.
The creation of heat through impacts, such as a hammer pounding a piece of metal, was explained as the result of the caloric being squeezed out of the metal through compression. If the caloric was resting within the nooks and crannies in matter, then smashing the matter left less room for the caloric to hide, and some of it would be ejected.
But if one hammers a room temperature piece of metal, which is not hot to begin with, where did the caloric come from? The calorists then argued that materials possessed “latent heat” — basically, caloric that is inert due to interaction with matter. In short, caloric was thought to come in two forms: free caloric, which caused the observable phenomenon of heat, and latent caloric, which was bound to matter and not directly observable.
If all of this starts to sound familiar, it is because the calorists had a very powerful analogy to draw from: electricity. In 1733, the French chemist Charles François de Cisternay du Fay had argued, based on a series of experimental tests, that there are two types of electricity, which he labeled “vitreous” and “resinous” (and which we would call positively and negatively charged, respectively), which he viewed as two distinct electrical fluids. He also found the fundamental result that opposite types of electricity attract and similar types of electricity repel. With this, and the caloric theory, it probably looked to researchers in the late 1700s that much of physics could be explained through a “Standard Model of Fluids.”
It should be noted that there were also advocates for a theory of heat as motion, but they were in the minority, and the aesthetic connection between the caloric theory and the electrical theory was no doubt appealing to scientists of the era. And both theories were able to explain almost everything observable about heat, so the choice at the time seemed a matter of taste.
A weak link existed in the chain of caloric reasoning, however: the heat given off due to friction. When two objects are rubbed together, they produce heat. There is no visible compression of the objects in the process, so a different explanation was needed. The calorists argued that the process of friction caused some of the material to be rubbed off in powder form, and that in powder form, the material has less heat capacity. In the powdering process, then, heat must be released. Superficially, this sounds quite reasonable; any trivial experiment, however — experiments that the calorists did not make — casts immediate doubt on this explanation. If I rub the heel of my palm on my wooden desktop, for instance, I can generate a lot of heat right away without turning either my hand or my desk into powdered form.
Nevertheless, by the end of the 18th century, the calorists felt like they had a solid explanation of the physics of heat. The situation is curiously analogous to one that would occur at the end of the 19th century, when physicists felt like almost everything in nature could be explained by existing laws, with a few troubling inconsistencies that they were certain would soon be resolved. Those inconsistencies, however, would turn out to be due to quantum effects, and would spark a revolution in science. A similar thing would happen to the calorists: those small inconsistencies would eventually result in a major change in the way we understand nature.
Into this state of affairs would come Count Rumford (1753-1814): inventor, soldier, scientist, nobility and all-around enterprising fellow. Rumford would end up presenting the strongest challenge to the caloric theory yet, through a remarkably serendipitous observation.
Count Rumford¹ would be a man of many hats throughout his life, and those hats would all influence his eventual discovery. Born Benjamin Thompson in the rural town of Woburn, Massachussetts, he showed an early aptitude in science and mathematics, as well as a curiosity which did not allow him to end a project until he had solved it to his satisfaction. At age 13 he became an apprentice to a merchant in Salem, but this did not dampen his taste for experimenting. Not only did he take up engraving as a hobby in his free time, but — ironically in hindsight — he attempted to build a perpetual motion machine. This latter exploit ended in failure, and he became convinced of its impossibility.
Thompson’s curious nature got him into serious danger in these early years. The Stamp Act of 1765, imposed by the British government on the American Colonies, not only added a new tax but required that many documents printed in the Americas be printed on a special stamped paper directly from the homeland. This tax was levied without any input from the colonists, and led to the famous statement “no taxation without representation.” The Act placed a huge cost burden on merchants, and a popular outcry led to it being repealed only a year later.
Salem wanted to have a fireworks display to celebrate the repeal of the act but, due to the lack of any professional pyrotechnics experts in town, Thompson volunteered to make the fireworks himself. In his attempts, however, he sparked an explosion that temporarily blinded him and left him near death. He was incapacitated for weeks, but it is an indication of his drive and determination that he carried on correspondence about scientific questions with a friend while he healed. And he went right back to work as soon as he was able.
But his career as a merchant wouldn’t last. Additional taxes levied by the crown on the Colonies led to the Americans creating a boycott of British goods, which started with the Boston Non-importation Agreement of 1768. With the reduced trade, Thompson was no longer needed as a clerk, and he returned home to live with his mother in Woburn. In 1769 he apparently sustained himself through teaching science and mathematics, and also worked as an assistant to a medical doctor named Hay, apparently with the intention of becoming licensed to practice medicine.
