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

by Paul Sen

Thermodynamics is a dreadful name for what is arguably the most useful and universal scientific theory ever conceived. The word suggests a narrow discipline concerned only with the behavior of heat. Here indeed lie the subject’s origins.

At its heart are three concepts—energy, entropy, and temperature. Without an understanding of these and the laws they obey, all science—physics, chemistry, and biology—would be incoherent. The laws of thermodynamics govern everything from the behavior of atoms to that of living cells, from the engines that power our world to the black hole at the center of our galaxy. Thermodynamics explains why we must eat and breathe, how the lights come on, and how the universe will end. Thermodynamics is the field of knowledge on which the modern world is based.

From sewage pumps to jet engines, from a reliable electricity supply to the biochemistry of lifesaving drugs, all the technology that we take for granted needs an understanding of energy, temperature, and entropy. Yet despite its importance, thermodynamics is the Cinderella of the sciences.

We count calories, pay energy bills, worry about the temperature of the planet, without appreciating the principles underpinning those actions. The Cinderella status of thermodynamics is reflected in the way Einstein’s science is remembered.

In his so-called miracle year of 1905, he published four papers that transformed physics, including the one featuring the equation E = mc2. This work did not emerge from nowhere. For in the previous three years, Einstein had published three papers on thermodynamics, and the first two of the miracle-year papers—one on the atomic structure of matter and the other on the quantum nature of light—were continuations of that work.

Of thermodynamics Einstein said, “It is the only physical theory of universal content, which I am convinced… will never be overthrown.”

Einstein’s interest in refrigerator design was that, in 1926, he read an article in a Berlin newspaper about a family—which included several children—who died because their malfunctioning refrigerator had leaked lethal fumes. Einstein’s response was to initiate a project to design safer refrigerators.

In early 2012, while producing a television documentary, I came across Reflections on the Motive Power of Fire, a slim book self-published in Paris in 1824 by a reclusive young Frenchman called Sadi Carnot. Carnot had died of cholera at thirty-six, believing that his work would be forgotten. Yet within two decades of his death, he was considered the founding father of the science of thermodynamics. Later in the nineteenth century, the great physicist Lord Kelvin said of Carnot’s text, “that little essay was indeed an epoch-making gift to science.”

Carnot’s work was unlike any other work of fundamental physics, combining algebraic calculus and physical insight with Carnot’s thoughts on what would constitute a happier, fairer society. Caring deeply for humanity, Carnot believed science was the key to progress.

Reflections was as much the product of two revolutions—the French and the Industrial—as it was of Carnot’s brilliant mind.

I shall therefore celebrate the heroes and heroines of science and show their quest to discover the truth about the universe as the ultimate creative endeavor. Sadi Carnot, William Thomson (Lord Kelvin), James Joule, Hermann von Helmholtz, Rudolf Clausius, James Clerk Maxwell, Ludwig Boltzmann, Albert Einstein, Emmy Noether, Claude Shannon, Alan Turing, Jacob Bekenstein, and Stephen Hawking are among the smartest humans who ever lived.

Ludwig Boltzmann, one of the heroes of this story, put it this way: “It must be splendid to command millions of people in great national ventures, to lead a hundred thousand to victory in battle. But it seems to me greater still to discover fundamental truths in a very modest room with very modest means—truths that will still be foundations of human knowledge when the memory of these battles is painstakingly preserved only in the archives of the historian.”

The number of steam engines has multiplied prodigiously. —French economist and businessman Jean-Baptiste Say on visiting Britain

On September 19, 1814, Jean-Baptiste Say, a forty-seven-year-old French businessman and economist, embarked on a ten-week spying mission to Britain.

As spying missions go, Say’s was neither dangerous nor clandestine. He made no secret of his reasons for being in Britain. A gregarious Anglophile, he crisscrossed the country, obtaining access to mines, factories, and ports and, in his leisure time, to theaters and country houses. And since his last visit twenty-six years earlier, Say witnessed a nation transformed. He began his tour in Fulham, a village to the west of London where he’d spent time in his youth. He found it unrecognizable.

Above all else, one piece of technology caught Say’s eye and his imagination: “Everywhere, the number of steam engines has multiplied prodigiously. Thirty years ago, there were only two or three of them in London; now there are thousands.… Industrial activity can no longer be profitably sustained without the powerful aid they give.” Above all, steam power had revolutionized Britain’s mining industry. Mines, like water wells, are shafts dug into the ground and are prone to flooding.

But by 1820, steam technology had advanced to the point where engines could easily pump water out of shafts that were over three hundred yards deep. This lowered the cost of mining coal, which, because coal is a crucial ingredient in the manufacture of iron, made iron more abundant, too. Between 1750 and 1805, production of the metal soared ninefold from 28,000 to 250,000 tons a year.

