Ludwig Boltzmann

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https://en.wikipedia.org/wiki/Ludwig_Boltzmann

 

Ludwig Boltzmann
Boltzmann in 1902
Born	Ludwig Eduard Boltzmann 20 February 1844 Vienna, Austrian Empire, German Confederation
Died	5 September 1906 (aged 62) Tybein, Princely County of Gorizia and Gradisca, Austria-Hungary
Resting place	Vienna Central Cemetery
Alma mater	University of Vienna (PhD; Dr. habil., 1869)
Known for	Boltzmann distribution (1868) Boltzmann equation (1872) Introducing the H-theorem (1872) Boltzmann's entropy formula (1875) Expanding the equipartition theorem (1876) Describing canonical ensemble (1884) Stefan–Boltzmann law (1884)
Spouse	Henriette von Aigentler ​ ​ (m. 1876)​
Children	4
Awards	ForMemRS (1899)
Scientific career
Fields	Statistical physics Thermodynamics
Institutions	University of Graz (1869–1873, 1876–1890) University of Vienna (1873–1876, 1894–1900, 1902–1906) University of Munich (1890–1894) University of Leipzig (1900–1902)
Thesis	Über die mechanische Bedeutung des zweiten Hauptsatzes der mechanischen Wärmetheorie (1866)
Doctoral advisor	Josef Stefan
Doctoral students	Ignaz Schütz (1894) Paul Ehrenfest (1904) Philipp Frank (1907)
Other notable students	Svante Arrhenius Gustav Herglotz Lise Meitner Walther Nernst Karl Přibram
Signature

Ludwig Eduard Boltzmann (/ˈbɔːltsˌmɑːn/ BAWLTS-mahn or /ˈboʊltsmən/ BOHLTS-muhn; German: [ˈluːtvɪç ˈeːduaʁt ˈbɔltsman]; 20 February 1844 – 5 September 1906) was an Austrian mathematician and theoretical physicist. His greatest achievements were the development of statistical mechanics and the statistical explanation of the second law of thermodynamics. In 1877 he provided the current definition of entropy, ${\displaystyle S=k_{\mathrm{B}}\ln \mathrm{\Omega }}$, where Ω is the number of microstates whose energy equals the system's energy, interpreted as a measure of the statistical disorder of a system. Max Planck named the constant k_B the Boltzmann constant.

Statistical mechanics is one of the pillars of modern physics. It describes how macroscopic observations (such as temperature and pressure) are related to microscopic parameters that fluctuate around an average. It connects thermodynamic quantities (such as heat capacity) to microscopic behavior, whereas, in classical thermodynamics, the only available option would be to measure and tabulate such quantities for various materials.

Biography

Childhood and education

Boltzmann was born in Erdberg, a suburb of Vienna into a Catholic family. His father, Ludwig Georg Boltzmann, was a revenue official. His grandfather, who had moved to Vienna from Berlin, was a clock manufacturer, and Boltzmann's mother, Katharina Pauernfeind, was originally from Salzburg. Boltzmann was home-schooled until the age of ten, and then attended high school in Linz, Upper Austria. When Boltzmann was 15, his father died.

Starting in 1863, Boltzmann studied mathematics and physics at the University of Vienna. He received his doctorate in 1866 and his venia legendi in 1869. Boltzmann worked closely with Josef Stefan, director of the institute of physics. It was Stefan who introduced Boltzmann to Maxwell's work.

Academic career

In 1869 at age 25, thanks to a letter of recommendation written by Josef Stefan, Boltzmann was appointed full Professor of Mathematical Physics at the University of Graz in the province of Styria. In 1869 he spent several months in Heidelberg working with Robert Bunsen and Leo Königsberger and in 1871 with Gustav Kirchhoff and Hermann von Helmholtz in Berlin. In 1873 Boltzmann joined the University of Vienna as Professor of Mathematics and there he stayed until 1876.

Ludwig Boltzmann and co-workers in Graz, 1887: (standing, from the left) Nernst, Streintz, Arrhenius, Hiecke, (sitting, from the left) Aulinger, Ettingshausen, Boltzmann, Klemenčič, Hausmanninger

In 1872, long before women were admitted to Austrian universities, he met Henriette von Aigentler, an aspiring teacher of mathematics and physics in Graz. She was refused permission to audit lectures unofficially. Boltzmann supported her decision to appeal, which was successful. On 17 July 1876 Ludwig Boltzmann married Henriette; they had three daughters: Henriette (1880), Ida (1884) and Else (1891); and a son, Arthur Ludwig (1881). Boltzmann went back to Graz to take up the chair of Experimental Physics. Among his students in Graz were Svante Arrhenius and Walther Nernst. He spent 14 happy years in Graz and it was there that he developed his statistical concept of nature.

Boltzmann was appointed to the Chair of Theoretical Physics at the University of Munich in Bavaria, Germany in 1890.

In 1894, Boltzmann succeeded his teacher Joseph Stefan as Professor of Theoretical Physics at the University of Vienna.