The next year he took up a job with a merchant again, this time in Boston, but that effort was doomed due to the growing political turmoil in the colonies. Thompson was in town when the infamous Boston Massacre took place on March 5, 1770, in which British soldiers shot and killed 5 locals in an angry mob. Thompson was apparently nearby when the shooting took place, and was ready to go out to the aid of the Colonists, if the violence had spread.
But these fights with the crown took their toll on the merchant community, and Thompson found himself without a job again. He returned home to Woburn again, but remained undaunted — he and a friend walked to sit in on scientific lectures at Harvard, which was about ten miles each way! When they got home, they would put together their own versions of the experiments they had seen demonstrated. Thompson also began experimenting with gunpowder again, though he was much wiser and cautious after his near-fatal earlier accident.
Thompson’s career prospects were dire at this point, but his energy and zeal finally paid off for him as people recognized it. He was invited to run an academy in Rumford, New Hampshire (today known as Concord, New Hampshire), and his success at that job gave him an opening into high society. During that time, he met Sarah Rolfe, a wealthy widower who was thirteen years his senior, and the two were married in 1772. This happy occasion, which occurred when Thompson was only 20, led to even more opportunities for the young man. After meeting him at a social event, the Governor of New Hampshire appointed Thompson as a Major in the New Hampshire militia, a prestigious role for someone so young who had not served in the military before. Apparently, in that time of heated political passions, the Governor appreciated Thompson’s pointed neutrality on the subject of American independence. Thompson’s daughter Sarah was born in October of 1774, adding to the sense that things were finally going his way.
But political turmoil would finally completely upend his entire life. People were simply not allowed to remain neutral in such a turbulent time, and other soldiers in Thompson’s militia, who had been passed over for promotion in favor of him, further suggested that his loyalties lay with the crown. In November of 1774 a mob descended on Thompson’s home, with the goal of tarring and feathering him. He was forced to flee to Boston, leaving his wife and child behind.
What followed was a tragic attempt by Thompson to prove his alliance to the Colonial cause. He attempted to enlist in Washington’s army, but found himself denied a commission due to the same suspicions of being a British loyalist. When actual war broke out, Thompson was tried on suspicion of being a traitor to the American cause. The court found that there was no evidence of a crime on Thompson’s part, but also did not acquit him of all suspicions, much to his chagrin.
As the war heated up, Thompson at last found himself without any real home among his fellow Americans. He was not allowed to return home to his family, but he was not trusted enough to be given a role in the burgeoning Revolution. Finally, in mid-1775, he ended up joining the British military as an advisor. He would never see his wife again, and he left the Americas after the war with the defeated British forces.
But, as we have already seen, Thompson was not a man easily discouraged. Even while advising the British during the war, he found time to perform more experiments on the force of exploding gunpowder, and his results were published in 1781 in the prestigious Philosophical Transactions of the Royal Society. This work cemented his reputation as a scientist. His ability to impress important officials remained undiminished, as well. When he had an opportunity to meet Major-General Maximilian of Deux-Ponts, who would later become King of Bavaria, the two traded stories of the American Revolutionary War. The discussion led Maximilian to suggest that Thompson might find good employment and appreciation of his talents in Bavaria, and Thompson moved there in 1785.
In Bavaria, working under the Prince-elector Charles Theodore, he implemented many reforms of both the military and society, trying to make the former more efficient and the latter more humane. He argued that permanent garrisons and arsenals for soldiers was key to efficiency, and these places were built and staffed. He established workhouses for those poor people able to work, and invented “Rumford’s soup” as an inexpensive but nutritious meal for the poor and soldiers alike. He also created the Englischer Garten in Munich, a large public park, in 1789. In recognition of his efforts, Benjamin Thompson was made a count of the Holy Roman Empire in 1791, and he took the name “Count Rumford” after the town where his life’s prospects first started to look up. In 1795, he returned to England, and in fact became a truly international figure, getting invitations to various European countries. He brought his daughter over from the Americas to join him, and introduced her to high society. Sadly, his wife had died several years earlier.
And with this rather lengthy introduction to Count Rumford — his life story becomes more fascinating the more one looks into it — we can return to the discussion of Rumford and the caloric theory of heat. In the late 1790s, Rumford was still advising the Bavarian government and working with their military on improvements. While supervising the boring of cannons at the arsenal in Munich, he started to ponder the tremendous amount of heat produced by friction in the process. As he would write in the introduction to his paper on the subject, published² in 1798 in the Philosophical Transactions of the Royal Society,
It frequently happens, that in the ordinary affairs and occupations of life, opportunities present themselves of contemplating some of the most curious operations of nature; and very interesting philosophical experiments might often be made, almost without trouble or expence, by means of machinery contrived for the mere mechanical purposes of the arts and manufactures.
