THERMODYNAMICS

CONCEPT

Thermodynamics is the study of the relationships between heat, work, and energy. Though rooted in physics, it has a clear application to chemistry, biology, and other sciences: in a sense, physical life itself can be described as a continual thermodynamic cycle of transformations between heat and energy. But these transformations are never perfectly efficient, as the second law of thermodynamics shows. Nor is it possible to get "something for nothing," as the first law of thermodynamics demonstrates: the work output of a system can never be greater than the net energy input. These laws disappointed hopeful industrialists of the early nineteenth century, many of whom believed it might be possible to create a perpetual motion machine. Yet the laws of thermodynamics did make possible such highly useful creations as the internal combustion engine and the refrigerator.

HOW IT WORKS

Historical Context

Machines were, by definition, the focal point of the Industrial Revolution, which began in England during the late eighteenth and early nineteenth centuries. One of the central preoccupations of both scientists and industrialists thus became the efficiency of those machines: the ratio of output to input. The more output that could be produced with a given input, the greater the production, and the greater the economic advantage to the industrialists and (presumably) society as a whole.

At that time, scientists and captains of industry still believed in the possibility of a perpetual motion machine: a device that, upon receiving an initial input of energy, would continue to operate indefinitely without further input. As it emerged that work could be converted into heat, a form of energy, it began to seem possible that heat could be converted directly back into work, thus making possible the operation of a perfectly reversible perpetual motion machine. Unfortunately, the laws of thermodynamics dashed all those dreams.

SNOW'S EXPLANATION.

Some texts identify two laws of thermodynamics, while others add a third. For these laws, which will be discussed in detail below, British writer and scientist C. P. Snow (1905-1980) offered a witty, nontechnical explanation. In a 1959 lecture published as The Two Cultures and the Scientific Revolution, Snow compared the effort to transform heat into energy, and energy back into heat again, as a sort of game.

The first law of thermodynamics, in Snow's version, teaches that the game is impossible to win. Because energy is conserved, and thus, its quantities throughout the universe are always the same, one cannot get "something for nothing" by extracting more energy than one put into a machine.

The second law, as Snow explained it, offers an even more gloomy prognosis: not only is it impossible to win in the game of energy-work exchanges, one cannot so much as break even. Though energy is conserved, that does not mean the energy is conserved within the machine where it is used: mechanical systems tend toward increasing disorder, and therefore, it is impossible for the machine even to return to the original level of energy.

The third law, discovered in 1905, seems to offer a possibility of escape from the conditions imposed in the second law: at the temperature of absolute zero, this tendency toward breakdown drops to a level of zero as well. But the third law only proves that absolute zero cannot be attained: hence, Snow's third observation, that it is impossible to step outside the boundaries of this unwinnable heat-energy transformation game.

Work and Energy

Work and energy, discussed at length elsewhere in this volume, are closely related. Work is the exertion of force over a given distance to displace or move an object. It is thus the product of force and distance exerted in the same direction. Energy is the ability to accomplish work.

There are many manifestations of energy, including one of principal concern in the present context: thermal or heat energy. Other manifestations include electromagnetic (sometimes divided into electrical and magnetic), sound, chemical, and nuclear energy. All these, however, can be described in terms of mechanical energy, which is the sum of potential energy—the energy that an object has due to its position—and kinetic energy, or the energy an object possesses by virtue of its motion.

MECHANICAL ENERGY.

Kinetic energy relates to heat more clearly than does potential energy, discussed below; however, it is hard to discuss the one without the other. To use a simple example—one involving mechanical energy in a gravitational field—when a stone is held over the edge of a cliff, it has potential energy. Its potential energy is equal to its weight (mass times the acceleration due to gravity) multiplied by its height above the bottom of the canyon below. Once it is dropped, it acquires kinetic energy, which is the same as one-half its mass multiplied by the square of its velocity.

Just before it hits bottom, the stone's kinetic energy will be at a maximum, and its potential energy will be at a minimum. At no point can the value of its kinetic energy exceed the value of the potential energy it possessed before it fell: the mechanical energy, or the sum of kinetic and potential energy, will always be the same, though the relative values of kinetic and potential energy may change.

CONSERVATION OF ENERGY.

What mechanical energy does the stone possess after it comes to rest at the bottom of the canyon? In terms of the system of the stone dropping from the cliffside to the bottom, none. Or, to put it another way, the stone has just as much mechanical energy as it did at the very beginning. Before it was picked up and held over the side of the cliff, thus giving it potential energy, it was presumably sitting on the ground away from the edge of the cliff. Therefore, it lacked potential energy, inasmuch as it could not be "dropped" from the ground.

If the stone's mechanical energy—at least in relation to the system of height between the cliff and the bottom—has dropped to zero, where did it go? A number of places. When it hit, the stone transferred energy to the ground, manifested as heat. It also made a sound when it landed, and this also used up some of its energy. The stone itself lost energy, but the total energy in the universe was unaffected: the energy simply left the stone and went to other places. This is an example of the conservation of energy, which is closely tied to the first law of thermodynamics.

But does the stone possess any energy at the bottom of the canyon? Absolutely. For one thing, its mass gives it an energy, known as mass or rest energy, that dwarfs the mechanical energy in the system of the stone dropping off the cliff. (Mass energy is the other major form of energy, aside from kinetic and potential, but at speeds well below that of light, it is released in quantities that are virtually negligible.) The stone may have electromagnetic potential energy as well; and of course, if someone picks it up again, it will have gravitational potential energy. Most important to the present discussion, however, is its internal kinetic energy, the result of vibration among the molecules inside the stone.

Heat and Temperature

Thermal energy, or the energy of heat, is really a form of kinetic energy between particles at the atomic or molecular level: the greater the movement of these particles, the greater the thermal energy. Heat itself is internal thermal energy that flows from one body of matter to another. It is not the same as the energy contained in a system—that is, the internal thermal energy of the system. Rather than being "energy-in-residence," heat is "energy-in-transit."

This may be a little hard to comprehend, but it can be explained in terms of the stone-and-cliff kinetic energy illustration used above. Just as a system can have no kinetic energy unless something is moving within it, heat exists only when energy is being transferred. In the above illustration of mechanical energy, when the stone was sitting on the ground at the top of the cliff, it was analogous to a particle of internal energy in body A. When, at the end, it was again on the ground—only this time at the bottom of the canyon—it was the same as a particle of internal energy that has transferred to body B. In between, however, as it was falling from one to the other, it was equivalent to a unit of heat.

TEMPERATURE.

In everyday life, people think they know what temperature is: a measure of heat and cold. This is wrong for two reasons: first, as discussed below, there is no such thing as "cold"—only an absence of heat. So, then, is temperature a measure of heat? Wrong again.

Imagine two objects, one of mass M and the other with a mass twice as great, or 2 M. Both have a certain temperature, and the question is, how much heat will be required to raise their temperature by equal amounts? The answer is that the object of mass 2 M requires twice as much heat to raise its temperature the same amount. Therefore, temperature cannot possibly be a measure of heat.

What temperature does indicate is the direction of internal energy flow between bodies, and the average molecular kinetic energy in transit between those bodies. More simply, though a bit less precisely, it can be defined as a measure of heat differences. (As for the means by which a thermometer indicates temperature, that is beyond the parameters of the subject at hand; it is discussed elsewhere in this volume, in the context of thermal expansion.)

MEASURING TEMPERATURE AND HEAT.

Temperature, of course, can be measured either by the Fahrenheit or Centigrade scales familiar in everyday life. Another temperature scale of relevance to the present discussion is the Kelvin scale, established by William Thomson, Lord Kelvin (1824-1907).

Drawing on the discovery made by French physicist and chemist J. A. C. Charles (1746-1823), 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 (discussed below) as −273.15°C (−459.67°F). The Kelvin and Celsius scales are thus directly related: Celsius temperatures can be converted to Kelvins (for which neither the word nor the symbol for "degree" are used) by adding 273.15.

MEASURING HEAT AND HEAT CAPACITY.

Heat, on the other hand, is measured not by degrees (discussed along with the thermometer in the context of thermal expansion), but by the same units as work. Since energy is the ability to perform work, heat or work units are also units of energy. The principal unit of energy in the SI or metric system is the joule (J), equal to 1 newton-meter (N · m), and the primary unit in the British or English system is the foot-pound (ft · lb). One foot-pound is equal to 1.356 J, and 1 joule is equal to 0.7376 ft · lb.

Two other units are frequently used for heat as well. In the British system, there is the Btu, or British thermal unit, equal to 778 ft · lb. or 1,054 J. Btus are often used in reference, for instance, to the capacity of an air conditioner. An SI unit that is also used in the United States—where British measures typically still prevail—is the kilocalorie. This is equal to the heat that must be added to or removed from 1 kilogram of water to change its temperature by 1°C. As its name suggests, a kilocalorie is 1,000 calories. A calorie is the heat required to change the temperature in 1 gram of water by 1°C—but the dietary Calorie (capital C), with which most people are familiar is the same as the kilocalorie.

A kilocalorie is identical to the heat capacity for one kilogram of water. Heat capacity (sometimes called specific heat capacity or specific heat) is the amount of heat that must be added to, or removed from, a unit of mass for a given substance to change its temperature by 1°C. this is measured in units of J/kg · °C (joules per kilogram-degree Centigrade), though for the sake of convenience it is typically rendered in terms of kilojoules (1,000 joules): kJ/kg · °c. Expressed thus, the specific heat of water 4.185—which is fitting, since a kilocalorie is equal to 4.185 kJ. Water is unique in many aspects, with regard to specific heat, in that it requires far more heat to raise the temperature of water than that of mercury or iron.

REAL-LIFE APPLICATIONS

Hot and "Cold"

Earlier, it was stated that there is no such thing as "cold"—a statement hard to believe for someone who happens to be in Buffalo, New York, or International Falls, Minnesota, during a February blizzard. Certainly, cold is real as a sensory experience, but in physical terms, cold is not a "thing"—it is simply the absence of heat.

People will say, for instance, that they put an ice cube in a cup of coffee to cool it, but in terms of physics, this description is backward: what actually happens is that heat flows from the coffee to the ice, thus raising its temperature. The resulting temperature is somewhere between that of the ice cube and the coffee, but one cannot obtain the value simply by averaging the two temperatures at the beginning of the transfer.

For one thing, the volume of the water in the ice cube is presumably less than that of the water in the coffee, not to mention the fact that their differing chemical properties may have some minor effect on the interaction. Most important, however, is the fact that the coffee did not simply merge with the ice: in transferring heat to the ice cube, the molecules in the coffee expended some of their internal kinetic energy, losing further heat in the process.

COOLING MACHINES.