The technology had proliferated not because Britons were especially inventive, but because their country was so replete with coal that even poorly designed and wasteful engines were profitable.

“Newcomen engines” work as follows: Heat from burning coal creates steam. This flows via an inlet valve into a large cylinder in which a piston can move up and down. Initially the piston rests at the top of the cylinder. Once this is full of steam, the inlet valve closes. Cold water is sprayed into the cylinder, cooling the steam inside, causing it to condense into water. Because water occupies much less space than steam, this creates a partial vacuum below the piston. Atmospheric air will always try to fill a void, and the only way it can do so in this arrangement is by pushing the piston down. This is the source of the engine’s power.

Newcomen engines consumed prodigious amounts of coal. They burned a bushel—84 pounds—of coal to raise between 5 to 10 million pounds of water by one foot.

By modern standards, these engines were very inefficient, wasting around 99.5 percent of the heat energy released as the coal burned.

At the time of Say’s visit, Britain’s mines produced 16 million tons every year, and in the new industrial towns of Leeds and Birmingham, coal often sold at less than ten shillings per ton. At these prices, poor engine design mattered little.

some sections of the public also grew wary of science because many of its practitioners, such as Joseph Priestley, the discoverer of oxygen, publicly supported the radical politics of the French Revolution.

Jean-Baptiste Say published his observations on Britain’s economic and industrial transformation in a book entitled De l’Angleterre et des Anglais, in 1816. His report, and those of others, convinced French engineers, businessmen, and politicians that the way to catch up with Britain economically was to exploit steam power. But they faced a problem: coal was scarce south of the Channel. French mines produced a million tons annually, and as most of these were in the remote Languedoc region, the price never dropped below twenty-eight shillings per ton, three times higher than in England’s industrial heartland.

One calorie is the amount of heat needed to elevate by one degree centigrade one kilogram of water.”

(A few decades later, scientists redefined the calorie to mean the amount of heat needed to raise the temperature of one gram of water, rather than one kilogram of water, by one degree Celsius, which means that one of Clément’s calories is equivalent to one thousand calories now.)

A body of water, no matter how vast, will not produce motive power unless it can flow downhill. So, too, even a prodigious quantity of heat will not create motive power if there’s no temperature difference it can “flow down.” A steam engine inside a vast hot furnace will not work despite the presence of abundant heat because there is no way to cool and liquefy the steam so the piston can be pushed back to the top of the cylinder. Carnot writes: “The production of heat alone is not sufficient to give birth to the impelling power: it is necessary that there should also be cold; without it, the heat would be useless.” That sentence marks the first step in the history of thermodynamics.

Carnot asks his reader to picture an ideal steam engine—one that, for a given flow of heat from a hot place to a cold one, can produce the maximum amount of motive power possible, i.e., it can lift a given weight to the greatest possible height. (For simplicity, I’ll refer to the source of the heat as the furnace and the cooler place where the heat ends up as the sink.) Next, Carnot proposes a hypothetical machine that does the same process in reverse—i.e., it uses up motive power to move heat from a cool place to a warmer one. In the modern world, we call such devices heat pumps or refrigerators.

He reasons that if the flow of heat from a hot place to a cooler one can create motive power and raise a weight, then a machine can exist that does the opposite. In this machine, the motive power obtained from a falling weight will force heat to flow “uphill” from cool sink to hot furnace. There is a direct analogy with water mills and water pumps. The former uses the downward flow of water to produce motive power; the latter uses power to push water uphill.

Carnot’s next step is a touch of genius. He conjures up another hypothetical engine that uses an alternative gas to steam, such as air or alcohol vapor; but the imagined gas he proposes using is better than steam.

Steam engines waste heat flow in a similar way. How could this be corrected? One way, Carnot argues, is to use atmospheric air as the substance that pushes the piston. Because air contains oxygen, fuel can burn and generate heat inside the cylinder and not in an external boiler as happens in a steam engine. “Considerable loss could thus be prevented” is how Carnot puts it. Air has another advantage—it has a lower “specific heat” than steam. That means, roughly, that the same amount of heat can raise the temperature of a quantity of air by a greater amount than an equivalent quantity of steam.

Carnot writes, “The use of atmospheric air for the development of the motive power of heat… would doubtless offer a notable advantage over the vapor of water.” This prediction was borne out in the late nineteenth century by the arrival of the internal combustion engine, a device that burns petrol or diesel to raise the air temperatures in its cylinders to well over 1,000°. Rudolf Diesel, who published his theories on how to build such an engine in 1893, was inspired by Carnot’s ideas.

Internal combustion engines, jets, the giant turbines that generate electricity, and even the rockets that took humans to the moon, all are based on Carnot’s discovery that the flow of heat from hot to cold is required to generate motive power.

