Chapter 6 from Universe Down to Earth
One of the greatest triumphs of 18th and 19th century physics was the formal understanding of heat energy and its interchangeability with mechanical energy. Out of these efforts was born the branch of physics called thermodynamics, which was pioneered through the efforts of many scientists, including the Scottish engineer James Watt (born 1736), who perfected the modern condensing steam engine; the American physicist Benjamin Thompson (born 1753, later Count Rumford), who first proposed that heat is a form of energy; the French engineer Nicolas Léonard Sadi Carnot (born 1796), who provided the first analysis of heat engines; the British physicist James Joule (born 1818), who performed careful experiments to prove that heat is, indeed, a form of energy; and the British physicist William Thompson (born 1824, later Lord Kelvin), who helped to formulate a consistent physical theory.
Modern society owes its industrial success primarily to the invented machines that allow work to be accomplished from energy that is not supplied by the physical labor of humans or of other animals. It is no accident that the 19th century industrial revolution coincided with the development of thermodynamics. A curious 20th century analog is that computers allow certain computational tasks to be completed without the intellectual labor of humans, so that society can now substitute machines for both our body and our brain. Meanwhile, back in the rest of the cosmos, the conversion of one form of energy to another plays a major role in stellar evolution, stellar orbits, and in the fate of the universe itself.
There are many different types of energy, although not all of them manifest themselves in everyday life. Among those that do, there is one type of energy that kills more people per year than any other. It is the energy you have by simply being in motion, which is known in the world of physics as your kinetic energy.
When you start your car and accelerate to 50 miles per hour onto the freeway and drive for a few hundred miles, you may notice that there is less fuel in your tank than when you started. During your trip, you converted the stored chemical energy of the gasoline into heat energy from the friction of the car’s internal moving parts, and into the kinetic of your entire car plus its occupants. When you apply your brakes to return to zero miles per hour, your car’s kinetic energy must go somewhere. It transforms to heat by way of the friction between your brake pads and your wheels, and if you skid, between your rubber tires and the road.
In a head-on collision, you also slow, for example, from 50 miles per hour to zero miles per hour, except that this does not happen with the help of your brakes. The kinetic energy of car-plus-driver at 50 miles per hour must go somewhere. It becomes the sole source of energy for the deafening sound of the collision, the crunch of the car’s front end, the smashed face and skull of any unseatbelted passenger, the damaged guard rail alongside the road, and any toppled lamp posts. The kinetic energy wielded by an object depends on its mass and on its velocity. But it only takes a small change in velocity to induce a big change in the kinetic energy. More precisely stated, the kinetic energy depends on the mass and on the square of the velocity
Kinetic Energy = ½ × mass × velocity²
This formula, translated into a proverb, would read “speed kills.” A sobering example is that at 70 miles per hour, you have nearly twice the kinetic energy of what you had at 50 miles per hour. In other words, if you were to drive 70 miles per hour rather than 50 miles per hour, then every aspect of a car accident would be twice as worse. Not only would the sounds be louder, but, on average, the damage to your car would be twice as costly, and you would be twice as likely to die. Yes, speed does kill.
While departments of transportation try to help people stay alive on the highways, the United States Department of Defense tries to find ways to kill people. Using the principle that speed kills, a rifle was invented that fires a relatively small bullet (0.22 caliber), but achieves a muzzle velocity of 3,250 feet per second, which is about three times the speed of sound—you would be hit with the bullet before you hear the rifle fire. This weapon is the M-16 assault rifle designed by Eugene Stoner in 1959, which was widely used by the American forces in the Vietnam War. It replaced the Thompson sub-machine gun that was used throughout the Korean War, which fired relatively slow-moving, fat (0.45 caliber) bullets. Stoner realized that high muzzle velocity is more important than massive bullets. This physical principle had not escaped the Russian weapons designer Mikhail Kalashnikov. His AK-47 rifle, the Russian high velocity counterpart to the M-16, was widely used by the North Vietnamese. It is the kinetic energy of the bullet, obtained from the stored chemical energy of explosive powder, that transfers to the target, which in the case of human flesh can be quite devastating. A letter home from Vietnam, written by Army Corporal George Olsen in 1969 contains the following passage
…we crawled within six feet of one group [of the North Vietnamese Army] and then charged, and all hell broke loose…One [of them] went down fighting; [he] shot our point man in the ankle at fistfighting range, [but] then was blown apart by the sergeant leading us. I won’t go into detail, but it is unbelievable what an M-16 will do to a man—particularly at close range. The only conceivable comparison is swatting a bug with a chain-mail glove. Enough said—perhaps too much.
