The Physics Book

MEASUREMENT AND MOTION 49 See also: Free falling 32–35 ■ Laws of motion 40–45 ■ The heavens 270–71 ■ Models of the universe 272–73 ■ Special relativity 276–79 ■ The equivalence principle 281 ■ Gravitational waves 312–15 and a feather on NASA’s Apollo 15 0 ft/s mission. With no air resistance at 32 ft/s the moon’s surface, the two objects hit the ground at the same time. 65 ft/s Newton’s apple 98 ft/s While the story of an apple falling on Isaac Newton’s head Grimaldi is apocryphal, watching the fruit and Riccioli drop to the ground did spark his showed that curiosity. By the time Newton gravity causes started thinking seriously about objects to fall at 131 ft/s gravity in the 1660s, much important groundwork had already been the same speed achieved. In his seminal work regardless of their Principia, Newton credited the mass. If air work of Italian physicist Giovanni resistance is Borelli (1608–1679) and French eliminated, astronomer Ismael Bullialdus (1605– objects accelerate 164 ft/s 1694), who both described the The New Almagest, a 1651 work by sun’s gravity exerting an attractive at a constant rate Riccioli, illustrates the tussle between force. Bullialdus believed incorrectly of 32.15 ft/s (9.8 m/s) faster rival models of planetary motion: Tycho that the sun’s gravity attracted a with each passing second. Brahe’s Earth-centric theory is shown planet at its aphelion (the point on outweighing heliocentrism. its orbital curve when it is furthest motion states that there is an exact from the sun) but repulsed it at the mathematical relationship between been wrong: if all things orbited perihelion (when it is closest). a planet’s distance from the sun Earth, Jupiter’s moons could not and the length of time it takes exist. Galileo also observed the The work of Johannes Kepler to complete a full orbit. phases of Venus, demonstrating was probably the greatest influence that it orbits the sun. on Newton’s ideas. The German In 1670, English natural astronomer’s third law of orbital philosopher Robert Hooke argued Galileo also challenged the idea that gravitation applies to all that heavy objects fall to the ground If the Earth should cease to celestial bodies and that its power more quickly than light objects. His attract its waters to itself all decreases with distance, and—in contention was supported by Italian the waters of the sea would be the absence of any other attractive Jesuit priests Giovanni Battista raised and would flow to the forces—moves in straight lines. By Riccioli and Francesco Maria 1679, he had concluded that the Grimaldi, who in the 1640s dropped body of the moon. inverse square law applied, so objects from a Bologna tower and Johannes Kepler gravity weakens in proportion to timed their descent to the street the square of the distance from a below. Their calculations provided body. In other words, if the distance reasonably accurate values for between the sun and another body the rate of acceleration due to is doubled, the force between them gravity, now known to be 32.15 ft/s2 reduces to only one quarter of the (9.8 m/s2). Their experiment was original force. However, whether recreated in 1971 by US astronaut this rule could be applied close to David Scott, who dropped a hammer the surface of a large planetary body such as Earth was unknown. ❯❯

50 LAWS OF GRAVITY Newton argued that gravity is a universal, attractive force that applies to all matter, however large or small. Its Universality of free fall strength varies according to how much mass the objects have, and how far they are from each other. The principle of universality of free fall was empirically The greater an object’s The further apart two objects discovered by Galileo and mass, the stronger its are, and the less mass they have, others, then mathematically gravitational pull the weaker the gravitational pull proven by Newton. It states that all materials, heavy or Universal gravitation the speed of the cannonball was light, fall at the same rate in Newton published his own laws of relatively slow it would fall back to a uniform gravitational field. motion and gravitation in Principia Earth, but if it was fired at a much Consider two falling bodies in 1687, asserting “Every particle faster velocity it would continue to of different weight. Since attracts every other particle … with circle Earth in a circular orbit; this Newton’s theory of gravity a force directly proportional to the would be its orbital velocity. If its says that the greater the mass product of their masses.” He velocity was faster still, the ball of an object, the greater the explained how all matter exerts would continue to travel around gravitational force, the heavy an attractive force—gravity—that Earth in an elliptical orbit. If it object should fall faster. pulls other matter toward its center. reached a speed that was faster However, his second law of It is a universal force, the strength than 7 miles/s (11.2 km/s), it would motion tells us that a larger of which depends on the mass of leave Earth’s gravitational field and mass does not accelerate as the object. For instance, the sun travel onward into outer space. quickly as a smaller one if the has a greater gravitational strength applied force is the same, so it than Earth, which in turn has more More than three centuries will fall more slowly. In fact, gravitational strength than the later, modern-day physics has put the two cancel each other out, moon, which in turn has more Newton’s theories into practice. so the light and heavy objects gravitational strength than a ball The cannonball phenomenon will fall with the same dropped upon it. Gravitational can be seen when a satellite or acceleration as long as no strength can be expressed with the spacecraft is launched into orbit. other forces—such as air Instead of the gunpowder that resistance—are present. equation F = Gm1m2/r2, where F is the force, m1 and m2 are the masses Nonsense will fall of its The Asinelli tower in Bologna, of the two bodies, r is the distance own weight, by a sort of Italy, was the chosen site for the between their centers, and G is the intellectual law of gravitation. free-fall experiments of Riccioli And a new truth will go and Grimaldi, in which Galileo’s gravitational constant. theory was put to the test. Newton continued to refine his into orbit. Cecilia Payne-Gaposchkin views long after the publication of Principia. His cannonball thought- British–American astronomer experiment speculated on the trajectory of a ball fired from a cannon on top of a very high mountain in an environment in which there was no air resistance. If gravity was also absent, he argued that the cannonball would follow a straight line away from Earth in the direction of fire. Assuming gravity is present, if

MEASUREMENT AND MOTION 51 blasted Newton’s imaginary as its gravitational mass? Repeated An object moving faster At 17,000 mph projectile, powerful rocket engines experiments have shown that the than 25,000 mph (27,000 km/h), lift the satellite from Earth’s surface two properties are the same, a fact (40,000 km/h) will an object will and give it forward speed. When that fascinated Albert Einstein, escape Earth’s go into orbit it reaches its orbital velocity, the who used it as a basis for his theory gravitational pull spacecraft’s propulsion ceases and of general relativity. At under it falls all the way around Earth, 7,000 mph never hitting the surface. The angle Reinterpreting gravitation (11,300 km/h), of the satellite’s path is determined Newton’s ideas on universal it will fall by its initial angle and speed. The gravitation and motion were back to success of space exploration has unchallenged until 1905, when Earth relied heavily on Newton’s laws Einstein’s theory of special of gravitation. relativity was published. Whereas Newton correctly predicted that Newton’s theory depended on the objects would orbit Earth if they were Understanding mass assumption that mass, time, and launched at the correct speed. If a An object’s inertial mass is its distance remain constant, Einstein’s satellite moves quickly enough, the inertial resistance to acceleration theory treats them as fluid entities curvature of its fall is less than that from any force, gravitational or not. that are defined by the observer’s of Earth, so it stays in orbit, never It is defined by Newton’s second frame of reference. A person returning to the ground. standing on Earth as it spins on law of motion as F = ma, where F its axis orbits the sun—and moves observed from two very different is the force applied, m is its inertial through the universe in a different frames of reference. In this mass, and a is acceleration. If a frame of reference to an astronaut instance, scientists must rely on flying through space in a spacecraft. Einstein’s theories of relativity. known force is applied to the object, Einstein’s theory of general relativity Classical mechanics and Einstein’s by measuring its acceleration the also states that gravity is not a force, theories of relativity agree as long but rather the effect of the distortion as an object’s speed is low or the inertial mass is found to be F/a. In of spacetime by massive objects. gravitational field it experiences is small. ■ contrast, according to Newton’s law Newton’s laws are adequate for of universal gravitation, gravitational most day-to-day applications, but mass is the physical property of they cannot explain the differences an object that causes it to interact in motion, mass, distance, and with other objects through the time that result when bodies are gravitational force. Newton was troubled by the question: is the inertial mass of an object the same Isaac Newton Born in the English village of over who had discovered Woolsthorpe on Christmas Day calculus, and Robert Hooke 1642, Newton went to school regarding the inverse square in Grantham and studied law. As well as being a keen at Cambridge University. In scientist, Newton was very Principia, he formulated the interested in alchemy and laws of universal gravitation and biblical chronology. He died motion, which formed the basis in London in 1727. of classical mechanics until the early 20th century when they Key works were partially superseded by Einstein’s theories of relativity. 1684 On the Motion of Bodies Newton also made important in an Orbit contributions to mathematics and 1687 Philosophiae Naturalis optics. Sometimes a controversial Principia Mathematica character, he had long-running (Mathematical Principles disputes with Gottfried Leibniz of Natural Philosophy)

52 EOVSECRILYLWAHTIEORNEIS HARMONIC MOTION IN CONTEXT P eriodic motion—motion in the opposite direction to the repeated in equal time displacement from the center. While KEY FIGURE intervals—is found in many tending to restore the string toward Leonhard Euler (1707–1783) natural and artificial phenomena. the center, it overshot to the other Studies of pendulums in the 16th side, creating a repeating cycle. BEFORE and 17th centuries, for instance, 1581 Galileo discovers the helped lay the foundations for This type of movement, with link between the length of Isaac Newton’s laws of motion. But a specific relationship between a pendulum and its period groundbreaking though these laws displacement and restoring force, of motion. were, physicists still faced major is today known as simple harmonic barriers in applying them to real- motion. As well as vibrating 1656 Christiaan Huygens world problems involving systems strings, it encompasses phenomena builds a pendulum clock that (interacting groups of items) that such as a swinging pendulum and uses the periodic motion of were more complex than Newton’s a weight bouncing on the end of a a pendulum to regulate a idealized, freely-moving bodies. spring. Bernoulli also discovered timekeeping mechanism. that harmonic oscillations plotted AFTER Musical oscillations Displacement wave 1807 Joseph Fourier, a French One particular area of interest was physicist, shows that any the vibration of musical strings— Direction of travel periodic process can be another form of periodic motion. Acceleration wave treated as the sum of simple In Newton’s day, the principle For any system in simple harmonic harmonic oscillations overlaid that strings vibrate at different motion, the displacement and on each other. frequencies to produce different acceleration can be described by sounds was well established, but sine wave oscillations that are mirror 1909 German engineer the exact form of the vibrations was images of each other. Hermann Frahm develops a unclear. In 1732, Swiss physicist “dynamic vibration absorber,” and mathematician Daniel Bernoulli a device that absorbs energy found a means of applying Newton’s from oscillations and releases second law of motion to each it out of sync in order to segment of a vibrating string. reduce vibration. He showed that the force on the string grew as it moved further from the center line (its stationary starting point), and always acted

MEASUREMENT AND MOTION 53 See also: Measuring time 38–39 ■ Laws of motion 40–45 ■ Kinetic energy and potential energy 54 ■ Music 164–167 Nothing takes place in Bernoulli’s earlier work and Leonhard Euler the world whose meaning eventually hit upon a form that mirrored the structure of Newton’s Born into a religious family is not that of some second law. In 1752, Euler was the in Basel, Switzerland, in 1707, maximum or minimum. first person to express that famous Leonhard Euler was the most law in the now familiar equation important mathematician of Leonhard Euler his generation, taking an F = ma (the force acting on a body interest in pure math and its on a graph form a sine wave—a many applications—including mathematical function that is is equal to its mass multiplied by ship design, mechanics, easily manipulated to find solutions its acceleration). In parallel, his astronomy, and music theory. to physical problems. Harmonic equation for rotation states that: motion can also be applied in Entering Basel’s university some more surprising places. L = I d/dt, where L is the torque at the age of 13, Euler studied For instance, both circular motion under Johann Bernoulli. He (for example, a satellite orbiting (the rotational force acting on the spent 14 years teaching and Earth) and the rotation of objects researching at the Imperial (Earth spinning on its axis) could object), I is the object’s “moment Russian Academy in St. be treated as oscillations back and Petersburg, before Frederick forth in two or more directions. of inertia” (broadly speaking, its the Great invited him to Berlin. Despite losing his sight resistance to turning), and d/dt in one eye in 1738 and the other in 1766, Euler continued is the rate of change of its angular to work at a prodigious rate, velocity  (in other words, its establishing several entirely “angular acceleration”). new areas of mathematical investigation. On his return to Simple harmonic motion St. Petersburg, he continued has proved to have countless to work until he died of a applications, including in fields brain hemorrhage in 1783. that were not dreamt of in Euler’s time, ranging from harnessing Key works the oscillations of electrical and magnetic fields in electric circuits 1736 Mechanics to mapping the vibrations of 1744 A method for finding electrons between energy levels curved lines enjoying properties in atoms. ■ of maximum or minimum 1749 Naval science Using Newton’s law 1765 Theory on the motion Swiss mathematician and physicist of solid or rigid bodies Leonhard Euler was intrigued by the forces that cause ships to pitch (bob up and down lengthwise from bow to stern) and roll (tilt side to side). Around 1736, he realized that the motion of a ship could be split into a translation element (a movement between two places) and a rotational element. Searching for an equation to describe the rotation part of the movement, Euler built on Daniel As a young medic in the Russian navy, Leonhard Euler became fascinated by the way in which waves affect the motion of ships.