In the summer of 1824 Carnot published Reflections on the Motive Power of Fire at his own expense. He was twenty-eight years old.

Carnot put it in his notes, “It would be difficult to explain why, in the development of the motive power of heat, a cold body is necessary.” This problem of how to reconcile Carnot’s insight that heat must flow from hot to cold to produce motive power with this imaginary caloric fluid provides the next turn in our story. Tragically, though, Carnot would play no further part. In 1832, for reasons that remain obscure, Carnot entered a mental asylum in Ivry, on the outskirts of Paris.

The ledger at the asylum reads, “Mr. Carnot Lazare Sadi, ex-military engineer, admitted 3 August 1832, for mania. Cured of mania. Dead from cholera, 21 August 1832.” He was thirty-six years old.

I have neither propelled vessels, carriages, nor printing presses. My object has been, first to discover correct principles. —James Joule

James Prescott Joule, the second of a brewer’s five children, was born in 1818 in Salford in Lancashire.

Between 1801 and 1830, the population roughly doubled to around 140,000, as people flocked in from all over the country to toil in a city that became known as Cottonopolis. The Joules, being brewers, prospered.

The family’s wealth meant that when Joule was sixteen, his father enrolled him for private lessons with the famous chemist John Dalton. Joule started work in the family brewery while in his teens and would play an active role in running the business for nearly two decades. In the early years, he attended the brewery daily from 9:00 a.m. to 6:00 p.m.

The family brewery did employ a steam engine, and Joule knew how much his business spent on coal. So, with an eye to the bottom line mixed in with a good measure of scientific curiosity, he wondered if a recent invention, the battery-powered electric motor, could drive the brewery’s pumps and stirrers more cheaply than burning coal. Electric motors had been invented in the early 1830s, and within a few years they had become a craze. “Electrical Euphoria” swept the Western world.

By 1840, ensconced in a laboratory he’d set up in the family home, Joule was building batteries, electromagnets, and motors, and investigating their behavior. One of his earliest observations was his most significant. He noticed that as an electric current runs through a wire, the wire becomes warmer. Electricity, in other words, can produce heat as well as do work by turning a motor. (From now on I shall use the word work to mean what Carnot called motive power

there is a mathematical relationship between the heat produced, the magnitude of the current, and the resistance of the wire through which it flows. Joule was convinced this was an important discovery, deserving of a wider audience than the readers of the Annals, so he sent a paper describing it to Britain’s most prestigious scientific publication, The Transactions of the Royal Society. Though the equation Joule derived is now taught as part of high school physics and is the basis of every electric toaster, the editor rejected it, allowing only a brief summary to be printed in a lowlier sister journal.

Through 1840 and 1841, Joule was becoming ever more skilled at working with electricity, and he focused on comparing the cost of extracting work from an electric motor with that of obtaining it from a steam engine.

To Joule, the implications were clear. He wrote with unequivocal confidence, “We have therefore in magneto-electricity an agent capable by simple mechanical means of destroying or generating heat.”

This implied that the ultimate source of the heat in this arrangement was the work, with the electricity acting as an intermediary. Joule’s next step was to try to quantify this process. If work can be turned into heat, how much of it is needed to create a given quantity of heat? To Joule, work and heat had become interconvertible, the one into the other much like the dollar and the pound.

Naming this “the Mechanical Equivalent of Heat,” he set out to discover its value. To do so, Joule connected his dynamo to a falling weight via a system of ropes and pulleys. As the weight fell, it turned the dynamo, generating first electricity and then heat, which as before warmed a tube of water. Joule could now equate the height by which a known weight fell to the amount of heat that was created. In other words, he could measure the Mechanical Equivalent of Heat.

His confidence stemmed in part from his upbringing and beliefs. Politically conservative and a devout Christian, Joule saw his scientific endeavors as “essentially a holy undertaking,” convinced as he was that a divine being had endowed the universe with a fixed amount of an immaterial substance that enabled change and movement. Electricity, work, and heat were simply different facets of this. They might be converted from one to the other, but the total amount was invariable.

What Joule called the grand agents of nature we today know as energy. For what lay behind Joule’s religious words was the elaboration of a principle known to scientists today as the conservation of energy and also as the first law of thermodynamics.

Joule recognized the usefulness to him of making small things visible. So he commissioned Dancer to design a thermometer, which with the aid of a lens, allowed minute movements in a thin column of mercury to be magnified and measured accurately. Dancer’s thermometers, Joule claimed, enabled him to measure temperatures to an accuracy of better than one-tenth of a degree Fahrenheit. When used with the paddle-wheel apparatus, their readings supported the conclusions from Joule’s dynamo experiments.