Even cooling machines, such as refrigerators and air conditioners, actually use heat, simply reversing the usual process by which particles are heated. The refrigerator pulls heat from its inner compartment—the area where food and other perishables are stored—and transfers it to the region outside. This is why the back of a refrigerator is warm.

Inside the refrigerator is an evaporator, into which heat from the refrigerated compartment flows. The evaporator contains a refrigerant—a gas, such as ammonia or Freon 12, that readily liquifies. This gas is released into a pipe from the evaporator at a low pressure, and as a result, it evaporates, a process that cools it. The pipe takes the refrigerant to the compressor, which pumps it into the condenser at a high pressure. Located at the back of the refrigerator, the condenser is a long series of pipes in which pressure turns the gas into liquid. As it moves through the condenser, the gas heats, and this heat is released into the air around the refrigerator.

An air conditioner works in a similar manner. Hot air from the room flows into the evaporator, and a compressor circulates refrigerant from the evaporator to a condenser. Behind the evaporator is a fan, which draws in hot air from the room, and another fan pushes heat from the condenser to the outside. As with a refrigerator, the back of an air conditioner is hot because it is moving heat from the area to be cooled.

Thus, cooling machines do not defy the principles of heat discussed above; nor do they defy the laws of thermodynamics that will be discussed at the conclusion of this essay. In accordance with the second law, in order to move heat in the reverse of its usual direction, external energy is required. Thus, a refrigerator takes in energy from a electric power supply (that is, the outlet it is plugged into), and extracts heat. Nonetheless, it manages to do so efficiently, removing two or three times as much heat from its inner compartment as the amount of energy required to run the refrigerator.

Transfers of Heat

It is appropriate now to discuss how heat is transferred. One must remember, again, that in order for heat to be transferred from one point to another, there must be a difference of temperature between those two points. If an object or system has a uniform level of internal thermal energy—no matter how "hot" it may be in ordinary terms—no heat transfer is taking place.

Heat is transferred by one of three methods: conduction, which involves successive molecular collisions; convection, which requires the motion of hot fluid from one place to another; or radiation, which involves electromagnetic waves and requires no physical medium for the transfer.

CONDUCTION.

Conduction takes place best in solids and particularly in metals, whose molecules are packed in relatively close proximity. Thus, when one end of an iron rod is heated, eventually the other end will acquire heat due to conduction. Molecules of liquid or nonmetallic solids vary in their ability to conduct heat, but gas—due to the loose attractions between its molecules—is a poor conductor.

When conduction takes place, it is as though a long line of people are standing shoulder to shoulder, passing a secret down the line. In this case, however, the "secret" is kinetic thermal energy. And just as the original phrasing of the secret will almost inevitably become garbled by the time it gets to the tenth or hundredth person, some energy is lost in the transfer from molecule to molecule. Thus, if one end of the iron rod is sitting in a fire and one end is surrounded by air at room temperature, it is unlikely that the end in the air will ever get as hot as the end in the fire.

Incidentally, the qualities that make metallic solids good conductors of heat also make them good conductors of electricity. In the first instance, kinetic energy is being passed from molecule to molecule, whereas in an electrical field, electrons—freed from the atoms of which they are normally a part—are able to move along the line of molecules. Because plastic is much less conductive than metal, an electrician will use a screwdriver with a plastic handle. Similarly, a metal pan typically has a handle of wood or plastic.

CONVECTION.

There is a term, "convection oven," that is actually a redundancy: all ovens heat through convection, the principal means of transferring heat through a fluid. In physics, "fluid" refers both to liquids and gases—anything that tends to flow. Instead of simply moving heat, as in conduction, convection involves the movement of heated material—that is, fluid. When air is heated, it displaces cold (that is, unheated) air in its path, setting up a convection current.

Convection takes place naturally, as for instance when hot air rises from the land on a warm day. This heated air has a lower density than that of the less heated air in the atmosphere above it, and, therefore, is buoyant. As it rises, however, it loses energy and cools. This cooled air, now more dense than the air around it, sinks again, creating a repeating cycle.

The preceding example illustrates natural convection; the heat of an oven, on the other hand, is an example of forced convection—a situation in which some sort of pump or mechanism moves heated fluid. So, too, is the cooling work of a refrigerator, though the refrigerator moves heat in the opposite direction.

Forced convection can also take place within a natural system. The human heart is a pump, and blood carries excess heat generated by the body to the skin. The heat passes through the skin by means of conduction, and at the surface of the skin, it is removed from the body in a number of ways, primarily by the cooling evaporation of moisture—that is, perspiration.

RADIATION.

If the Sun is hot—hot enough to severely burn the skin of a person who spends too much time exposed to its rays—then why is it cold in the upper atmosphere? After all, the upper atmosphere is closer to the Sun. And why is it colder still in the empty space above the atmosphere, which is still closer to the Sun? The reason is that in outer space there is no medium for convection, and in the upper atmosphere, where the air molecules are very far apart, there is hardly any medium. How, then, does heat come to the Earth from the Sun? By radiation, which is radically different from conduction or convection. The other two involve ordinary thermal energy, but radiation involves electromagnetic energy.

A great deal of "stuff" travels through the electromagnetic spectrum, discussed in another essay in this book: radio waves, microwaves for television and radar, infrared light, visible light, x rays, gamma rays. Though the relatively narrow band of visible-light wavelengths is the only part of the spectrum of which people are aware in everyday life, other parts—particularly the infrared and ultraviolet bands—are involved in the heat one feels from the Sun. (Ultraviolet rays, in fact, cause sunburns.)

Heat by means of radiation is not as "other-worldly" as it might seem: in fact, one does not have to point to the Sun for examples of it. Any time an object glows as a result of heat—as for example, in the case of firelight—that is an example of radiation. Some radiation is emitted in the form of visible light, but the heat component is in infrared rays. This also occurs in an incandescent light bulb. In an incandescent bulb, incidentally, much of the energy is lost to the heat of infrared rays, and the efficiency of a fluorescent bulb lies in the fact that it converts what would otherwise be heat into usable light.

The Laws of Thermodynamics

Having explored the behavior of heat, both at the molecular level and at levels more easily perceived by the senses, it is possible to discuss the laws of thermodynamics alluded to throughout this essay. These laws illustrate the relationships between heat and energy examined earlier, and show, for instance, why a refrigerator or air conditioner must have an external source of energy to move heat in a direction opposite to its normal flow.

The story of how these laws came to be discovered is a saga unto itself, involving the contributions of numerous men in various places over a period of more than a century. In 1791, Swiss physicist Pierre Prevost (1751-1839) put forth his theory of exchanges, stating correctly that all bodies radiate heat. Hence, as noted earlier, there is no such thing as "cold": when one holds snow in one's hand, cold does not flow from the snow into the hand; rather, heat flows from the hand to the snow.

Seven years later, an American-British physicist named Benjamin Thompson, Count Rumford (1753) was boring a cannon with a blunt drill when he noticed that this action generated a great deal of heat. This led him to question the prevailing wisdom, which maintained that heat was a fluid form of matter; instead, Thompson began to suspect that heat must arise from some form of motion.

CARNOT'S ENGINE.

The next major contribution came from the French physicist and engineer Sadi Carnot (1796-1832). Though he published only one scientific work, Reflections on the Motive Power of Fire (1824), this treatise caused a great stir in the European scientific community. In it, Carnot made the first attempt at a scientific definition of work, describing it as "weight lifted through a height." Even more important was his proposal for a highly efficient steam engine.

A steam engine, like a modern-day internal combustion engine, is an example of a larger class of machine called heat engine. A heat engine absorbs heat at a high temperature, performs mechanical work, and, as a result, gives off heat a lower temperature. (The reason why that temperature must be lower is established in the second law of thermodynamics.)

For its era, the steam engine was what the computer is today: representing the cutting edge in technology, it was the central preoccupation of those interested in finding new ways to accomplish old tasks. Carnot, too, was fascinated by the steam engine, and was determined to help overcome its disgraceful inefficiency: in operation, a steam engine typically lost as much as 95% of its heat energy.

In his Reflections, Carnot proposed that the maximum efficiency of any heat engine was equal to (T_H-T_L)/T_H, where T_H is the highest operating temperature of the machine, and T_L the lowest. In order to maximize this value, T_L has to be absolute zero, which is impossible to reach, as was later illustrated by the third law of thermodynamics.

In attempting to devise a law for a perfectly efficient machine, Carnot inadvertently proved that such a machine is impossible. Yet his work influenced improvements in steam engine design, leading to levels of up to 80% efficiency. In addition, Carnot's studies influenced Kelvin—who actually coined the term "thermodynamics"—and others.

THE FIRST LAW OF THERMODYNAMICS.

During the 1840s, Julius Robert Mayer (1814-1878), a German physicist, published several papers in which he expounded the principles known today as the conservation of energy and the first law of thermodynamics. As discussed earlier, the conservation of energy shows that within a system isolated from all outside factors, the total amount of energy remains the same, though transformations of energy from one form to another take place.

The first law of thermodynamics states this fact in a somewhat different manner. As with the other laws, there is no definitive phrasing; instead, there are various versions, all of which say the same thing. One way to express the law is as follows: Because the amount of energy in a system remains constant, it is impossible to perform work that results in an energy output greater than the energy input. For a heat engine, this means that the work output of the engine, combined with its change in internal energy, is equal to its heat input. Most heat engines, however, operate in a cycle, so there is no net change in internal energy.

Earlier, it was stated that a refrigerator extracts two or three times as much heat from its inner compartment as the amount of energy required to run it. On the surface, this seems to contradict the first law: isn't the refrigerator putting out more energy than it received? But the heat it extracts is only part of the picture, and not the most important part from the perspective of the first law.

A regular heat engine, such as a steam or internal-combustion engine, pulls heat from a high-temperature reservoir to a low-temperature reservoir, and, in the process, work is accomplished. Thus, the hot steam from the high-temperature reservoir makes possible the accomplishment of work, and when the energy is extracted from the steam, it condenses in the low-temperature reservoir as relatively cool water.

A refrigerator, on the other hand, reverses this process, taking heat from a low-temperature reservoir (the evaporator inside the cooling compartment) and pumping it to a high-temperature reservoir outside the refrigerator. Instead of producing a work output, as a steam engine does, it requires a work input—the energy supplied via the wall outlet. Of course, a refrigerator does produce an "output," by cooling the food inside, but the work it performs in doing so is equal to the energy supplied for that purpose.

THE SECOND LAW OF THERMODYNAMICS.

Just a few years after Mayer's exposition of the first law, another German physicist, Rudolph Julius Emanuel Clausius (1822-1888) published an early version of the second law of thermodynamics. In an 1850 paper, Clausius stated that "Heat cannot, of itself, pass from a colder to a hotter body." He refined this 15 years later, introducing the concept of entropy—the tendency of natural systems toward breakdown, and specifically, the tendency for the energy in a system to be dissipated.