As discussed earlier in this post, the caloric theory explained the release of frictional heat as due to a change in the heat capacity of the powdered material produced. That is: powdered metal produced in friction must have a lower heat capacity than solid metal, resulting in a release of heat during the powdering process.
Rumford’s first experiment was to test this friction hypothesis. He compared the heat properties of some of the metal chips that had been produced in the boring process, along with an equal weight of metal that had been sliced off of the barrel, producing no heat. Bringing these two samples to the temperature of boiling water, he then dropped them into equal quantities of cold water. If the chips had less heat capacity, they should have heated the water much less than the sliced metal; Rumford, however, found that they heated the water equally. Evidently, the heat capacity of the chips was unchanged from the bulk metal — this was in direct contradiction with the caloric theory.
But if the heat was not being released from the metal, where was it coming from? Here, Rumford needed a much more elaborate experimental apparatus. He took a brass cylinder, that would normally be used to make a six-pound cannon, and ground the exterior to produce one long section that could be held and turned in the borer, connected by a thin metal rod to a compact section that would serve as the actual experimental apparatus. Figure 1 below shows the initial cylinder, and Figure 2 shows the result after shaping.
It is worth drawing a more detailed illustration of the short section of the barrel that is the main part of the experiment. The whole barrel was rotated by the action of horses, causing the fixed metal borer to grind away on the inside of the cylinder, producing frictional heat. A small second hole was made to allow a thermometer to be dropped in for instantaneous temperature readings. This thin connection to the main barrel was presumably made to minimize thermal contact between the experimental apparatus and the rest of the metal.
In Rumford’s first test, he did the grinding in air, with a flannel cover over the cylinder to prevent excessive heat loss. In this test, he wanted to estimate how much “caloric” was released, by weight, in the frictional heating process.
His numbers were astounding. The cylinder was raised roughly 70 degrees Fahrenheit in temperature over the course of the grinding, and about 1/1000th of the mass of the barrel was converted into metal chips, about 1/10th of a pound. But this indicated, to Rumford, that apparently that 1/10th of a pound carried enough caloric to create 70,000° F worth of temperature! (1/1000th of the mass was able to make the entire mass 70°.)
In modern terms, this is a terrible, awkward, and inconsistent way to quantify the heat released in a physical process, but for Rumford, it highlighted the absurdity of the caloric theory. How could such a tiny amount of material contain so much heat within it, and yet be apparently unchanged in its heat capacity when measured in another experiment?
One possible explanation for this effect is that the caloric was not coming from the metal itself, but from the air around it, through some unknown mechanism. The interior of the borehole was open to the air, and therefore the effectively unlimited amount of air around the experimental apparatus could be providing the caloric seemingly observed. For Rumford’s second experiment, he placed a leather piston around the opening of the borehole and the iron rod, effectively blocking the free passage of air into and out of the hole. But this second experiment showed that the amount of heat produced was unchanged; evidently, caloric from the air was not producing the heat inside the borehole.
Now, however, Rumford worried that friction between the spinning leather piston and the iron rod might be interacting with the air outside to produce the same effect. So, for his third experiment, he submerged the entire apparatus in a box of water, as illustrated below.
For the results of this experiment, we should quote Rumford himself:
The result of this beautiful experiment was very striking, and the pleasure it afforded me amply repaid me for all the trouble I had had, in contriving and arranging the complicated machinery used in making it.
The cylinder, revolving at the rate of about 32 times in a minute, had been in motion but a short time, when I perceived, by putting my hand into the water, and touching the outside
of the cylinder, that heat was generated; and it was not long before the water which surrounded the cylinder began to be sensibly warm.
At the end of 1 hour I found, by plunging a thermometer into the water in the box, (the quantity of which fluid amounted to 18.771b. avoirdupois, or 2 1/4 wine gallons,) that its temperature had been raised no less than 47 degrees; being now 107° of Fahrenheit’s scale.
When 30 minutes more had elapsed, or 1 hour and 30 minutes after the machinery had been put in motion, the heat of the water in the box was 142°.
At the end of 2 hours, reckoning from the beginning of the experiment, the temperature of the water was found to be raised to 178°.
At 2 hours 20 minutes it was at 200°; and at 2 hours 30 minutes it ACTUALLY BOILED!