54 DOTHEFSEFRTORERUICSCETNIOON KINETIC ENERGY AND POTENTIAL ENERGY IN CONTEXT I saac Newton’s laws of motion Du Châtelet concluded that each incorporated the fundamental ball’s vis viva (broadly the same KEY FIGURE idea that the sum of momentum concept as the modern kinetic Émilie du Châtelet across all objects involved is the energy attributed to moving (1706–1749) same before as after a collision. He particles) was proportional to its had little to say, however, about the mass but also to the square of its BEFORE concept of energy as understood 1668 John Wallis proposes today. In the 1680s, Gottfried Leibniz velocity (mv2). She hypothesized a law of conservation of noted that another property of momentum—the first in its moving bodies, which he called that since vis viva was clearly modern form. vis viva (“living force”), also seemed conserved (or transferred wholesale) to be conserved. in such collisions, it must exist in a AFTER different form when the weight was 1798 American-born British Leibniz’s idea was widely suspended before its fall. This form physicist Benjamin Thompson, rejected by Newton’s followers, who is now known as potential energy Count Rumford, makes felt that energy and momentum and is attributed to an object’s measurements that suggest should be indistinguishable, but it position within a force field. ■ heat is another form of kinetic was revived in the 1740s. French energy, contributing to the philosopher Marquise Émilie du Physics is an immense total energy of a system. Châtelet, who was working on a building that surpasses the translation of Newton’s Principia, 1807 British polymath Thomas proved vis viva’s significance. She powers of a single man. Young first uses the term repeated an experiment—first Émilie du Châtelet “energy” for the vis viva carried out by Dutch philosopher investigated by du Châtelet. Willem ‘s Gravesande—in which she dropped metal balls of differing 1833 Irish mathematician weights into clay from various William Rowan Hamilton heights and measured the depth of shows how the evolution of the resulting craters. This showed a mechanical system can be that a ball traveling twice as fast thought of in terms of the made a crater four times as deep. changing balance between potential and kinetic energies. See also: Momentum 37 ■ Laws of motion 40–45 ■ Energy and motion 56–57 ■ Force fields and Maxwell’s equations 142–147

MEASUREMENT AND MOTION 55 ENNNEOIERTRHDGEEYRSCTCARRNOEYBAETEDED THE CONSERVATION OF ENERGY IN CONTEXT T he law of conservation often given to British physicist of energy states that the James Joule. In 1845, Joule KEY FIGURE total energy of an isolated published the results of a key James Joule (1818–1889) system remains constant over experiment. He designed an time. Energy cannot be created or apparatus with a falling weight to BEFORE destroyed, but can be transformed spin a paddle wheel in an insulated 1798 Benjamin Thompson, from one form to another. cylinder of water, using gravity Count Rumford, uses a cannon to do the mechanical work. By barrel immersed in water and Although German chemist and measuring the increase in water bored with a blunted tool to physicist Julius von Mayer first temperature, he calculated the show that heat is created advanced the idea in 1841, credit is precise amount of heat an exact from mechanical motion. amount of mechanical work would create. He also showed that no AFTER energy was lost in the conversion. 1847 In his paper “On the Conservation of Force,” Joule’s discovery that heat had German physicist Hermann been created mechanically was not von Helmholtz explains the widely accepted until 1847, when convertibility of all forms Hermann von Helmholtz proposed of energy. a relationship between mechanics, heat, light, electricity, and 1850 Scottish civil engineer magnetism—each a form of energy. William Rankine is the first Joule’s contribution was honored to use the phrase “the law of when the standard unit of energy the conservation of energy” was named after him in 1882. ■ to describe the principle. For his experiment, Joule used this 1905 In his theory of relativity, vessel, filled with water, and the brass Albert Einstein introduces his paddle wheel, turned by falling weights. principle of mass–energy The water’s rising temperature showed equivalence—the idea that that mechanical work created heat. every object, even at rest, has See also: Energy and motion 56–57 ■ Heat and transfers 80–81 ■ Internal energy energy equivalent to its mass. and the first law of thermodynamics 86–89 ■ Mass and energy 284–285

56 OANNEMWECTHRAENAITCISSE ENERGY AND MOTION IN CONTEXT T hroughout the 18th equations of the first kind” were century, physics advanced simply a structure of equation KEY FIGURE considerably from the laws that allowed constraints to be Joseph-Louis Lagrange of motion set out by Isaac Newton considered as separate elements (1736–1813) in 1687. Much of this development in determining the movement was driven by mathematical of an object or objects. BEFORE innovations that made the central 1743 French physicist and principles of Newton’s laws easier to Even more significant were mathematician Jean Le Rond apply to a wider range of problems. the equations “of the second d’Alembert points out that kind,” which abandoned the the inertia of an accelerating A key question was how best “Cartesian coordinates” implicit body is proportional and to tackle the challenge of systems in Newton’s laws. René Descartes’ opposite to the force causing with constraints, in which bodies pinning-down of location in three the acceleration. are forced to move in a restricted dimensions (commonly denoted way. An example is the movement 1744 Pierre-Louis Maupertuis, of the weight at the end of a fixed x, y, and z) is intuitively easy to a French mathematician, pendulum, which can’t break free shows that a “principle of from its swinging rod. Adding any interpret, but makes all but the least length” for the motion form of constraint complicates simplest problems in Newtonian of light can be used to find Newtonian calculations its equations of motion. considerably—at each point in an Newton was the greatest object’s movement, all the forces genius that ever existed, AFTER acting on it must be taken into and the most fortunate, for we 1861 James Clerk Maxwell account and their net effect found. cannot find more than once applies the work of Lagrange and William Rowan Hamilton Langrangian equations a system of the world to calculate the effects of In 1788, French mathematician to establish. electromagnetic force fields. and astronomer Joseph-Louis Lagrange proposed a radical new Joseph-Louis Lagrange 1925 Erwin Schrödinger approach he called “analytical derives his wave equation mechanics.” He put forward two from Hamilton’s principle. mathematical techniques that allowed the laws of motion to be more easily used in a wider variety of situations. The “Lagrangian

MEASUREMENT AND MOTION 57 See also: Laws of motion 40–45 ■ The conservation of energy 55 ■ Force fields and Maxwell’s equations 142–147 ■ Reflection and refraction 168–169 Newton’s laws of motion It is very difficult to describe motion in calculate complex problems of motion using Cartesian coordinates (3-D Cartesian coordinates. x-, y-, and z-coordinates). This revealed that Joseph-Louis Lagrange Joseph-Louis objects usually move along devised equations that Lagrange allowed problems of motion the path that requires the Born in Turin, Italy, in least energy. to be solved using the 1736, Lagrange studied law most appropriate before becoming interested coordinate system. in mathematics at the age of 17. From then on, he taught physics very hard to calculate. The the path that requires the least himself and developed his method developed by Lagrange energy. Using this principle, he knowledge rapidly, lecturing allowed calculations to be made proved that any mechanical system on mathematics and ballistics with whatever coordinate system could be described by solving it with at Turin’s military academy. was most appropriate for the a mathematical method similar to He subsequently became a problem under investigation. The identifying the turning points on founding member of the Turin generalization set out by Lagrange a graph. Academy of Sciences, and he for equations of the second kind published work that attracted was not just a mathematical tool, Finally, in 1833, Hamilton set the attention of others, but also pointed the way to a out a powerful new approach to including Leonhard Euler. deeper understanding of the mechanics through equations nature of dynamic systems. that described the evolution of a In 1766, he moved to Berlin, mechanical system over time, in where he succeeded Euler as Solving systems terms of generalized coordinates head of mathematics at the Between 1827 and 1833, Irish and the total energy of the system Academy of Science. There, he mathematician William Rowan produced his most important Hamilton expanded on Lagrange’s (denoted H and now known as the work on analytical mechanics work and took mechanics to a new and addressed astronomical level. Drawing on the “principle of “Hamiltonian”). Hamilton’s problems such as the least time” in optics, first proposed equations allowed the system’s gravitational relationship by French mathematician Pierre balance of kinetic and potential between three bodies. He de Fermat in the 17th century, energies to be calculated for a moved to Paris in 1786, where Hamilton developed a method to particular time, and therefore he spent the remainder of his calculate the equations of motion predicted not just the trajectories career until his death in 1813. for any system based on a principle of objects, but their exact locations. of least (or stationary) action. This Alongside his general principle of Key works is the idea that objects, just like “least time,” they would prove to light rays, will tend to move along have applications in several other 1758–73 Miscellanea areas of physics, including Taurinensia: papers published gravitation, electromagnetism, by the Turin Academy of and even quantum physics. ■ Sciences 1788–89 Analytical Mechanics

TWHE EMUHSET ALOVOEKNTSO FTOHR TEHE EMEAASRURTE HOF SI UNITS AND PHYSICAL CONSTANTS



60 SI UNITS AND PHYSICAL CONSTANTS IN CONTEXT Measurements used to be defined by referring to a “standard unit” (such as the International Prototype Kilogram, KEY FIGURE Bryan Kibble or IPK). These standard units changed with time. (1938–2016) Values for universal physical constants in these standard units BEFORE 1875 The Meter Convention were determined through experiment. is agreed by 17 nations. 1889 The International Universal physical constants are based Prototype Kilogram and Meter on things in nature that are known to be invariant. are constructed. 1946 New definitions of the By fixing a value for a physical constant, a unit ampere and ohm are adopted. can be defined in terms of a true invariant. AFTER 1967 The second is redefined M easurement of a physical nature. The meter, for example, in terms of frequencies linked quantity requires the was defined as a fraction of Earth’s with the cesium atom. specification of a unit circumference along the Paris 1983 The meter is redefined (such as the meter for length), and meridian. In 1799, the prototype comparing measurements requires platinum meter and platinum in terms of c, the speed of that each party defines the unit in kilogram were created, and copies exactly the same way. Although were sent out for display in public light in a vacuum. standard units had been developed places all over France; the meter 1999 A new derived SI unit by ancient cultures, such as the length was also etched in stone on measuring catalytic activity, Romans, the growth of international sites across Paris and other cities. the katal, is introduced. trade and industrialization in the 2019 All SI base units are 17th and 18th centuries made Over the next century, other redefined in terms of universal the need for uniformity and countries in Europe and some in physical constants. precision imperative. South America adopted the metric system. In 1875, concerned about Each molecule, throughout The metric system was wear and tear to the existing the universe, bears impressed introduced in the 1790s, during platinum prototypes, and their the French Revolution, in order to tendency to warp, representatives on it the stamp of a metric rationalize measurement, simplify from 30 nations met in Paris, with system as distinctly as trade, and unite France. At the the aim of establishing a global does the meter of the time, hundreds of thousands of standard for measurements. Archives at Paris. different units were in use, varying James Clerk Maxwell from village to village. The idea The resulting treaty, the Meter was to replace them with universal, Convention (Convention du Mètre), permanent standards for length, stipulated new prototypes for the area, mass, and volume based on meter and kilogram, made out of a platinum–iridium alloy. These

MEASUREMENT AND MOTION 61 See also: Measuring distance 18–19 ■ Measuring time 38–39 ■ The development of statistical mechanics 104–111 ■ Electric charge 124–127 ■ The speed of light 275 were kept in Paris, and copies were The metric system came into use in and time. Gauss’s idea was that produced for the national standards France around 1795. This engraving by all physical quantities could be institutes of the 17 signatory L.F. Labrousse shows people using the measured in these units, or nations. The Convention outlined new decimal units to measure things, combinations of them. Each procedures for periodically and includes a list of metric units, each fundamental quantity would have calibrating the national standards followed by the unit being replaced. one unit, unlike some traditional against the new prototypes, and systems that used several different also set up the Bureau International make a foot—some everyday sums units for a quantity (for example, ❯❯ des Poids et Mesures (International are easy, but more complicated Bureau of Weights and Measures), arithmetic can be unwieldy. The or BIPM, to oversee them. metric system specifies only decimal ratios (counting in units of 10), The SI (Système international, making arithmetic much easier; it or International System) version is clear that 1/10th of 1/100th of a of the metric system, initiated in meter is 1/1000th of a meter. 1948, was approved by signatory nations in Paris in 1960. Since The metric system also then, it has been used for almost specifies names of prefixes and all scientific and technological and abbreviations for many multiples, many everyday measurements. such as kilo- (k) for multiplication There are still exceptions, such by 1,000, centi- (c) for one hundredth, as road distances in the UK and and micro- (µ) for one millionth. US, but even British imperial and US The prefixes allowed by the SI customary units such as the yard range from yocto- (y), meaning and the pound have been defined 10–24, to yotta- (Y), meaning 1024. in terms of metric standards. CGS, MKS, and SI Units of 10 In 1832, German mathematician With traditional systems of units Carl Gauss proposed a system that use ratios of 2, 3, and their of measurement based on three multiples—for example, 12 inches fundamental units of length, mass, The IPK is just 4 cm tall and is The IPK emerged between cylinders. kept under three glass bell jars at the Since other base units depended BIPM (Bureau International des Poids For 130 years, the kilogram was on the definition of the kilogram, et Mesures) in Paris, France. defined by a platinum–iridium this drift affected measurements cylinder, the IPK (International of many quantities. As scientists Prototype Kilogram) or “Le Grand and industry demanded greater K.” Copies of the cylinder were held precision for experiments and by national metrology institutes technology, the instability of the around the world, including the IPK became a serious problem. NPL (National Physical Laboratory, UK) and NIST (National Institute In 1960, when the meter was of Standards and Technology, US), redefined in terms of a particular and compared with the IPK about wavelength of light emitted by once every 40 years. a krypton atom, the kilogram became the only base unit whose Although the platinum–iridium standard depended on a physical alloy is extremely stable, over time, object. With the redefinition of SI discrepancies of up to 50µg in 2019, this is no longer the case.