Final years and death

Boltzmann spent a great deal of effort in his final years defending his theories. He did not get along with some of his colleagues in Vienna, particularly Ernst Mach, who became a professor of philosophy and history of sciences in 1895. That same year Georg Helm and Wilhelm Ostwald presented their position on energetics at a meeting in Lübeck. They saw energy, and not matter, as the chief component of the universe. Boltzmann's position carried the day among other physicists who supported his atomic theories in the debate. In 1900, Boltzmann went to the University of Leipzig, on the invitation of Wilhelm Ostwald. Ostwald offered Boltzmann the professorial chair in physics, which became vacant when Gustav Heinrich Wiedemann died. After Mach retired due to bad health, Boltzmann returned to Vienna in 1902. In 1903, Boltzmann, together with Gustav von Escherich and Emil Müller, founded the Austrian Mathematical Society. His students included Karl Přibram, Paul Ehrenfest and Lise Meitner.

In Vienna, Boltzmann taught physics and also lectured on philosophy. Boltzmann's lectures on natural philosophy were very popular and received considerable attention. His first lecture was an enormous success: people stood all the way down the staircase outside the largest available lecture hall, and the Emperor invited him to a reception.

In 1905, he gave an invited course of lectures in the summer session at the University of California in Berkeley, which he described in a popular essay A German professor's trip to El Dorado.

In May 1906, Boltzmann's deteriorating mental condition (described in a letter by the Dean as "a serious form of neurasthenia") forced him to resign his position. His symptoms indicate he experienced what might today be diagnosed as bipolar disorder. Four months later he died by suicide on 5 September 1906, by hanging himself while on vacation with his wife and daughter in Duino, near Trieste (then Austria). He is buried in the Viennese Zentralfriedhof. His tombstone bears the inscription of Boltzmann's entropy formula: ${\displaystyle S=k\cdot \log W}$.

Philosophy

Boltzmann's kinetic theory of gases seemed to presuppose the reality of atoms and molecules, but almost all German philosophers and many scientists like Ernst Mach and the physical chemist Wilhelm Ostwald disbelieved their existence. Boltzmann had been exposed to molecular theory by James Clerk Maxwell’s paper, "Illustrations of the Dynamical Theory of Gases," which described temperature as dependent on the speed of the molecules. This inspired Boltzmann to embrace atomism, introducing statistics into physics and extending the theory.

Boltzmann wrote treatises on philosophy such as "On the question of the objective existence of processes in inanimate nature" (1897). He was a realist. In his work "On Thesis of Schopenhauer's", Boltzmann refers to his philosophy as materialism and says further: "Idealism asserts that only the ego exists, the various ideas, and seeks to explain matter from them. Materialism starts from the existence of matter and seeks to explain sensations from it."

Physics

Boltzmann's most important scientific contributions were in the kinetic theory of gases based upon the Second law of thermodynamics. This was important because Newtonian mechanics did not differentiate between past and future motion, but Rudolf Clausius’ invention of entropy to describe the second law was based on disgregation or dispersion at the molecular level so that the future was one-directional. Boltzmann was twenty-five years of age when he came upon James Clerk Maxwell's work on the kinetic theory of gases which hypothesized that temperature was caused by collision of molecules. Maxwell used statistics to create a curve of molecular kinetic energy distribution from which Boltzmann clarified and developed the ideas of kinetic theory and entropy based upon statistical atomic theory creating the Maxwell–Boltzmann distribution as a description of molecular speeds in a gas. It was Boltzmann who derived the first equation to model the dynamic evolution of the probability distribution Maxwell and he had created. Boltzmann's key insight was that dispersion occurred due to the statistical probability of increased molecular "states". Boltzmann went beyond Maxwell by applying his distribution equation to not solely gases, but also liquids and solids. Boltzmann also extended his theory in his 1877 paper beyond Carnot, Rudolf Clausius, James Clerk Maxwell and Lord Kelvin by demonstrating that entropy is contributed to by heat, spatial separation, and radiation. Maxwell–Boltzmann statistics and the Boltzmann distribution remain central in the foundations of classical statistical mechanics. They are also applicable to other phenomena that do not require quantum statistics and provide insight into the meaning of temperature.

He made multiple attempts to explain the second law of thermodynamics, with the attempts ranging over many areas. He tried Helmholtz's monocycle model, a pure ensemble approach like Gibbs, a pure mechanical approach like ergodic theory, the combinatorial argument, the Stoßzahlansatz, etc.

Boltzmann's 1898 I₂ molecule diagram showing atomic "sensitive region" (α, β) overlap

Most chemists, since the discoveries of John Dalton in 1808, and James Clerk Maxwell in Scotland and Josiah Willard Gibbs in the United States, shared Boltzmann's belief in atoms and molecules, but much of the physics establishment did not share this belief until decades later. Boltzmann had a long-running dispute with the editor of the preeminent German physics journal of his day, who refused to let Boltzmann refer to atoms and molecules as anything other than convenient theoretical constructs. Only a couple of years after Boltzmann's death, Perrin's studies of colloidal suspensions (1908–1909), based on Einstein's theoretical studies of 1905, confirmed the values of the Avogadro constant and the Boltzmann constant, convincing the world that the tiny particles really exist.