[Our point man’s] wound, of itself, wasn’t serious, but the power and shock of a modern rifle bullet is absolutely unbelievable and within two minutes of being hit he was fighting for his life in shock…1
Chemical energy is not the only way to set something into motion. Gravity is well known for this ability. For example, if you set a pan of freshly baked peach cobbler to cool on the narrow sill of your open window on the 8th floor of an apartment building, and if, by chance, it accidentally flies out of the window, it will increase speed (gain kinetic energy) all the way to the ground. Unless you have lived in the basement all your life, this airborne fate of your peach cobbler comes as no surprise. What was the source of energy that became the kinetic energy of the cobbler? It was not gasoline. We presume it was not gun powder. It was you (or your elevator). You carried the peaches. You carried the flour. You carried the brown sugar. You carried the eggs. You carried all ingredients from the ground level to the 8th floor against the will of gravity. This common consequence of a shopping trip endows your food with the potential to recover the work you did against gravity. In genuine terms of physics, the food was given gravitational potential energy simply by being lifted to some height above the ground. The higher above the ground the food is taken, the more potential energy it gains, and the faster it will hit the ground after it flies out of the window. What then happens to the kinetic energy? It promptly explodes the food in a manner that is commonly described with the word “splat.” It also may damage the ground.
On an average day, Earth plows through about 1,000 tons of meteors. As they fall toward Earth’s surface, most of these meteors lose all their kinetic energy in a spectacular way as friction with the atmosphere makes them burn. They become what we all identify as “falling” stars in the nighttime sky. Some of the larger meteors actually survive the trip through Earth’s atmosphere, and hit the ground with tremendous kinetic energy. What then happens to the kinetic energy? It digs holes. The 25,000 year old Barringer crater near Coon Butte, in Coconino County, Arizona, is an impressive example of a hole “dug” by the impact energy of an iron meteor. It is 14 football fields in diameter and about 500 feet deep.
When astronauts re-enter Earth’s lower atmosphere from orbit, their heat shields get hot. What is not widely appreciated is that these shields are the thermal repository for the loss of the spacecraft’s kinetic energy. Heat shields do not simply serve as protection, they are a way of slowing down. One might even call them “airbrakes.”
Spongy objects such as foam, springs, and car airbags, make excellent kinetic energy absorbers. If a pole vaulter chooses to land on a slab of concrete after a 20 foot vault, then the kinetic energy of the fall would be used to fracture bones and rupture body tissue upon impact. This is the splat effect that the peach cobbler experienced. Organizers of track and field events wisely place fluffy things near the pole vault and high jump to absorb the kinetic energy of impact. The task of absorbing the kinetic energy is now passed from the human body to these spongy pillows, which is why pillows are normally preferred to concrete. What then becomes of this absorbed energy? It is converted immediately to heat within the absorbers and then dissipated to the atmosphere. Springs, however, take longer to convert kinetic energy into heat. If our pole vaulter landed on springs, then the kinetic energy would swap back and forth with the mechanical potential energy of the spring. You would watch the vaulter bob up and down until the energy was converted to heat within the springs.
Children’s toys are no exception to these rules. When you shove the clown of a jack-in-the-box back into its box, you are providing energy that is stored in the inner spring. When the lid is released and the clown pops out, the spring converts its stored mechanical energy into the kinetic energy of the clown. Only when the bobbing stops has the spring converted all available energy into heat, which dissipates to the atmosphere. Many toys require that you “wind up” some sort of device that stores mechanical potential energy. The stored energy is then converted to kinetic energy, such as a truck that rolls, a robot that walks, or perhaps even a baby doll that pees. In other toys, this mechanical potential energy is converted to sound energy as the robot or doll speaks to you. The only difference between toys that use batteries and toys that need to be wound is that batteries use stored chemical energy obtained from the battery manufacturer, and wind-up toys use stored mechanical energy obtained from you.
The conversion of gravitational potential energy to kinetic energy is a fundamental ingredient in star formation and stellar evolution. In the final collapse of a gas cloud to form a star, there is a precipitous rise in the kinetic energy of the individual atoms of the cloud. Because the cloud is gaseous, the individual atoms cannot fall straight to the cloud’s center. Instead, the increase in kinetic energy is revealed through an increase in atomic collisions and an associated increase in temperature. Some of this kinetic energy is also converted to photons of light, which escape into space. Eventually, if the gas cloud contains enough mass, the core temperature will become high enough to trigger thermonuclear fusion.