The second law of thermodynamics begins from the fact that the natural flow of heat is always from a high-temperature reservoir to a low-temperature reservoir. As a result, no engine can be constructed that simply takes heat from a source and performs an equivalent amount of work: some of the heat will always be lost. In other words, it is impossible to build a perfectly efficient engine.

Though its relation to the first law is obvious, inasmuch as it further defines the limitations of machine output, the second law of thermodynamics is not derived from the first. Elsewhere in this volume, the first law of thermodynamics—stated as the conservation of energy law—is discussed in depth, and, in that context, it is in fact necessary to explain how the behavior of machines in the real world does not contradict the conservation law.

Even though they mean the same thing, the first law of thermodynamics and the conservation of energy law are expressed in different ways. The first law of thermodynamics states that "the glass is half empty," whereas the conservation of energy law shows that "the glass is half full." The thermodynamics law emphasizes the bad news: that one can never get more energy out of a machine than the energy put into it. Thus, all hopes of a perpetual motion machine were dashed. The conservation of energy, on the other hand, stresses the good news: that energy is never lost.

In this context, the second law of thermodynamics delivers another dose of bad news: though it is true that energy is never lost, the energy available for work output will never be as great as the energy put into a system. A car engine, for instance, cannot transform all of its energy input into usable horsepower; some of the energy will be used up in the form of heat and sound. Though energy is conserved, usable energy is not.

Indeed, the concept of entropy goes far beyond machines as people normally understand them. Entropy explains why it is easier to break something than to build it—and why, for each person, the machine called the human body will inevitably break down and die, or cease to function, someday.

THE THIRD LAW OF THERMODYNAMICS.

The subject of entropy leads directly to the third law of thermodynamics, formulated by German chemist Hermann Walter Nernst (1864-1941) in 1905. The third law states that at the temperature of absolute zero, entropy also approaches zero. From this statement, Nernst deduced that absolute zero is therefore impossible to reach.

All matter is in motion at the molecular level, which helps define the three major phases of matter found on Earth. At one extreme is a gas, whose molecules exert little attraction toward one another, and are therefore in constant motion at a high rate of speed. At the other end of the phase continuum (with liquids somewhere in the middle) are solids. Because they are close together, solid particles move very little, and instead of moving in relation to one another, they merely vibrate in place. But they do move.

Absolute zero, or 0K on the Kelvin scale of temperature, is the point at which all molecular motion stops entirely—or at least, it virtually stops. (In fact, absolute zero is defined as the temperature at which the motion of the average atom or molecule is zero.) As stated earlier, Carnot's engine achieves perfect efficiency if its lowest temperature is the same as absolute zero; but the second law of thermodynamics shows that a perfectly efficient machine is impossible. This means that absolute zero is an unreachable extreme, rather like matter exceeding the speed of light, also an impossibility.

This does not mean that scientists do not attempt to come as close as possible to absolute zero, and indeed they have come very close. In 1993, physicists at the Helsinki University of Technology Low Temperature Laboratory in Finland used a nuclear demagnetization device to achieve a temperature of 2.8 · 10⁻¹⁰ K, or 0.00000000028K. This means that a fragment equal to only 28 parts in 100 billion separated this temperature from absolute zero—but it was still above 0K. Such extreme low-temperature research has a number of applications, most notably with superconductors, materials that exhibit virtually no resistance to electrical current at very low temperatures.

WHERE TO LEARN MORE

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison-Wesley, 1991.

Brown, Warren. Alternative Sources of Energy. Introduction by Russell E. Train. New York: Chelsea House, 1994.

Encyclopedia of Thermodynamics (Web site). <http://therion.minpet.unibas.ch/minpet/groups/thermodict/> (April 12, 2001).

Entropy and the Second Law of Thermodynamics (Web site). <http://www.2ndlaw.com> (April 12, 2001).

Fleisher, Paul. Matter and Energy: Principles of Matter and Thermodynamics. Minneapolis, MN: Lerner Publications, 2002.

Macaulay, David. The New Way Things Work. Boston: Houghton Mifflin, 1998.

Moran, Jeffrey B. How Do We Know the Laws of Thermodynamics? New York: Rosen Publishing Group, 2001.

Santrey, Laurence. Heat. Illustrated by Lloyd Birmingham. Mahwah, N.J.: Troll Associates, 1985.

Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996.

"Temperature and Thermodynamics" PhysLINK.com (Web site). <http://www.physlink.com/ae_thermo.cfm> (April 12, 2001).

KEY TERMS

ABSOLUTE ZERO:

The temperature, defined as 0K on the Kelvin scale, at which the motion of molecules in a solid virtually ceases. The third law of thermodynamics establishes the impossibility of actually reaching absolute zero.

BTU (BRITISH THERMAL UNIT):

A measure of energy or heat in the Britishsystem, often used in reference to the capacity of an air conditioner. A Btu is equal to 778 foot-pounds, or 1,054 joules.

CALORIE:

A measure of heat or energy in the SI or metric system, equal to the heat that must be added to or removed from 1 gram of water to change its temperature by 33.8°F (1°C). The dietary Calorie (capital C) with which most people are familiar is the same as the kilocalorie.

CONDUCTION:

The transfer of heat by successive molecular collisions. Conduction is the principal means of heat transfer in solids, particularly metals.

CONSERVATION OF ENERGY:

A law of physics which holds that within a system isolated from all other outside factors, the total amount of energy remains the same, though transformations of energy from one form to another take place. The first law of thermodynamics is the same as the conservation of energy.

CONSERVE:

In physics, "to conserve" something means "to result in no net loss of" that particular component. It is possible that within a given system, the component may change form or position, but as long as the net value of the component remains the same, it has been conserved.

CONVECTION:

The transfer of heat through the motion of hot fluid from oneplace to another. In physics, a "fluid" can be either a gas or a liquid, and convection is the principal means of heat transfer, for instance, in air and water.

ENERGY:

The ability to accomplishwork.

ENTROPY:

The tendency of natural systems toward breakdown, and specifically, the tendency for the energy in a system to be dissipated. Entropy is closely related to the second law of thermodynamics.

FIRST LAW OF THERMODYNAMICS:

A law which states the amount of energy in a system remains constant, and therefore it is impossible to perform work that results in an energy output greater than the energy input. This is the same as the conservation of energy.

FOOT-POUND:

The principal unit of energy—and thus of heat—in the British or English system. The metric or SI unit is the joule. A foot-pound (ft · lb) is equal to 1.356 J.

HEAT:

Internal thermal energy that flows from one body of matter to another. Heat is transferred by three methods conduction, convection, and radiation.

HEAT CAPACITY:

The amount of heat that must be added to, or removed from, a unit of mass of a given substance to change its temperature by 33.8°F (1°C). Heat capacity is sometimes called specific heat capacity or specific heat. A kilocalorie is the heat capacity of 1 gram of water.

HEAT ENGINE:

A machine that absorbs heat at a high temperature, performs mechanical work, and as a result gives off heat at a lower temperature.

KINETIC ENERGY:

The energy that an object possesses by virtue of its motion.

JOULE:

The principal unit of energy—and thus of heat—in the SI or metric system, corresponding to 1 newton-meter (N · m). A joule (J) is equal to 0.7376 foot-pounds.

KELVIN SCALE:

Established by William Thomson, Lord Kelvin (1824-1907), 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.) The Kelvin and Celsius scales are directly related; hence Celsius temperatures can be converted to Kelvins by adding273.15.

KILOCALORIE:

A measure of heat or energy in the SI or metric system, equal to the heat that must be added to or removed from 1 kilogram of water to change its temperature by 33.8°F (1°C). As its name suggests, a kilocalorie is 1,000 calories. The dietary Calorie (capital C) with which most people are familiar is the same as the kilocalorie.

MECHANICAL ENERGY:

The sum of potential energy and kinetic energy in a given system.

POTENTIAL ENERGY:

The energy that an object possesses due to its position.

RADIATION:

The transfer of heat by means of electromagnetic waves, which require no physical medium (e.g., water or air) for the transfer. Earth receives the Sun's heat by means of radiation.

SECOND LAW OF THERMODYNAMICS:

A law of thermodynamics which states that no engine can be constructed that simply takes heat from a source and performs an equivalent amount of work. Some of the heat will always be lost, and therefore it is impossible to build a perfectly efficient engine. This is a result of th efact that the natural flow of heat is always from a high-temperature reservoir to alow-temperature reservoir—a fact expressed in the concept of entropy. The second law is sometimes referred to as "the law of entropy."

SYSTEM:

In physics, the term "system" usually refers to any set of physical interactions isolated from the rest of the universe. Anything outside of the system, including all factors and forces irrelevant to a discussion of that system, is known as the environment.

TEMPERATURE:

The direction of internal energy flow between bodies when heat is being transferred. Temperature measures the average molecular kinetic energy in transit between those bodies.

THERMAL ENERGY:

Heat energy, a form of kinetic energy produced by the movement of atomic or molecular particles. The greater the movement of the separticles, the greater the thermal energy.

THERMODYNAMICS:

The study of the relationships between heat, work, and energy.

THIRD LAW OF THERMODYNAMICS:

A law of thermodynamics which states that at the temperature of absolute zero, entropy also approaches zero. Zero entropy would contradict the second law of thermodynamics, meaning that absolute zero is therefore impossible to reach.

WORK:

The exertion of force over a given distance to displace or move an object. Work is thus the product of force and distance exerted in the same direction.

Thermodynamics

Historical background

Temperature

Expansion coefficients

Thermostats

Water

Conservation of energy

Heat

The first law of thermodynamics

Specific heats; the calorie

Change of phase

Equations of state; work

Equations of state

Work

The second law of thermodynamics

Heat engines

Resources

Thermodynamics, within physics, is the science that deals with work and heat, and the transformation of one into the other. It is a macroscopic theory, dealing with matter in bulk, disregarding the molecular nature of materials. The corresponding microscopic theory, based on the fact that materials are made up of a vast number of molecules, is called statistical mechanics.

Historical background

American physicist Benjamin Thompson (Count von Rumford) (1753–1814) recognized from observing the boring of cannons that the work (or mechanical energy) involved in the boring process was being

converted to heat by friction, causing the temperature of the cannon to rise. With the experiments of English physicist James Joule (1818–1889), it was recognized that heat is a form of energy that is transferred from one object to another, and that work can be converted to heat without limit. However, the opposite is found not to be true: that is, there are limiting factors in the conversion of heat to work. The research of French physicist Nicolas Leonard Sadi Carnot (1796–1832), of British mathematician and physicist William Thomson (Lord Kelvin) (1824–1907), and of German mathematical physicist Rudolph Clausius (1822–1888), among others, has led to an understanding of these limitations.