To quote Planck, "The logarithmic connection between entropy and probability was first stated by L. Boltzmann in his kinetic theory of gases". This famous formula for entropy S is $${\displaystyle S=k_{\mathrm{B}}\ln W}$$ where k_B is the Boltzmann constant, and ln is the natural logarithm. W (for Wahrscheinlichkeit, a German word meaning "probability") is the probability of occurrence of a macrostate or, more precisely, the number of possible microstates corresponding to the macroscopic state of a system – the number of (unobservable) "ways" in the (observable) thermodynamic state of a system that can be realized by assigning different positions and momenta to the various molecules. Boltzmann's paradigm was an ideal gas of N identical particles, of which N_i are in the ith microscopic condition (range) of position and momentum. W can be counted using the formula for permutations $${\displaystyle W=N!\prod _i\frac{1}{N_i!}}$$ where i ranges over all possible molecular conditions, and where ${\displaystyle !}$ denotes factorial. The "correction" in the denominator account for indistinguishable particles in the same condition.

Boltzmann could also be considered one of the forerunners of quantum mechanics due to his suggestion in 1877 that the energy levels of a physical system could be discrete, although Boltzmann used this as a mathematical device with no physical meaning.

An alternative to Boltzmann's formula for entropy, above, is the information entropy definition introduced in 1948 by Claude Shannon. Shannon's definition was intended for use in communication theory but is applicable in all areas. It reduces to Boltzmann's expression when all the probabilities are equal, but can, of course, be used when they are not. Its virtue is that it yields immediate results without resorting to factorials or Stirling's approximation. Similar formulas are found, however, as far back as the work of Boltzmann, and explicitly in Gibbs (see reference).

Boltzmann equation

Main article: Boltzmann equation

Boltzmann's bust in the courtyard arcade of the main building, University of Vienna

The Boltzmann equation was developed to describe the dynamics of an ideal gas. $${\displaystyle \frac{\mathrm{\partial }f}{\mathrm{\partial }t}+v\frac{\mathrm{\partial }f}{\mathrm{\partial }x}+\frac{F}{m}\frac{\mathrm{\partial }f}{\mathrm{\partial }v}=\frac{\mathrm{\partial }f}{\mathrm{\partial }t}{\frac{}{}|}_{\mathrm{c}\mathrm{o}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}}}$$ where ƒ represents the distribution function of single-particle position and momentum at a given time (see the Maxwell–Boltzmann distribution), F is a force, m is the mass of a particle, t is the time and v is an average velocity of particles.

This equation describes the temporal and spatial variation of the probability distribution for the position and momentum of a density distribution of a cloud of points in single-particle phase space. (See Hamiltonian mechanics.) The first term on the left-hand side represents the explicit time variation of the distribution function, while the second term gives the spatial variation, and the third term describes the effect of any force acting on the particles. The right-hand side of the equation represents the effect of collisions.

In principle, the above equation completely describes the dynamics of an ensemble of gas particles, given appropriate boundary conditions. This first-order differential equation has a deceptively simple appearance, since f can represent an arbitrary single-particle distribution function. Also, the force acting on the particles depends directly on the velocity distribution function f. The Boltzmann equation is notoriously difficult to integrate. David Hilbert spent years trying to solve it without any real success.

The form of the collision term assumed by Boltzmann was approximate. However, for an ideal gas the standard Chapman–Enskog solution of the Boltzmann equation is highly accurate. It is expected to lead to incorrect results for an ideal gas only under shock wave conditions.

Boltzmann tried for many years to "prove" the second law of thermodynamics using his gas-dynamical equation – his famous H-theorem. However the key assumption he made in formulating the collision term was "molecular chaos", an assumption which breaks time-reversal symmetry as is necessary for anything which could imply the second law. It was from the probabilistic assumption alone that Boltzmann's apparent success emanated, so his long dispute with Loschmidt and others over Loschmidt's paradox ultimately ended in his failure.

Finally, in the 1970s E. G. D. Cohen and J. R. Dorfman proved that a systematic (power series) extension of the Boltzmann equation to high densities is mathematically impossible. Consequently, nonequilibrium statistical mechanics for dense gases and liquids focuses on the Green–Kubo relations, the fluctuation theorem, and other approaches instead.

Second thermodynamics law as a law of disorder

Boltzmann's grave in the Zentralfriedhof, Vienna, with bust and entropy formula

The idea that the second law of thermodynamics or "entropy law" is a law of disorder (or that dynamically ordered states are "infinitely improbable") is due to Boltzmann's view of the second law of thermodynamics.

In particular, it was Boltzmann's attempt to reduce it to a stochastic collision function, or law of probability following from the random collisions of mechanical particles. Following Maxwell, Boltzmann modeled gas molecules as colliding billiard balls in a box, noting that with each collision nonequilibrium velocity distributions (groups of molecules moving at the same speed and in the same direction) would become increasingly disordered leading to a final state of macroscopic uniformity and maximum microscopic disorder or the state of maximum entropy (where the macroscopic uniformity corresponds to the obliteration of all field potentials or gradients). The second law, he argued, was thus simply the result of the fact that in a world of mechanically colliding particles disordered states are the most probable. Because there are so many more possible disordered states than ordered ones, a system will almost always be found either in the state of maximum disorder – the macrostate with the greatest number of accessible microstates such as a gas in a box at equilibrium – or moving towards it. A dynamically ordered state, one with molecules moving "at the same speed and in the same direction", Boltzmann concluded, is thus "the most improbable case conceivable...an infinitely improbable configuration of energy."