62 SI UNITS AND PHYSICAL CONSTANTS SI base units meters per second (m s–1). As well as these derived units, there are Today, SI base units are defined in terms of physical constants whose currently 22 “derived units with numerical values are fixed, and—apart from the second and the mole—of special names”—including force, definitions of other base units. which is measured in newtons (N), where 1 N = 1 kg m s–2. Time Second vThe second (s) is defined by fixing ∆ cs, the Length (s) Increasing accuracy unperturbed ground-state hyperfine transition As theory and technology have Mass frequency of the cesium-133 atom, to be advanced, SI base units have been Electric 9 192 631 770 Hz (i.e. 9 192 631 770 s–1). redefined. Modern metrology—the current science of measurement—depends Meter cThe meter (m) is defined by fixing , the speed of light on instruments of great precision. (m) British metrologist Bryan Kibble’s in a vacuum, to be 299 792 458 m s–1, where the second development of the moving-coil watt balance in 1975 greatly vis defined in terms of ∆ cs. increased the accuracy with which the ampere could be defined. The Kilogram hThe kilogram (kg) is defined by fixing , the Planck watt balance compares the power (kg) developed by a moving mass to constant, to be 6.626 070 15 × 10–34 J s, (i.e. 6.626 070 15 × the current and voltage in an 10–34 kg m2 s–1, where the meter and the second are electromagnetic coil. c vdefined in terms of and ∆ cs). Kibble went on to collaborate with Ian Robinson at the UK’s Ampere The ampere (A) is defined by fixing e, the elementary National Physical Laboratory (NPL) (A) charge, to be 1.602 176 634 × 10–19 C (i.e. 1.602 176 634 × in 1978, creating a practical instrument—the Mark I—that v10–19 A s, where the second is defined in terms of ∆ cs). enabled the ampere to be measured with unprecedented accuracy. The Thermo- Kelvin The kelvin (K) is defined by fixing k, the Boltzmann Mark II balance followed in 1990. dynamic (K) constant, to be 1.380 649 × 10–23 J K–1 (i.e. 1.380 649 × Constructed in a vacuum chamber, temperature 10–23 kg m2 s–2 K–1, where the kilogram, meter, and this instrument made it possible Amount of Mole to measure Planck’s constant substance (mol) h c vsecond are defined in terms of , and ∆ cs). accurately enough to allow for the redefinition of the kilogram. The mole (mol) is defined by fixing NA, the Avogadro Later models of Kibble’s balance constant, to be exactly 6.022 140 76 × 1023 mol–1 have contributed significantly to (i.e. one mole of a substance contains 6.02214076 × the most recent version of the SI. 1023 particles such as atoms, molecules, or electrons). Historically, definitions were Luminous Candela The candela (cd) is defined by fixing Kcd, the luminous made in terms of physical artifacts intensity (cd) efficacy of radiation of frequency 540 × 1012 Hz, to be (such as the IPK) or measured 683 lm W–1 (i.e. 683 cd sr kg–1 m–2 s3, where sr is the solid properties (such as the frequency angle in steradians, and kilogram, meter, and second are of radiation emitted by a particular type of atom), and included one or h c vdefined in terms of , , and ∆ cs). more universal physical constants. inch, yard, and furlong for length). including the meter (m) for length, These constants (such as c, the In 1873, British physicists proposed kilogram (kg) for mass, and second speed of light in a vacuum, or ∆vcs, the centimeter, gram, and second (s) for time. These fundamental (CGS) as the fundamental units. quantities are considered to be a frequency associated with an This CGS system worked well for independent of each other, although electron moving between particular many years, but gradually gave the definitions of their units are energy levels—the “hyperfine way to the MKS (meter, kilogram, not—for instance, length and time transition”—in a cesium atom) and second) system. Both were are independent, but the definition superseded by the SI, which of the meter is dependent on the included standardized units in definition of the second. newer areas of study, such as electricity and magnetism. Other quantities are measured in “derived units,” which are Base and derived SI units combinations of base units, The SI specifies seven “base units” according to the relationship (and abbreviations) to measure between the quantities. For seven fundamental quantities, example, speed, which is distance per unit time, is measured in

MEASUREMENT AND MOTION 63 It is natural for man to relate radiation emitted by the cesium The Kibble balance at NIST produces the units of distance by which hyperfine transition. This number incredibly accurate measurements, he travels to the dimensions of was obtained experimentally, by and has contributed to the recent redefinition of all base measurement the globe that he inhabits. comparing ∆vcs with the most units in terms of physical constants. Pierre-Simon Laplace rigorous definition of the second is fixed, and the kilogram has French mathematician and then existing, which was based on been redefined to fit with this philosopher Earth’s orbit around the sun. Today, numerical value. the definition is subtly different. are natural invariants. In other The new SI now has a stronger words, universal physical constants The constant—here, the value foundation for its redefinition of are the same over all time and units. For practical purposes, most space, and so are more stable than of ∆vcs—is first explicitly defined are unchanged, but their stability any experimental determination of and precision at very small or very them, or any material artifact. (as 9 192 631 770). This expresses large scales is markedly improved. ■ SI units redefined our confidence that ∆vcs never The 2019 redefinition of SI units in terms of fundamental physical changes. It does not really matter constants was a philosophical shift. what numerical value is assigned Prior to 2019, definitions of units to it because the size of the unit were explicit. For example, since it is measured in is arbitrary. 1967, the second had been defined However, there is an existing, as 9 192 631 770 cycles of the convenient unit—the second— that can be refined, so it is assigned a value that makes the newly defined second as close as possible to the second by the old definition. In other words, instead of having a fixed definition of the second, and measuring ∆vcs relative to it, metrologists fix a convenient number for ∆vcs and define the second relative to that. Under the old definition of the kilogram, the IPK was considered a constant. Under the new definition, the value of Planck’s constant (6.626 070 15  10–34 joule-seconds) Bryan Kibble Born in 1938, British physicist and enabled measurements (initially metrologist Bryan Kibble showed of the ampere) to be made with an early aptitude for science and great accuracy without won a scholarship to study at the reference to a physical artifact. University of Oxford, where he After his death in 2016, the watt was awarded a DPhil in atomic balance was renamed the Kibble spectroscopy in 1964. After a balance in his honor. short post-doctoral period in Canada, he returned to the UK in Key works 1967 and worked as a researcher at the National Physical 1984 Coaxial AC Bridges Laboratory (NPL) until 1998. (with G.H. Raynor) 2011 Coaxial Electrical Kibble made several significant Circuits for Interference-Free contributions to metrology over Measurements (with Shakil his career, the greatest of which Awan and Jürgen Schurr) was his development of the moving-coil watt balance, which

EANNEDRMGYATT materials and heat

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66 INTRODUCTION The Greek philosophers Isaac Newton suggests James Watt creates British physicist and Democritus and Leucippus that atoms are held an efficient steam inventor Benjamin together by an engine, which proves Thompson, Count establish the school of invisible force to be the motive force atomism, believing the of attraction. of the Industrial Rumford, provides an world to be made from authoritative definition small, indestructible Revolution. of the conservation fragments. of energy. 5TH CENTURY BCE 1704 1769 1798 1678 1738 1787 1802 English polymath Swiss mathematician Jacques Charles discovers Joseph-Louis Gay-Lussac Robert Hooke publishes Daniel Bernoulli the relationship between rediscovers Charles’s the volume of a gas and gas law and also the Hooke’s law, which discovers that a fluid’s describes the way pressure decreases its temperature at relationship between objects deform constant pressure, but a gas’s temperature under tension. as its velocity does not publish his work. increases. and pressure. S ome things in our universe Long before the Greeks, early were powered by water in its are tangible, things we can humans had used the materials gaseous form of steam. Heat was touch and hold in our hands. around them in order to achieve the key to creating steam from Others seem ethereal and unreal the desired task. Every now water. In the 1760s, Scottish until we observe the effect they and then, a new material was engineers Joseph Black and James have on those objects we hold. discovered, mostly by accident but Watt made the important discovery Our universe is constructed from sometimes through trial-and-error that heat is a quantity, while tangible matter but it is governed by experiments. Adding coke (carbon) temperature is a measurement. the exchange of intangible energy. to iron produced steel, a stronger Understanding how heat is but more brittle metal that made transferred and how fluids move Matter is the name given to better blades than iron alone. became crucial to success in the anything in nature with shape, industrial world, with engineers form, and mass. The natural The age of experimentation and physicists vying to build the philosophers of ancient Greece were In Europe during the 17th century, biggest and best machines. the first to propose that matter was experimentation gave way to made from many small building laws and theories, and these ideas Experiments with the physical blocks called atoms. Atoms collect led toward new materials and properties of gases began with the together to form materials, made methods. During the European creation of the vacuum pump by of one or more different atoms Industrial Revolution (1760–1840), Otto von Guericke in Germany combined in various ways. Such engineers selected materials to in 1650. Over the next century, differing microscopic structures build machines that could chemists Robert Boyle in England give these materials very different withstand large forces and and Jacques Charles and Joseph- properties, some stretchy and temperatures. These machines Louis Gay-Lussac in France elastic, others hard and brittle. discovered three laws that related

ENERGY AND MATTER 67 Sadi Carnot analyzes the James Joule Dutchman Johannes German physicist Max efficiencies of steam discovers that heat Diderik van der Waals Planck proposes a new is a form of energy proposes his equation theory for blackbody engines and develops the and that other forms of state to describe idea of a reversible process, radiation, and of energy can be mathematically the introduces the idea initiating the science converted to heat. behavior of gases as they of thermodynamics. of the quantum condense to a liquid. of energy. 1824 1844 1873 1900 1803 1834 1865 1874 British chemist John Dalton Frenchman Émile German physicist Irish-born engineer and physicist proposes his modern atomic Clapeyron combines Rudolf Clausius William Thomson (later Lord Kelvin) the gas laws of Boyle, introduces the model from the ratio with Charles, Gay-Lussac, and modern definition formally states the second law which certain chemical Amedeo Avogadro into of thermodynamics, which elements combine to the ideal gas equation. of entropy. eventually leads to the form compounds. thermodynamic arrow of time. the temperature, volume, and Physicists designed new heat particles that make up a system. pressure of a gas. In 1834, these engines to squeeze as much work as Heat flowing only from hot to cold laws were combined into a single they could from every last bit of heat. was a specialized example of the equation to simply show the Frenchman Sadi Carnot discovered second law of thermodynamics, relationship between gas pressure, the most efficient way to achieve which states that the entropy and volume, and temperature. this theoretically, placing an upper disorder of an isolated system can limit on the amount of work only ever increase. Experiments conducted by obtainable for each unit of heat British physicist James Joule exchanged between two reservoirs The variables of temperature, showed that heat and mechanical at different temperatures. He volume, pressure, and entropy seem work are interchangeable forms of confirmed that heat only moved to only be averages of microscopic the same thing, which we today spontaneously from hot to cold. processes involving innumerable call energy. Industrialists desired Machines were imagined that did particles. The transition from mechanical work in exchange for the opposite, but these refrigerators microscopic huge numbers to a heat. Vast quantities of fossil fuels, were only constructed years later. singular macroscopic number mainly coal, were burned to boil was achieved through kinetic water and create steam. Heat Entropy and kinetic theory theory. Physicists were then able increased the internal energy The single direction of heat transfer to model complex systems in a of the steam before it expanded from hot to cold suggested an simplified way and link the kinetic and performed mechanical work, underlying law of nature, and the energy of particles in a gas to pushing pistons and turning idea of entropy emerged. Entropy its temperature. Understanding turbines. The relationship between describes the amount of disorder matter in all its states has helped heat, energy, and work was set out there is among the underlying physicists solve some of the deepest in the first law of thermodynamics. mysteries of the universe. ■

68 IN CONTEXT PUOTRHNFIEINTVHFCEIERIRPSSLEETS KEY FIGURE Democritus (c. 460–370 bce) MODELS OF MATTER BEFORE c.500 bce In ancient Greece, Heraclitus declares that everything is in a state of flux. AFTER c.300 bce Epicurus adds the concept of atomic “swerve” to atomism, allowing for some behavior to be unpredictable. 1658 French clergyman Pierre Gassendi’s Syntagma philosophicum (Philosophical Treatise), which attempts to marry atomism with Christianity, is published posthumously. 1661 Anglo-Irish physicist Robert Boyle defines elements in The Sceptical Chymist. 1803 John Dalton puts forward his atomic theory, based on empirical evidence. A mong the several mysteries that scholars have contemplated over millennia is the question of what everything is made of. Ancient philosophers—from Greece to Japan—tended to think of all matter as being made from a limited set of simple substances (“elements”), usually earth, air or wind, fire, and water, which combined in different proportions and arrangements to create all material things. Different cultures imagined these systems of elements in different ways, with some linking them to deities (as in Babylonian mythology) or tying them into

