CHARLES’S GAS LAW

France, 1787. At constant pressure, the volume occupied by a ﬁxed amount of gas is directly proportional to its absolute temperature.

Cross Reference: Joseph Louis Gay-Lussac, Leonardo da Vinci, Guillaume Amontons, and Amontons’s Law of Friction.

In 1787, American inventor John Fitch launched a steamboat on the Delaware River. William Herschel discovered two moons of Uranus, which his sons later named Titania and Oberon.

The Constitutional Convention in Philadelphia adopted the U.S.

Constitution.

Charles’s Gas Law, also known as Gay-Lussac’s Law, states that the volume occupied by a ﬁxed amount of gas varies directly with the absolute temperature (i.e., the temperature in degrees kelvin). The law can be expressed as

V=kT,

whereVis the volume at a constant pressure,Tis the temperature, and kis a constant. French chemist and physicist Joseph Louis Gay-Lussac (1778–1850) ﬁrst published the law in 1802, where he referenced unpub- lished work from around 1787 by French chemist and physicist Jacques Charles.

Physicists have discovered that a gas increases approximately by 1/273 (0.003663) of its volume at 0^◦C for each ^◦C rise of temperature. Very slight deviations from 1/273 have been observed, but because they are so slight, the constant 1/273 is generally used as an approximate expansion coefficient for gases. For example, French physicist Henri-Victor Regnault (1810–1878) found values of 0.0036613 for hydrogen and 0.0037099 for car- bon dioxide. Note that although the coefficients of expansion of different gases are nearly the same, different solids or liquids have very different coefficients.

As the temperature of the gas increases, the gas molecules move more quickly and hit the walls of their container with more force—thus increas- ing the volume of gas, assuming that the container volume is able to expand. For a more speciﬁc example, consider warming the air within a balloon. As the temperature increases, the speed of the moving gas molecules increases inside the surface of the balloon. This in turn increases the rate at which the gas molecules bombard the surface. Because the surface of the balloon can stretch, the surface expands as a result of the increased internal bombardment. The volume of gas increases, and its

density decreases. The act of cooling the gas inside a balloon will have the opposite effect and cause the pressure to be reduced and the balloon to shrink.

Charles’s Law is sometimes expressed as V1

T₁ = V2

T₂,

where the subscripts 1 and 2 refer to the volume and temperature of a gas before and after the volume or temperature has changed. Notice that we do not need to know the value of the constantkin order to make practical use of the law when comparing two volumes. For example, let us suppose we have a sample of gas at 15^◦C and at one atmosphere pressure, with a volume of 2.50 liters. We want to know what volume this gas will occupy at 40^◦C at the same atmospheric pressure. In other words, for this problem, the pressure remains the same, while the volume and temperature change.

Our ﬁrst step is to convert the temperature in degrees Celsius to degrees kelvin by adding 273 to both temperature values. Thus, we have 2.50 L÷ 288^◦K =V2 ÷ 313^◦K; thus,V2= 2.72 liters. The temperature has increased slightly, and the volume also increases slightly.

Jacques Charles (1746–1823), French mathematician, physicist, and inventor who studied the thermal expansion of gases and who was the ﬁrst person to ascend in a hydrogen balloon (with Nicolas Robert).

CURIOSITY FILE: In the world of ballooning, Charles invented the nacelle, the basket suspended beneath the balloon by ropes and held in place by a hoop. This nacelle holds the passengers and their belongings. • Local peasants were so frightened by the landing of one of Charles’s balloons that they tore it apart, believing it to be the work of the devil.

Almost nothing is known of Charles’s family or his upbringing, except that he received a liberal, nonscientiﬁc education. [Later] Charles published almost nothing of signiﬁcance.

—J. B. Gough, “Jacques Charles,” inDictionary of Scien- tiﬁc Biography

Charles’s view from the balloon was phenomenal, and as soon as they touched down, the ecstatic Jacques Charles jumped from the basket, crying out to the assembled onlookers his newly sworn creed: “I care not what may 166 ^| a r c h i m e d e s t o h a w k i n g

be the condition of the Earth—it is the sky that is for me now. What serenity! What a ravishing scene!”

—Richard Hamblyn,The Invention of Clouds

Jacques Charles was born in Beaugency-sur-Loire, France, and later conducted research in many fields that ranged from electricity to gases to the flight of balloons. Very little is known about his family and early life, but we do know his education was liberal and did not focus on science. His first job was a low-level position in the bureau of finances in Paris. In 1779, at the same time that Ben Franklin was in Paris, Charles was fired from his job and became inspired to learn about those experimental sciences that did not require much mathematical sophistication.

Less than two years later, Charles had evolved into such a good science lecturer that his presentations in physics and chemistry attracted large audiences. He was named a resident member of the Académie des Sciences in 1795, and later he became professor of experimental physics at the Conservatoire des Arts et Metiers (Conservatory of Arts and Trades).

In 1804, he married a woman described in the literature merely as an

“attractive young lady.”

Charles was most famous to his contemporaries for his various exploits and inventions pertaining to the science of ballooning and other practical sciences. For example, Charles

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promoted the idea of using hydrogen instead of hot air in balloons

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invented thevalve line, which enables gas release for balloon descent

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invented theappendix, a tube that enables gas to escape to prevent balloon rupture

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invented the megascope, a device for projecting and magnifying objects

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invented a goniometer for measuring crystal angles

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developed ways to make balloons less porous in order to hold the hydrogen gas.

