Exploring the Science and History of Thermodynamics
From the boilers that heat water in our homes to the engines in our vehicles that allow us to travel with ease, thermodynamics are an often-invisible part of our everyday lives.
Published May 1, 2006
By John H. Lienhard
Academy Contributor
The president of France, Sadi Carnot, was stabbed by an anarchist on June 24, 1894. The vein to his liver was severed, and he bled to death in the hospital. This touches our story in two ways:
First, the darkness of venous blood was one of the “tells” that led people to accept the idea of energy conservation, the first law of thermodynamics. Questions about how blood manages human body temperatures had helped people to see that our bodies achieve both work and heating from the chemical energy of food.
Second, President Carnot’s uncle, also Sadi Carnot, and his grandfather, Lazare Carnot, were key players in the struggle to understand the rules that govern heat and work. Their efforts led to what we call the second law of thermodynamics, the idea that no engine can ever be 100 percent efficient, and that all natural processes degrade energy. Yet neither senior Carnot accepted the first law of thermodynamics – the idea of energy conservation.
Black and Phlogiston
Many towns in France have a square, avenue, or street named Carnot but it is hard to tell which Carnot it honors: Lazare, best known as the “organizer of victory” during the revolutionary wars of the 1790s; his son, Sadi, who died at 36 having published just one work, yet whose name is inextricably linked to the origins of thermodynamics; or Sadi’s nephew who presided over the French Republic from 1887 until his assassination.
The story of the thermodynamical Carnots best begins about the time of Lazare Carnot’s birth, in 1753. Heat was then regarded as the “subtle fluid” phlogiston – the “substance” released during combustion. The young Scottish chemist Joseph Black was still thinking of heat as wedded to chemical change, but was asking just how much phlogiston it took to increase a material’s temperature one degree.
The Kindred Concept of Latent Heat
Black recognized that the amount must vary from material to material. By this time, both Fahrenheit and Celsius had provided excellent means for measuring the intensity of heat – its temperature. But should one not also have means for measuring its extent – its quantity? Black realized that he could heat a mass of water by transferring energy to it from another material. Since the heat leaving one mass is the same as that entering another, he could determine the heat capacity of any material by heating or cooling a known amount of water.
He also took an interest in the kindred concept of latent heat. At the transition points where a liquid boils or condenses (or a solid melts or freezes) it does so with no change in temperature. To measure the latent heat transferred in, say, melting, Black surrounded a known mass of ice with a known mass of hot water; then he measured how much the water temperature fell as the ice melted away.
These experiments led naturally to the British thermal unit or Btu (the energy needed to raise the temperature of a pound of cold water one degree Fahrenheit).
The Rise of Caloric
Black at first thought he was manipulating chemical changes in matter, but he began to see that heat was not some component of matter, as phlogiston was imagined to be. Rather, it flowed in and out of matter. Phlogiston was about to be displaced by the new term caloric. Caloric gained its full definition in 1779 when Black’s student, William Cleghorn, set down rules for its behavior. Cleghorn’s rules helped to make a useful tool of caloric, but they also helped expose its eventual failings.
Cleghorn determined that caloric had to be a subtle invisible fluid. He explained thermal expansion by imagining caloric to be elastic, with particles that repelled each other. Cool bodies attracted caloric to different extents. That explained heat conduction and specific heats. Caloric had to take a latent form as water boiled at 212° F. It was “sensible” when it raised a material’s temperature. Caloric had to have weight because metals gained weight when they were heated.
Today we know that bodies expand as they are heated because their molecules repel one another. We recognize the gain in weight in metals as a chemical change, oxidation.
Not the Whole Story
Black knew Cleghorn’s rules were not the whole story, but he allowed that they correctly explained the experiments of Benjamin Franklin and others. He cautiously called the caloric theory, “the most probable of any that I know.” Antoine Lavoisier, the French chemist, also liked the idea and coined the term calorique.
So the caloric theory remained for about seventy years. Not until atoms were far better understood would we realize that heat merely reflected atomic motion. However, in everyday life, we still speak of heat flow, or of bodies holding their heat, as if heat were behaving like a caloric fluid.
In our bones (or more accurately, in our muscles) we have always known that we can create heat by doing work. But how could frictional heating be reconciled with heat as a fluid? Caloric theorists tried to resolve that with increasingly tenuous arguments about how friction or deformation “released” caloric. They looked at frictional heating and saw, not a contradiction, but a phenomenon to be explained in terms of caloric. All the while, it was perfectly clear to everyone that the amount of caloric they could create was limited only by their own stamina.
A New Science of Thermodynamics
So the stage was set for the last act in the drama of writing a new science of thermodynamics. What had to be digested was the fact that thermal energy and mechanical work can be traded back and forth (the essence of the first law of thermodynamics).