ENERGY AND MATTER 69 See also: Changes of state and making bonds 100–103 ■ Atomic theory 236–237 ■ The nucleus 240–241 ■ Subatomic particles 242–243 The classical system of elements of atomism on the idea that it must Democritus focused on earth, water, air, and fire. be impossible to continue dividing This illustration, from a manuscript matter eternally. He argued that Democritus was born into a dated c. 1617, shows these elements all matter must therefore be made wealthy family in Abdera, in within a divine universe. up of tiny particles that are too the historic region of Thrace small to see. He named these in southeast Europe around grander philosophical frameworks particles “atoms” from the word 460 bce. He traveled at length (such as the Chinese philosophy atomos, meaning uncuttable. through parts of western Asia of Wu Xing). and Egypt as a young man According to Democritus, before arriving in Greece to On the Indian subcontinent, atoms are infinite and eternal. familiarize himself with for instance, as early as the 8th The properties of an object depend natural philosophy. century bce, the Vedic sage Aruni not just on the size and shape of had described “particles too small its atoms but how these atoms are Democritus acknowledged to be seen [which] mass together assembled. Objects could, he his teacher Leucippus as his into the substances and objects stated, change over time through greatest influence, and of experience.” A number of shifts in their atomic arrangement. classicists have sometimes other Indian philosophers had For example, he proposed bitter struggled to distinguish independently developed their foods were made of jagged atoms between their contributions own atomic theories. that tore the tongue as they were to philosophy—particularly chewed; sweet foods, on the as none of the original works A materialist approach other hand, consisted of smooth has survived to this day. In the 5th century bce, the Greek atoms that flowed smoothly philosopher Democritus and his over the tongue. Best known for formulating teacher Leucippus also took a “atomism,” Democritus is also more materialist approach to these While modern atomic theory recognized as an early pioneer systems of elements. Democritus, looks very different from the theory in aesthetics, geometry, and who valued rational reasoning over put forward by Leucippus and epistemology. He believed observation alone, based his theory Democritus almost 2,500 years that rational reasoning was a ago, their idea that the properties necessary tool to seek truth of substances are affected by because observations made how atoms are arranged remains through human senses would relevant today. ❯❯ always be subjective. By convention sweet Democritus was a modest and by convention bitter, by man and is said to have convention hot, by convention taken a humorous approach cold, by convention color; but to scholarship, giving him his nickname: “The Laughing in reality atoms and void. Philosopher.” He died Democritus around 370 bce.

70 MODELS OF MATTER Europe effectively abandoned the Keep These fragments are concept of atomism for several dividing an object, atoms, which exist centuries, Islamic philosophers and eventually it can be such as Al-Ghazali (1058–1111) divided no further. in a void. developed their own distinct forms of atomism. Indian Buddhist philosophers such as Dhamakirti in the 7th century described atoms as point-like bursts of energy. The features Atoms come in Atomism revival and arrangement different shapes The birth of the Renaissance in of these atoms are what 14th-century Italy revived classical and sizes. arts, science, and politics across gives substances their properties. Europe. It also saw the rebirth of the theory of atomism, as had been described by Leucippus and Democritus. Atomism was According to Democritus, only atoms and the void are real. controversial, however, because of its link with Epicureanism, which many people believed violated strict Christian teachings. In the 17th century, French Around 300 bce, the Greek fire was made up of tiny tetrahedra, clergyman Pierre Gassendi philosopher Epicurus refined which—with their sharp points and dedicated himself to reconciling Democritus’s ideas, by proposing edges—made it more mobile than Christianity with Epicureanism, the notion of atomic “swerve.” This earth, which was made of stable including atomism. He put forward idea, that atoms can deviate from and squat cubes. Plato’s student a version of Epicurean atomism in their expected actions, introduces Aristotle—who loathed Democritus which atoms have some of the unpredictability at the atomic scale and reputedly wanted to burn his physical features of the objects and allowed for the preservation works—proposed that there were they make up, such as solidity of “free will,” a core belief held by five elements (adding the celestial and weight. Most importantly, Epicurus. Atomic swerve could be element of “ether”) and no basic Gassendi’s theory stated that God seen as an ancient iteration of the unit of matter. Although Western had created a finite number of uncertainty at the core of quantum mechanics: since all objects have Each particle is fixed in one Particles are closely packed Particles move freely, wave-like properties, it is impossible position, giving solids a but random, giving liquid giving gas no fixed to accurately measure their position fixed shape and volume fixed volume but fluid shape shape or volume and momentum at the same time. The rejection of atomism Solid Liquid Gas Some of the most influential Greek philosophers rejected Dalton’s atomic theory proposed that solids, liquids, atomism and instead backed the and gases consist of particles (atoms or molecules). The theory of four or five fundamental motion of the particles and distances between them vary. elements. In 4th-century Athens, Plato proposed that everything was composed of five geometric solids (the Platonic solids), which gave types of matter their characteristics. For instance,

ENERGY AND MATTER 71 size; and atoms in gases are mobile and distant from each other, resulting in a substance with no fixed shape or volume. Oxygen atom Hydrogen atoms Water molecule The atom is divisible Atoms are the smallest ordinary 16 mass units 1 mass unit each 18 mass units object to have the properties of an element. However, they are no longer John Dalton proposed that atoms combine to produce considered indivisible. In the two molecules in simple ratios of mass. For example, two atoms of centuries since Dalton built modern hydrogen (each with a mass of 1) combine with one of oxygen atomic theory, it has been adapted (with a mass of 16) to create a water molecule with a mass of 18. to explain new discoveries. For instance, plasma—the fourth basic atoms at the beginning of the they can be bonded or broken state of matter after solids, liquids, universe, arguing that everything apart from other atoms to form and gases—can only be fully could be made up of these atoms new substances. explained if atoms can be divided and still be ruled by God. This idea further. Plasma is created when helped steer atomism back into the Dalton’s theory was confirmed electrons are delocalized (stripped mainstream among European in 1905, when Albert Einstein away) from their atoms. scholars, aided by the endorsement used mathematics to explain the of Isaac Newton and Robert Boyle. phenomenon of Brownian motion— In the late 19th and early 20th the jiggling of tiny pollen grains in century, scientists found atoms In 1661, Boyle published The water—using atomic theory. are made up of several subatomic Sceptical Chymist, which rejected According to Einstein, the pollen particles—electrons, protons, and Aristotle’s theory of five elements is constantly bombarded by the neutrons; and those neutrons and instead defined elements as random motion of many atoms. and protons are composed of “perfectly unmingled bodies.” Disputes over this model were even smaller, subatomic particles. According to Boyle, many different settled in 1911 when French This more complex model has elements such as mercury and physicist Jean Perrin verified allowed physicists to understand sulfur were made of many particles that atoms were responsible for phenomena that Democritus and of different shapes and sizes. Brownian motion. The concept Dalton could never have imagined, that atoms are bonded to or split such as radioactive beta decay and How elements combine from other atoms to form different matter–antimatter annihilation. ■ In 1803, British physicist John substances is simple but remains Dalton created a basic model of useful for understanding everyday [Epicurus] supposes not only all how atoms combine to form these phenomena, such as how atoms mixt bodies, but all others to be elements. It was the first model of iron and oxygen combine to built from a scientific basis. From form rust. produced by the various and his experiments, Dalton noticed casual occursions of atoms, that the same pairs of elements, States of matter moving themselves to and such as hydrogen and oxygen, Plato taught that the consistency fro … in the … infinite vacuum. could be combined in different of substances depended on the ways to form various compounds. geometric shapes from which they Robert Boyle They always did so with whole were made, but Dalton’s atomic number mass ratios (see diagram theory more accurately explains above). He concluded that each the states of matter. As illustrated element was composed of its own opposite, atoms in solids are closely atom with unique mass and other packed, giving them a stable shape properties. According to Dalton’s and size; atoms in liquids are atomic theory, atoms cannot be weakly connected, giving them divided, created, or destroyed, but indefinite shapes but mostly stable

72 IN CONTEXT FESAOXSOTRTTECHHNEEESION, KEY FIGURES Robert Hooke (1635–1703), STRETCHING AND SQUEEZING Thomas Young (1773–1829) BEFORE 1638 Galileo Galilei explores the bending of wooden beams. AFTER 1822 French mathematician Augustin-Louis Cauchy shows how stress waves move through an elastic material. 1826 Claude-Louis Navier, a French engineer and physicist, develops Young’s modulus into its modern form, the elastic modulus. 1829 German miner Wilhelm Albert demonstrates metal fatigue (weakening of metal due to stress). 1864 French physicist Jean Claude St-Venant and German physicist Gustav Kirchhoff discover hyperelastic materials. B ritish physicist and polymath Robert Hooke made many crucial contributions in the Scientific Revolution of the 17th century, but he became interested in springs in the 1660s because he wanted to make a watch. Up to then, timepieces were typically pendulum-driven, and pendulum clocks became erratic when used on ships. If Hooke could create a timepiece driven by a spring and not a pendulum, he could make a clock that could keep time at sea, thus solving the key navigational problem of the age—calculating a ship’s longitude (east–west distance) required accurate timekeeping. Using a spring

ENERGY AND MATTER 73 See also: Pressure 36 ■ Measuring time 38–39 ■ Laws of motion 40–45 ■ Kinetic energy and potential energy 54 ■ The gas laws 82–85 Metal wound as a coil Hanging a weight on a spring can be stretched coil spring makes it grow longer. and squeezed. The stretching of an The amount the spring Robert Hooke elastic material is grows longer varies Born on the Isle of Wight proportional to the directly with the weight. in 1635, Robert Hooke went force stretching it. on to make his way through Oxford University, where he As the extension, so the force. gained a passion for science. In 1661, the Royal Society pendulum also meant that Hooke summarized in a simple equation, debated an article on the could make a watch small enough phenomenon of rising water to be put in a pocket. F = kx, in which F is the force, x is in slender glass pipes; Hooke’s the distance stretched, and k is a explanation was published in Spring force a journal. Five years later, the In the 1670s, Hooke heard that constant (a fixed value). This simple Royal Society hired Hooke as Dutch scientist Christiaan Huygens law proved to be a key platform for their curator of experiments. was also developing a spring-driven understanding how solids behave. watch. Anxious not to be beaten, The range of Hooke’s Hooke set to work with master Hooke wrote his idea down scientific achievements is clockmaker Thomas Tompion to as a Latin anagram, ceiiinosssttvu, huge. Among his many make his watch. a common way for scientists at the inventions were the ear time to keep their work secret until trumpet and the spirit level. As Hooke worked with Tompion, they were ready to publish it. ❯❯ He also founded the science he realized that a coil spring must of meteorology, was the great unwind at a steady rate to keep The most ingenious book pioneer of microscope studies time. Hooke experimented with I ever read in my life. (discovering that living things stretching and squeezing springs Samuel Pepys are made from cells), and and discovered the simple developed the key law on relationship embodied in the law English diarist, elasticity, known as Hooke’s on elasticity that was later given on Hooke’s book Micrographia law. He also collaborated with his name. Hooke’s law says that Robert Boyle on the gas laws, the amount a spring is squeezed or and with Isaac Newton on the stretched is precisely proportional laws of gravity. to the force applied. If you apply twice the force, it stretches twice Key works as far. The relationship can be 1665 Micrographia 1678 “Of Spring” 1679 Collection of Lectures

74 STRETCHING AND SQUEEZING Deciphered, the anagram read Hooke’s spring balance used metallic bonds between their Ut tensio sic vis, which means the stretching of a spring to show the atoms. Although scientists would “as the extension, so the force”— weight of something. Hooke used this not understand this for another that is, the extension is proportional illustration to explain the concept in 200 years, the Industrial Revolution’s to the force. Once the watch was his “Of Spring” lecture. engineers soon realized the benefits made, Hooke went on to publish his of Hooke’s law when they began to ideas about springs two years later, constantly collided with each other build bridges and other structures in his 1678 pamphlet “de Potentia (anticipating the kinetic theory of with iron in the 1700s. Restitutiva” (“Of Spring”). He began gases by more than 160 years). by outlining a simple demonstration He suggested that squeezing a Engineering math for people to try at home—twist solid pushed the particles closer In 1694, Swiss mathematician wire into a coil, then hang different and increased collisions making it Jacob Bernoulli applied the weights to see how far the coil more resistant; stretching it reduced phrase “force per unit area” to the stretches. He had invented the collisions so that the solid became deforming force—the stretching or spring balance. less able to resist the pressure of squeezing force. Force per unit area the air around itself. came to be called “stress” and the However, Hooke’s paper was of amount the material was stretched lasting importance. Not only was it There are clear parallels or squeezed came to be known as a simple observation of how springs between Hooke’s law, published the “strain.” The direct relationship behaved, but it also provided a in 1678, and Boyle’s law (1662) on between stress and strain varies— key insight into the strength of gas pressure, which Robert Boyle for example, some materials will materials and the behavior of solids called “the spring of the air.” deform much more under a certain under stress—factors that are Furthermore, Hooke’s vision of stress than others. In 1727, another central to modern engineering. the role of invisible particles in the Swiss mathematician, Leonhard strength and elasticity of materials Euler, formulated this variation Mini springs seems remarkably close to our in stress and strain in different In trying to find an explanation modern understanding. We now materials as the coefficient (a for the behavior of springs, Hooke know that strength and elasticity number by which another number suspected that it was tied to a do indeed depend on a material’s fundamental property of matter. molecular structure and bonding. is multiplied) “E”, and Hooke’s He speculated that solids were Metals are hugely resilient, for equation became  = E, in which made of vibrating particles that instance, because of special  is the stress and  is the strain. Spring x When the FForce ( ) of weight 2 x Fforce ( ) is Fdoubled (2 ), stretches spring by spring stretches xa distance of twice as far to a 2xdistance of F Hooke’s law shows that the amount a 2F spring is squeezed or stretched is precisely proportional to the force applied. If you apply twice the force, it stretches twice as far.

