Einstein's Fridge: How the Difference Between Hot and Cold Explains the Universe

by Paul Sen

On April 28, 1847, he gave a lecture to the general public in a church in Manchester, where he presented his evidence and repeated his claim that energy conservation was part of a divine plan. A local paper, the Manchester Courier, published the lecture in full, and Joule sent copies to his friends. The scientific community, however, remained uninterested.

The organizers told Joule, who was due to speak to a group of chemists, that they were now too busy for his lecture. So, instead, they asked him to speak to some physicists, who had time available. The organizers made it clear to Joule that he should make his talk as brief as possible. For Joule and for science, however, this organizational snafu was serendipitous. Finally, after a decade of scientific obscurity, chance had placed someone in the audience who seemed interested in Joule’s work.

The interrogator was a twenty-three-year-old from Glasgow named William Thomson, who was already regarded as one of his nation’s leading scientific minds. Years later he, too, vividly recalled the encounter and the feelings of both intrigue and alarm it had evoked: “I felt strongly impelled at first to rise and say that Joule must be wrong,” but “as I listened on and on, I saw that Joule had certainly a great truth and a great discovery, and a most important measurement to bring forward.”

William Thomson, however, possessed remarkable scientific intuition. In his mind, Carnot’s theory and Joule’s experiments both rang true despite appearing incompatible. Could they both be right? If so, how?

According to Thomson, while on a walking holiday a few weeks after that first meeting, he’d run into Joule near the Alpine resort town of Chamonix. Joule was on his honeymoon, but he’d left his bride in a nearby carriage while, thermometer in hand, he searched for a waterfall to confirm a theory that the temperature at the top is cooler than at the bottom.

Caino? Je ne connais pas cet auteur.

—Paris bookseller to William Thomson

Thomson was in Paris undergoing the final stages of an education designed from boyhood to prepare him for scientific greatness. Born in Belfast in 1824, he’d moved to Glasgow eight years later with his family when his father had been appointed mathematics professor at the city’s university. Aged fifteen, Thomson won the class prize at the same institution for an analysis of how the earth’s shape had formed. A year later his precocious mathematical talent further manifested when he encountered The Analytical Theory of Heat by the French polymath Joseph Fourier.

An example is a metal bar that is hot at one end and cold at the other. Experience tells us that heat will diffuse from hot to cold until the bar’s temperature equalizes. Fourier showed how this kind of diffusion can be described mathematically. His approach was unusual for the time, and Fourier had critics. Aged sixteen, Thomson published a detailed defense of the Frenchman’s methods in the scholarly Cambridge Mathematics Journal.

Thomson’s father began hatching a plan for him to become Glasgow University’s next professor of natural philosophy.

With the incumbent old and in poor health, Thomson senior’s one concern was that the post would not be open to a youthful candidate whose only credentials were a Cambridge mathematics degree—a qualification that showed a talent for abstract reasoning but not necessarily for demonstrating physical phenomena to students, a highly valued skill at Glasgow University, the leading educational establishment in an industrial city that prized practicality.

He urged his son to obtain letters of introduction to eminent French savants, travel to Paris, and get his hands dirty once he’d received his Cambridge degree.

it was in Paris—“without doubt the Alma Mater of my scientific youth”—where Thomson encountered the ideas of Sadi Carnot.

Joule’s conviction that heat and work could be turned into each other flew in the face of a key assumption that Carnot had made, namely that heat, being caloric, could not be created or destroyed. Then, in the autumn of 1848, William Thomson obtained a copy of Carnot’s original treatise. Whatever doubts Joule had seeded in his mind, Thomson was now convinced the Frenchman’s work was too important to remain in scientific obscurity.

“An Account of Carnot’s Theory of the Motive Power of Heat with Numerical Results Deduced from Regnault’s Experiments on Steam,” undersells its importance. It is not merely an English rendition of the French original; rather, the paper is one of the most significant Thomson wrote over a long and illustrious career, not least because with it he introduced a new word into the scientific lexicon: thermodynamic.

The main body goes to great lengths to demonstrate both theoretical and experimental support for Carnot’s treatise. But at regular intervals, Thomson introduces footnotes referring to Joule’s work that serve as troublesome critiques. The paper captures the conflict between Carnot and Joule in Thomson’s mind. Though he can’t resolve it, by juxtaposing each side of this internal debate in the same text, he would enable others to join in.

Then unexpectedly, within a few months, new evidence emerged that, on the face of it, favored Carnot over Joule. This evidence came from James, William’s older brother, who had devised an ingenious way of testing Carnot’s ideas.