It would be difficult to describe the surprise and astonishment expressed in the countenances of the by-standers, on seeing so large a quantity of cold water heated, and actually made to boil, without any fire.
This is evidently one of the first, if not the first, cases in which water was boiled without a flame. It seems apparent that most scientists, up to this point, felt that large amounts of caloric could only be produced efficiently through combustion; Rumford demonstrated that this was not the case.
In his report to the Royal Society, Rumford himself could not suppress a bit of adorable giddiness over the findings:
Though there was, in fact, nothing that could justly be considered as surprising in this event, yet I acknowledge fairly that it afforded me a degree of childish pleasure, which, were I ambitious of the reputation of a grave philosopher, I ought most certainly rather to hide than to discover.
In this experiment, air had been taken entirely out of the picture; that potential objection to his results had been eliminated. He performed one more experiment — his fourth — in which he took the piston off of the cylinder while it was immersed in water, letting the borer be surrounded by water instead of air; he found no difference in his results.
Rumford finally came to a conclusion which was a huge departure from the caloric theory, and potentially a big step forward for the understanding of the physics of heat:
And, in reasoning on this subject, we must not forget to consider that most remarkable circumstance, that the source of the heat generated by friction, in these experiments, appeared evidently to be inexhaustible.
It is hardly necessary to add, that any thing which any insulated body, or system of bodies, can continue to furnish without limitation, cannot possibly be a material substance: and it
appears to me to be extremely difficult, if not quite impossible, to form any distinct idea of any thing, capable of being excited, and communicated, in the manner the heat was excited and communicated in these experiments, except it be MOTION.
In short: Rumford argued that the heat was being conveyed to the experimental device through the motion of the system, and that heat itself must be a form of motion. His work appeared to deal a devastating blow to the caloric theory, and heavily favored the concept of heat as motion.
The calorists, however, were not so easily defeated. Their theory was still nebulous enough that it could be adapted to explain even these effects, albeit by adding even more hypotheses to it. Furthermore, that other fundamental fluid, electricity, was already known to be able to be create through friction in seemingly inexhaustible quantities; it was not too difficult for those people invested in a “Standard Model of Fluids” to assume that caloric was somehow produced in a similar manner.
So Rumford’s experiments, though fascinating and quite important historically, did not immediately have an impact on the thinkers of the era. It would take the work of a doctor and a brewer in the 1840s to really dispose of the caloric theory and introduce a theory of energy.
But Rumford himself did not suffer from this rejection. Even long before this, in 1789, he had been welcomed back into the American fold with a Foreign Honorary Membership in the American Academy of Arts & Sciences. In 1799, he co-founded the Royal Institution of Great Britain, an organization dedicated to scientific research and education which still exists today; its scientific Christmas lectures are world-renowned. The first one of these was given by Michael Faraday in 1825, and I’ve blogged about one of his lectures previously.
Rumford is also known for another important invention associated with heat that he made at roughly the same time as his cannon experiments: the Rumford fireplace. It was designed to both reflect heat more effectively into a room as well as draw smoke more efficiently out of the chimney; after Rumford introduced his design, it became standard in homes for some 50 years. In 1802, Rumford also introduce the Rumford furnace, which could be used in the industrial production of quicklime.
Rumford himself endowed medals at both the Royal Society and American Society, as well as a professorship at Harvard University, where he had walked to take classes so many years ago.
Do you remember Antoine Lavoisier, the great proponent of the caloric theory? Lavoisier died in 1794; in 1804, Rumford married his widow, Marie-Anne Paulze Lavoisier, who was a chemist in her own right and had often helped her husband with his experiments.
Rumford’s daughter Sarah became the Countess Rumford upon his death, and used her inherited wealth to become a noted philanthropist, helping out the poor, the motherless, the mentally ill, and widows. She never married, but traveled extensively throughout her life before settling back to her childhood home in Concord, New Hampshire, where she lives with her adopted daughter until her death.
The Rumford family as a whole left a big impact on society. It is somewhat ironic that Rumford’s greatest scientific achievement, his experiments on the nature of heat, is probably the least recognized thing associated with his name. But, as we have hinted, the 1800s would bring more unlikely discoveries from more unlikely discoverers, leading to a revolution in science and the discovery of energy as a conserved quantity in nature.
¹ Much of the history of Count Rumford comes from the 1848 book, Lives of Count Rumford, Zebulon Montgomery Pike, and Samuel Gorton.
² Count Rumford, “An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction,” Phil. Trans. Roy. Soc. 88 (1798), 80-102.