ENERGY AND MATTER 75 Tensile strength When materials are stretched of iron wires of various lengths.” beyond their elastic limit, they We now know that structural will not return to their original steel has a high tensile strength size, even when the stress is of over 400 MPa (megapascals). removed. If they are stretched even further, they may eventually A pascal is the measurement snap. The maximum stress that unit for pressure: 1 Pa is defined a material can take in tension— as 1 N (newton) per square being pulled longer—before it meter. Pascals are named after snaps is known as its tensile mathematician and physicist strength, and is crucial in deciding Blaise Pascal. the suitability of a material for a particular task. Structural steel is often used for today’s suspension bridges, Some of the first tests of tensile such as the George Washington strength were carried out by Bridge in New Jersey (see left). Leonardo da Vinci, who wrote in Carbon nanotubes can be over 1500 about “Testing the strength a hundred times as strong as structural steel (63,000 MPa). Young’s measure strength of various materials to between a material’s stress During experiments carried out derive his measures. Young’s and strain is linear. Young’s in 1782, Italian scientist Giordano modulus is a measure of a chosen contributions about the strength of Riccati had discovered that steel material’s ability to resist stretching materials, and also their resistance was about twice as resistant to or squeezing in one direction. It is to stress, were of huge value to stretching and squeezing as brass. the ratio of the stress to the strain. engineers. Young’s modulus and Riccati’s experiments were very A material such as rubber has a low his equations opened the door to similar in concept to the work of Young’s modulus—less than 0.1 Pa the development of a whole series Euler and also, 25 years later, the (pascals)—so it will stretch a lot of calculation systems that allow work of Thomas Young. with very little stress. Carbon fiber engineers to work out the stresses has a modulus of around 40 Pa, and strains on proposed structures Young was, like Robert Hooke, which means it is 400 or more precisely before they are built. a British polymath. He earned times more resistant to stretching These calculation systems are his living as a physician but his than rubber. fundamental to constructing scientific achievements were wide everything from sports cars to ranging and his work on stress and Elastic limit suspension bridges. Total collapses strain in materials was a keystone Young realized that the linear of these structures are rare. ■ for 19th-century engineering. relationship (in which one quantity In 1807, Young revealed the increases directly proportionally A permanent alteration mechanical property that was to another) between a material’s of form limits the strength stress and strain works over a of materials with regard Euler’s coefficient “E”. In his limited range. This varies between materials, but in any material to practical purposes. remarkable series of lectures, subjected to too much stress, a Thomas Young during the same year, entitled nonlinear (disproportionate) “Natural Philosophy and the relationship between stress and Mechanical Arts,” Young strain will eventually develop. If introduced the concept of a the stress continues, the material “modulus” or measure to describe will reach its elastic limit (the point the elasticity of a material. at which it stops returning to its original length after the stress is Stress and strain removed). Young’s modulus only Young was interested in what he applies when the relationship called the “passive strength” of a material, by which he meant the elasticity, and he tested the

76 IN CONTEXT PRMTAHAARPETTITMDSEIMRNOUOFATTREIEONIN KEY FIGURE Daniel Bernoulli (1700–1782) FLUIDS BEFORE 1647 Blaise Pascal defines the transmission of pressure change in a static fluid. 1687 Isaac Newton explains a fluid’s viscosity in Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). AFTER 1757 Influenced by Bernoulli, Leonhard Euler writes on fluid mechanics. 1859 James Clerk Maxwell explains the macroscopic qualities of gases. 1918 German engineer Reinhold Platz designs the airfoil of the Fokker D.VII aircraft to produce greater lift. A fluid is defined as a phase of matter that has no fixed shape, yields easily to external pressure, deforms to the shape of its container, and flows from one point to another. Liquids and gases are among the most common types. All fluids can be compressed to some degree, but a great deal of pressure is required to compress a liquid by just a small amount. Gases are more easily compressed since there is more space between their atoms and molecules. One of the greatest contributors to the field of fluid dynamics—the study of how forces affect the motion of fluids—was Swiss mathematician and physicist Daniel Bernoulli,

ENERGY AND MATTER 77 See also: Pressure 36 ■ Laws of motion 40–45 ■ Kinetic energy and potential energy 54 ■ The gas laws 82–85 ■ The development of statistical mechanics 104–111 An increase in a fluid’s A decrease in a fluid’s speed causes a reduction speed causes an increase in its pressure. in its pressure. This principle is known as Daniel Bernoulli Bernoulli’s law. Born in 1700 in Groningen in whose 1738 Hydrodynamica and the fluid leaving the hole. the Netherlands into a family (Hydrodynamics) laid the basis The velocity at which the fluid of prominent mathematicians, for the kinetic theory of gases. His leaves the hole is proportional to Bernoulli studied medicine principle states that an increase in the height of fluid above the hole. at the University of Basel in the speed of motion of a fluid occurs Switzerland, Heidelberg simultaneously with a reduction in So, v = 2gh where g is the University in Germany, and its pressure or potential energy. the University of Strasbourg acceleration due to gravity. ❯❯ (at the time also in Germany). From bath tubs to barrels He gained a doctorate in Bernoulli’s principle built on the Top surface hAs droplets fall 1 anatomy and botany in 1721. discoveries of earlier scientists. The hand 2, they reach first major work on fluids was On h( ) of fluid Bernoulli’s 1724 paper Floating Bodies by the ancient Greek the same velocity on differential equations and philosopher Archimedes. This as fluids flowing the physics of flowing water 3rd-century bce text states that a from holes 1 and 2 earned him a post at the body immersed in a liquid receives Academy of Sciences in St. a buoyant force equal to the weight h Petersburg, Russia, where of the fluid it displaces, a fact that he taught and produced Archimedes is said to have realized h1 important mathematical when taking a bath, leading to the work. Hydrodynamica was famous cry “Eureka!” (“I found it!”). v1 1 published after his return to the University of Basel. He Centuries later, in 1643, Italian Fluid flows with worked with Leonhard Euler mathematician and inventor low velocity ( 1) on the flow of fluids, especially Evangelista Torricelli formulated 1 and doesn’t blood in the circulatory Torricelli’s law. This principle of h v v2 system, and also worked on fluid dynamics explains that the the conservation of energy in squirt far from fluids. He was elected to the velocity of flow (v) of a fluid leaving the container Royal Society of London in a hole in a container, where h is the 1750, and died in 1782 in v2 2 Basel, Switzerland, aged 82. depth of fluid above the hole, is the same as the velocity that a droplet v2 Key work of fluid would acquire falling freely Fluid flows with 1738 Hydrodynamica from a height h. If h increases, so (Hydrodynamics) vhigh velocity ( 2) do the velocity of the falling droplet and squirts further Under Torricelli’s law, fluid squirts from holes 1 and 2—placed at a depth h hof 1 and 2 from the top of the fluid— hin a container. As increases, the velocity of the fluid also increases. The same applies for droplets in free fall.

78 FLUIDS Pressure Aeronautics makes use of Bernoulli’s law: since air Boyle’s discovery that the pressure difference travels faster above a curved wing than below it, low of a given mass of gas, at a constant creates lift pressure above the wing causes the wing to lift. temperature, increases as the volume of the container holding Low pressure it decreases. Bernoulli argued Airflow is that gases are made up of huge faster over numbers of molecules moving the top of the randomly in all directions, and that wing, so the their impact on a surface causes air pressure pressure. He wrote that what is is lower experienced as heat is the kinetic energy of their motion, and that— Curve of the High pressure Airflow is slower given the random motion of top surface underneath the molecules—motion and pressure of the wing wing, so the air increase as temperatures rise. forces air to pressure is greater flow faster By drawing these conclusions, Bernoulli laid the basis of the Another breakthrough came easily, while high-viscosity fluids kinetic theory of gases. It was in 1647, when French scientist resist deformation and do not flow not widely accepted at the time Blaise Pascal proved that for an easily. According to Newton’s of publication in 1738, since the incompressible fluid inside a viscosity law, a fluid’s viscosity principle of the conservation of container, any change in pressure is its “shear stress” divided by its energy would not be proven for is transmitted equally to every part “shear rate.” While not all liquids more than a century. Bernoulli of that fluid. This is the principle follow this law, those that do are discovered that as fluids flow more behind the hydraulic press and called Newtonian liquids. Shear quickly, they produce less pressure the hydraulic jack. stress and rate can be pictured as and, conversely, when fluids flow a fluid sandwiched between two more slowly, they produce greater Pascal also proved that plates. One is fixed below the fluid, pressure. This became known hydrostatic pressure (the pressure and the other drifts slowly on the as Bernoulli’s law, which now has of a fluid due to the force of gravity) surface of the fluid. The fluid is many applications, such as the lift depends not on the weight of fluid subject to shear stress (the force generated by airflow in aeronautics. above it, but on the height between moving the upper plate, divided that point and the top of the liquid. by the plate’s area). The shear rate A diagram in Bernoulli’s In Pascal’s famous (if apocryphal) is the velocity of the moving plate Hydrodynamica depicts air molecules barrel experiment, he is said to divided by the distance between colliding with the walls of a container, have inserted a long, narrow, water- the plates. creating enough pressure to support a filled pipe into a water-filled barrel. weight resting on a movable surface. When the pipe was raised above Later studies showed that there the barrel, the increased hydrostatic are also different kinds of fluid flow. pressure burst the barrel. A flow is described as “turbulent” when it exhibits recirculation, Viscosity and flow eddying, and apparent randomness. In the 1680s, Isaac Newton studied Flows that lack these characteristics fluid viscosity—how easily fluids are described as “laminar.” flow. Almost all fluids are viscous, exerting some resistance to Bernoulli’s law deformation. Viscosity is a measure Bernoulli studied pressure, density, of a fluid’s internal resistance to and velocity in static and moving flow: fluids with low viscosity fluids. He was familiar both with possess low resistance and flow Newton’s Principia and with Robert

ENERGY AND MATTER 79 Nature always equation to describe a distribution As the atoms are cooled, they tends to act in the curve, now known as the Maxwell– start piling into the lowest Boltzmann distribution, that showed possible energy state. simplest ways. the range of different speeds of Lene Hau Daniel Bernoulli gas molecules. He also calculated the mean free path (the average Danish physicist, on superfluids Kinetic theory distance traveled by gas molecules While Bernoulli and other scientists between collisions) and the number exhibited zero viscosity, flowing laid the foundations for the kinetic of collisions at a given temperature, without losing kinetic energy. At theory of gases, Scottish scientist and found that the higher the such low temperatures, atoms James Clerk Maxwell attempted temperature, the faster the molecular almost stop moving. The scientists to quantify the nature of molecular movement, and the greater the had discovered a “superfluid.” motion within them. He explained number of collisions. He concluded the macroscopic qualities of gases: that the temperature of a gas is a When superfluids are stirred, their pressure, temperature, measure of its mean kinetic energy. vortices form that can rotate viscosity, and thermal conductivity. Maxwell also confirmed Italian indefinitely. They have greater Along with Austrian physicist scientist Amedeo Avogadro’s law thermal conductivity than any Ludwig Boltzmann, Maxwell of 1811, which states that equal known substance—hundreds of developed a statistical means volumes of two gases, at equal times greater than copper, which of describing this theory. temperatures and pressures, contain itself has high thermal conductivity. equal numbers of molecules. Superfluids called “Bose–Einstein In the mid-19th century, most condensates” have been used scientists assumed that all gas Superfluid discoveries experimentally as coolants, and in molecules travel at the same speed, Findings in the 20th century 1998 Danish physicist Lene Hau but Maxwell disagreed. In his 1859 revealed how fluids behave at used them to slow the speed of paper “Illustration of the Dynamic very cold temperatures. In 1938, light to 10mph (17km/h). Such “slow Theory of Gases,” he produced an Canadian physicists John F. Allen light” optical switches could cut and Don Misener and Russian power requirements dramatically. ■ physicist Pyotr Kapitsa discovered that a helium isotope behaved strangely when cooled to a temperature close to absolute zero. Below its boiling point of –452.1 °F (–268.94 °C) it behaved as a normal colorless liquid, but below –455.75 °F (–270.97 °C), it Applied fluid dynamics costs, and maintain quality. CFD CFD is a branch of fluid has its roots in the work of French dynamics that uses flow Predicting how fluids behave engineer Claude-Louis Navier. modeling and other tools to is fundamental to many modern Building on earlier work by Swiss analyze problems and predict technological processes. For physicist Leonhard Euler, in 1822 flows. It can take into account instance, factory-based food Navier published equations that variables such as changes production systems are designed applied Isaac Newton’s second law in a fluid’s viscosity due to to convey ingredients and final of motion to fluids. Later known temperature, altered flow foodstuffs—from binding syrups as Navier–Stokes equations after speeds caused by phase to soups—through pipes and further contributions from Anglo- change (such as melting, ducts. Integral to this process Irish physicist George Stokes in freezing, and boiling), and it is computational fluid dynamics the mid-19th century, they were can even predict the effects (CFD), a branch of fluid dynamics able to explain, for example, the of turbulent flow in parts of that can maximize efficiency, cut movement of water in channels. a pipe system.