Boltzmann accomplished the feat of showing that the second law of thermodynamics is only a statistical fact. The gradual disordering of energy is analogous to the disordering of an initially ordered pack of cards under repeated shuffling, and just as the cards will finally return to their original order if shuffled a gigantic number of times, so the entire universe must some-day regain, by pure chance, the state from which it first set out. (This optimistic coda to the idea of the dying universe becomes somewhat muted when one attempts to estimate the timeline which will probably elapse before it spontaneously occurs.) The tendency for entropy increase seems to cause difficulty to beginners in thermodynamics, but is easy to understand from the standpoint of the theory of probability. Consider two ordinary dice, with both sixes face up. After the dice are shaken, the chance of finding these two sixes face up is small (1 in 36); thus one can say that the random motion (the agitation) of the dice, like the chaotic collisions of molecules because of thermal energy, causes the less probable state to change to one that is more probable. With millions of dice, like the millions of atoms involved in thermodynamic calculations, the probability of their all being sixes becomes so vanishingly small that the system must move to one of the more probable states.

Legacy and impact on modern science

Ludwig Boltzmann's contributions to physics and philosophy have left a lasting impact on modern science. His pioneering work in statistical mechanics and thermodynamics laid the foundation for some of the most fundamental concepts in physics. For instance, Max Planck in quantizing resonators in his Black Body theory of radiation used the Boltzmann constant to describe the entropy of the system to arrive at his formula in 1900. However, Boltzmann's work was not always readily accepted during his lifetime, and he faced opposition from some of his contemporaries, particularly in regard to the existence of atoms and molecules. Nevertheless, the validity and importance of his ideas were eventually recognized, and they have since become cornerstones of modern physics. Here, we delve into some aspects of Boltzmann's legacy and his influence on various areas of science.

Atomic theory and the existence of atoms and molecules

Boltzmann's kinetic theory of gases was one of the first attempts to explain macroscopic properties, such as pressure and temperature, in terms of the behaviour of individual atoms and molecules. Although many chemists were already accepting the existence of atoms and molecules, the broader physics community took some time to embrace this view. Boltzmann's long-running dispute with the editor of a prominent German physics journal over the acceptance of atoms and molecules underscores the initial resistance to this idea.

It was only after experiments, such as Jean Perrin's studies of colloidal suspensions, confirmed the values of the Avogadro constant and the Boltzmann constant that the existence of atoms and molecules gained wider acceptance. Boltzmann's kinetic theory played a crucial role in demonstrating the reality of atoms and molecules and explaining various phenomena in gases, liquids, and solids.

Statistical mechanics and the Boltzmann constant

Statistical mechanics, which Boltzmann pioneered, connects macroscopic observations with microscopic behaviors. His statistical explanation of the second law of thermodynamics was a significant achievement, and he provided the current definition of entropy (${\displaystyle S=k_{\mathrm{B}}\ln \mathrm{\Omega }}$), where k_B is the Boltzmann constant and Ω is the number of microstates corresponding to a given macrostate.

Max Planck later named the constant k_B as the Boltzmann constant in honor of Boltzmann's contributions to statistical mechanics. The Boltzmann constant is now a fundamental constant in physics and across many scientific disciplines.

Boltzmann equation and modern uses

Because the Boltzmann equation is practical in solving problems in rarefied or dilute gases, it has been used in many diverse areas of technology. It has been used to calculate Space Shuttle re-entry in the upper atmosphere. It is the basis for Neutron transport theory, and ion transport in Semiconductors.

Influence on quantum mechanics

Boltzmann's work in statistical mechanics laid the groundwork for understanding the statistical behavior of particles in systems with a large number of degrees of freedom. In his paper published in 1877, he used discrete energy levels of physical systems as a mathematical device and went on to show that the same approach could be applied to continuous systems. This might be seen as a forerunner to the development of quantum mechanics. One biographer of Boltzmann says that Boltzmann’s approach “pav[ed] the way for Planck.”

Quantization of energy levels became a fundamental postulate in quantum mechanics, leading to groundbreaking theories like quantum electrodynamics and quantum field theory. Thus, Boltzmann's early insights into the quantization of energy levels had a profound influence on the development of quantum physics.

Awards and honours

In 1885 he became a member of the Imperial Austrian Academy of Sciences and in 1887 he became the President of the University of Graz. He was elected a member of the Royal Swedish Academy of Sciences in 1888 and a Foreign Member of the Royal Society (ForMemRS) in 1899. He was awarded honorary membership of the Manchester Literary and Philosophical Society in 1892. Numerous things are named in his honour.

