English chemist John Dalton (1766-1844) was the first to recognize that nature is composed of tiny particles. In putting forward his idea, Dalton adopted a concept from the Greek philosopher Democritus (c. 470-380 B.C. ), who proposed that matter is made up of tiny units he called atomos, or "indivisible."
Dalton recognized that the structure of atoms in a particular element or compound is uniform, and maintained that compounds are made up of compound atoms: in other words, that water, for instance, is composed of "water atoms." Soon after Dalton, however, Avogadro clarified the distinction between atoms and molecules. Neither Dalton nor Avogadro offered much in the way of a theory regarding atomic or molecular behavior; but another scientist had already introduced the idea that matter at the smallest levels is in a constant state of motion.
This was Daniel Bernoulli (1700-1782), a Swiss mathematician and physicist whose studies of fluids—a term which encompasses both gases and liquids—provided a foundation for the field of fluid mechanics. (Today, Bernoulli's principle, which relates the velocity and pressure of fluids, is applied in the field of aerodynamics, and explains what keeps an airplane aloft.) Bernoulli published his fluid mechanics studies in Hydrodynamica (1700-1782), a work in which he provided the basis for what came to be known as the kinetic theory of gases.
Because he came before Dalton and Avogadro, and, thus, did not have the benefit of their atomic and molecular theories, Bernoulli was not able to develop his kinetic theory beyond the seeds of an idea. The subsequent elaboration of kinetic theory, which is applied not only to gases but (with somewhat less effectiveness) to liquids and solids, in fact, resulted from an accidental discovery.
In 1827, Scottish botanist Robert Brown (1773-1858) was studying pollen grains under a microscope, when he noticed that the grains underwent a curious zigzagging motion in the water. The pollen assumed the shape of a colloid, a pattern that occurs when particles of one substance are dispersed—but not dissolved—in another substance. Another example of a colloidal pattern is a puff of smoke.
At first, Brown assumed that the motion had a biological explanation—that is, that it resulted from life processes within the pollen—but later, he discovered that even pollen from long-dead plants behaved in the same way. He never understood what he was witnessing. Nor did a number of other scientists, who began noticing other examples of what came to be known as Brownian motion: the constant but irregular zigzagging of colloidal particles, which can be seen clearly through a microscope.
A generation after Brown's time, kinetic theory came to maturity through the work of Maxwell and Austrian physicist Ludwig E. Boltzmann (1844-1906). Working independently, the two men developed a theory, later dubbed the Maxwell-Boltzmann theory of gases, which described the distribution of molecules in a gas. In 1859, Maxwell described the distribution of molecular velocities, work that became the foundation of statistical mechanics—the study of large systems—by examining the behavior of their smallest parts.
A year later, in 1860, Maxwell published a paper in which he presented the kinetic theory of gases: the idea that a gas consists of numerous molecules, relatively far apart in space, which interact by colliding. These collisions, he proposed, are responsible for the production of thermal energy, because when the velocity of the molecules increases—as it does after collision—the temperature increases as well. Eight years later, in 1868, Boltzmann independently applied statistics to the kinetic theory, explaining the behavior of gas molecules by means of what would come to be known as statistical mechanics.
Kinetic theory offered a convincing explanation of the processes involved in Brownian motion. According to the kinetic view, what Brown observed had nothing to do with the pollen particles; rather, the movement of those particles was simply the result of activity on the part of the water molecules. Pollen grains are many thousands of times larger than water molecules, but since there are so many molecules in even one drop of water, and their motion is so constant but apparently random, the water molecules are bound to move a pollen grain once every few thousand collisions.
In 1905, Albert Einstein (1879-1955) analyzed the behavior of particles subjected to Brownian motion. His work, and the confirmation of his results by French physicist Jean Baptiste Perrin (1870-1942), finally put an end to any remaining doubts concerning the molecular structure of matter. The kinetic explanation of molecular behavior, however, remains a theory.
Maxwell's and Boltzmann's work helped explain characteristics of matter at the molecular level, but did so most successfully with regard to gases. Kinetic theory fits with a number of behaviors exhibited by gases: their tendency to fill any container by expanding to fit its interior, for instance, and their ability to be easily compressed.
This, in turn, concurs with the gas laws (discussed in a separate essay titled "Gas Laws")—for instance, Boyle's law, which maintains that pressure decreases as volume increases, and vice versa. Indeed, the ideal gas law, which shows an inverse relationship between pressure and volume, and a proportional relationship between temperature and the product of pressure and volume, is an expression of kinetic theory.
The operations of the gas laws are easy to visualize by means of kinetic theory, which portrays gas molecules as though they were millions upon billions of tiny balls colliding at random. Inside a cube-shaped container of gas, molecules are colliding with every possible surface, but the net effect of these collisions is the same as though the molecules were divided into thirds, each third colliding with opposite walls inside the cube.