His first balloon journey took place in 1783, and his adoring audience of thousands watched as the balloon drifted. The balloon ascended to a height of nearly 3,000 feet (914 meters) and seems to have finally landed in a field outside of Paris, where it was destroyed by terrified peasants. In fact, the locals believed that the balloon was some kind of evil spirit or beast from which they heard sighs and groans, accompanied by a noxious odor.

The initial ﬁlling of this balloon had been quite a task. According to Charles M. Evans’sWar of the Aeronauts: The History of Ballooning in the Civil War,

c h a r l e s ’ s g a s l a w | 167

Charles used a crude hydrogen generator that consisted of a large wooden barrel containing iron filings. . . . Hinged doors were fash- ioned into the top of the barrel, which allowed Charles to pour sulfuric acid over the filings, causing the chemical reaction that produced hydrogen. The inflation process . . . took over four days to complete. More than 200 pints of acid and a ton of iron filings were consumed. . . .

The balloon craze had thus begun. Here are some quick highlights: In 1784, John Jeffries and Jean-Pierre F. Blanchard flew a hydrogen balloon at various altitudes above England as they collected temperature and mois- ture data. In January of 1785, Jeffries and Blanchard crossed the English Channel from England to France. In June of 1785, Jean-François Pilâtre de Rozie and Pierre Romain attempted to cross the Channel from France to England in a double balloon, consisting of an upper gas balloon and a lower hot-air balloon. At an altitude of about 1,000 meters, the craft burst into flames, killing both de Rozier and Romain, who were the first to die in a balloon accident. The first flight made by a woman took place in 1894 when Marie Thible of Lyons, France, ascended to 8,500 feet in a 45-minute flight. The first balloon flight in America was undertaken by Blanchard in 1793 and witnessed by George Washington.

Charles had started a fad, but despite his initial fame, he rarely published his scientific findings, and his famous 1878 gas law was first made public by Gay-Lussac, who also improved upon Charles’s experimental procedures.

Note that the relationshipP=kT, wherePstands for pressure, is a relationship that is usually not attributed in an eponymous fashion, although it is often seemingly mistakenly called Gay-Lussac’s Law. Note also that French physicist Guillaume Amontons (1663–1705) also investigated the relationship between pressure and temperature in gases, although he did not have access to accurate thermometers. He did show that that the pressure of a gas increases as its temperature is raised while holding the volume and the amount of gas constant.

Amontons also discovered a relationship, which some have called Amontons’s Law, that characterizes the friction between two surfaces. In particular, Amontons showed that the frictional force is directly proportional to the force normal (perpendicular) to the surfaces in contact, with a constant of proportionality (a frictional coefﬁcient) that is constant and independent of the size of the contact area. These kinds of relationships were ﬁrst suggested by Leonardo da Vinci and rediscovered by Amontons.

Several studies have been conducted in the early years of the twenty-ﬁrst century to determine the extent to which Amontons’s Law 168 ^| a r c h i m e d e s t o h a w k i n g

actually applies for materials at length scales from nanometers to millime- ters. In particular, the validity of Amontons’s Law is of concern today for researchers in the area of MEMS (micro-electromechanical systems), which make use of tiny devices such as those now used in inkjet printers and as accelerometers in car airbag systems. MEMS uses microfabrication technology to integrate mechanical elements, sensors, and electronics on a silicon substrate. Amontons’s Law, which is often useful when studying traditional machines and moving parts, may not be applicable to larger machines, such as those the size of a pinhead and larger. [For additional principles in this book that relate to the ﬁeld of tribology (friction), see Coulomb’s Law of Friction, discussed in the entry for Coulomb.]

Returning to the life of Jacques Charles, his spirit of adventure and zest for life are exempliﬁed by the joy he felt while traveling in his balloons.

Richard Hamblyn, author ofThe Invention of Clouds: How an Amateur Meteorologist Forged the Language of the Skies, describes Charles’s feel- ings while on one of his solo ﬂights:

Charles rose even higher on this second [ﬂight of the evening], bringing the Sun back into view, where he stayed aloft until he watched its second setting, ravished by the sight, “hearing himself live.” . . . When he ﬁnally relanded . . . he emerged from the basket more rhapsodic than ever, with the image of the twin sunsets, viewed from the vantage of a soaring balloon, scored indelibly onto his mind.

A lunar crater with a diameter of 1 kilometer was named after Charles and approved in 1976 by the International Astronomical Union General Assembly.

1800–1900

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Science will continue to surprise us with what it dis- covers and creates; then it will astound us by devising new methods to surprise us. At the core of science’s self-modiﬁcation is technology. New tools enable new structures of knowledge and new ways of discovery. The achievement of science is to know new things; the evolu- tion of science is to know them in new ways. What evolves is less the body of what we know and more the nature of our knowing.

—Kevin Kelly, “Speculations on the Future of Science”

When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong.

—Arthur C. Clarke,Proﬁles of the Future, 1962

When, however, the lay public rallies round an idea that is denounced by distinguished but elderly scientists and supports that idea with great fervor and emotion—the distinguished but elderly scientists are then, after all, probably right.

—Isaac Asimov,Quasar, Quasar, Burning Bright, 1976 As the nineteenth century drew to a close, scientists could reﬂect with satisfaction that they had pinned down most of the mysteries of the physical world: electricity, mag- netism, gases, optics, acoustics, kinetics, and statistical mechanics . . . all had fallen into order before them. They had discovered the X ray, the cathode ray, the electron, and radioactivity, invented the ohm, the watt, the Kelvin, the joule, the amp, and the little erg.

—Bill Bryson,A Short History of Nearly Everything

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Dalam dokumen archimedes to hawking laws of science and the great minds behind them (Halaman 180-188)

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FURTHER READING

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