On reading these calculations, William Thomson was elated. He now had a way of testing Carnot’s theory in his laboratory at Glasgow University. If he could measure the drop in the freezing point of water as it’s put under pressure to be a value predicted by his brother, it would provide evidence that Carnot’s theory was correct.

So, in late 1849, William Thomson commissioned one of his students, Robert Mansell, to build a thermometer sensitive enough to detect temperature changes of less than one one-hundredth of a degree Celsius.

Thomson measured the temperature at which water froze under differing amounts of pressure. Much to William Thomson’s satisfaction, the results vindicated his brother and, by extension, Carnot.

The Thomson brothers had also, without knowing it, explained how glaciers move. The pressure on the ice at the bottom of a glacier is so great that it melts, even though the temperature there is 0°C or lower. A layer of water is thus created under the glacier, allowing it to slide downhill.

Thomson knew, however, that though the ice experiment was evidence for Carnot, it was not evidence against Joule.

In fact, Joule’s work amplified another doubt Thomson had about the theory, which was this: Though the flow of heat from hot to cold can produce work, this flow doesn’t always do so.

As caloric flows unimpeded down an iron bar from the hot to cold end, it doesn’t make a splashing sound or anything equivalent. So what happens to the power it could have produced? Thomson had no answer.

In March 1850, he wrote to Thomson saying, “There ought to be some connecting link between the results I have arrived at and those deduced from Carnot’s theory. Perhaps you will succeed before long in discovering it. For my own part it quite baffles me.”

It is a spectacle for the gods to see the muscle working like the cylinder of a steam engine. —The Berlin-based physiologist Emil du Bois-Reymond

Walk in von Moltke’s footsteps today and you see much the same sights. But some are missing, notably a footbridge, which was intended to appear ruined and beneath which flowed a powerful stream of water. A few hundred yards past it, one would have heard a strange sound, now also long gone—an insistent clattering and puffing, emanating from within a villa that would not have seemed out of place in Renaissance Florence. Entering, one would have seen a steam engine, one of the earliest in Prussia and designed by an engineer trained in England.

This was the society in which the young Hermann Helmholtz grew up. He took full advantage, forming long-lasting friendships with other ambitious young physicians, physicists, and chemists. A like-minded group coalesced with the common mission of bringing the study of living organisms in line with existing research into the inanimate world. In modern terms, they wanted to show that living organisms obeyed the same mathematical, physical, and chemical laws as everything else.

Many scientists of the day believed in vitalism, the idea that living organisms, in addition to the sustenance they received from food, water, air, and so on, also possessed a “vital,” life-giving force. While an organism was alive, this vital force controlled the physical and chemical processes that took place within it. Logically, therefore, when it died, that vital force disappeared, leaving the dead organism to decay as if it were inanimate. Helmholtz and his friends opposed this “vitalist” view and felt disproving it was a crucial step to putting biology on the same footing as physics and chemistry.

The feeling in the anti-vitalist camp was that if they could demonstrate that the way warm-blooded creatures generate their warmth is akin to a slowed-down form of burning, not different in principle to the combustion of coal, a telling blow would be struck against vitalism. This hypothesis had been promoted as far back as the 1780s, by the great French chemist Antoine Lavoisier, who pictured the lungs as a torpid fireplace where food burned: “Respiration is then a combustion, admittedly very slow, but nevertheless completely analogous to that of charcoal.”

He saw that the muscle movement caused a reduction in the amount of material that dissolved in water, which was exactly balanced by an increase of material that dissolved in alcohol. Muscle movement, in other words, was accompanied by the change of a water-soluble substance into an alcohol-soluble substance. The lesson was clear: muscle movement was driven by chemical energy released as one substance turned into another, again, in principle, no different to combustion.

For Helmholtz, this type of analysis enabled very different-seeming phenomena—gravity, motion, electricity—to be related to each other quantitatively. Every type of energy has a “best possible” exchange rate into another form of energy, which is embedded in the laws of nature. Helmholtz also introduced another important idea in his paper, which today is called potential energy but which he referred to as tensional forces. In simple terms, this means that energy can be stored and released later.

Helmholtz pointed out that foods are stores of chemical potential energy, and as animals digest them, they “use up a certain quantity of chemical tensional forces and… generate heat and mechanical force.” This perspective led him to conclude that the ultimate source of chemical potential energy in food must be sunlight.