History of thermodynamics

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/History_of_thermodynamics 

The history of thermodynamics is a fundamental strand in the history of physics, the history of chemistry, and the history of science in general. Due to the relevance of thermodynamics in much of science and technology, its history is finely woven with the developments of classical mechanics, quantum mechanics, magnetism, and chemical kinetics, to more distant applied fields such as meteorology, information theory, and biology (physiology), and to technological developments such as the steam engine, internal combustion engine, cryogenics and electricity generation. The development of thermodynamics both drove and was driven by atomic theory. It also, albeit in a subtle manner, motivated new directions in probability and statistics; see, for example, the timeline of thermodynamics.

Antiquity

The ancients viewed heat as that related to fire. In 3000 BC, the ancient Egyptians viewed heat as related to origin mythologies. The ancient Indian philosophy including Vedic philosophy believed that five classical elements (or pancha mahā bhūta) are the basis of all cosmic creations. In the Western philosophical tradition, after much debate about the primal element among earlier pre-Socratic philosophers, Empedocles proposed a four-element theory, in which all substances derive from earth, water, air, and fire. The Empedoclean element of fire is perhaps the principal ancestor of later concepts such as phlogiston and caloric. Around 500 BC, the Greek philosopher Heraclitus became famous as the "flux and fire" philosopher for his proverbial utterance: "All things are flowing." Heraclitus argued that the three principal elements in nature were fire, earth, and water.

Vacuum-abhorrence

Main article: Horror vacui (physics)

The 5th century BC Greek philosopher Parmenides, in his only known work, a poem conventionally titled On Nature, uses verbal reasoning to postulate that a void, essentially what is now known as a vacuum, in nature could not occur. This view was supported by the arguments of Aristotle, but was criticized by Leucippus and Hero of Alexandria. From antiquity to the Middle Ages various arguments were put forward to prove or disapprove the existence of a vacuum and several attempts were made to construct a vacuum but all proved unsuccessful.

Heating a body, such as a segment of protein alpha helix (above), tends to cause its atoms to vibrate more, and the body itself to expand—or change phase, if heating is continued; an axiom of nature noted by Herman Boerhaave in the 1700s.

Atomism

Atomism is a central part of today's relationship between thermodynamics and statistical mechanics. Ancient thinkers such as Leucippus and Democritus, and later the Epicureans, by advancing atomism, laid the foundations for the later atomic theory. Until experimental proof of atoms was later provided in the 20th century, the atomic theory was driven largely by philosophical considerations and scientific intuition.

17th century

Early thermometers

Main article: Thermometer § Early developments

The European scientists Cornelius Drebbel, Robert Fludd, Galileo Galilei and Santorio Santorio in the 16th and 17th centuries were able to gauge the relative "coldness" or "hotness" of air, using a rudimentary air thermometer (or thermoscope). This may have been influenced by an earlier device which could expand and contract the air constructed by Philo of Byzantium and Hero of Alexandria.

"Heat is motion" (Francis Bacon)

Francis Bacon

Main article: Kinetic theory of gases § History

The idea that heat is a form of motion is perhaps an ancient one and is certainly discussed by the English philosopher and scientist Francis Bacon in 1620 in his Novum Organum. Bacon surmised: "Heat itself, its essence and quiddity is motion and nothing else."^[3] "not ... of the whole, but of the small particles of the body."

René Descartes

Precursor to work

Main article: Work (physics) § History

René Descartes

In 1637, in a letter to the Dutch scientist Christiaan Huygens, the French philosopher René Descartes wrote:

Lifting 100 lb one foot twice over is the same as lifting 200 lb one foot, or 100 lb two feet.

In 1686, the German philosopher Gottfried Leibniz wrote essentially the same thing: The same force ["work" in modern terms] is necessary to raise body A of 1 pound (libra) to a height of 4 yards (ulnae), as is necessary to raise body B of 4 pounds to a height of 1 yard.^[6]

Quantity of motion

Main article: Momentum § Quantity of motion

In Principles of Philosophy (Principia Philosophiae) from 1644, Descartes defined "quantity of motion" (Latin: quantitas motus) as the product of size and speed, and claimed that the total quantity of motion in the universe is conserved.

If x is twice the size of y, and is moving half as fast, then there's the same amount of motion in each.

[God] created matter, along with its motion ... merely by letting things run their course, he preserves the same amount of motion ... as he put there in the beginning.

He claimed that merely by letting things run their course, God preserves the same amount of motion as He created, and that thus the total quantity of motion in the universe is conserved.

Boyle's law

Main article: Boyle's law § History

Boyle's law

Irish physicist and chemist Robert Boyle in 1656, in coordination with English scientist Robert Hooke, built an air pump. Using this pump, Boyle and Hooke noticed the pressure-volume correlation: PV=constant. In that time, air was assumed to be a system of motionless particles, and not interpreted as a system of moving molecules. The concept of thermal motion came two centuries later. Therefore, Boyle's publication in 1660 speaks about a mechanical concept: the air spring. Later, after the invention of the thermometer, the property temperature could be quantified. This tool gave Gay-Lussac the opportunity to derive his law, which led shortly later to the ideal gas law.