Temperature

the idea of temperature is well known to everyone, but the need to define it so that it can be used for measurements is far more complex than the simple concepts of hot and cold. If a rod of metal is placed in an ice-water bath and the length is measured, and then placed in a steam bath and the length again measured, it will be found that the rod has lengthened. This is an illustration of the fact that, in general, materials expand when heated, and contract when cooled (however, under some conditions rubber can do the opposite, while water is a very special case and is treated below). One could therefore use the length of a rod as a measure of temperature. However, that would not be useful, since different materials expand different amounts for the same increase in temperature. Therefore, everyone would need to have exactly the same type of rod to make certain that they obtained the same value of temperature under the same conditions.

However, it turns out that practically all gases, at sufficiently low pressures, expand in volume exactly the same amount with a given increase in temperature. This has given rise to the constant volume gas thermometer, which consists of a flask to hold the gas, attached to a system of glass and rubber tubes containing mercury. A small amount of any gas is introduced into the (otherwise empty) flask, and the top of the mercury in the glass column on the left is placed at some mark on the glass (by moving the right hand glass column up or down). The difference between the heights of the two mercury columns gives the difference between atmospheric pressure and the pressure of the gas in the flask. The gas pressure changes with a change in temperature of the flask, and can be used as a definition of the temperature by taking the temperature to be proportional to the pressure; the proportionality factor can be found in the following manner.

If the temperature at the freezing point of water is assigned the value 0° and that at the boiling point is called 100°, the temperature scale is called the Celsius scale (formerly called Centigrade); if those points are taken at 32° and 212°, it is known as the Fahrenheit scale. The relationship between them can be found as follows. If the temperature in the Celsius scale is T(°C), and that in the Fahrenheit scale is T(°F), they are related by T(°F) = (9/5) T(°C) + 32°. The importance of using the constant volume gas thermometer to define the temperature is that it gives the same value for the temperature no matter what gas is used (as long as the gas is used at a very low pressure), so that anyone at any laboratory would be able to find the same temperature under the same conditions. Of course, a variety of other types of thermometers are used in practice (mercury-in-glass, or the change in the electrical resistance of a wire, for example), but they all must be calibrated against a constant volume gas thermometer as the standard.

Expansion coefficients

An important characteristic of a material is how much it expands for a given increase in temperature. The amount that a rod of material lengthens is given by L= L₀ [1+α (T–T₀)], where L₀ is the length of the rod at some temperature T₀, and L is the length at some other temperature T;ψα (Greek alpha) is called the coefficient of linear expansion. Some typical values for α × 10⁶ (per °C) are: aluminum, 24.0; copper, 16.8; glass, 8.5; steel, 29.0 (this notation means that, for example, aluminum expands at a rate of 24.0/1,000,000 for each degree Celsius change in temperature). Volumes, of course, also expand with a rise in temperature, obeying a law similar to that for linear expansion; coefficients of volume expansion are approximately three times as large as that for linear expansion for the same material. It is interesting to note that, if a hole is cut in a piece of material, the hole expands just as if there were the same material filling it!

Thermostats

since various metals expand at different rates, a thermostat can be made to measure changes in temperature by securely fastening together two strips of metal with different expansion coefficients. If they are straight at one temperature, they will be bent at any other temperature, since one will have expanded or contracted more than the other. These are used in many homes to regulate the temperature by causing an electrical contact to be made or broken as temperature changes cause the end of the strips to move.

Water

water has the usual property of contracting when the temperature decreases, but only down to 39.2°F (4°C); below that temperature it expands until it reaches 32°F(0°C). It then forms ice at 0°C, expanding considerably in the process; the ice then behaves normally, contracting as the temperature decreases. Since the density of a substance varies inversely to the volume (as a given mass of a substance expands, its density decreases), this means that the density of water increases as the temperature decreases until 4°C, when it reaches its maximum density. The density of the water then decreases from 4 to 0°C; the formation of the ice also involves a decrease in density. The ice then increases its density as its temperature falls below 0°C. Thus, as a lake gets colder, the water at the top cools off and, since its density is increasing, this colder water sinks to the bottom. However, when the temperature of the water at the top becomes lower than 4°C, it remains at the top since its density is lower than that of the water below it. The pond then ices over, with the ice remaining at the top, while the water below remains at 4°C (until, if ever, the entire lake freezes). Fish are thus able to live in lakes even when ice forms at the top, since they have the 4°C water below it to live in.

Conservation of energy

The conservation of energy is well known from mechanics, where energy does not disappear but only changes its form. For example, the potential energy of an object at some height is converted to the kinetic energy of its motion as it falls. Thermodynamics is concerned with the internal energy of an object and those things that affect it; conservation of energy applies in this case, as well.

Heat

as noted in the introduction, doing work on an object (for example, by drilling a hole in a piece of metal, or by repeatedly bending it) causes its temperature to rise. If this object is placed in contact with a cooler object it is found that they eventually come to the same temperature, and remain that way as long as there are no outside influences (this is known as thermal equilibrium). This series of events is viewed as follows. Consistent with the concept of the conservation of energy, the energy due to the work done on the object is considered to be stored in the object as (what may be called) internal energy. In the particular example above, the increase in the internal energy of the object is recognized by the increase in temperature, but there are processes where the internal energy increases without a change in temperature. By then placing it in contact with an object of lower temperature, energy flows from the hotter to the colder one in the form of heat, until the temperatures become the same. Thus, heat should be viewed as a type of energy that can flow from one object to another by virtue of a temperature difference. It makes no sense to talk of an object having a certain amount of heat in it; whenever it is placed in contact with a lower-temperature object, heat will flow from the hotter to the cooler one.

The first law of thermodynamics

These considerations may be summarized in the first law of thermodynamics: the internal energy of an object is increased by the amount of work done on it, and by the amount of heat added to it. Mathematically, if U_f is the internal energy of an object at the end of some process, and U_i is the internal energy at the beginning of the process, then U_f– U_i= W + Q, where W is the amount of work done on the object, and Q is the amount of heat added to the object (negative values are used if work is done by the object, or heat is transferred from the object). As is usual for an equation, all quantities must be expressed in the same units; the usual mechanical unit for energy (in the International System of Units (SI)—formerly the MKS system) is the joule, where 1 joule equals 1 kg-m²/s².

Specific heats; the calorie

An important characteristic of materials is how much energy in the form of heat it takes to raise the temperature of some material by one degree. It depends upon the type of material being heated as well as its amount. The traditional basic unit, the calorie, is defined as the amount of heat that is needed to raise one gram of water by one degree Celsius. In terms of mechanical energy units, one calorie equals 4.186 joules (J).

The corresponding amount of heat necessary to raise the temperature of other materials is given by the specific heat capacity of a material, usually denoted by c. It is the number of kilojoules (kJ) needed to raise 1 kg of the material by 1°C. By definition, the value for water is 4.186 kilojoules. Typical values for c in kilojoules per kg (kJ/kg), at 0°C, are: ice, 2.11; aluminum, 0.88; copper, 0.38; iron, 0.45. It should be noted that water needs more heat to bring about a given rise in temperature than most other common substances.

Change of phase

The process of water changing to ice or to steam is a familiar one, and each is an example of a change in phase. Suppose a piece of ice were placed in a container and heated at a uniform rate; that is, a constant amount of heat per second is transferred to the material in the container. The ice (the solid phase of water) first rises in temperature at a uniform rate until its temperature reaches 32°F(0°C), when it begins to melt, that is, some of the ice changes to water (in its liquid phase); this temperature is called the melting point. It is important to note that the temperature of the ice-water mixture remains at 32°F(0°C) until all the ice has turned to water. The water temperature then rises until it reaches 212°F(100°C), when it begins to vaporize, that is, turns to steam (the gaseous phase of water); this temperature is called the boiling point. Again, the water-steam mixture remains at 212°F(100°C) until all the liquid water turns into steam. Thereafter, the temperature of the steam rises as more heat is transferred to the container. It is important to recognize that during a change in phase the temperature of the mixture remains constant. (The energy being transferred to the mixture goes into breaking molecular bonds rather than in increasing the temperature.)

Many substances undergo similar changes in phase as heat is applied, going from solid to liquid to gas, with the temperature remaining constant during each phase change. (Some substances, such as glass, do not have such a well-defined melting point.) The amount of heat needed to melt a gram of a material is known as the heat of fusion; that to vaporize it is the heat of vaporization. On the other hand, if steam is cooled at a uniform rate, it would turn to liquid water at the condensation temperature (equal to the boiling point, 212°F [100°C]), and then turn to ice at the solidification temperature (equal to the melting point, 32°F [0°C]). The heat of condensation is the amount of heat needed to be taken from a gram of a gas to change it to its liquid phase; it is equal to the heat of vaporization. Similarly, there is a heat of solidification that is equal to the heat of fusion. Some typical values are shown in Table 1.

It is interesting to note that water has much larger heats of fusion and of vaporization than many other usual substances. The melting and boiling points depend upon the pressure (the values given in the table are for atmospheric pressure). It is for this reason that water boils at a lower temperature in high-altitude Denver, Colorado, than at sea level in New Orleans, Louisiana.

Finally, below certain pressures it is possible for a substance to change directly from the solid phase to the gaseous one; this case of sublimation is best illustrated by the disappearance of dry ice when it is exposed to the atmosphere.

Equations of state; work

When an object of interest (usually called the system) is left alone for a sufficiently long time, and is subject to no outside influences from the surroundings, measurements of the properties of the object do not change with time; it is in a state of thermal equilibrium. It is found experimentally that there are certain measurable quantities that give complete information about the state of the system in thermal equilibrium (this is similar to the idea that measurements of the velocity and acceleration of an object give complete information about the mechanical state of a system). For each state, relationships can be found that hold true over a wide range of values of the quantities. These relationships are known as equations of state.

Equations of state

Thermodynamics applies to many different types of systems; gases, elastic solids (solids that can be stretched and return to their original form when the stretching force is removed), and mixtures of chemicals are all examples of such systems. Each system has its own equation of state, which depends upon the variables that need to be measured in order to describe its internal state. The relevant variables for a system can only be determined by experiment, but one of those variables will always be the temperature.

