The Law That Sets the Limit
The first law of thermodynamics tells you that energy is conserved. The second tells you that entropy always increases, that every natural process has a direction it cannot reverse. Together, these two principles define what energy can do. But there is a third law, less famous yet equally fundamental, that tells you what energy cannot do. It says you can never reach absolute zero. No matter how ingenious your cooling technique, no matter how many stages of refrigeration you stack upon one another, the temperature of a physical system can approach zero kelvins but never arrive there. This is the third law of thermodynamics, and it was first formulated in 1906 by the German physical chemist Walther Nernst.
Where the first two laws emerged from the work of many hands over decades, the third law is unusual in having a single, clear origin. Nernst’s heat theorem was a precise, quantitative statement about the behaviour of entropy at extremely low temperatures, and it completed the theoretical framework that makes modern thermodynamics possible. Without it, we could not assign absolute values to entropy, could not construct the thermodynamic tables that chemists and engineers depend on, and could not fully understand why the coldest temperature in nature remains forever out of reach.
Walther Nernst: The Man Behind the Third Law
From Prussia to the Nobel Prize
Walther Hermann Nernst was born in 1864 in Briesen, West Prussia (now Wabrzezno, Poland). He studied physics under Ludwig Boltzmann in Graz and under Friedrich Kohlrausch in Wurzburg before settling into a career that bridged physics and chemistry with unusual fluency. In 1891 he became a professor at the University of Gottingen, where he established one of Germany’s leading physical chemistry laboratories. He later moved to the University of Berlin, where he would spend the most productive years of his career.
Nernst was a practical scientist as much as a theoretical one. He invented the Nernst lamp, an early electric light that used a ceramic rod instead of a filament, and he contributed important work on electrochemistry, including the Nernst equation that relates electrode potential to ion concentration. But his greatest achievement was the heat theorem he announced in 1906, a statement about the behaviour of chemical reactions near absolute zero that would earn him the Nobel Prize in Chemistry in 1920.
A Difficult Later Life
Nernst’s later years were marked by personal tragedy and political upheaval. He lost two sons in the First World War. When the National Socialists came to power in 1933, Nernst, though not Jewish himself, openly opposed the regime’s persecution of Jewish scientists. He refused to dismiss his Jewish colleagues and withdrew from public life. He died in 1941 on his country estate in Zibelle, largely forgotten by the regime he despised. His reputation, however, has only grown since.
The Heat Theorem of 1906
What Nernst Actually Said
Nernst’s original formulation concerned the entropy change in chemical reactions. He proposed that as the temperature of a system approaches absolute zero, the entropy change associated with any isothermal process approaches zero. In mathematical terms, as T approaches 0 K, the change in entropy (delta S) tends to zero.
This was a bold claim. The first two laws of thermodynamics place no constraint on what entropy does at very low temperatures. Nernst’s theorem supplied the missing boundary condition. It said, in effect, that all substances converge toward the same entropic behaviour as they are cooled to the lowest temperatures, and that the differences between them vanish.
Planck’s Extension: The Absolute Zero of Entropy
Max Planck later strengthened Nernst’s result into a more powerful statement. Planck proposed that the entropy of a perfect crystal at absolute zero is not merely approaching a minimum but is exactly zero. This gave thermodynamics something it had previously lacked: an absolute reference point for entropy. Just as the Celsius scale needs a fixed point (the freezing point of water) to be useful, entropy calculations need a zero point to yield absolute values. The third law provides that zero point.
For a perfect crystal, one in which every atom sits in its correct lattice position with no disorder whatsoever, there is only one possible microscopic arrangement at absolute zero. Since entropy measures the number of possible microscopic configurations (a relationship formalised by Boltzmann’s famous equation S = k log W), a single configuration means W = 1, and therefore S = 0. The absolute zero entropy of a perfect crystal is exactly zero.
Why the Third Law Matters
Making Thermodynamic Tables Possible
The practical importance of the third law is difficult to overstate. Chemists routinely use thermodynamic tables listing the standard molar entropy of thousands of substances. These tables allow them to predict whether a chemical reaction will proceed spontaneously, to calculate equilibrium constants, and to design industrial processes. Every value in those tables depends on the third law, because every value is measured relative to the zero-entropy reference point that the third law establishes.
Without Nernst’s theorem, entropy values would be defined only up to an arbitrary constant, much as altitude could be measured only as a difference between two points if we had no agreed-upon sea level. The third law gives thermodynamics its sea level.
