Water boiling on a stove and hot air rising from the asphalt on a parking lot in summertime are both examples of heat transfer by convection. Think about the water in the pot. Heat from the stove causes the molecules of water in the bottom layer of the pan to move faster. Some heat travels up through the water by conduction, but the process is too slow and cumbersome to move all the energy that is pouring in. The water at the bottom heats up, expands, and rises, to be replaced by cold water from the upper regions of the pot. When this heated water gets to the top it cools off and sinks, to be replaced by newly heated water from the bottom. The cycle of heating and cooling goes on, creating what is known as a convection cell. Convection depends on heat being carried from one place to another by the bulk motion of warmed materials, rather than through collisions between individual atoms.
Hold your hand out toward a fire and you feel warmth, even though neither convection nor conduction is operating. Heat reaches you by radiation. In this case, infrared radiation (an invisible cousin of ordinary light) travels from the fire to your hand, carrying energy in the process. Every object in the universe gives off heat by radiation. Indeed, for something like a satellite or a star in the vacuum of space, radiation is the only way that heat can be given off.
Heat, Temperature, and Absolute Zero
The words “temperature” and “heat” are often used interchangeably, but scientists think of the two terms in quite distinct ways. Heat refers to the total amount of atomic kinetic and potential energy in a material. Two gallons of ice water hold twice as much heat energy as one gallon. Temperature, on the other hand, is a relative term. Two objects are at the same temperature if no heat flows between them. Put a pound of metal into a gallon of ice water and they will soon be at the same temperature—32° Fahrenheit. But the metal and ice water do not hold the same amount of heat energy, because it takes more energy to make the atoms of water vibrate.
The time and temperature display at your local bank probably gives temperatures in degrees Fahrenheit and degrees Celsius, two scales in common use. The choice of which scale to use is arbitrary—there is no “correct” way to report temperature. All you have to do is pick two easily reproducible temperature reference points, assign a number to each, and then split the gap between the numbers into convenient intervals that you call “degrees.” The Celsius scale, for example, uses the freezing and boiling points of water as its two reference points, calling the former zero, the latter 100, and defining a degree Celsius as a hundredth of the interval between the two. The Fahrenheit scale works the same way, with zero signifying the coldest temperature Daniel Fahrenheit could produce in his laboratory back in 1717 and 100 being his best determination of human body temperature. Today, the Fahrenheit scale is defined in terms of the freezing and boiling points of water (32° and 212° respectively), and human body temperature is the more familiar 98.6°F.
Insofar as there is a “scientific” scale, however, it is what scientists call the Kelvin scale, named after William Thomson, Lord Kelvin (1824–1907), one of the founders of thermodynamics. The degree in the Kelvin scale is the same as a degree Celsius, but, unlike other scales, it is anchored by the only temperature that refers to a fundamental physical process.
The zero in the Kelvin scale is taken to be absolute zero—the lowest temperature attainable by any natural system. In the nineteenth century, absolute zero was pictured as the temperature at which all atomic motion stopped—at which everything just froze. Today, the laws of quantum mechanics have changed this picture slightly, and we define absolute zero as the temperature at which no more heat can be extracted from a system. Either way, absolute zero is cold. It measures-273.16°C (or-453°F). On the Kelvin scale, water freezes at 273.16 K, room temperature is about 300 K, and a wood fire ignites at about 650 K.
BAD NEWS—THE SECOND LAW
The first law tells us that energy can be converted from one form to another and that the total amount of energy in a closed system is fixed, but it says nothing about whether a particular store of energy can be used to do anything useful. There is, for example, a great deal of energy stored in the vibrational energy of water in the ocean. According to the first law, that energy could, in principle, be used to power a ship. The fact that no one has devised a ship to tap this reservoir of energy is a consequence of the second law of thermodynamics. This law places limitations on the ways that heat can be converted to useful work, and, in the process, produces a gloomy picture of the evolution of the universe.
Like other fundamental laws, the second law is deceptively simple, but belies a great deal of depth. Unlike most of the other laws we will encounter, however, the second law can be stated in ways that appear at first to be quite different. In fact, they are all logically equivalent—any one statement implies (and is implied by) the others. First statement:
Heat energy always flows spontaneously from hot to cold.
If you put an ice cube on the table, heat will flow into it from the table and the surrounding air. The ice cube doesn’t get successively colder as heat flows out of it into the air. This commonplace experience is one illustration of the second law.
It is important to realize that the second law does not say that heat never flows from cold to hot. When you make ice in a refrigerator, that’s exactly what happens. What the second law says is that if you want heat to flow “against the grain,” you have to put energy into the system. In a refrigerator, energy comes into the system through the electric power cord. In fact, we like to say that there is another statement of the second law, namely:
A refrigerator won’t work unless it’s plugged in.
Second statement:
It is impossible to build an engine that operates on a cycle whose only effect is to convert heat into an equivalent amount of work.