Which takes the story back to venous blood. Natural philosophers were beginning to suspect that chemical reactions turned blood from red to dark. But estimates of the extent of chemical heating were too low to account fully for the heat.
Eighteenth-century physiologists had attributed blood heat to friction despite the caloric theory, and they continued to think that friction accounted for blood heat, well into the 19th century. Not until 1843, did French chemist Pierre Dulong have accurate enough data to show that chemical heating accounted for virtually all of blood heat. In an ironic twist, Dulong effectively bolstered the lingering caloric theory when he removed frictional heating from physiology.
Everyone who has ever studied the history of heat has struggled with the obviousness of mechanical friction. Yet even the idea that blood is heated by friction had failed to animate an anti-caloric movement. The recognition of friction as an instance of the convertibility of heat and work replaced caloric as a competing theory only in the 19th century, after cannon-boring experiments made in Bavaria by American expatriate Benjamin Thompson/Count Rumford. Thompson had become Count Rumford in Bavaria after a rapid and convoluted series of moves that began when he had to flee colonials who learned he was spying for the British.
Count Rumford’s Canon
As a result of tests in which he generated unlimited caloric by boring cannon with blunt bits under water, Rumford was able to state quite plainly, Anything which an 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.
Rumford continued his advocacy of a mechanical theory of heat after he left Bavaria and returned to England and France. At that point he took up a four-year relationship with Lavoisier’s widow, Marie, which ended in a short and disastrous marriage. It’s quite possible that the scientifically savvy Marie Lavoisier egged him on in his attack on caloric. In any case, before the marriage Rumford crowed: “I think I shall live to drive caloric off the stage as the late M. Lavoisier drove away Phlogiston. What a singular destiny for the wife of two Philosophers!!”
With that kind of rhetoric, we can hardly be surprised that the marriage failed. Rumford did indeed help drive caloric “off the stage” by setting a foundation for the first law of thermodynamics. But that would not happen yet.
An anti-caloric faction failed to arise, even after Rumford, for this is where Lazare and Sadi Carnot enter the story.
Lazare Carnot, Revolutionary Leader
Lazare Carnot was a remarkable figure. He was born in 1753 – the same year as Benjamin Thompson – and was educated in mathematics and military engineering. During his military service, he competed for mathematics prizes, and also had political dealings with the infamous Robespierre. While he was on garrison duty in the 1780s, Lazare Carnot began an intense affair with an aristocrat’s daughter.
Unbeknownst to Carnot, her father arranged her marriage to another aristocrat. Carnot, furious, went to the fiancé and revealed the affair. That broke up the marriage plans, but the father had Carnot thrown in jail for conduct unbecoming an officer and gentleman. This was 1789. The first events of the French Revolution were just taking place, and they led to Carnot being retrieved from prison after only two months.
His life had been pretty static up to that point. Now it began moving very rapidly. He was soon married (to someone else) and was elected to the Assembly. His skills in administering military missions led to his selection in 1793 as one of the 12 men on the Committee of Public Safety and, in 1796, as a member of France’s five-man ruling group, The Directory. They reorganized the government and ran it until Napoleon took power. Carnot served longer than any revolutionary leader except Napoleon.
A Mathematician and Technocrat
Carnot also started the Little Corporal on his rapid ascent to power by appointing him head of the Army of Italy, and Carnot would rally to Napoleon as his Minister of Interior when he returned from Elba. However, after Napoleon’s fall, the returning monarchy remembered Carnot’s vote to behead Louis XVI and he spent the rest of his life exiled to Germany.
Lazare Carnot was first a mathematician, yet strongly interested in technology. Also, he advocated active defense in fortification design, including what became known as Carnot walls – the high, heavy, detached walls built in front of forts, with loopholes for the exchange of fire. He befriended the Montgolfier Brothers, and Robert Fulton, who showed up in France trying to sell submarine designs. Carnot was an excellent violinist, but he thought like a technocrat. He once remarked: If real mathematicians were to take up economics and apply experimental methods, a new science would be created – a science which would only need to be animated by the love of humanity in order to transform government.
From Waterwheel to Steam Engine
Lazare Carnot’s attention naturally turned to power production. Imagine a perfect waterwheel, he said, in which no energy is wasted or dissipated. Water is stationary before it enters and stationary at the exit. Then he reached a very important insight: all motions would be completely reversible. Run the perfect waterwheel backward, and it would become the perfect pump.