If the cube were doubled in size, the molecules bouncing back and forth between two sets of walls would have twice as far to travel between each collision. Their speed would not change, but the time between collisions would double, thus, cutting in half the amount of pressure they would exert on the walls. This is an illustration of Boyle's law: increasing the volume by a factor of two leads to a decrease in pressure to half of its original value.
On the other hand, if the size of the container were decreased, the molecules would have less distance to travel from collision to collision. This means they would be colliding with the walls more often, and, thus, would have a higher degree of energy—and, hence, a higher temperature. This illustrates another gas law, Charles's law, which relates volume to temperature: as one of the two increases or decreases, so does the other. Thus, it can be said, in light of kinetic theory, that the average kinetic energy produced by the motions of all the molecules in a gas is proportional to the absolute temperature of the gas.
The term "absolute temperature" refers to the Kelvin scale, established by William Thomson, Lord Kelvin (1824-1907). Drawing on Charles's discovery that gas at 0°C (32°F) regularly contracts by about 1/273 of its volume for every Celsius degree drop in temperature, Thomson derived the value of absolute zero (−273.15°C or −459.67°F). The Kelvin and Celsius scales are directly related; hence, Celsius temperatures can be converted to Kelvins by adding 273.15.
The Kelvin scale measures temperature in relation to absolute zero, or 0K. (Units in the Kelvin system, known as Kelvins, do not include the word or symbol for degree.) But what is absolute zero, other than a very cold temperature? Kinetic theory provides a useful definition: the temperature at which all molecular movement in a gas ceases. But this definition requires some qualification.
First of all, the laws of thermodynamics show the impossibility of actually reaching absolute zero. Second, the vibration of atoms never completely ceases: rather, the vibration of the average atom is zero. Finally, one element—helium—does not freeze, even at temperatures near absolute zero. Only the application of pressure will push helium past the freezing point.
Kinetic theory is more successful when applied to gases than to liquids and solids, because liquid and solid molecules do not interact nearly as frequently as gas particles do. Nonetheless, the proposition that the internal energy of any substance—gas, liquid, or solid—is at least partly related to the kinetic energies of its molecules helps explain much about the behavior of matter.
The thermal expansion of a solid, for instance, can be clearly explained in terms of kinetic theory. As discussed in the essay on elasticity, many solids are composed of crystals, regular shapes composed of molecules joined to one another, as though on springs. A spring that is pulled back, just before it is released, is an example of potential energy: the energy that an object possesses by virtue of its position. For a crystalline solid at room temperature, potential energy and spacing between molecules are relatively low. But as temperature increases and the solid expands, the space between molecules increases—as does the potential energy in the solid.
An example of a liquid displaying kinetic behavior is water in the process of vaporization. The vaporization of water, of course, occurs in boiling, but water need not be anywhere near the boiling point to evaporate. In either case, the process is the same. Speeds of molecules in any substance are distributed along a curve, meaning that a certain number of molecules have speeds well below, or well above, the average. Those whose speeds are well above the average have enough energy to escape the surface, and once they depart, the average energy of the remaining liquid is less than before. As a result, evaporation leads to cooling. (In boiling, of course, the continued application of thermal energy to the entire water sample will cause more molecules to achieve greater energy, even as highly energized molecules leave the surface of the boiling water as steam.)
The vaporization of water is an example of a change of phase—the transition from one phase of matter to another. The properties of any substance, and the points at which it changes phase, are plotted on what is known as a phase diagram. The latter typically shows temperature along the x-axis, and pressure along the y-axis. It is also possible to construct a phase diagram that plots volume against temperature, or volume against pressure, and there are even three-dimensional phase diagrams that measure the relationship between all three—volume, pressure, and temperature. Here we will consider the simpler two-dimensional diagram we have described.
For simple substances such as water and carbon dioxide, the solid form of the substance appears at a relatively low temperature, and at pressures anywhere from zero upward. The line between solids and liquids, indicating the temperature at which a solid becomes a liquid at any pressure above a certain level, is called the fusion curve. Though it appears to be a line, it is indeed curved, reflecting the fact that at high pressures, a solid well below the normal freezing point for that substance may be melted to create a liquid.
Liquids occupy the area of the phase diagram corresponding to relatively high temperatures and high pressures. Gases or vapors, on the other hand, can exist at very low temperatures, but only if the pressure is also low. Above the melting point for the substance, gases exist at higher pressures and higher temperatures. Thus, the line between liquids and gases often looks almost like a 45° angle. But it is not a straight line, as its name, the vaporization curve, indicates. The curve of vaporization reflects the fact that at relatively high temperatures and high pressures, a substance is more likely to be a gas than a liquid.
There are several other interesting phenomena mapped on a phase diagram. One is the critical point, which can be found at a place of very high temperature and pressure along the vaporization curve. At the critical point, high temperatures prevent a liquid from remaining a liquid, no matter how high the pressure. At the same time, the pressure causes gas beyond that point to become more and more dense, but due to the high temperatures, it does not condense into a liquid. Beyond the critical point, the substance cannot exist in anything other than the gaseous state. The temperature component of the critical point for water is 705.2°F (374°C)—at 218 atm, or 218 times ordinary atmospheric pressure. For helium, however, critical temperature is just a few degrees above absolute zero. This is why helium is rarely seen in forms other than a gas.