An engine is a device that takes energy stored in some form and produces useful work. The engine in your car, for example, takes chemical energy stored in gasoline and produces kinetic energy to make the car move. The second law says that no engine can operate at 100 percent efficiency.
At one level this isn’t too surprising, especially for real engines. Every real machine must have moving parts, and every time parts move, some energy is lost as frictional heat. Heat always flows from hot to cold, so the frictional heat dissipates; it flows out to the machine’s surroundings and that lost energy can do no further work through the machine. When you drive your car, some of the potential energy of the gasoline is lost as engine heat, as tire wear and friction, or even as sound energy as the car speeds along.
But even if there were no friction in an engine, the second law tells us that the efficiency with which heat can be converted to useful work must be less than 100 percent; some energy must always be dissipated into the environment as waste heat. The reason for this is that every engine, no matter what its design, must operate on a cycle, and must always be returned to its original position so that it can start its cycle over again. In your car, for example, the gasoline-air mixture that explodes in your cylinder drives the piston down. This motion, through a number of intermediate steps, eventually becomes the force that turns the wheels of the car, moving it forward. In principle (but not in practice) this operation could be carried out with 100 percent efficiency—all the stored energy of the fuel converted into the kinetic energy of the car. The important point, however, is that at the end of this operation, the piston is at the bottom of the cylinder. It has to be returned to the top before it can make the car move farther. To return the piston to the top, you have to cool the cylinder down so that the air you are compressing doesn’t finish the cycle at a higher temperature than it had at the beginning. In your car, this heat (as well as some of that generated by the explosion) is carried away from the cylinder by the cooling system and transferred to the atmosphere by the radiator.
According to the second law, every engine, no matter how cleverly designed, must take some of its original store of energy and transfer it to a lower-temperature reservoir
in order to return the engine to its original position. In most cases, this reservoir is the atmosphere or the ocean. In that reservoir the energy be comes unusable, because to tap it we would have to build an engine that could deposit its waste heat in some still cooler reservoir that doesn’t exist. To argue otherwise is equivalent to saying you can make a refrigerator that will work when it isn’t plugged in.
The second law leads to the intuitively reasonable notion that energy sources appear in a hierarchy, with high-grade sources producing very high temperatures and dumping heat to lower-temperature reservoirs, heat from those reservoirs dumping heat to those at a still lower temperature until, at the end of the chain, the accumulated waste heat ends up in the environment.
This idea has important technological consequences. The second law tells us, for instance, that if we burn coal with perfect efficiency, only slightly more than a third of the energy locked in the coal can ultimately appear as electricity in your home. The rest of the coal’s chemical energy must go into the atmosphere—a fact that explains the presence of giant cooling towers at large generator sites. The true efficiency of a generating plant must be even smaller than this to take into account the effects of things like friction. To give credit to our engineering colleagues, we should point out that the efficiency of modern generators is within a few percentage points of the limit allowed by the second law.
Every few years for the past two centuries enthusiastic inventors have come forth with claims of perpetual motion machines—miracle devices that run forever with no additional energy input. So far none of the machines has worked. (One of our colleagues boasts that he keeps a complete collection of successful perpetual motion devices in his desk drawer.) New claims are met with universal skepticism by the scientific community, but not because scientists are too conservative or unwilling to listen to new ideas. Such machines would violate the second law, and would be equivalent to refrigerators that work when they’re not plugged in. Third statement:
The amount of disorder in any isolated system cannot decrease with time.
If you placed 100 black marbles in the bottom of a jar, put a layer of 100 red marbles above them, then put a layer of 100 green marbles on top and shook the jar vigorously, you know what would result. In a short time black, red, and green marbles would be all mixed together. You could keep shaking for a million years and still never come close to duplicating the original orderly configuration.
This example illustrates an important point about nature. Isolated systems naturally tend to move from order to disorder. Put another way, time has a definite direction, with disordered systems occurring later than ordered ones. This idea is deeply ingrained since your life is full of examples of the second law. Just play your favorite video backwards and see how many things look wrong. It’s easier to make an omelet than to unmake it, easier to scratch the side of your car than to paint it, easier to mess up your room than to clean it, and so on. All of these examples express the same idea of the directionality of time in nature.
“Entropy” is the scientist’s measure of a system’s randomness or disorder. The third statement of the second law says that in any closed system entropy either increases or (at best) remains the same over time. Disorder never decreases. Having said this, however, we have to admit that some systems can become more ordered—but at the expense of making things more disordered someplace else. You can vacuum your room, but you also have to pay the electric bill. When you make an ice cube in your refrigerator the water becomes more ordered as it freezes. The refrigerator, however, is not an isolated system—it is connected to the power plant that generates its electricity. The second law says that the increase in the orderliness of the water’s atoms must be balanced by an increase in disorder in the atmosphere around the generating plant, an increase that is sure to result from waste heat.