Gas laws in brief

Robert Boyle. 1627–1691

• Boyle's law (1662)
• Charles's law was first published by Joseph Louis Gay-Lussac in 1802, but he referenced unpublished work by Jacques Charles from around 1787. The relationship had been anticipated by the work of Guillaume Amontons in 1702.
• Gay-Lussac's law (1802)

Steam digester

Main article: Steam digester

Denis Papin

Denis Papin, an associate of Boyle's, built in 1679 a bone digester, which is a closed vessel with a tightly fitting lid that confines steam until a high pressure is generated. Later designs implemented a steam release valve to keep the machine from exploding. By watching the valve rhythmically move up and down, Papin conceived of the idea of a piston and cylinder engine. He did not however follow through with his design. Nevertheless, in 1697, based on Papin's designs, Thomas Newcomen greatly improved upon engineer Thomas Savery's earlier "fire engine" by incorporating a piston. This made it suitable for mechanical work in addition to pumping to heights beyond 30 feet, and is thus often considered the first true steam engine.

Heat transfer (Halley and Newton)

Main articles: Hadley cell § Formulation and discovery, and Newton's law of cooling

Edmond Halley

The phenomenon of heat conduction is immediately grasped in everyday life. The fact that warm air rises and the importance of the phenomenon to meteorology was first realised by Edmond Halley in 1686.

In 1701, Sir Isaac Newton published his law of cooling.

18th century

Phlogiston theory

Main article: Phlogiston theory

The theory of phlogiston arose in the 17th century, late in the period of alchemy. Its replacement by caloric theory in the 18th century is one of the historical markers of the transition from alchemy to chemistry. Phlogiston was a hypothetical substance that was presumed to be liberated from combustible substances during burning, and from metals during the process of rusting.

The world's first ice-calorimeter, used in the winter of 1782–83, by Antoine Lavoisier and Pierre-Simon Laplace, to determine the heat evolved in various chemical changes; calculations which were based on Joseph Black's prior discovery of latent heat. These experiments mark the foundation of thermochemistry.

Limit to the "degree of cold"

Main article: Absolute zero § History

In 1702 Guillaume Amontons introduced the concept of absolute zero based on observations of gases.

Kinetic theory (18th century)

Main article: Kinetic theory of gases § History

An early scientific reflection on the microscopic and kinetic nature of matter and heat is found in a work by Mikhail Lomonosov, in which he wrote: "Movement should not be denied based on the fact it is not seen. ... leaves of trees move when rustled by a wind, despite it being unobservable from large distances. Just as in this case motion ... remains hidden in warm bodies due to the extremely small sizes of the moving particles."

During the same years, Daniel Bernoulli published his book Hydrodynamics (1738), in which he derived an equation for the pressure of a gas considering the collisions of its atoms with the walls of a container. He proved that this pressure is two thirds the average kinetic energy of the gas in a unit volume. Bernoulli's ideas, however, made little impact on the dominant caloric culture. Bernoulli made a connection with Gottfried Leibniz's vis viva principle, an early formulation of the principle of conservation of energy, and the two theories became intimately entwined throughout their history.

Thermochemistry and steam engines

See also: History of chemistry

Heat capacity

Joseph Black

Bodies were capable of holding a certain amount of this fluid, leading to the term heat capacity, named and first investigated by Scottish chemist Joseph Black in the 1750s.

In the mid- to late 19th century, heat became understood as a manifestation of a system's internal energy. Today heat is seen as the transfer of disordered thermal energy. Nevertheless, at least in English, the term heat capacity survives. In some other languages, the term thermal capacity is preferred, and it is also sometimes used in English.

Steam engines

Main article: History of the steam engine

A Watt steam engine, the steam engine that propelled the Industrial Revolution in Britain and the world

Prior to 1698 and the invention of the Savery engine, horses were used to power pulleys, attached to buckets, which lifted water out of flooded salt mines in England. In the years to follow, more variations of steam engines were built, such as the Newcomen engine, and later the Watt engine. In time, these early engines would eventually be utilized in place of horses. Thus, each engine began to be associated with a certain amount of "horse power" depending upon how many horses it had replaced. The main problem with these first engines was that they were slow and clumsy, converting less than 2% of the input fuel into useful work. In other words, large quantities of coal (or wood) had to be burned to yield only a small fraction of work output. Hence the need for a new science of engine dynamics was born.

Caloric theory

Main article: Caloric theory

In the mid- to late 18th century, heat was thought to be a measurement of an invisible fluid, known as the caloric. Like phlogiston, caloric was presumed to be the "substance" of heat that would flow from a hotter body to a cooler body, thus warming it. The utility and explanatory power of kinetic theory, however, soon started to displace the caloric theory. Nevertheless, William Thomson, for example, was still trying to explain James Joule's observations within a caloric framework as late as 1850. The caloric theory was largely obsolete by the end of the 19th century.

Calorimetry

Main articles: Calorimeter and Calorimetry

Antoine Lavoisier

Joseph Black and Antoine Lavoisier made important contributions in the precise measurement of heat changes using the calorimeter, a subject which became known as thermochemistry. The development of the steam engine focused attention on calorimetry and the amount of heat produced from different types of coal. The first quantitative research on the heat changes during chemical reactions was initiated by Lavoisier using an ice calorimeter following research by Joseph Black on the latent heat of water.