The system usually given as an example is a gas, where the relevant thermodynamic variables are the pressure of the gas (P), its volume (V), and, of course, the temperature (T). (These variables are the relevant ones for any simple chemical system, e.g., water, in any of its phases.) The amount of gas may be specified in grams or kilograms, but the usual way of measuring mass in thermodynamics (as well as in some other fields) is in terms of the number of moles. One kilo-mole (kmol) is defined as equal to M kilograms, where M is the molecular weight of the substance, with carbon-12 being taken as M = 12. (One mole of any substance contains 6.02× 10²³ molecules, known as Avogadro’s number.) Thus, one kilomole of oxygen has a mass of 70.56 lb (32 kg); of nitrogen, 61.76 lb (28.01 kg); the molar mass of air (which is, of course, actually a mixture of gases) is commonly taken as 63.87 lb (28.97 kg). It is found, by experiment, that most gases at sufficiently low pressures have an equation of state of the form: PV = NRT, where P is in Newtons/m², V is in m³, N is the number of kilomoles of the gas, T is the temperature in K, and R = 8.31 kJ/kmol-K is known as the universal gas constant. The temperature is in Kelvin (K), which is given in terms of the Celsius temperature as T(K)= T(°C)+ 273.15°C. It should be noted that real gases obey this ideal gas equation of state to within a few percent accuracy at atmospheric pressure and below.

The equation of state of substances other than gases is more complicated than the above ideal gas law. For example, an elastic solid has an equation of state that involves the length of the stretched material, the stretching force, and the temperature, in a relationship somewhat more complex than the ideal gas law.

Work

work is defined in mechanics in terms of force acting over a distance; that definition is exactly the same in thermodynamics. This is best illustrated by calculating the work done by a force F in compressing a volume of gas. If a volume (V) of gas is contained in a cylinder at pressure (P), the force needed on the piston is (by the definition of pressure) equal to PA, where A is the area of the piston. Let the gas now be compressed in a manner that keeps the pressure constant (by letting heat flow out, so that the temperature also decreases); suppose the piston moves a distance (d). Then the work done is W = Fd = PAd. However, Ad is the amount that the volume has decreased, V_i – V_f, where V_i is the initial volume and V_f is the final volume. (Note that this volume difference gives a positive value for the distance, in keeping with the fact that work done on a gas is taken as positive.) Therefore, the work done on a gas during a compression at constant pressure is P(V_i– V_f).

The first law thus gives a straightforward means to determine changes in the internal energy of an object (and it is only changes in the internal energy that can be measured), since the change in internal energy is just equal to the work done on the object in the absence of any heat flow. Heat flow to or from the object can be minimized by using insulating materials, such as fiberglass or, even better, styrofoam. The idealized process where there is zero heat flow is called an adiabatic process.

The second law of thermodynamics

One of the most remarkable facts of nature is that certain processes take place in only one direction. For example, if a high temperature object is placed in contact with one of lower temperature, heat flows from the hotter to the cooler until the temperatures become equal. In this case (where there is no work done), the first law simply requires that the energy lost by one object should be equal to that gained by the other object (through the mechanism of heat flow), but does not prescribe the direction of the energy flow. Yet, in a situation like this, heat never flows from the cooler to the hotter object. Similarly, when a drop of ink is placed in a glass of water that is then stirred, the ink distributes itself throughout the water. Yet no amount of stirring will make the uniformly distributed ink go back into a single drop. An open bottle of perfume placed in the corner of a room will soon fill the room with its scent, yet a room filled with perfume scent will never become scent-free with the perfume having gone back into the bottle. These are all examples of the second law of thermodynamics, which is usually stated in two different ways. Although the two statements appear quite different, it can be shown that they are equivalent and that each one implies the other.

Clausius statement of the second law

The Clausius statement of the second law is: No process is possible whose only result is the transfer of heat from a cooler to a hotter object. The most common example of the transfer of heat from a cooler object to a hotter one is the refrigerator (air conditioners and heat pumps work the same way). When, for example, a bottle of milk is placed in a refrigerator, the refrigerator takes the heat from the bottle of milk and transfers it to the warmer kitchen. (Similarly, a heat pump takes heat from the cool ground and transfers it to the warmer interior of a house.) An idealized view of the refrigerator is as follows. The heat transfer is accomplished by having a motor, driven by an electrical current, run a compressor. A gas is compressed to a liquid, a phase change that generates heat (heat is taken from the gas to turn it into its liquid state). This heat is dissipated to the kitchen by passing through tubes (the condenser) in the back of (or underneath) the refrigerator. The liquid passes through a valve into a low-pressure region, where it expands and becomes a gas, and flows through tubes inside the refrigerator. This change in phase from a liquid to a gas is a process that absorbs heat, thus cooling whatever is in the refrigerator. The gas then returns to the compressor where it is again turned into a liquid. The Clausius statement of the second law asserts that the process can only take place by doing work on the system; this work is provided by the motor that drives the compressor. However, the process can be quite efficient, and considerably more energy in the form of heat can be taken from the cold object than the work required to do it.

Kelvin-Planck statement of the second law

Another statement of the second law is due to Lord Kelvin and German physicist Maxwell Planck (1858– 1947): No process is possible whose only result is the conversion of heat into an equivalent amount of work. Suppose that a cylinder of gas fitted with a piston had heat added, which caused the gas to expand. Such an expansion could, for example, raise a weight, resulting in work being done. However, at the end of that process the gas would be in a different state (expanded) than the one in which it started, so that this conversion of all the heat into work had the additional result of expanding the working fluid (in this case, the gas).

If the gas were, on the other hand, then made to return to its original volume, it could do so in three possible ways: (a) the same amount of work could be used to compress the gas, and the same amount of heat as was originally added would then be released from the cylinder; (b) if the cylinder were insulated so that no heat could escape, then the end result would be that the gas is at a higher temperature than originally; (c) something in-between. In the first case, there is no net work output or heat input. In the second, all the work was used to increase the internal energy of the gas, so that there is no net work and the gas is in a different state from which it started. Finally, in the third case, the gas could be returned to its original state by allowing some heat to be transferred from the cylinder. In this case the amount of heat originally added to the gas would equal the work done by the gas plus the heat removed (the first law requires this). Thus, the only way in which heat could be (partially) turned into work and the working fluid returned to its original state is if some heat were rejected to an object having a temperature lower than the heating object (so that the change of heat into work is not the only result). This is the principle of the heat engine (an internal combustion engine or a steam engine are examples).

Heat engines

The working fluid (say, water for a steam engine) of the heat engine receives heat Q_h from the burning fuel (diesel oil, for example), which converts it to steam. The steam expands, pushing on the piston so that it does work, W; as it expands, it cools and the pressure decreases. It then traverses a condenser, where it loses an amount of heat Q_c to the coolant (cooling water or the atmosphere, for example), which returns it to the liquid state. The second law says that,

KEY TERMS

Adiabatic process —A process during which no heat is transferred between the system and surroundings is described as adiabatic.

Avogadro’s number —The number of molecules present in one mole of whatever the compound is always equal to 6.0229 × 10²³. It was named for Italian physicist Amedeo Avogadro.

Boiling point —The boiling point of a liquid is the temperature at which it boils, also the temperature at which its vapor condenses.

Calorie —The amount of heat necessary to increase the temperature of water by one degree Celsius.

Celsius temperature (°C) —The temperature scale on which the freezing point of water is 0° and the boiling point is 100°.

Change in phase —Change in the form and characteristics of a substance, e.g., changes from gas to liquid, or liquid to solid.

Coefficient of linear expansion —The fractional rate of change in length of an object with a change in temperature.

Condensation temperature —The temperature at which a gas changes into a liquid (equal to the boiling point).

Equation of state —Relationship among the (experimentally determined) variables, which give complete information about the state of a system.

Fahrenheit temperature (°F) —The temperature scale on which the freezing point of water is 32°and the boiling point is 212°.

First law of thermodynamics —The internal energy of a system is increased by the amount of work done on the system and the heat flow to the system (conservation of energy).

Heat of condensation —The amount of heat needed to be removed from a gas to change it to its liquid phase (equal to the heat of vaporization).

Heat of fusion —The amount of heat needed to be added to a solid to change it to its liquid phase.

Heat of solidification —The amount of heat needed to be removed from a liquid to change it to its solid phase (equal to the heat of fusion).

Heat of vaporization —The amount of heat needed to be added to a liquid to change it to its gaseous phase.

Ideal gas— A gas obeying the ideal gas equation of state, pV = nRT, where, e.g., p is in Newtons/meter², Visinm³, n is the number of kilomoles of the gas, T is the temperature in K, and R = 8.31 kJ/kmolK.

Internal energy —The change in the internal energy of a system is equal to the amount of adiabatic work done on the system.

Kelvin temperature (K) —The Celsius temperature plus 273.15°C.

Kilomole (kmol) —A quantity of matter equal to M kilograms, where M is the molecular weight of the substance, with carbon-12 being taken as M←= 12 (one kilomole equals 1,000 moles).

Macroscopic theory —A theory which ignores the molecular nature of matter.

Melting point —The temperature at which a solid changes into a liquid.

Microscopic theory —A theory that is based on the molecular nature of matter.

Second law of thermodynamics —No process is possible whose only result is the transfer of heat from a cooler to a hotter object (Clausius statement). No process is possible whose only result is the conversion of heat into an equivalent amount of work (Kelvin Planck statement).

Solidification temperature —The temperature at which a liquid changes into a solid (equal to the melting point).

Specific heat —The amount of heat needed to increase the temperature of a mass of material by one degree.

Statistical mechanics —The microscopic theory of matter for which the macroscopic theory is thermodynamics, or the molecular basis of thermodynamics.

Sublimation —The change of a material from its solid phase directly to its gaseous phase.

Temperature (T) —The (experimentally determined) variable which determines the direction of heat flow; the variable which is common to all equations of state.

Thermal equilibrium —A condition between two or more objects in direct thermal contact in which no energy as heat flows from one to the other. The temperatures of such objects are identical.

Universal gas constant (R) —The constant in the ideal gas equation of state (as well as elsewhere); equal to 8.31 kJ/kmolK.

if the working fluid (in this case the water) is to be returned to its original state so that the heat-work process could begin all over again, then some heat must be rejected to the coolant. Since the working fluid is returned to its original state, there is no change in its internal energy, so that the first law demands that Q_h – Q_c = W. The efficiency of the process is the amount of work obtained for a given cost in heat input: E = W/Q_h. Thus, combining the two laws, E = (Q_h – Q_c)/Q_h. It can be seen therefore that a heat engine can never run at 100% efficiency.

It is important to note that the laws of thermodynamics are of very great generality, and are of importance in understanding such diverse subjects as chemical reactions, very low temperature phenomena, and the changes in the internal structure of solids with changes in temperature, as well as engines of various kinds.

See also Gases, properties of.

Resources

BOOKS

Burshtein, A.I. Introduction to Thermodynamics and Kinetic Theory of Matter. Weinheim, Germany: Wiley-VCH, 2005.