Living systems are the most highly ordered form of matter we know. Staggering numbers of atoms must fit together in a precisely dictated way to make even the simplest cell. Creationists sometimes argue that evolution theories violate the second law because they assume that life appeared spontaneously. Nothing so ordered, they argue, could arise from disorder, because of the second law. Just as was the case with the ice cube, however, you have to consider the energy and randomness of the entire system in which life arose. That system includes not just Earth, but Earth’s energy source—the sun—as well. The relative increase in order seen in living systems on the surface of our planet is more than balanced by the disorder created by the nuclear furnace that supplies the sun with energy; and the total entropy of the Earth-sun system increases all the time.
The second law tells us that in nature, as in life, you have to pay for what you get. There is no free lunch!
FRONTIERS—NEW ENERGY SOURCES
One of the great problems humanity will face in the twenty-first century will be to find a way of generating energy without burning fossil fuels. Fossil fuels—coal, oil, and natural gas—result from energy in the form of sunlight falling on the Earth millions of years ago being converted to chemical energy in plants and animals and, upon their death, being stored in geological formations until they are mined by humans. By the end of the twentieth century, over 90 percent of all energy used by humans was derived from these fossil fuels. This fact should not be surprising, because these fuels represent a high-grade source of energy that is easily accessible and easy to use.
However, this energy strategy has two serious drawbacks. First, fossil fuels cannot last forever. Indeed, many analysts believe that more than half of all easily recovered petroleum has already been used up and that supplies will decline sharply in the twenty-first century. Furthermore, burning fossil fuels adds carbon dioxide to the atmosphere, an effect, as we shall see in Chapter 15, that may lead to global warming and other environmental problems. Thus, finding other ways of generating energy has become a major goal of scientific and technological research.
Many promising sources of energy do not involve fossil fuels. Two of these—nuclear fission and nuclear fusion—will be discussed in Chapter 8. Two others, involving energy sources that America has in abundance, are wind and solar power.
Wind energy is one of humanity’s oldest sources of energy Basically, the rotation of the Earth and the energy carried by incoming sunlight produce winds, and these winds can be used to turn windmill blades and generate electricity. The United States has huge energy resources in windswept places like the Dakotas, Colorado, and many coastal areas, and by the beginning of the twenty-first century the technology of wind turbines had developed to the point that wind energy is economically competitive with fossil fuels. The future energy strategy of the United States will likely involve a significant fraction of energy from this source.
Solar energy is also abundant in the United States, particularly in the deserts of the Southwest. Converting incoming sunlight into electricity is technically possible through the use of semiconducting diodes (see Chapter 7), but the problem has always been to make this conversion at a cost that would make solar electricity comparable to electricity generated by coal. In the 1980s, for example, the cost of solar electricity was twenty times higher than that of coal. This disparity has been falling, however, and by the beginning of the twenty-first century the cost of solar electricity was only five times that of coal. It is expected that when the cost of solar electricity is reduced further, it will also provide a significant fraction of the national energy budget.
CHAPTER THREE
Electricity and Magnetism
6A.M. ANOTHER WEEKDAY. The clock-radio blares, but you lie in bed a few minutes longer, listening to the news and weather and gathering energy to face the day. Turn on the light, start the coffee, wake the children, shower and dress. Grab the orange juice from the refrigerator—a note on the door reminds you that the kids have basketball practice after school. Eat a piece of toast, maybe some cereal. Brush your teeth, feed the cat, turn on the answering machine, and out the door to work. By 7 A.M. you�
��re on your way to another busy day.
Gravity is not the only natural force you experience daily, nor even the strongest. In just one hour you’ve had dozens of run-ins with electricity and magnetism. A magnet clings to your refrigerator door, easily overcoming the gravitational force that the entire Earth, pulling down, exerts on it. Static cling holds your clothes together, and you have to exert a force to pull them apart. These effects are not caused by gravity.
Electricity and magnetism are familiar forces and they appear everywhere in nature. Four laws of nature, Maxwell’s equations, summarize everything we know about the phenomena of electricity and magnetism. The most important statement made in these equations is:
Electricity and magnetism are two aspects
of the same force.
Lightning, static cling, friction, radio transmission, and the little magnets you use to hold notes on your refrigerator are all siblings.
MAXWELL’S EQUATIONS
Once Isaac Newton demonstrated the power of the scientific method in mechanics, it was natural that the method would be applied to other areas. Eighteenth-century researchers with now familiar names like Alessandro Volta and André-Marie Ampère studied electrical and magnetic phenomena as curiosities of the laboratory. They constructed batteries, examined the effects of electric sparks, passed current through various materials, and performed hundreds of other experiments. Driven by a desire to understand fascinating natural phenomena, these researchers never dreamed that electricity might someday transform society. Today we would say they were doing basic research.
Science Matters Page 5