Over and above his direct contributions to science, Prof. Magnus exercised a powerful indirect influence, through the kindly aid and countenance which he lent to young inquirers. —From the 1870 obituary in Nature of Gustav Magnus, written by the Anglo-Irish physicist John Tyndall

A few months after Helmholtz had published his tract on the conservation of energy, Magnus brought it before the colloquium. To scrutinize it, he selected Rudolf Clausius, a twenty-six-year-old from Köslin, a town in Prussia (now in Poland). The sixth son of a Lutheran pastor, Clausius had attended a school run by his father before going on to Berlin University, where he was awarded a doctorate for investigating the colors of the sky. Though the explanation in his dissertation was wrong, Clausius’s gift for abstract reasoning swayed the examiners, a gift amply displayed in a career in which he eschewed experiments and instead sought truth with the aid of logic and mathematics.

Clausius reasoned as follows: Carnot had been wrong to say that all the heat flowing into an engine eventually flows out. But some does. This is not converted into work but is wasted. You can feel this if you put your hand near the exhaust pipe of your car. The warmth you sense is evidence that no matter how well engineered the system, some heat will always escape.

Heat never flows from cold to hot unless it’s forced to—i.e., without some input of work.

In the final publication, he removed the biblical reference but was no less bleak about the future: “Within a finite period of time past, the earth must have been, and within a finite period of time to come, the earth must again be, unfit for the habitation of man as at present constituted.” This idea that the universe will wind down and die as all the heat in it dissipates became known as the heat death of the universe.

Die Entropie der Welt strebt einem Maximum zu. —Rudolf Clausius

Predicting the end of time wasn’t enough for William Thomson. Soon after, he conceived an idea that wrote his name into the scientific lexicon. This was the so-called absolute temperature scale.

Thanks to Thomson, temperature can be seen as a fundamental property of any object, just like its mass. Different objects, whether a fried egg or a nugget of gold or a volume of air, all weigh a certain number of kilograms, irrespective of what they consist of. The Kelvin scale permits a similar claim for their temperature. Just as with mass, physicists can investigate the behavior and effects of temperature with mathematical equations confident that its definition is not contingent on the arbitrary properties of a substance. We can even speak of black holes having temperature.

The fruit of this labor was the definition of a new concept, entropy, a physical quantity that matches energy for importance. It was a secret buried in the way heat flows.

Similarly, when a quantity of heat flows out of a hot room, the fall in entropy there is smaller than the increase that occurs when that heat enters a cold room. In summary, to say the entropy of a system increases is to say the heat within it is becoming more widely dispersed. But, though Clausius’s equation says this always tends to happen, it doesn’t specify the rate at which it does so.

Once the house reaches this state of maximum entropy, the engines will stop working. The heat in the house will no longer be of any use.

Increasing entropy is thus a measure of the decreasing usefulness of heat.

In 1865, Clausius revisited the two laws of thermodynamics that he had first stated in his paper of fifteen years prior. He updated them by employing the word energy instead of Kraft, and he added his own coinage, entropy. The laws state: 1. The energy of the universe is constant. 2. The entropy of the universe tends to a maximum. (Universe means any system that’s closed or sealed off. But because the universe we live in has nothing beyond it, it is true that its energy cannot change and its entropy tends to rise. More intuitively, the second law can be stated: the entropy of any closed system tends to increase.)

In the same way that geographical maps give us an immediate understanding of a landscape, Gibbs pioneered the idea of thermodynamic maps—charts that show how the physical properties of a substance change as, for example, it’s heated or cooled, squeezed or stretched. These reveal the laws of thermodynamics at work in the material world.

Now, imagine doing the identical experiment in La Rinconada, Peru, the highest town on earth. The altitude is fifty-one hundred meters, and the atmospheric pressure there is about half that at sea level. You note two differences from when doing the experiment at the first location: the water boils much cooler at 83°C, and it remains as a water-steam mixture for longer. Darwin noted this effect while camping in the Andes. Despite potatoes being boiled all night, they weren’t soft enough to eat.

I am conscious of being only an individual struggling weakly against the stream of time. —Ludwig Boltzmann

The first and most constructive criticism Boltzmann received was from his friend and mentor Josef Loschmidt. The latter’s motivation was that he disliked the way the second law of thermodynamics predicted that the universe would eventually die, degenerating into a never-changing state in which all heat had dissipated throughout the cosmos. If this was true, wrote Loschmidt, the second law is a “terroristic nimbus cloud, which appears to be a destructive principle to all life in the universe.”