Thermal conduction and thermal radiation

Main article: Thermal conduction

Carl Wilhelm Scheele distinguished heat transfer by thermal radiation (radiant heat) from that by convection and conduction in 1777.

Pierre Prévost

In the 17th century, it came to be believed that all materials had an identical conductivity and that differences in sensation arose from their different heat capacities. Suggestions that this might not be the case came from the new science of electricity in which it was easily apparent that some materials were good electrical conductors while others were effective insulators. Jan Ingen-Housz in 1785-9 made some of the earliest measurements, as did Benjamin Thompson during the same period.

In 1791, Pierre Prévost showed that all bodies radiate heat, no matter how hot or cold they are. In 1804, Sir John Leslie observed that a matte black surface radiates heat more effectively than a polished surface, suggesting the importance of black-body radiation.

Heat and friction (Rumford)

Main article: An Inquiry Concerning the Source of the Heat Which Is Excited by Friction

See also: Benjamin Thompson § Mechanical equivalent of heat

Benjamin Thompson

In the 19th century, scientists abandoned the idea of a physical caloric. The first substantial experimental challenges to the caloric theory arose in a work by Benjamin Thompson's (Count Rumford) from 1798, in which he showed that boring cast iron cannons produced great amounts of heat which he ascribed to friction. His work was among the first to undermine the caloric theory.

As a result of his experiments in 1798, Thompson suggested that heat was a form of motion, though no attempt was made to reconcile theoretical and experimental approaches, and it is unlikely that he was thinking of the vis viva principle.

Early 19th century

Modern thermodynamics (Carnot)

Main article: Nicolas Léonard Sadi Carnot § Reflections on the Motive Power of Fire

Sadi Carnot (1796–1832): the "father" of thermodynamics

Although early steam engines were crude and inefficient, they attracted the attention of the leading scientists of the time. One such scientist was Sadi Carnot, the "father of thermodynamics", who in 1824 published Reflections on the Motive Power of Fire, a discourse on heat, power, and engine efficiency. Most cite this book as the starting point for thermodynamics as a modern science. (The name "thermodynamics", however, did not arrive until 1854, when the British mathematician and physicist William Thomson (Lord Kelvin) coined the term thermo-dynamics in his paper On the Dynamical Theory of Heat.)

Carnot defined "motive power" to be the expression of the useful effect that a motor is capable of producing. Herein, Carnot introduced us to the first modern day definition of "work": weight lifted through a height. The desire to understand, via formulation, this useful effect in relation to "work" is at the core of all modern day thermodynamics.

Even though he was working with the caloric theory, Carnot in 1824 suggested that some of the caloric available for generating useful work is lost in any real process.

Reflection, refraction, and polarisation of radiant heat

Main article: Macedonio Melloni § Work

Though it had come to be suspected from Scheele's work, in 1831 Macedonio Melloni demonstrated that radiant heat could be reflected, refracted and polarised in the same way as light.

Kinetic theory (early 19th century)

Main articles: John Herapath and John James Waterston § Kinetic theory

John Herapath independently formulated a kinetic theory in 1820, but mistakenly associated temperature with momentum rather than vis viva or kinetic energy. His work ultimately failed peer review, even from someone as well-disposed to the kinetic principle as Humphry Davy, and was neglected.

John James Waterston in 1843 provided a largely accurate account, again independently, but his work received the same reception, failing peer review.

Further progress in kinetic theory started only in the middle of the 19th century, with the works of Rudolf Clausius, James Clerk Maxwell, and Ludwig Boltzmann.

Mechanical equivalent of heat

Main article: Mechanical equivalent of heat

Quantitative studies by Joule from 1843 onwards provided soundly reproducible phenomena, and helped to place the subject of thermodynamics on a solid footing. In 1843, Joule experimentally found the mechanical equivalent of heat. In 1845, Joule reported his best-known experiment, involving the use of a falling weight to spin a paddle-wheel in a barrel of water, which allowed him to estimate a mechanical equivalent of heat of 819 ft·lbf/Btu (4.41 J/cal). This led to the theory of conservation of energy and explained why heat can do work.

Absolute zero and the Kelvin scale

Main articles: Absolute zero § Lord Kelvin's work, and Lord Kelvin § Thermodynamics

The idea of absolute zero was generalised in 1848 by Lord Kelvin.

Late 19th century

Entropy and the second law of thermodynamics

Main articles: History of entropy and Second law of thermodynamics § History

Lord Kelvin

In March 1851, while grappling to come to terms with the work of Joule, Lord Kelvin started to speculate that there was an inevitable loss of useful heat in all processes. The idea was framed even more dramatically by Hermann von Helmholtz in 1854, giving birth to the spectre of the heat death of the universe.

William Rankine

In 1854, William John Macquorn Rankine started to make use of what he called thermodynamic function in calculations. This has subsequently been shown to be identical to the concept of entropy formulated by the famed mathematical physicist Rudolf Clausius.^[14]

Rudolf Clausius

Main article: Rudolf Clausius § Entropy

In 1865, Clausius coined the term "entropy" (das Wärmegewicht, symbolized S) to denote heat lost or turned into waste. ("Wärmegewicht" translates literally as "heat-weight"; the corresponding English term stems from the Greek τρέπω, "I turn".) Clausius used the concept to develop his classic statement of the second law of thermodynamics the same year.