Connecting Microscopic and Macroscopic Physics
The third law also serves as a bridge between the macroscopic world of classical thermodynamics and the microscopic world of statistical mechanics. It confirms that as thermal energy is removed from a system, the number of accessible quantum states decreases until, at absolute zero, only the ground state remains. This deep connection between temperature, entropy, and quantum mechanics gives the third law a significance that extends well beyond chemistry.
The Unattainability of Absolute Zero
A Fundamental Impossibility
One of the most striking consequences of the third law is the unattainability of absolute zero. It is not merely that we lack the technology to cool a system to 0 K. The third law implies that no finite sequence of operations can bring any system to absolute zero. Each successive cooling step removes less and less entropy, and the steps needed to reach zero temperature would require an infinite number of operations or an infinite amount of time. Absolute zero is an asymptote, a limit that can be approached ever more closely but never reached.
This principle was formalised by Nernst himself and is sometimes called the unattainability principle. It stands alongside the impossibility of perpetual motion machines (forbidden by the first and second laws) as one of thermodynamics’ fundamental prohibitions.
How Close Can We Get?
Modern experiments have pushed temperatures astonishingly close to absolute zero. Laser cooling and evaporative cooling techniques, developed in the late twentieth century, routinely achieve temperatures in the nanokelvin range, billionths of a degree above absolute zero. In 2021, researchers at the University of Bremen achieved an effective temperature of approximately 38 picokelvin (trillionths of a kelvin) in a freely falling Bose-Einstein condensate. These experiments confirm that while nature permits us to approach absolute zero with extraordinary precision, the final step to zero itself remains forever out of reach.
Applications: What the Third Law Makes Possible
Cryogenics and Superconductivity
The science of producing and maintaining extremely low temperatures, known as cryogenics, is built on the thermodynamic principles that the third law completes. At temperatures near absolute zero, materials exhibit remarkable behaviours. Many metals and ceramics become superconductors, losing all electrical resistance below a critical temperature. Superconducting magnets, cooled by liquid helium to a few kelvins, generate the powerful magnetic fields used in MRI machines and particle accelerators.
Bose-Einstein Condensates
When certain gases are cooled to nanokelvin temperatures, their atoms lose their individual identities and collapse into a single quantum state known as a Bose-Einstein condensate. Predicted by Einstein in 1924 (building on work by Satyendra Nath Bose) and first achieved experimentally in 1995, these condensates allow physicists to observe quantum mechanical behaviour at a macroscopic scale. The third law’s framework is essential for understanding why these exotic states of matter appear only at temperatures vanishingly close to absolute zero.
Quantum Computing
Modern quantum computers require operating temperatures in the millikelvin range, colder than outer space, to protect the fragile quantum states of their superconducting qubits from thermal noise. The dilution refrigerators that cool quantum processors to these temperatures are sophisticated cryogenic machines whose design and operation depend on a thorough understanding of thermodynamic behaviour near absolute zero. In this sense, every advance in quantum computing is built, in part, on the foundation that Nernst laid in 1906.
The Third Law in Beautifully Designed Books
Nernst’s heat theorem completed the edifice of classical thermodynamics that began with the study of heat engines and culminated in the statistical mechanical insights of Boltzmann and Planck. The quantum hypothesis that Planck introduced in 1900, which ultimately explained why entropy reaches zero at absolute zero, is presented in its original form in our collector’s edition of Max Planck’s three foundational publications, a book designed to honour the beauty of the ideas it contains.
The revolution in physics that Nernst’s generation helped create extended far beyond thermodynamics. Einstein’s theory of relativity, developed in the same intellectual milieu of early twentieth-century German physics, reshaped our understanding of space, time, and energy. Our edition of Einstein’s Relativity brings readers face to face with one of the defining works of modern science. And for those who wish to see the people behind these ideas, Portraying Science collects the portraits of the men and women who built the foundations of contemporary physics and chemistry.
The Quiet Power of the Third Law
Of the three laws of thermodynamics, the third is the least dramatic but perhaps the most elegant. It does not announce the conservation of energy or the relentless march of disorder. Instead, it draws a quiet, absolute line at the bottom of the temperature scale and says: this far, no further. Walther Nernst, working in his Berlin laboratory at the turn of the twentieth century, identified that line and gave it mathematical precision. In doing so, he completed the theoretical framework that governs everything from the design of chemical reactors to the operation of quantum computers. The Nernst heat theorem remains, more than a century after its formulation, one of the most consequential ideas in the history of physical science.
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