80 FOSIEURATER-TCSHHEECINRGET HEAT AND TRANSFERS IN CONTEXT I n the early 1600s, thermoscopes The introduction of the first began to appear across Europe. successful steam engine in 1712 by KEY FIGURES These liquid-filled glass tubes British inventor Thomas Newcomen Joseph Black (1728–1799), (shown opposite) were the first ever sparked huge interest in heat. In James Watt (1736–1819) instruments for measuring how hot a 1761 lecture, Scottish chemist things are. In 1714, German-born Joseph Black spoke of experiments BEFORE Dutch scientist and instrument- he had done on melting. These 1593 Galileo Galilei creates maker Daniel Fahrenheit created showed that the temperature did not the thermoscope for showing the first modern thermometer, filled change when ice melted to water, changes in hotness. with mercury—he established his yet melting the ice required the famous temperature scale in 1724. same heat as it took to warm water 1654 Ferdinando II de Medici, Swedish scientist Anders Celsius from melting point to 140°F (60°C). Grand Duke of Tuscany, makes invented the more convenient Black realized that heat must be the first sealed thermometer. centigrade scale in 1742. absorbed when ice melted, and he 1714 Daniel Fahrenheit makes When ice melts to water, there is no temperature change. the first mercury thermometer. It takes the same amount Water must absorb 1724 Fahrenheit establishes of heat to melt water as heat when it melts—it a temperature scale. to raise its temperature becomes latent. 1742 Anders Celsius invents to 140°F (60°C). the centigrade scale. AFTER 1777 Carl Scheele identifies radiant heat. c. 1780 Jan Ingenhousz clarifies the idea of heat conduction. Heat and temperature must be different.

ENERGY AND MATTER 81 See also: The gas laws 82–85 ■ Internal energy and the first law of thermodynamics 86–89 ■ Heat engines 90–93 ■ Entropy and the second law of thermodynamics 94–99 ■ Thermal radiation 112–117 Galilean thermoscopes are tubes filled with a liquid (often ethanol), holding liquid-filled “floats.” Heat causes the density of all the liquids to change, making the floats rise or fall. The heat which disappears of cold water barely affects the cold Meanwhile, around 1780, Dutch in the conversion of water water’s temperature, but bubbling scientist Jan Ingenhousz pinned a little steam through the water down a third kind of heat transfer: into vapor is not lost, brings it quickly to a boil. conduction. This is when atoms but is retained in vapor. in a hot part of a solid vibrate a How heat moves lot, collide with their neighboring Joseph Black In 1777, an apothecary in Sweden, atoms, and by doing so transfer Carl Scheele, made a few simple energy (heat). Ingenhousz coated called the heat absorbed “latent yet crucial observations—such wires of different metals with wax, heat.” The latent (hidden) heat is as the fact that on a cold day you heated one end of each wire, and the energy required to change a can feel the heat of a glowing noted how quickly the wax melted material to another state. Black had fire a few feet away while still for each metal. ■ made a crucial distinction between seeing your breath on the cold heat, which we now know is a form air. This is radiant heat, and is of energy, and temperature, which infrared radiation (emitted from is a measurement of energy. a source, such as fire or the sun), which travels like light—radiation James Watt also discovered the is quite different from convective concept of latent heat in 1764. Watt heat. Convection is how heat was conducting experiments on moves through a liquid or gas; steam engines and noticed that heat causes the molecules and adding a little boiling water to a lot atoms to spread out—for example, when air above a stove is warmed it will then rise. James Watt Scottish engineer James Watt was Watt noticed that the engine one of the pivotal figures in the wasted a lot of steam, and history of the steam engine. The came up with a revolutionary son of a ship’s instrument-maker, improvement—introducing Watt became highly skilled in a second cylinder with one making instruments, in his running hot and the other cold. father’s workshop and in London This change transformed the as an apprentice. He then steam engine from a pump of returned to Glasgow to make limited use to the universal instruments for the university. source of power that drove the Industrial Revolution. In 1764, Watt was asked to repair a model Newcomen steam Key inventions engine. Before making practical adjustments to the model, Watt 1775 Watt steam engine conducted some scientific 1779 Copying machine experiments, during which he 1782 Horsepower discovered latent heat.

82 IN CONTEXT EPTLOHAWESAETIRIRCIANL KEY FIGURES Robert Boyle (1627–1691), THE GAS LAWS Jacques Charles (1746–1823), Joseph Gay-Lussac (1778–1850) BEFORE 1618 Isaac Beeckman suggests that, like water, air exerts pressure. 1643 Italian physicist Evangelista Torricelli makes the first barometer and measures air pressure. 1646 French mathematician Blaise Pascal shows that air pressure varies with height. AFTER 1820 British scientist John Herapath introduces the kinetic theory of gases. 1859 Rudolf Clausius shows that pressure is related to the speed of gas molecules. T he fact that gases are so transparent and seemingly insubstantial meant that it took natural philosophers a long time to appreciate that they have any physical properties at all. However, during the 17th and 18th centuries, European scientists gradually realized that, like liquids and solids, gases do indeed have physical properties. These scientists discovered the crucial relationship between the temperature, pressure, and volume of gases. Over a period of 150 years, studies carried out by three individuals—Robert Boyle in Britain and Frenchmen Jacques

ENERGY AND MATTER 83 See also: Pressure 36 ■ Models of matter 68–71 ■ Fluids 76–79 ■ Heat engines 90–93 ■ Changes of state and making bonds 100–103 ■ The development of statistical mechanics 104–111 Gases (including air) have physical properties, such as volume, pressure, and temperature. When a gas When a gas is When a gas is heated is subjected to heated, it takes up in a sealed container, pressure, the volume more space (the volume pressure increases. it occupies expands. it occupies expands). There is a three-way relationship between a gas’s volume, pressure, and temperature. Charles and Joseph Gay-Lussac— limit was instead the maximum after Robert Boyle. The youngest finally produced the laws that weight of water the pressure of son of Richard Boyle, 1st Earl of explain the behavior of gases. air outside could support. Cork and once the richest man in Ireland, Robert Boyle used his The pressure of air To prove his point, Torricelli inherited wealth to set up in ❯❯ Early in the 17th century, Dutch filled a tube closed at one end scientist Isaac Beeckman with mercury, a far denser liquid Evangelista Torricelli used a suggested that, just like water, than water, then turned it upside column of mercury to measure air air exerts pressure. The great down. The mercury dropped pressure. He deduced that air pressing Italian scientist Galileo Galilei to about 30 in (76 cm) below the down on the mercury in the cistern disagreed, but Galileo’s young closed end, then stopped falling. balanced the column in the tube. protégé Evangelista Torricelli He concluded that this was the not only proved Beeckman right maximum height the pressure but showed how to measure of air outside could support. The pressure by inventing the world’s height of mercury in the tube first barometer. would vary slightly in response to changes in air pressure, which Galileo had observed that a is why this is described as the siphon could never raise water above first barometer. 33 ft (10 m). At the time, vacuums were thought to “suck” liquids, and Boyle’s “spring of the air” Galileo wrongly thought this was Torricelli’s groundbreaking the maximum weight of water that invention paved the way for the a vacuum above it could draw up. discovery of the first of the gas In 1643, Torricelli showed that the laws, known as Boyle’s law,

84 THE GAS LAWS Air when reduc’d discovery to Boyle’s friend Richard same rate as it cooled. If plotted to half Its wonted extent Townley, and a friend of Townley, on a graph, it showed the volume physician Henry Power. Boyle would shrink to zero at –460°F, [volume] obtained … himself called the idea “Townley’s now known as absolute zero, and twice as forcible hypothesis,” but it was Boyle who the zero point on the Kelvin scale. made the idea well known. Charles had discovered a law that a Spring [pressure]. describes how volume varies with Robert Boyle Charles’s hot air discovery temperature provided the pressure Just over a century later, French stays steady. Oxford his own private scientific scientist and balloon pioneer research laboratory, the first ever. Jacques Charles added in a third Charles never wrote down his Boyle was a pioneering advocate element to the relationship between ideas. Instead they were described of experimental science and it volume and pressure—temperature. and clarified in the early 1800s in was here that he conducted crucial Charles was the first person to a paper written by fellow French experiments on air pressure that experiment with balloons filled with scientist Joseph Gay-Lussac, at he described in his book known in hydrogen rather than hot air, and on much the same time as English short as Touching the Spring and August 27, 1783, in Paris, he sent scientist John Dalton showed that Weight of the Air (published in up the first large hydrogen balloon. the rule applied universally to 1662). “Spring” was his word for all gases. pressure—he viewed squeezed In 1787, Charles conducted an air acting as if it had springs experiment with a container of gas A third dimension that recoil when pushed. in which the volume could vary Gay-Lussac added a third gas freely. He then heated up the gas law to those of Boyle and Charles. Inspired by Torricelli’s and measured the volume as the Known as Gay-Lussac’s law, barometer, Boyle poured mercury temperature rose. He saw that for it showed that if the mass and into a J-shaped glass tube sealed at each degree temperature rise, the volume of a gas are held constant the lower end. He could see that the gas expanded by 1⁄273 of its volume then pressure rises in line with the volume of air trapped in the lower at 32ºF (0°C). It contracted at the temperature. As was soon clear, tip of the J varied according to how much mercury he added. One weight In other words, there was a clear represents relationship between how much pressure inside mercury the air could support a fixed volume and its volume. container Two weights Boyle argued that the volume (v) represent increased of a gas and its pressure (p) vary pressure Particles at a low in inverse proportion, provided temperature move the temperature stays the same. slowly Mathematically this is expressed Hot particles as pv = k, a constant (an move faster and create more unchanging number). In other pressure words, if you decrease the volume of a gas, its pressure increases. Gay-Lussac’s law states that for a fixed mass Heat Some people credit the crucial of “ideal” gas (one with zero interparticle forces) at constant volume, the pressure is directly proportional to the absolute temperature. As more heat is applied, the particles move faster and pressure inside the container rises.

ENERGY AND MATTER 85 Joseph Gay-Lussac employed atmospheric balloons for several experiments. In this 1804 ascent with Jean-Baptiste Biot, he studied how Earth’s electromagnetic intensity varied with altitude. there is a simple three-way molecules varies exactly with the Joseph Gay-Lussac relationship between the volume, volume. This is called Avogadro’s pressure, and temperature of gases. hypothesis, and it explained Gay- French chemist and physicist This relationship applies to ideal Lussac’s discovery that gases Joseph Gay was the son of a gases (gases with zero interparticle combine in particular proportions. wealthy lawyer. The family forces), although it is approximately owned so much of the village true for all gases. Crucially, Avogadro’s hypothesis of Lussac in southwestern indicated that oxygen by itself France that, in 1803, both How gases combine existed as double-atom molecules, father and son incorporated Gay-Lussac went on to make which split to combine with Lussac into their names. another important contribution two atoms of hydrogen in water Joseph studied chemistry to our understanding of gases. In vapor—this must be so if there in Paris before working as a 1808, he realized that when gases are to be as many water molecules researcher in Claude-Louis combine, they do so in simple as there were molecules of hydrogen Berthollet’s laboratory. By age proportions by volume—and that and oxygen. 24, he had already discovered when two gases react, the volume the gas law named after him. of gases produced depends on the This work was important to the original volumes. So, two volumes development of atomic theory and Gay-Lussac was also a of hydrogen join to one volume of the relationship between atoms and balloon pioneer and in 1804 oxygen in a ratio of 2:1 to create molecules. It was also vital to the he ascended in a balloon to two volumes of water vapor. kinetic theory of gases developed more than 22,965 ft (7,000 m) by James Clerk Maxwell and others. with fellow French physicist Two years later, Italian scientist This states that gas particles move Jean-Baptiste Biot to sample Amedeo Avogadro explained this randomly and produce heat when air at different heights. From discovery by tying it in with the they collide. It helps explain the these experiments, he showed rapidly emerging ideas about atoms relationship between pressure, that the composition of the and other particles. He theorized volume, and temperature. ■ atmosphere does not change that at a given temperature and with height and decreasing pressure, equal volumes of all Compounds of gaseous pressure. In addition to his gases have the same number of substances with each other work on gases, Gay-Lussac “molecules.” Indeed, the number of are always formed in very also discovered two new elements, boron and iodine. simple ratios, so that representing one of the Key works terms by unity, the other 1802 “On the Expansion of is 1, 2, or at most 3. Gases and Vapors,” Annals Joseph Gay-Lussac of Chemistry 1828 Lessons of Physics