Roy, Bimalendu Naravan. Fundamentals of Classical and Statistical Thermodynamics. West Sussex, UK, and New York: John Wiley, 2002.

Turns, Stephen R. Thermodynamics: Concepts and Applications. New York: Cambridge University Press, 2006.

David Mintzer

Thermodynamics

Thermodynamics is the science that deals with work and heat , and the transformation of one into the other. It is a macroscopic theory, dealing with matter in bulk, disregarding the molecular nature of materials. The corresponding microscopic theory, based on the fact that materials are made up of a vast number of molecules, is called statistical mechanics .

Historical background

Benjamin Thompson, Count von Rumford (1753-1814) recognized from observing the boring of cannon that the work (or mechanical energy ) involved in the boring process was being converted to heat by friction , causing the temperature of the cannon to rise. With the experiments of James Joule (1818-1889), it was recognized that heat is a form of energy that is transferred from one object to another, and that work can be converted to heat without limit. However, the opposite is found not to be true: that is, there are limiting factors in the conversion of heat to work. The research of Sadi Carnot (1796-1832), of Lord Kelvin (1824-1907), and of Rudolph Clausius (1822-1888), among others, has led to an understanding of these limitations.

Temperature

The idea of temperature is well known to everyone, but the need to define it so that it can be used for measurements is far more complex than the simple concepts of "hot" and "cold." If a rod of metal is placed in an icewater bath and the length is measured, and then placed in a steam bath and the length again measured, it will be found that the rod has lengthened. This is an illustration of the fact that, in general, materials expand when heated, and contract when cooled (however, under some conditions rubber can do the opposite, while water is a very special case and is treated below). One could therefore use the length of a rod as a measure of temperature, but that would not be useful, since different materials expand different amounts for the same increase in temperature, so that everyone would need to have exactly the same type of rod to make certain that they obtained the same value of temperature under the same conditions.

However, it turns out that practically all gases, at sufficiently low pressures, expand in volume exactly the same amount with a given increase in temperature. This has given rise to the constant volume gas thermometer , which consists of a flask to hold the gas, attached to a system of glass and rubber tubes containing mercury. A small amount of any gas is introduced into the (otherwise empty) flask, and the top of the mercury in the glass column on the left is placed at some mark on the glass (by moving the right hand glass column up or down). The difference between the heights of the two mercury columns gives the difference between atmospheric pressure and the pressure of the gas in the flask. The gas pressure changes with a change in temperature of the flask, and can be used as a definition of the temperature by taking the temperature to be proportional to the pressure; the proportionality factor can be found in the following manner. If the temperature at the freezing point of water is assigned the value 0° and that at the boiling point is called 100°, the temperature scale is called the Celsius scale (formerly called Centigrade); if those points are taken at 32° and 212°, it is known as the Fahrenheit scale. The relationship between them can be found as follows. If the temperature in the Celsius scale is T(°C), and that in the Fahrenheit scale is T(°F), they are related by T(°F)=(9/5)T(°C)+32°. The importance of using the constant volume gas thermometer to define the temperature is that it gives the same value for the temperature no matter what gas is used (as long as the gas is used at a very low pressure), so that anyone at any laboratory would be able to find the same temperature under the same conditions. Of course, a variety of other types of thermometers are used in practice (mercury-in-glass, or the change in the electrical resistance of a wire, for example), but they all must be calibrated against a constant volume gas thermometer as the standard.

Expansion coefficients

An important characteristic of a material is how much it expands for a given increase in temperature. The amount that a rod of material lengthens is given by L=L0 [1+ α (T-T0)], where L0 is the length of the rod at some temperature T0, and L is the length at some other temperature T; α (Greek alpha) is called the coefficient of linear expansion. Some typical values for α ×106 (per °C) are: aluminum , 24.0; copper , 16.8; glass, 8.5; steel , 29.0 (this notation means that, for example, aluminum expands at a rate of 24.0/1,000,000 for each degree Celsius change in temperature). Volumes, of course, also expand with a rise in temperature, obeying a law similar to that for linear expansion; coefficients of volume expansion are approximately three times as large as that for linear expansion for the same material. It is interesting to note that, if a hole is cut in a piece of material, the hole expands just as if there were the same material filling it!

Thermostats

Since various metals expand at different rates, a thermostat can be made to measure changes in temperature by securely fastening together two strips of metal with different expansion coefficients. If they are straight at one temperature, they will be bent at any other temperature, since one will have expanded or contracted more than the other. These are used in many homes to regulate the temperature by causing an electrical contact to be made or broken as temperature changes cause the end of the strips to move.

Water

Water has the usual property of contracting when the temperature decreases, but only down to 39.2°F (4°C); below that temperature it expands until it reaches 32°F (0°C). It then forms ice at 0°C, expanding considerably in the process; the ice then behaves "normally," contracting as the temperature decreases. Since the density of a substance varies inversely to the volume (as a given mass of a substance expands, its density decreases), this means that the density of water increases as the temperature decreases until 4°C, when it reaches its maximum density. The density of the water then decreases from 4°C to 0°C; the formation of the ice also involves a decrease in density. The ice then increases its density as its temperature falls below 0°C. Thus, as a lake gets colder, the water at the top cools off and, since its density is increasing, this colder water sinks to the bottom. However, when the temperature of the water at the top becomes lower than 4°C, it remains at the top since its density is lower than that of the water below it. The pond then ices over, with the ice remaining at the top, while the water below remains at 4°C (until, if ever, the entire lake freezes). Fish are thus able to live in lakes even when ice forms at the top, since they have the 4°C water below it to live in.

Conservation of energy

The conservation of energy is well known from mechanics, where energy does not disappear but only changes its form. For example, the potential energy of an object at some height is converted to the kinetic energy of its motion as it falls. Thermodynamics is concerned with the internal energy of an object and those things that affect it; conservation of energy applies in this case, as well.

Heat

As noted in the introduction, doing work on an object (for example, by drilling a hole in a piece of metal, or by repeatedly bending it) causes its temperature to rise. If this object is placed in contact with a cooler object it is found that they eventually come to the same temperature, and remain that way as long as there are no outside influences (this is known as thermal equilibrium). This series of events is viewed as follows. Consistent with the concept of the conservation of energy, the energy due to the work done on the object is considered to be "stored" in the object as (what may be called) internal energy. In the particular example above, the increase in the internal energy of the object is recognized by the increase in temperature, but there are processes where the internal energy increases without a change in temperature. By then placing it in contact with an object of lower temperature, energy flows from the hotter to the colder one in the form of heat, until the temperatures become the same. Thus heat should be viewed as a type of energy which can flow from one object to another by virtue of a temperature difference. It makes no sense to talk of an object having a certain amount of heat in it; whenever it is placed in contact with a lower-temperature object, heat will flow from the hotter to the cooler one.

The first law of thermodynamics

These considerations may be summarized in the first law of thermodynamics: the internal energy of an object is increased by the amount of work done on it, and by the amount of heat added to it. Mathematically, if Uf is the internal energy of an object at the end of some process, and Ui is the internal energy at the beginning of the process, then Uf - Ui = W + Q, where W is the amount of work done on the object, and Q is the amount of heat added to the object (negative values are used if work is done by the object, or heat is transferred from the object). As is usual for an equation, all quantities must be expressed in the same units; the usual mechanical unit for energy (in the International System of Unitsformerly the MKS system) is the joule, where 1 joule equals 1 kg-m2/s2.

Specific heats; the calorie

An important characteristic of materials is how much energy in the form of heat it takes to raise the temperature of some material by one degree. It depends upon the type of material being heated as well as its amount. The traditional basic unit, the calorie , is defined as the amount of heat that is needed to raise one gram of water by one degree Celsius. In terms of mechanical energy units, one calorie equals 4.186 joules (J).

The corresponding amount of heat necessary to raise the temperature of other materials is given by the specific heat capacity of a material, usually denoted by c. It is the number of kilojoules (kJ) needed to raise 1 kg of the material by 1°C. By definition, the value for water is 4.186 kilojoules. Typical values for c in kilojoules per kg (kJ/kg), at 0°C, are: ice, 2.11; aluminum, 0.88; copper, 0.38; iron , 0.45. It should be noted that water needs more heat to bring about a given rise in temperature than most other common substances.

Change of phase

The process of water changing to ice or to steam is a familiar one, and each is an example of a change in phase. Suppose a piece of ice were placed in a container and heated at a uniform rate, that is, a constant amount of heat per second is transferred to the material in the container. The ice (the solid phase of water) first rises in temperature at a uniform rate until its temperature reaches 32°F (0°C), when it begins to melt, that is, some of the ice changes to water (in its liquid phase); this temperature is called the melting point. It is important to note that the temperature of the ice-water mixture remains at 32°F (0°C) until all the ice has turned to water. The water temperature then rises until it reaches 212°F (100°C), when it begins to vaporize, that is, turns to steam (the gaseous phase of water); this temperature is called the boiling point. Again, the water-steam mixture remains at 212°F (100°C) until all the liquid water turns into steam. Thereafter, the temperature of the steam rises as more heat is transferred to the container. It is important to recognize that during a change in phase the temperature of the mixture remains constant. (The energy being transferred to the mixture goes into breaking molecular bonds rather than in increasing the temperature.) Many substances undergo similar changes in phase as heat is applied, going from solid to liquid to gas, with the temperature remaining constant during each phase change. (Some substances, such as glass, do not have such a well-defined melting point.) The amount of heat needed to melt a gram of a material is known as the heat of fusion; that to vaporize it is the heat of vaporization. On the other hand, if steam is cooled at a uniform rate, it would turn to liquid water at the condensation temperature (equal to the boiling point, 212°F [100°C]), and then turn to ice at the solidification temperature (equal to the melting point, 32°F [0°C]). The heat of condensation is the amount of heat needed to be taken from a gram of a gas to change it to its liquid phase; it is equal to the heat of vaporization. Similarly, there is a heat of solidification which is equal to the heat of fusion. Some typical values are shown in Table 1.

It is interesting to note that water has much larger heats of fusion and of vaporization than many other usual substances. The melting and boiling points depend upon the pressure (the values given in the table are for atmospheric pressure). It is for this reason that water boils at a lower temperature in high-altitude Denver than at sea level .

Finally, below certain pressures it is possible for a substance to change directly from the solid phase to the gaseous one; this case of sublimation is best illustrated by the "disappearance" of dry ice when it is exposed to the atmosphere.

Equations of state; work

When an object of interest (usually called the system) is left alone for a sufficiently long time , and is subject to no outside influences from the surroundings, measurements of the properties of the object do not change

with time; it is in a state of thermal equilibrium. It is found experimentally that there are certain measurable quantities that give complete information about the state of the system in thermal equilibrium (this is similar to the idea that measurements of the velocity and acceleration of an object give complete information about the mechanical state of a system). For each such state relationships can be found which hold true over a wide range of values of the quantities. These relationships are known as equations of state.