Here Lazare’s son, Sadi, claimed his inheritance. In 1824, one year after his father died, 28-year-old Sadi Carnot wrote his sole monograph, Reflections on the Motive Power of Heat. In it, he asks us to conceive a perfectly reversible steam engine. If we could build such a machine, we could run it in reverse and pump heat from a low-temperature condenser to a high-temperature boiler. When the first refrigerators appeared 36 years later, they were exactly the reversed heat engines that Sadi Carnot had described.
Sadi “operated” his perfect engine in a thought experiment. In his mental engine, he used an ideal gas instead of steam. When he assumed the not-yet-fully-accepted fact that no engine can possibly act as a perpetual motion machine, he was able to show that the work of one kilogram of air in such an engine depends only upon the temperatures at which the air is heated and cooled.
The Basis for Carnot’s Theorem
That was the basis for Carnot’s Theorem: The motive force of a perfectly reversible engine depends solely upon the high and the low operating temperatures. (Those would be the boiler and condenser temperatures in a steam engine.) This sole dependence on temperature was the first step toward the second law of thermodynamics.
Carnot’s theorem would be true whether the engine used steam, air, or any other fluid. His ideal engine mirrored his father’s perfect waterwheel – a waterwheel that depends solely upon how far water falls through it. Yet neither father nor son accepted the conversion of work into heat or vice versa. (I can find no evidence that Lazare Carnot and his contemporary, Count Rumford, ever communicated.)
Sadi Carnot assumed that caloric was conserved as it passed through an engine, just as water passing through a waterwheel is conserved. Today we know that only part of the heat flowing into a boiler turns into useful work. A good fraction of the heat passes into the condenser. But since Carnot had couched his work in terms of indestructible caloric, the validity of what he said about steam engine performance seemed to bolster the caloric theory.
Clausius and Entropy
This strange turn of affairs meant that the demise of caloric had to await a new generation. Rudolf Clausius, born in 1822, finally synthesized our science of thermodynamics from these seemingly contradictory parts. Clausius showed how Carnot’s theorem and the conservation of energy complemented one another. Energy conservation said that less heat left a steam engine than entered it – the difference being converted into useful work. While that contradicted Carnot, it left Carnot’s theorem intact.
Clausius saw that something was being conserved in Carnot’s perfectly reversible engine – but something other than heat. He called it entropy, and defined it as the heat flow from a body divided by its absolute temperature. Entropy changes in a perfectly reversible engine balance out. As heat flows from the boiler to the steam, the boiler’s entropy is reduced. As it flows into the condenser coolant, the coolant’s entropy increases by the same amount.
No heat flows as steam expands in the cylinder or as condensed water is compressed back to the boiler pressure. Therefore, the entropy of the water or steam changes only when heat flows to and from the condenser and the boiler. The net entropy change is zero in that perfectly reversible engine and its surroundings. Under Clausius’s definition of entropy he was able to show that everything Sadi Carnot had claimed was true – except the part about heat or caloric being conserved.
Carnot’s Single Error
Once he corrected Carnot’s single error, Clausius could conclude that the efficiency of a perfectly reversible heat engine did indeed depend upon nothing other than the temperatures of the boiler and the condenser, just as Carnot had said it must. Carnot’s belief in caloric denied him the specific use of the word efficiency, but his central deduction remained intact.
Sadi Carnot died of cholera in 1832 and the image of his fevered blood brings to mind the dark venous blood of his nephew, Lazare’s grandson, its life-giving energy spent. What bizarre convergences these three generations offer – contradiction and resolution, terrorist politics and idealism, maddening complexity and elegant simplicity – and a crucial path along the road to understanding how things work.
Also read: Lockheed Martin Challenge Inspires Innovative Ideas
References
1. Brown, S. C. 1981. Benjamin Thompson, Count Rumford, MIT Press, Cambridge, MA.
2. Carnot, S. 1897. Réflexions sur la Puissance Motrice du Feu (Reflections on the Motive Power of Heat), R. H. Thurston, Ed. John Wiley, New York.
3. Gillespie, C. C. 1970-1979. The Dictionary of Scientific Biography, Charles Scribner’s Sons, New York.
4. Lienhard, J. H. June 2006. How Invention Begins: Echoes of Old Voices in the Rise of New Machines, Oxford University Press, Oxford, New York. Much of the material in this article, and all the resources used in its making, are in this book.
5. Lienhard, J. H. Engines of Our Ingenuity radio program Web site. www.uh.edu/engines. Short essays on many of the themes of this article can be found and heard here.
About the Author
John H. Lienhard is M. D. Anderson Professor Emeritus of Mechanical Engineering and of History at the University of Houston, and the author and voice of The Engines of Our Ingenuity, a radio program heard nationally on Public Radio. His latest book is the forthcoming, How Invention Begins: Echoes of Old Voices in the Rise of New Machines. (Oxford University Press)