There is also a certain temperature and pressure, called the triple point, at which some substances—water and carbon dioxide are examples—will be a liquid, solid, and gas all at once. Another interesting phenomenon is the sublimation curve, or the line between solid and gas. At certain very low temperatures and pressures, a substance may experience sublimation, meaning that a gas turns into a solid, or a solid into a gas, without passing through a liquid stage. A well-known example of sublimation occurs when "dry ice," which is made of carbon dioxide, vaporizes at temperatures above (−109.3°F [−78.5°C]). Carbon dioxide is exceptional, however, in that it experiences sublimation at relatively high pressures, such as those experienced in everyday life: for most substances, the sublimation point occurs at such a low pressure point that it is seldom witnessed outside of a laboratory.
One interesting and useful application of phase change is the liquefaction of gases, or the change of gas into liquid by the reduction in its molecular energy levels. There are two important properties at work in liquefaction: critical temperature and critical pressure. Critical temperature is that temperature above which no amount of pressure will cause a gas to liquefy. Critical pressure is the amount of pressure required to liquefy the gas at critical temperature.
Gases are liquefied by one of three methods: (1) application of pressure at temperatures below critical; (2) causing the gas to do work against external force, thus, removing its energy and changing it to the liquid state; or (3) causing the gas to do work against some internal force. The second option can be explained in terms of the operation of a heat engine, as explored in the Thermodynamics essay.
In a steam engine, an example of a heat engine, water is boiled, producing energy in the form of steam. The steam is introduced to a cylinder, in which it pushes on a piston to drive some type of machinery. In pushing against the piston, the steam loses energy, and as a result, changes from a gas back to a liquid.
As for the use of internal forces to cool a gas, this can be done by forcing the vapor through a small nozzle or porous plug. Depending on the temperature and properties of the gas, such an operation may be enough to remove energy sufficient for liquefaction to take place. Sometimes, the process must be repeated before the gas fully condenses into a liquid.
Like the steam engine itself, the idea of gas lique-faction is a product of the early Industrial Age. One of the pioneering figures in the field was the brilliant English physicist Michael Faraday (1791-1867), who liquefied a number of high-critical temperature gases, such as carbon dioxide.
Half a century after Faraday, French physicist Louis Paul Cailletet (1832-1913) and Swiss chemist Raoul Pierre Pictet (1846-1929) developed the nozzle and porous-plug methods of liquefaction. This, in turn, made it possible to liquefy gases with much lower critical temperatures, among them oxygen, nitrogen, and carbon monoxide.
By the end of the nineteenth century, physicists were able to liquefy the gases with the lowest critical temperatures. James Dewar of Scotland (1842-1923) liquefied hydrogen, whose critical temperature is −399.5°F (−239.7°C). Some time later, Dutch physicist Heike Kamerlingh Onnes (1853-1926) successfully liquefied the gas with the lowest critical temperature of them all: helium, which, as mentioned earlier, becomes a gas at almost unbelievably low temperatures. Its critical temperature is −449.9°F (−267.7°C), or just 5.3K.
Liquefied natural gas (LNG) and liquefied petroleum gas (LPG), the latter a mixture of by-products obtained from petroleum and natural gas, are among the examples of liquefied gas in daily use. In both cases, the volume of the liquefied gas is far less than it would be if the gas were in a vaporized state, thus enabling ease and economy in transport.
Liquefied gases are used as heating fuel for motor homes, boats, and homes or cabins in remote areas. Other applications of liquefied gases include liquefied oxygen and hydrogen in rocket engines, and liquefied oxygen and petroleum used in welding. The properties of liquefied gases also figure heavily in the science of producing and studying low-temperature environments. In addition, liquefied helium is used in studying the behavior of matter at temperatures close to absolute zero.
Physicists at a Colorado laboratory in 1995 revealed a highly interesting aspect of atomic motion at temperatures approaching absolute zero. Some 70 years before, Einstein had predicted that, at extremely low temperatures, atoms would fuse to form one large "superatom." This hypothesized structure was dubbed the Bose-Einstein Condensate after Einstein and Satyendranath Bose (1894-1974), an Indian physicist whose statistical methods contributed to the development of quantum theory.
Because of its unique atomic structure, the Bose-Einstein Condensate has been dubbed a "new" form of matter. It represents a quantum mechanical effect, relating to a cutting-edge area of physics devoted to studying the properties of subatomic particles and the interaction of matter with radiation. Thus it is not directly related to molecular dynamics; nonetheless, the Bose-Einstein Condensate is mentioned here as an example of the exciting work being performed at a level beyond that addressed by molecular dynamics. Its existence may lead to a greater understanding of quantum mechanics, and on an everyday level, the "superatom" may aid in the design of smaller, more powerful computer chips.
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