Equations of state

Thermodynamics applies to many different types of systems; gases, elastic solids (solids that can be stretched and return to their original form when the stretching force is removed), and mixtures of chemicals are all examples of such systems. Each system has its own equation of state, which depends upon the variables that need to be measured in order to describe its internal state. The relevant variables for a system can only be determined by experiment, but one of those variables will always be the temperature.

The system usually given as an example is a gas, where the relevant thermodynamic variables are the pressure of the gas (P), its volume (V), and, of course, the temperature. (These variables are the relevant ones for any simple chemical system, e.g., water, in any of its phases.) The amount of gas may be specified in grams or kilograms, but the usual way of measuring mass in thermodynamics (as well as in some other fields) is in terms of the number of moles . One kilomole (kmol) is defined as equal to M kilograms, where M is the molecular weight of the substance, with carbon-12 being taken as M = 12. (One mole of any substance contains 6.02 × 1023 molecules, known as Avogadro's number.) Thus one kilomole of oxygen has a mass of 70.56 lb (32 kg); of nitrogen , 61.76 lb (28.01 kg); the molar mass of air (which is, of course, actually a mixture of gases) is commonly taken as 63.87 lb (28.97 kg). It is found, by experiment, that most gases at sufficiently low pressures have an equation of state of the form: PV = NRT, where P is in Newtons/m2, V is in m3, N is the number of kilomoles of the gas, T is the temperature in K, and R = 8.31 kJ/kmol-K is known as the universal gas constant. The temperature is in degrees Kelvin (K), which is given in terms of the Celsius temperature as T(K) = T(°C)+273.15°C. It should be noted that real gases obey this ideal gas equation of state to within a few percent accuracy at atmospheric pressure and below.

The equation of state of substances other than gases is more complicated than the above ideal gas law. For example, an elastic solid has an equation of state which involves the length of the stretched material, the stretching force, and the temperature, in a relationship somewhat more complex than the ideal gas law.

Work

Work is defined in mechanics in terms of force acting over a distance; that definition is exactly the same in thermodynamics. This is best illustrated by calculating the work done by a force F in compressing a volume of gas. If a volume of gas V is contained in a cylinder at pressure P, the force needed on the piston is (by the definition of pressure) equal to PA, where A is the area of the piston. Let the gas now be compressed in a manner which keeps the pressure constant (by letting heat flow out, so that the temperature also decreases); suppose the piston moves a distance d. Then the work done is W = Fd = PAd. But Ad is the amount that the volume has decreased, Vi - Vf, where Vi is the initial volume and Vf is the final volume. (Note that this volume difference gives a positive value for the distance, in keeping with the fact that work done on a gas is taken as positive.) Therefore, the work done on a gas during a compression at constant pressure is P(Vi - Vf).

The first law thus gives a straightforward means to determine changes in the internal energy of an object (and it is only changes in the internal energy that can be measured), since the change in internal energy is just equal to the work done on the object in the absence of any heat flow. Heat flow to or from the object can be minimized by using insulating materials, such as fiberglass or, even better, styrofoam. The idealized process where there is zero heat flow is called an adiabatic process.

The second law of thermodynamics

One of the most remarkable facts of nature is that certain processes take place in only one direction. For example, if a high temperature object is placed in contact with one of lower temperature, heat flows from the hotter to the cooler until the temperatures become equal. In this case (where there is no work done), the first law simply requires that the energy lost by one object should be equal to that gained by the other object (through the mechanism of heat flow), but does not prescribe the direction of the energy flow. Yet, in a situation like this, heat never flows from the cooler to the hotter object. Similarly, when a drop of ink is placed in a glass of water which is then stirred, the ink distributes itself throughout the water. Yet no amount of stirring will make the uniformly-distributed ink go back into a single drop. An open bottle of perfume placed in the corner of a room will soon fill the room with its scent, yet a room filled with perfume scent will never become scentfree with the perfume having gone back into the bottle. These are all examples of the second law of thermodynamics, which is usually stated in two different ways. Although the two statements appear quite different, it can be shown that they are equivalent and that each one implies the other.

Clausius statement of the second law

The Clausius statement of the second law is: No process is possible whose only result is the transfer of heat from a cooler to a hotter object. The most common example of the transfer of heat from a cooler object to a hotter one is the refrigerator (air conditioners and heat pumps work the same way). When, for example, a bottle of milk is placed in a refrigerator, the refrigerator takes the heat from the bottle of milk and transfers it to the warmer kitchen. (Similarly, a heat pump takes heat from the cool ground and transfers it to the warmer interior of a house.) An idealized view of the refrigerator is as follows. The heat transfer is accomplished by having a motor, driven by an electrical current, run a compressor. A gas is compressed to a liquid, a phase change which generates heat (heat is taken from the gas to turn it into its liquid state). This heat is dissipated to the kitchen by passing through tubes (the condenser) in the back of (or underneath) the refrigerator. The liquid passes through a valve into a low pressure region, where it expands and becomes a gas, and flows through tubes inside the refrigerator. This change in phase from a liquid to a gas is a process which absorbs heat, thus cooling whatever is in the refrigerator. The gas then returns to the compressor where it is again turned into a liquid. The Clausius statement of the Second Law asserts that the process can only take place by doing work on the system; this work is provided by the motor which drives the compressor. However, the process can be quite efficient, and considerably more energy in the form of heat can be taken from the cold object than the work required to do it.

Kelvin-Planck statement of the second law

Another statement of the second law is due to Lord Kelvin and Max Planck (1858-1947): No process is possible whose only result is the conversion of heat into an equivalent amount of work. Suppose that a cylinder of gas fitted with a piston had heat added, which caused the gas to expand. Such an expansion could, for example, raise a weight, resulting in work being done. However, at the end of that process the gas would be in a different state (expanded) than the one in which it started, so that this conversion of all the heat into work had the additional result of expanding the "working fluid" (in this case, the gas). If the gas were, on the other hand, then made to return to its original volume, it could do so in three possible ways: (a) the same amount of work could be used to compress the gas, and the same amount of heat as was originally added would then be released from the cylinder; (b) if the cylinder were insulated so that no heat could escape, then the end result would be that the gas is at a higher temperature than originally; (c) something in-between. In the first case, there is no net work output or heat input. In the second, all the work was used to increase the internal energy of the gas, so that there is no net work and the gas is in a different state from which it started. Finally, in the third case, the gas could be returned to its original state by allowing some heat to be transferred from the cylinder. In this case the amount of heat originally added to the gas would equal the work done by the gas plus the heat removed (the first law requires this). Thus, the only way in which heat could be (partially) turned into work and the working fluid returned to its original state is if some heat were rejected to an object having a temperature lower than the heating object (so that the change of heat into work is not the only result). This is the principle of the heat engine (an internal combustion engine or a steam engine are examples).

Heat engines

The working fluid (say, water for a steam engine) of the heat engine receives heat Qh from the burning fuel (diesel oil, for example) which converts it to steam. The steam expands, pushing on the piston so that it does work W; as it expands, it cools and the pressure decreases. It then traverses a condenser, where it loses an amount of heat Qc to the coolant (cooling water or the atmosphere, for example), which returns it to the liquid state. The second law says that, if the working fluid (in this case the water) is to be returned to its original state so that the heat-work process could begin all over again, then some heat must be rejected to the coolant. Since the working fluid is returned to its original state, there is no change in its internal energy, so that the first law demands that Qh - Qc=W. The efficiency of the process is the amount of work obtained for a given cost in heat input: E = W/Qh. Thus, combining the two laws, E = (Qh-Qc)/Qh. It can be seen therefore that a heat engine can never run at 100% efficiency.

It is important to note that the laws of thermodynamics are of very great generality, and are of importance in understanding such diverse subjects as chemical reactions , very low temperature phenomena, and the changes in the internal structure of solids with changes in temperature, as well as engines of various kinds.

See also Gases, properties of.

Resources

books

DiLavore, Philip, Energy: Insights from Physics. New York: Wiley, 1984.)

Goldstein, Martin, and Inge F. Goldstein. The Refrigerator and the Universe. Cambridge: Harvard University Press, Cambridge, 1993.

David Mintzer

KEY TERMS

Adiabatic process

—A process during which no heat is transferred between the system and surroundings is described as "adiabatic."

Avogadro's number

—The number of molecules present in one mole of whatever the compound is always equal to 6.0229 × 1023. It was named for the Italian physicist Amedeo Avogadro.

Boiling point

—The boiling point of a liquid is the temperature at which it boils, also the temperature at which its vapor condenses.

Calorie

—The amount of heat necessary to increase the temperature of water by one degree Celsius.

Celsius temperature (°C)

—The temperature scale on which the freezing point of water is 0° and the boiling point is 100°.

Change in phase

—Change in the form and characteristics of a substance, e.g., changes from gas to liquid, or liquid to solid.

Coefficient of linear expansion ( β. α)

—The fractional rate of change in length of an object with a change in temperature.

Condensation temperature

—The temperature at which a gas changes into a liquid (equal to the boiling point).

Equation of state

—Relationship among the (experimentally determined) variables, which give complete information about the state of a system.

Fahrenheit temperature (°F)

—The temperature scale on which the freezing point of water is 32° and the boiling point is 212°.

First law of thermodynamics

—The internal energy of a system is increased by the amount of work done on the system and the heat flow to the system (conservation of energy).

Heat of condensation

—The amount of heat needed to be removed from a gas to change it to its liquid phase (equal to the heat of vaporization).

Heat of fusion

—The amount of heat needed to be added to a solid to change it to its liquid phase.

Heat of solidification

—The amount of heat needed to be removed from a liquid to change it to its solid phase (equal to the heat of fusion).

Heat of vaporization

—The amount of heat needed to be added to a liquid to change it to its gaseous phase.

Ideal gas

—A gas obeying the ideal gas equation of state, pV = nRT, where, e.g., p is in Newtons/meter2, V is in m3, n is the number of kilomoles of the gas, T is the temperature in K, and R = 8.31 kJ/kmolK.

Internal energy

—The change in the internal energy of a system is equal to the amount of adiabatic work done on the system.

Kelvin temperature (K)

—The Celsius temperature plus 273.15°C.

Kilomole (kmol)

—A quantity of matter equal to M kilograms, where M is the molecular weight of the substance, with carbon-12 being taken as M = 12 (one kilomole equals 1,000 moles).

Macroscopic theory

—A theory which ignores the molecular nature of matter.

Melting point

—The temperature at which a solid changes into a liquid.

Microscopic theory

—A theory which is based on the molecular nature of matter.