Statistical thermodynamics

Main article: Statistical thermodynamics

Temperature is average kinetic energy of molecules

In his 1857 work On the nature of the motion called heat, Clausius for the first time clearly states that heat is the average kinetic energy of molecules.

Maxwell–Boltzmann distribution

Main article: Maxwell–Boltzmann distribution

Clausius' above statement interested the Scottish mathematician and physicist James Clerk Maxwell, who in 1859 derived the momentum distribution later named after him. The Austrian physicist Ludwig Boltzmann subsequently generalized this distribution for the case of gases in external fields. In association with Clausius, in 1871, Maxwell formulated a new branch of thermodynamics called statistical thermodynamics, which functions to analyze large numbers of particles at equilibrium, i.e., systems where no changes are occurring, such that only their average properties as temperature T, pressure P, and volume V become important.

Degrees of freedom

Main article: Degrees of freedom (physics and chemistry)

Boltzmann is perhaps the most significant contributor to kinetic theory, as he introduced many of the fundamental concepts in the theory. Besides the Maxwell–Boltzmann distribution mentioned above, he also associated the kinetic energy of particles with their degrees of freedom. The Boltzmann equation for the distribution function of a gas in non-equilibrium states is still the most effective equation for studying transport phenomena in gases and metals. By introducing the concept of thermodynamic probability as the number of microstates corresponding to the current macrostate, he showed that its logarithm is proportional to entropy.

Definition of entropy

Main article: Ludwig Boltzmann § Physics

In 1875, the Austrian physicist Ludwig Boltzmann formulated a precise connection between entropy S and molecular motion:

${\displaystyle S=k\log W}$

being defined in terms of the number of possible states W that such motion could occupy, where k is the Boltzmann constant.

Gibbs free energy

Main article: Gibbs free energy

In 1876, chemical engineer Willard Gibbs published an obscure 300-page paper titled: On the Equilibrium of Heterogeneous Substances, wherein he formulated one grand equality, the Gibbs free energy equation, which suggested a measure of the amount of "useful work" attainable in reacting systems.

Enthalpy

Main article: Enthalpy

Gibbs also originated the concept we now know as enthalpy H, calling it "a heat function for constant pressure". The modern word enthalpy would be coined many years later by Heike Kamerlingh Onnes, who based it on the Greek word enthalpein meaning to warm.

Stefan–Boltzmann law

Main article: Stefan–Boltzmann law § History

James Clerk Maxwell's 1862 insight that both light and radiant heat were forms of electromagnetic wave led to the start of the quantitative analysis of thermal radiation. In 1879, Jožef Stefan observed that the total radiant flux from a blackbody is proportional to the fourth power of its temperature and stated the Stefan–Boltzmann law. The law was derived theoretically by Ludwig Boltzmann in 1884.

20th century

Quantum thermodynamics

Main article: Quantum thermodynamics

In 1900 Max Planck found an accurate formula for the spectrum of black-body radiation. Fitting new data required the introduction of a new constant, known as the Planck constant, the fundamental constant of modern physics. Looking at the radiation as coming from a cavity oscillator in thermal equilibrium, the formula suggested that energy in a cavity occurs only in multiples of frequency times the constant. That is, it is quantized. This avoided a divergence to which the theory would lead without the quantization.

Third law of thermodynamics

Main article: Third law of thermodynamics

In 1906, Walther Nernst stated the third law of thermodynamics.

Erwin Schrödinger

Building on the foundations above, Lars Onsager, Erwin Schrödinger, Ilya Prigogine and others, brought these engine "concepts" into the thoroughfare of almost every modern-day branch of science.

Branches of thermodynamics

The following list is a rough disciplinary outline of the major branches of thermodynamics and their time of inception:

• Thermochemistry – 1780s
• Classical thermodynamics – 1824
• Chemical thermodynamics – 1876
• Statistical mechanics – c. 1880s
• Equilibrium thermodynamics
• Engineering thermodynamics
• Chemical engineering thermodynamics – c. 1940s
• Non-equilibrium thermodynamics – 1941
• Small systems thermodynamics – 1960s
• Biological thermodynamics – 1957
• Ecosystem thermodynamics – 1959
• Relativistic thermodynamics – 1965
• Rational thermodynamics – 1960s
• Quantum thermodynamics – 1968
• Black hole thermodynamics – c. 1970s
• Theory of critical phenomena and use of renormalization group theory in statistical physics – 1966-1974
• Geological thermodynamics – c. 1970s
• Biological evolution thermodynamics – 1978
• Geochemical thermodynamics – c. 1980s
• Atmospheric thermodynamics – c. 1980s
• Natural systems thermodynamics – 1990s
• Supramolecular thermodynamics – 1990s
• Earthquake thermodynamics – 2000
• Drug-receptor thermodynamics – 2001
• Pharmaceutical systems thermodynamics – 2002

Concepts of thermodynamics have also been applied in other fields, for example:

• Thermoeconomics – c. 1970s