86 IN CONTEXT IOTSHFECTOHENNESEUTRNAGINYVTERSE KEY FIGURE William Rankine ILNATWERONFATLHEENREMROGDYYANNADMTICHSE FIRST (1820–1872) BEFORE 1749 Émilie du Châtelet implicitly introduces the idea of energy and its conservation. 1798 Benjamin Thompson develops the idea that heat is a form of kinetic energy. 1824 French scientist Sadi Carnot concludes there are no reversible processes in nature. 1840s James Joule, Hermann von Helmholtz, and Julius von Mayer introduce the theory of conservation of energy. AFTER 1854 William Rankine introduces potential energy. 1854 Rudolf Clausius publishes his statement of the second law of thermodynamics. I n the late 18th century, scientists had begun to understand that heat was different from temperature. Joseph Black and James Watt had shown that heat was a quantity (while temperature was a measurement), and the development of steam engines throughout the Industrial Revolution focused scientific interest on how exactly heat gave those engines such power. At the time, scientists followed the “caloric” theory—the idea that heat was a mysterious fluid or weightless gas called caloric that flowed from hotter to colder bodies. The connection between heat and movement had long

ENERGY AND MATTER 87 See also: Kinetic energy and potential energy 54 ■ The conservation of energy 55 ■ Heat and transfers 80–81 ■ Heat engines 90–93 ■ Entropy and the second law of thermodynamics 94–99 ■ Thermal radiation 112–117 Generating electricity The burning of fossil fuels (coal, heat energy into kinetic energy), oil, and natural gas) to generate which generates electricity electricity is a classic example of (electrical potential energy). a chain of energy conversions. It Finally, the electricity is begins with solar energy from converted into useful forms the sun’s rays. Plants convert the of energy, such as light in light solar energy into chemical energy bulbs or sound in loudspeakers. as they grow—this then becomes Throughout all of these “stored” as chemical potential conversions, the total energy energy in the chemical bonds always remains the same. made. The stored energy is During the entire process, concentrated as the plants are energy is converted from one compressed into coal, oil, and gas. form to another, but it is never created or destroyed, and there The fuel is burned, creating is no loss of energy when one heat energy, which heats water form of energy is changed to to produce steam, and the steam another form. makes turbines turn (converting been recognized, but no one fully the metal. It seemed that the heat happen, just like muscle power. appreciated how fundamental must be in the movement. In other They would come to realize that all this link was. In the 1740s, French words, heat is kinetic energy—the forms of energy are interchangeable. mathematician Émilie du Châtelet energy of movement. But few people studied the concept of momentum accepted this idea and the caloric In 1840, Julius von Mayer had and introduced the idea of theory held for another 50 years. been looking at the blood of sailors mechanical “energy,” which is in the tropics and found that blood the capacity to make things The breakthrough came from returning to the lungs was still rich happen—though she did not several scientists simultaneously in in oxygen. In colder locations, a name it as such at the time. the 1840s, including James Joule person’s blood would return to the But it was becoming clear that in Britain, and Hermann von lungs carrying a lot less oxygen. moving objects had energy, later Helmholtz and Julius von Mayer in This meant that, in the tropics, the identified as “kinetic” energy. Germany. What they all saw was body needed to burn less oxygen that heat was a form of energy with to keep warm. Mayer’s conclusion Heat is energy the capacity to make something was that heat and all forms of energy In 1798, American-born physicist (including those in his observations: Benjamin Thompson, later known You see, therefore, that living muscle power, the heat of the as Count Rumford, conducted an force may be converted into body, and the heat of the sun) are experiment in a cannon foundry interchangeable and they can be in Munich. He wanted to measure heat, and heat may be changed from one form to another, the heat generated by the friction converted into living force. but never created. The total energy when the barrels of cannons were will remain the same. However, bored out. After many hours of James Joule Mayer was a medic and physicists continuous friction from a blunt paid his work little attention. boring machine, heat was still being generated, yet there was Converting energy no change in the structure of the Meanwhile, young James cannon’s metal—so it was clear Joule began experimenting in a that nothing physical (and no laboratory in the family home in caloric fluid) was being lost from Salford near Manchester. In 1841, he figured out just how much ❯❯

88 INTERNAL ENERGY AND THE FIRST LAW OF THERMODYNAMICS heat is made by an electric current. they expand—the basis of The commonest objects He then experimented with ways of refrigeration. Joule also made the are by science rendered converting mechanical movement first clear estimate of the average into heat and developed a famous speed of molecules in a gas. precious. experiment in which a falling William Rankine weight turns a paddle wheel in The first law water, heating the water (shown Throughout the next decade, Gottfried Leibniz had referred to below). By measuring the rise in Helmholtz and Thomson—along this as vis visa or “living force,” the water temperature Joule could with German Rudolf Clausius and which was a term still used by work out how much heat a certain Scotsman William Rankine—began Rankine. But it was only in the amount of mechanical work would to pull their findings together. 1850s that its full significance create. Joule’s calculations led him Thomson first used the phrase emerged, and the word “energy” to the belief that no energy is ever “thermo-dynamic” in 1849 to sum in its modern sense began to be lost in this conversion. But like up the power of heat. Over the used regularly. Mayer’s research, Joule’s ideas next year, Rankine and Clausius were initially largely ignored by (apparently independently) Clausius and Rankine worked the scientific community. developed what is now called on the concept of energy as a the first law of thermodynamics. mathematical quantity—in the Then, in 1847, Hermann von Like Joule, Rankine and Clausius same way that Newton had Helmholtz published a key paper, focused on work—the force used to revolutionized our understanding which drew from his own studies move an object a certain distance. of gravity by simply looking at it and those of other scientists, Throughout their studies, they saw as a universal mathematical rule, including Joule. Helmholtz’s paper a universal connection between without actually describing how summarized the theory of the heat and work. Significantly, Clausius it works. They were finally able conservation of energy. The same also began to use the word “energy” to banish the caloric idea of heat year, Joule presented his work at a to describe the capacity to do work. as a substance. Heat is energy, a meeting of the British Association capacity to do work, and heat in Oxford. After the meeting, Joule In Britain, Thomas Young had must therefore conform to another met William Thomson (who later coined the word “energy” in 1802 simple mathematical rule: the law became Lord Kelvin), and the two to explain the combined effect of conservation of energy. This law of them worked on the theory of of mass and velocity. Around the shows that energy cannot be gases and on how gases cool as late 17th century, German polymath created or destroyed; it can only be transferred from one place Winding Joule’s paddle wheel to another or converted into other drum experiment featured forms of energy. In simple terms, a paddle wheel inside a the first law of thermodynamics Pulley tank of water, powered is the law of conservation of energy by falling weights— applied to heat and work. Weight this caused the water temperature to rise. Clausius’ and Rankine’s ideas Water in Joule measured the and research had been inspired by insulated tank temperature to calculate trying to understand theoretically how much heat a certain how engines worked. So Clausius Paddle wheel amount of mechanical looked at the total energy in a closed turns and work would create. heats water Thermometer

ENERGY AND MATTER 89 system (a system where matter things. So he made a useful William Rankine cannot be moved in or out, but division of energy into two kinds: energy can be moved—like in the stored energy and work energy. Scotsman William Rankine cylinders of a steam engine) and Stored energy is energy held still, was born in Edinburgh in talked about its “internal energy.” ready to move—like a compressed 1820. He became a railroad You cannot measure the internal spring or a skier standing at the engineer, like his father, but energy of the system, but you can top of a slope. Today we describe having become fascinated by measure the energy going in and stored energy as potential energy. the science behind the steam out. Heat is a transfer of energy into Work is either the action done to engines he was working with, the system and a combination of store up the energy or it is the he later switched to studying heat and work is a transfer out. movement when that energy science instead. is unleashed. Rankine’s categorizing According to the energy of energy in this way was a simple Along with scientists conservation law, any change in and lastingly effective way of Rudolf Clausius and William internal energy must always be looking at energy in its resting Thomson, Rankine became the difference between the energy and moving phases. one of the founding fathers of moving into the system and the thermodynamics. He helped energy that is moving out—this also By the end of the 1850s, the establish the two key laws of equates to the total difference remarkable work of du Châtelet, thermodynamics, and defined between heat and work. Put more Joule, Helmholtz, Mayer, Thomson, the idea of potential energy. heat into the same system and you Rankine, and Clausius had Rankine and Clausius also get more work out, and also the other transformed our understanding independently described the way around—this adheres to the first of heat. This pioneering group of entropy function (the idea law of thermodynamics. This must young scientists had revealed the that heat is transferred in a be so because the total energy in the reciprocal relationship between disordered way). Rankine universe (all energy surrounding heat and movement. They had wrote a complete theory of the the system) is constant, so the also begun to understand and show steam engine, and of all heat transfers in and out must match. the universal importance of this engines, and contributed to relationship. They summed it up in the final move away from the Rankine’s categories the term “thermodynamics”—the caloric theory of heat as a Rankine was a mechanical idea that the total amount of energy fluid. He died in Glasgow, engineer, which meant that he in the universe must always be at the age of 52, in 1872. liked to put a practical spin on constant and cannot change. ■ Heat going into a closed system usually raises its internal energy. The amount of Work going out energy in the universe of the system lowers is constant. its energy. The change in internal energy is therefore the Key works difference between the heat going in and work going out. 1853 “On the General Law of Transformation of Energy” 1855 “Outlines of the Science of Energetics”

90 IN CONTEXT HMAEOCATATIUOCSNAENOBFE KEY FIGURE Sadi Carnot (1796–1832) HEAT ENGINES BEFORE c.50 ce Hero of Alexandria builds a small steam-driven engine known as the aeolipile. 1665 Robert Boyle publishes An Experimental History of Cold, an attempt to determine the nature of cold. 1712 Thomas Newcomen builds the first successful steam engine. 1769 James Watt creates his improved steam engine. AFTER 1834 British–American inventor Jacob Perkins makes the first refrigerator. 1859 Belgian engineer Étienne Lenoir develops the first successful internal combustion engine. I t is hard to overestimate the impact of the coming of the steam engine in the 18th century. Steam engines gave people a previously unimaginable source of power. They were practical machines, built by engineers, and were put to use on a grand scale to drive the Industrial Revolution. Scientists became fascinated by how the awesome power of steam engines was created, and their curiosity drove a revolution with heat at its heart. The idea of steam power is ancient. As long ago as the 3rd century bce, a Greek inventor in Alexandria called Ctesibius realized that steam jets out

ENERGY AND MATTER 91 See also: Kinetic energy and potential energy 54 ■ Heat and transfers 80–81 ■ Internal energy and the first law of thermodynamics 86–89 ■ Entropy and the second law of thermodynamics 94–99 To take away today from The first successful steam engine compatriot Joseph Black, that it England her steam-engines was invented by Thomas Newcomen to is heat, not temperature, that would be to take away at the pump water from mines. It worked by provides the motive power of same time her coal and iron. cooling steam in a cylinder to create a steam. Watt also realized that the partial vacuum and draw up a piston. efficiency of steam engines could Sadi Carnot be hugely improved by using not of air against the pulling power of one cylinder but two—one which powerfully from the spout of a eight strong horses. This discovery was kept hot all the time and a water-filled container heated over a opened up a new way of using separate cold one to condense fire. He began to play with the idea steam, very different from Hero’s the steam. Watt also introduced a of an aeolipile or wind ball, a hollow jets. French inventor Denis Papin crank to convert the up-and-down sphere on a pivot. When the water realized in the 1670s that if steam motion of the piston into the within boiled, the expanding steam trapped in a cylinder cools and rotary motion needed to drive a escaped in jets from two curved, condenses, it shrinks dramatically wheel. This smoothed the action directional nozzles, one on each to create a powerful vacuum, strong of the piston strokes to maintain side. The jets set the sphere enough to draw up a heavy piston, a constant power. Watt’s innovations spinning. About 350 years later, moving component of engines. So, were extraordinarily successful and another Alexandrian, named Hero, instead of using steam’s expansive could be said to have launched created a working design for an power, the new discovery utilized the age of steam. aeolipile—replicas of which have the massive contraction when it since been built. It is now known cools and condenses. Energy and that when liquid water turns to thermodynamics vapor (steam), the bonds holding Steam revolution The efficiency of steam engines its molecules to each other break In 1698, English inventor Thomas intrigued young French military down, causing it to expand. Savery built the first large steam engineer Sadi Carnot. He visited engine using Papin’s principle. factory after factory, studying not Hero’s device, though, was However, Savery’s engine used only their steam engines but also ❯❯ simply a plaything, and although high-pressure steam that made various inventors experimented it dangerously explosive and with steam, it was another 1,600 unreliable. A much safer engine, years before the first practical steam which used low-pressure steam, engine was built. The breakthrough was built by Devon iron seller was the discovery of the vacuum Thomas Newcomen in 1712. and the power of air pressure in Although Newcomen’s engine was the 17th century. In a famous so successful that it was installed demonstration in 1654, German in thousands of mines across physicist Otto von Guericke showed Britain and Europe by 1755, it was that atmospheric pressure was inefficient because the cylinder powerful enough to hold together had to be cooled at every stroke the two halves of a sphere drained to condense the steam, and this used a huge amount of energy. In the 1760s, to improve on the Newcomen engine, Scottish engineer James Watt conducted the first scientific experiments on the way heat moves in a steam engine. His experiments led to his discovery, along with his