Second law of thermodynamics

—No process is possible whose only result is the transfer of heat from a cooler to a hotter object (Clausius statement). No process is possible whose only result is the conversion of heat into an equivalent amount of work (Kelvin Planck statement).

Solidification temperature

—The temperature at which a liquid changes into a solid (equal to the melting point).

Specific heat

—The amount of heat needed to increase the temperature of a mass of material by one degree.

Statistical mechanics

—The microscopic theory of matter for which the macroscopic theory is thermodynamics, or the molecular basis of thermodynamics.

Sublimation

—The change of a material from its solid phase directly to its gaseous phase.

Temperature (T)

—The (experimentally determined) variable which determines the direction of heat flow; the variable which is common to all equations of state.

Thermal equilibrium

—A condition between two or more objects in direct thermal contact in which no energy as heat flows from one to the other. The temperatures of such objects are identical.

Universal gas constant (R)

—The constant in the ideal gas equation of state (as well as elsewhere); equal to 8.31 kJ/kmolK.

Thermodynamics

Thermodynamics is the science of heat and temperature and, in particular, of the laws governing the conversion of thermal energy into mechanical, electrical, or other forms of energy. It is a central branch of science that has important applications in chemistry, physics, biology, and engineering. Thermodynamics is a logical discipline that organizes the information obtained from experiments performed on systems and enables us to draw conclusions, without further experimentation, about other properties of the system. It allows us to predict whether a reaction will proceed and what the maximum yield might be.

Thermodynamics is a macroscopic science that deals with such properties as pressure, temperature, and volume. Unlike quantum mechanics , thermodynamics is not based on a specific model, and therefore it is unaffected by our changing concepts of atoms and molecules. By the same token, equations derived from thermodynamics do not provide us with molecular interpretations of complex phenomena. Furthermore, thermodynamics tells us nothing about the rate of a process except its likelihood.

Applications of thermodynamics are based on three fundamental laws that deal with energy and entropy changes. The laws of thermodynamics cannot be derived; their validity is based on the fact that they predict changes that are consistent with experimental observations.

The first law of thermodynamics is based on the law of conservation of energy, which states that energy can neither be created nor destroyed; therefore, the total energy of the universe is constant. It is convenient for scientists to divide the universe into two parts: the system (the part of the universe that is under study—for example, a beaker of solution) and the surroundings (the rest of the universe). For any process, then, the change in the energy of the universe is zero. Chemists are usually interested only in what happens to the system. Consequently, for a given process the first law can be expressed as

ΔU = q + w          (1)

where ΔU is the change in the internal energy of the system, q is the heat exchange between the system and the surroundings, and w is the work done by the system or performed on the system by the surroundings. The first law is useful in studying the energetics of physical processes, such as the melting or boiling of a substance, and chemical reactions—for example, combustion . The heat change occurring as part of a process is measured with a calorimeter. For a constant-volume process, the heat change is equated to the change in the internal energy ΔU of the system; for a constant-pressure process, which is more common, the heat change is equated to the change in the enthalpy ΔH of the system. Enthalpy H is a thermodynamic function closely related to the internal energy of the system, and is defined as

H = U + PV          (2)

where P and V are the pressure and volume of the system, respectively.

The first law of thermodynamics deals only with energy changes and cannot predict the direction of a process. It asks, for example: Under a given set of conditions of pressure, temperature, and concentration, will a specific reaction occur? To answer the question we need a new thermodynamic function called entropy S. To define entropy, we need to use a quantum mechanical concept. The entropy of a system is related to the distribution of energy among the available molecular energy levels at a given temperature. The greater the number of energy levels that have significant occupation, the greater the entropy.

The second law of thermodynamics states that the entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process. The mathematical statement of the second law of thermodynamics is given by

ΔS _univ = ΔS _sys + ΔS _surr ≥ 0          (3)

where the subscripts denote the universe, the system, and the surroundings, respectively. The greater than portion of the "greater than or equal to" sign corresponds to a spontaneous process, and the equal portion corresponds to a system at equilibrium. Because processes in the real world are spontaneous, the entropy of the universe therefore constantly increases with time.

As is not the case with energy and enthalpy , it is possible to determine the absolute value of entropy of a system. To measure the entropy of a substance at room temperature, it is necessary to add up entropy from the absolute zero up to 25°C (77°F). However, the absolute zero is unattainable in practice. This dilemma is resolved by applying the third law of thermodynamics, which states that the entropy of a pure, perfect crystalline substance is zero at the absolute zero of temperature. The increase in entropy from the lowest reachable temperature upward can then be determined from heat capacity measurements and enthalpy changes due to phase transitions.

Because it is inconvenient to use the change in entropy of the universe to determine the direction of a reaction, an additional thermodynamic function, called the Gibbs free energy (G ), is introduced to help chemists to focus only on the system. The Gibbs free energy of a system is defined as G = H − TS, where T is the absolute temperature. At constant temperature and pressure, ΔG is negative for a spontaneous process, is positive for an unfavorable process, and equals zero for a system at equilibrium. The change in Gibbs free energy can be related to the changes in enthalpy and entropy of a reaction, and also to the equilibrium constant of the reaction, according to the equation ΔG ° = −RT ln K, where ΔG ° is the change in Gibbs free energy under standard-state conditions (1 bar), R is the gas constant, and K is the equilibrium constant.

Many chemical reactions can be classified as either kinetically controlled or thermodynamically controlled. In a kinetically controlled process the products are thermodynamically more stable than the reactants, hence the reaction is favorable. However, the rate of reaction is often very slow due to a high activation energy barrier. The conversion of the less stable allotropic form of carbon, diamond, to the more stable graphite is an example: The process can take millions of years to complete. In a thermodynamically controlled reaction the reactants may have a number of kinetically accessible routes to follow to form different products, but what is eventually formed is governed by relative thermodynamic stability. In protein folding, for example, a denatured protein may have many possibilities of intermediate conformation; however, the conformation it finally assumes, which corresponds to the physiologically functioning protein, is the most stable state thermodynamically.

see also Chemistry and Energy; Energy; Heat; Kinetics; Physical Chemistry; Temperature.

Raymond Chang

Bibliography

Bent, Henry A. (1965). The Second Law: An Introduction to Classical and Statistical Thermodynamics. New York: Oxford University Press.

Berry, R. Stephen (1991). Understanding Energy: Energy, Entropy, and Thermodynamics for Everyman. River Edge, NJ: World Scientific.

Smith, E. Brian (1990). Basic Chemical Thermodynamics, 4th edition. New York: Oxford University Press.

Thermodynamics

Thermodynamics is the science that deals with work and heat—and the transformation of one into the other. It is a macroscopic theory, dealing with matter in bulk, disregarding the molecular nature of materials. The corresponding microscopic theory, based on the fact that materials are made up of a vast number of particles, is called statistical mechanics.

Historical background

The origins of thermodynamics can be traced to the late eighteenth century. English-American physicist Benjamin Thomson, Count Rumford (1753–1814), became intrigued by the physical changes accompanying the boring of cannons. (Boring is the process of making a hole—in this case the barrel of the cannon—with a twisting movement.) He found that the work (or mechanical energy) involved in the boring process was converted to heat as a result of friction, causing the temperature of the cannon to rise.

Some of the fundamental relationships involved in thermodynamics were later developed by English physicist James Joule (1818–1889), who showed that work can be converted to heat without limit. Other researchers found, however, that the opposite is not true—that is, that there are limiting factors that operate in the conversion of heat to work. The research of French physicist Sadi Carnot (1796–1832), British physicist William Thomson, Lord Kelvin (1824–1907), and German physicist Rudolf Clausius (1822–1888), among others, has led to an understanding of these limitations.

The laws of thermodynamics

The most basic facts about thermodynamics can be summarized in two general laws. The first law of thermodynamics is actually nothing other than the law of conservation of energy: energy can neither be created nor destroyed. It can be converted from one form to another, but the total amount of energy in a system always remains constant.

For example, consider the simple example of heating a beaker of water with a gas flame. One can measure the amount of heat energy given off by the flame. One also can measure the increase in the heat energy of the water in the beaker, the beaker itself, and any air surrounding the beaker. Under ideal circumstances, the total amount of energy produced by the flame is equal to the total amount of energy gained by the water, the beaker, and the air.

The first law of thermodynamics is sometimes stated in a somewhat different form because of the kinds of systems to which it is applied. Another statement is that the internal energy of a system is equal to the amount of work done on the system plus any heat added to the system. In this definition, the term work is used to describe all forms of energy other than heat.

The first law can be thought of as a quantitative law (involving measurement of some quantity or amount): the amount of energy lost by one system is equal to the amount of energy gained by a second system. The second law, in contrast, can be thought of as a qualitative law (involving quality or kind): the second law says that all natural processes occur in such a way as to result in an increase in entropy.

To understand this law, it is first necessary to explain the concept of entropy. Entropy means disorder. Consider the dissolving of a sugar cube in water. The sugar cube itself represents a highly ordered state in which every sugar particle is arranged in an exact position within the sugar crystal. The entropy of a sugar cube is low because there is little disorder.

Words to Know

Energy: The capacity for doing work.

Entropy: The amount of disorder in a system.

First law of thermodynamics: The internal energy of a system is increased by the amount of work done on the system and the heat flow to the system (Conservation of Energy).

Heat: A form of energy produced by the motion of molecules that make up a substance.

Second law of thermodynamics: All natural processes proceed in a direction that leads to an increase in entropy.

Submicroscopic level of phenomena: Phenomena that cannot be observed directly by any of the five human senses, aided or unaided.

Work: Transfer of energy by a force acting to move matter.

But consider what happens when the sugar cube is dissolved in water. The cube breaks apart, and sugar molecules are dispersed completely throughout the water. There is no longer any order among the sugar molecules at all. The entropy of the system has increased because the sugar molecules have become completely disorganized.

The second law of thermodynamics simply says that any time some change takes place in nature, there will be more entropy—more disorganization—than there was to begin with. As a practical example, consider the process by which electricity is generated in most instances in the United States today. Coal or oil is burned in a large furnace, heating water and changing it to steam. The steam then is used to run turbines and generators that manufacture electricity. The first law of thermodynamics says that all of the energy stored in coal and oil must ultimately be converted to some other form: electricity or heat, for example. But the second law says that some of the energy from coal and oil will end up as "waste" heat, heat that performs no useful function. It is energy that simply escapes into the surrounding environment and is distributed throughout the universe.

The second law is sometimes described as the "death of the universe" law because it means that over very long periods of time, all forms of energy will be evenly distributed throughout the universe. The waste energy produced by countless numbers of natural processes will add up over the millennia until that is the only form in which energy will remain in our universe.

[See also Gases, properties of; Heat; Temperature ]