92 HEAT ENGINES Water power Heat engines depend on a heat was a fluid. However, this depends on a difference temperature difference. misconception allowed him to in water levels that allows see a key analogy between water and steam power. Water power water to fall. depends on a head of water, a difference in water levels, that For a heat engine to work, there must be a cold allows water to fall. In the same place for heat to flow to. way, Carnot saw that a heat engine depends on a head of heat that The engine is driven by the flow of heat allows a “fall of caloric.” In other from hot to cold. words, for a heat engine to work there must not just be heat, but those driven by water power. systems driven by heat. This was also a cold place for it to flow to. In 1824, he wrote a short book, the first recognition of the true The engine is driven not by heat Reflections On the Motive Power significance of heat in the universe, but by the flow of heat from hot to of Heat. Carnot realized that heat is and provided the launchpad for the cold. So the motive power is the the basis of all motion on Earth, science of thermodynamics. difference between hot and cold, driving the winds and ocean not the heat by itself. currents, earthquakes and other Seeing and comparing water geological shifts, and the body’s and steam power in factories gave Perfect efficiency muscle movements. He saw the Carnot a key insight into the nature Carnot had a second key insight— cosmos as a giant heat engine made of heat engines. Like most of his that for the generation of maximum of countless smaller heat engines, contemporaries, he believed in the power there must be no wasted caloric theory—the false idea that flow of heat at any place or time. An ideal engine is one in which all the heat flow is converted into useful movement. Any loss of heat that does not generate motive power is a reduction in the heat engine’s efficiency. To model this, Carnot outlined a theoretical ideal heat engine reduced to its basics. Now known Sadi Carnot Born in Paris in 1796, Sadi Carnot In 1824, Carnot wrote his came from a family of renowned groundbreaking Reflections on scientists and politicians. His the Motive Power of Heat, which father Lazare was a pioneer in drew attention to the importance the scientific study of heat, as of heat engines and introduced well as ranking high in the the Carnot cycle. Little attention French Revolutionary Army. was paid to Carnot’s work Sadi followed his father into the at the time and before its military academy. After graduating significance as the starting in 1814, he joined the military point of thermodynamics could engineers as an officer and was be appreciated, he died of sent around France to make a cholera in 1832. report on its fortifications. Five years later, having become Key work fascinated by steam engines, he retired from the army to 1824 Reflections on the Motive pursue his scientific interests. Power of Heat

ENERGY AND MATTER 93 Carnot’s cycle Hot reservoir Cold reservoir Insulation The production of heat alone Movable Isothermal Ideal gas Adiabatic is not sufficient to give birth piston expansion particle that expansion Heated is cooled to the impelling power: ideal gas Heat it is necessary that there particle from hot reservoir should also be cold. Sadi Carnot Stage 1: There is a heat transfer from Stage 2: The gas, now insulated from the hot reservoir to the gas in the the reservoirs, continues to expand as a Carnot engine, this ideal cylinder. The gas expands, pushing up as weight is lifted from the piston. engine works in a cycle in four the piston. This stage is isothermal The gas cools as it expands, though stages. First, the gas is heated by because there is no temperature no heat is lost from the system overall. conduction from an external source change in the system. This expansion is adiabatic. (such as a reservoir of hot water) and expands. Second, the hot gas Heat Isothermal Ideal gas Adiabatic is kept insulated (inside a cylinder, released compression particle at compression for example) and as it expands it from Temperature normal does work on its surroundings system remains the temperature (such as pushing on a piston). As it same expands, the gas cools. Third, the surroundings push the piston Stage 3: Weight is added above Stage 4: More weight is added on down, compressing the gas. Heat the piston. Since heat is now able the piston, compressing the gas is transferred from the system to to transfer from the cylinder into in the cylinder. Since the gas is the cold reservoir. Finally, as the the cold reservoir, the gas does not now insulated from the reservoirs system is kept insulated and the increase in temperature, so this again, the compression causes its piston continues to push down, stage is isothermal. temperature to increase adiabatically. the gas temperature rises again. (the efficiency) can be expressed as Carnot’s work on heat was only just In the first two stages the gas is beginning when he died of cholera expanding, and in the second two (TH  TC)/TH = 1 (TC /TH). Even at the age of 36. Unfortunately, his it is contracting. But the expansion copious notes were burned to and contraction each go through two Carnot’s ideal engine is far from destroy the infection, so we will phases; isothermal and adiabatic. 100 percent efficient, but real never know how far he got. Two In the Carnot cycle, isothermal engines are much less efficient years after his death, Benoît Paul means there is an exchange of than Carnot’s engine. Unlike Émile Clapeyron published a heat with the surroundings, but no Carnot’s ideal engine, real engines summary of Carnot’s work using temperature change in the system. use irreversible processes. Once graphs to make the ideas clearer, Adiabatic means no heat goes oil is burned, it stays burned. So and updating it to remove the either into or out of the system. the heat available for transfer is caloric element. As a result, continually reduced. And some of Carnot’s pioneering work on Carnot calculated the efficiency the engine’s work output is lost as heat engines revolutionized of his ideal heat engine: if the heat through the friction of moving our understanding of the key parts. Most motor vehicle engines role of heat in the universe hottest temperature reached is TH are barely 25 percent efficient, and and laid the foundations of the and the coldest is TC, the fraction of even steam turbines are only 60 science of thermodynamics. ■ percent efficient at best, which heat energy that comes out as work means a lot of heat is wasted.

THE ENTROPY MOTFEATNHXDE IUSMNITVUEORMSAE ENTROPY AND THE SECOND LAW OF THERMODYNAMICS



96 ENTROPY AND THE SECOND LAW OF THERMODYNAMICS IN CONTEXT I n the mid-1800s, a group of No other part of science has physicists in Britain, Germany, contributed as much to the KEY FIGURE and France revolutionized liberation of the human spirit Rudolf Clausius (1822–1888) the understanding of heat. These scientists, including William as the second law of BEFORE Thomson and William Rankine in thermodynamics. 1749 French mathematician Britain; Hermann von Helmholtz, and physicist Émilie du Julius von Mayer, and Rudolf Peter William Atkins Châtelet introduces an early Clausius in Germany; and Sadi idea of energy and how it Carnot in France showed that British chemist is conserved. heat and mechanical work are interchangeable. They are both French military scientist Sadi 1777 In Sweden, pharmacist manifestations of what came to Carnot had envisaged an ideal Carl Scheele discovers how be called energy transfers. heat engine in which, contrary to heat can move by radiating what happened in nature, energy through space. In addition, the physicists found changes were reversible: when one that the interchange of heat and form of energy was converted to 1780 Dutch scientist Jan mechanical work is entirely another, it could be changed back Ingenhousz discovers that heat balanced: when one form of energy again with no loss of energy. In can be moved by conduction increases, another must decrease. reality, however, a large portion of through materials. The total energy can never be lost; the energy used by steam engines it simply switches form. This was not translated into mechanical AFTER came to be called the law of the movement but lost as heat. Even 1876 American scientist conservation of energy and was though engines of the mid-1800s Josiah Gibbs introduces the the first law of thermodynamics. It were more efficient than they had idea of free energy. was later broadened and reframed been in the 1700s, they were far by Rudolf Clausius as “the energy 1877 Austrian physicist of the universe is constant.” Ludwig Boltzmann states the relationship between entropy Heat flow and probability. Scientists quickly realized that there was another fundamental theory of thermodynamics concerning heat flow. In 1824, Rudolf Clausius The son of a headmaster and summaries of the laws of pastor, Rudolf Clausius was born thermodynamics: “The energy in Pomerania, Prussia (now in of the universe is constant” and Poland) in 1822. After studying “The entropy of the universe at the University of Berlin, he tends to a maximum.” Clausius became a professor at Berlin’s died in Bonn in 1888. Artillery and Engineering School. In 1855, he became professor of Key works physics at the Swiss Federal Institute of Technology in Zurich. 1850 “On the Moving Force He returned to Germany in 1867. of Heat” 1856 “On a Modified Form The publication of his paper of the Second Fundamental “On the Moving Force of Heat” Theorem in the Mechanical in 1850 marked a key step in the Theory of Heat” development of thermodynamics. 1867 The Mechanical Theory In 1865, he introduced the concept of Heat of entropy, leading to his landmark

ENERGY AND MATTER 97 See also: Kinetic energy and potential energy 54–55 ■ Heat and transfers 80–81 ■ Internal energy and the first law of thermodynamics 86–89 ■ Heat engines 90–93 ■ Thermal radiation 112–117 Clausius realized that in a real heat engine, it is impossible to extract an supplies available for work are not inexhaustible: in time, they are all Qamount of heat ( H) from a hot reservoir and use all the extracted heat to do reduced to heat and so everything W Qwork ( ). Some of the heat ( C) must be transferred to a cold reservoir. A has a limited lifespan. Qperfect heat engine, in which all the extracted heat ( H) can be used to Wdo work ( ), is impossible according to the second law of thermodynamics. Energy of the universe In the early 1850s, Clausius and QH QH Hot reservoir Thomson independently began to W W Cold reservoir speculate on whether Earth itself was a heat engine with a finite QC Perfect heat engine lifespan, and whether this could be true of the entire universe. In Real heat engine 1852, Thomson speculated that there would be a time when the below a 100 percent conversion rate. initially thought. It became clear sun’s energy would run out. The It was partly the scientists’ efforts to that heat engines are doomed to implications of this to Earth meant understand this energy loss that led inefficiency. However cleverly they that Earth must have a beginning them to discover the second law of are designed, some energy will and an end—a new concept. thermodynamics. Clausius realized, always leak away as heat, whether Thomson then attempted to work as did Thomson and Rankine, that as friction, exhaust (gas or steam), out how old Earth must be by heat flows only one way: from hot to or radiation, without doing any calculating the time it would cold, not from cold to hot. useful work. have taken to cool to its present temperature, given how long the External help Work is done by the flow of sun could generate heat as it slowly In 1850, Clausius wrote his first heat from one place to another. To collapsed under its own gravity. statement of the second law of Clausius and the other scientists thermodynamics: “heat cannot by researching thermodynamics, it Thomson’s calculation showed itself flow from a colder body to a soon became clear that if work is Earth to be just a few million years warmer one.” Clausius was not done by heat flow, there must be old, which brought him into bitter saying that heat can never flow from a concentration of energy stored conflict with geologists and cold to hot, but that it needs external in one place in order to initiate the evolutionists, who were convinced help to do so. It needs to do work: the flow; one area must be hotter than that it was considerably older. ❯❯ effect of energy. This is how modern another. However, if heat is lost refrigerators operate. Like heat every time work is done, then heat engines in reverse, they transfer gradually spreads out and becomes heat from cold regions inside the dissipated. Concentrations of heat device to hot regions outside, become smaller and rarer until no making the cold regions even cooler. more work can be done. Energy Such a transfer requires work, which is supplied by an expanding coolant. An eruption of the Sakurajima volcano in Japan transfers thermal Clausius soon realized that the energy from Earth’s super-hot interior implications of a one-way flow to the cooler exterior, demonstrating of heat were far more complex than the second law of thermodynamics.

98 ENTROPY AND THE SECOND LAW OF THERMODYNAMICS The explanation for the discrepancy more about the universe than I have intentionally formed is that nothing was then known Thomson could and no longer the word entropy so as to be about radioactivity and Einstein’s accept the heat death theory, as similar as possible to the 1905 discovery that matter can be although the universe’s ultimate turned into energy. It is the energy fate remains unknown. word energy. of matter that has kept Earth warm Rudolf Clausius for much longer than solar radiation Stating the second law alone. This pushes Earth’s history In 1865, Clausius introduced the random mess of low-level energy. back more than 4 billion years. word “entropy” (coined from the As a result, entropy is now Greek for “intrinsic” and “direction”) considered a measure of the degree Thomson went further still to sum up the one-way flow of heat. of dissipation, or more precisely and suggested that in time all the The concept of entropy brought the degree of randomness. But energy in the universe would be together the work that Clausius, Clausius and his peers were dissipated as heat. It would spread Thomson, and Rankine had been talking specifically about heat. out as a uniform “equilibrium” doing for the previous 15 years In fact, Clausius defined entropy mass of heat, with no concentrations as they developed what was to as a measure of the heat that a body of energy at all. At that point, become the second law of transfers per unit of temperature. nothing further would be able to thermodynamics. Yet entropy came When a body contains a lot of heat change in the universe and it would to mean much more than just one- but its temperature is low, the effectively be dead. However, way flow. As Clausius’s ideas took heat must be dissipated. Thomson also asserted that the shape, entropy developed into a “heat death” theory depended on mathematical measure of just how there being a finite amount of much energy dissipated. matter in the universe, which he believed was not the case. Clausius argued that because Because of this, he said, its a concentration of energy is needed dynamic processes would carry to hold the shape and order of the on. Cosmologists now know much universe, dissipation leads to a The fate of all things Clausius summed up his version of the second law of thermodynamics as “the entropy of the universe tends to a maximum.” Because this wording is vague, many people now imagine it applies to everything. It has become a metaphor for the fate of all things—which will ultimately be consumed by chaos. In 1854, however, Clausius was specifically talking about heat and energy. His definition contained the first mathematical formulation of entropy, though at the time he Crab Nebula is a supernova, an exploded star. According to the heat death theory, the heat released into space by such explosions will eventually lead to a thermal equilibrium.