A similar mechanism allows us to discover the presence of compact cosmic objects with high mass such as neutron stars and black holes. Unlike the Sun, most stars in the Galaxy do not travel though space alone. It is not uncommon to find binary, triple, or even quadruple star systems with all members in mutual orbit. If one star first collapses to become a black hole, and another star passes through the red giant phase, then the red giant may fill its Roche lobe and dump matter across its Lagrangian point onto the black hole. Rather than fall straight in, the gaseous matter is likely to spiral toward the black hole’s event horizon, like water that runs down a toilet bowl. Friction between the inner, fast-spinning regions and the outer slower-spinning regions heats the gas to enormous temperatures. As a consequence, the funneling gas emits copious quantities of ultraviolet light and X-rays, which is the calling-card of a massive, yet compact object. Such high energy emission would be uncharacteristic of an ordinary star. Once again, the gravitational potential energy is converted to the kinetic energy of atomic collisions rather than to the kinetic energy of descent.
There are many astrophysical systems where mechanical energy is not rapidly lost to heat. In clusters of galaxies, for example, where there are no galactic airbags or fluffy pillows, galaxies orbit the cluster center with a relatively constant average kinetic energy. For large clusters of hundreds or thousands of galaxies, this average kinetic energy is a direct and reliable measure of the total gravity, which remains the primary means by which the total mass of a galaxy cluster is determined. The same principles of energy and gravity are also invoked to compute the total mass of the larger open star clusters and of all globular star clusters. This method, however, derives total masses for galaxy clusters that are systematically higher (in some cases, by a factor of one hundred) than what you get if you summed the mass of each individual galaxy. The discrepancy was discovered in 1936 by the California Institute of Technology astrophysicist Fritz Zwicky, and it festers to this day as the infamous “missing mass” problem in the universe.
In the reverse of a collapsing gas cloud that gets hotter, the entire universe cools for every moment that it expands. The overall density of energy drops continuously. The temperature of the radiation that permeates all of space, which is the frigid remnant of a hot big bang, is now just under 3 kelvins. If the universe expands forever, then its contents will ultimately greet a cold and dark death as all the stars burn out and as the background temperature nears absolute zero.
How much energy does it take to throw a tomato straight up so that it never returns? It may surprise you to learn that the adage “what goes up must come down” is more a statement of human weakness than of the laws of physics. There is, in fact, a particular velocity that an object must have for it to leave Earth and never return. It is called, quite sensibly, the escape velocity. In the absence of atmospheric resistance, Earth’s escape velocity is about seven miles per second from the surface, which is 250 times faster than the fastest pitches thrown in professional baseball.
With rockets, or other launch apparatus, however, if you propel a tomato with at least Earth’s escape velocity, then you have endowed it with sufficient kinetic energy to leave the force of Earth’s gravity forever. Earth’s gravity does manage to slow the tomato down somewhat, but you have given it more kinetic energy than it would gain had it fallen to Earth from the edge of the universe. In genuine descriptive terms of physics, the escaping tomato has sufficient energy to climb out of Earth’s gravitational potential “well.” On this subject, an acquaintance once penned
Some of what goes up,
If launched with great ferocity,
Will never return—
It reached escape velocity.
Some of what goes up,
If propelled both high and far,
Burns upon return
To become a “falling star.”
The rest of what goes up,
Tossed slowly from the ground,
Started the old saying,
“What goes up, must come down!”
Comets that move with speeds near the local escape velocity of the solar system are only loosely bound to the Sun, and may be considered one-time events. Such comets are not uncommon and are often more spectacular than famous ones that are tightly bound such as Halley’s Comet. Earth is treated to one or two of the one-timers per decade.
There are four types of orbits that an object can have in a simple gravitational field. If all four varieties are given the same closest approach to the central object, then sequenced by increasing total energy (potential plus kinetic) they are the circle, the ellipse, the parabola, and the hyperbola. If an object’s speed is less than the escape velocity, then its orbit will be bound and assume the shape of a circle or of an ellipse. If an object’s speed equals the escape velocity then it will be unbound with a parabolic trajectory. If an object’s speed exceeds the escape velocity then its trajectory will be hyperbolic. The colloquial cool-down phrase, “Don’t get hyper!” does have genuine astrophysical relevance. And if “Don’t get hyper!” is too strong for your needs, then you can always substitute, “Don’t get parabolic!” or “Don’t get elliptical!”
For elliptical orbits, or more generally, for any orbit where the orbit distance varies, there is a continual exchange between an object’s kinetic energy and its gravitational potential energy. As the orbiting object moves closer, gravitational potential energy gets converted to kinetic energy—the object moves faster. This is precisely what happened with our defenestrated peach cobbler. In orbit, however, the object gets to move farther away again as some of its kinetic energy is converted back to gravitational potential energy. Amusement park roller coasters are living physics experiments on the conversion of gravitational potential energy to kinetic energy. In a typical gravity-driven roller coaster, the connected cabs are first dragged up to the highest point in the entire ride, which supplies the requisite gravitational potential energy to avoid getting stuck somewhere between two hills. Now comes the physics experiment: the cabs roll down-and-up and down-and-up and down-and-up in a continual exchange of potential energy with kinetic energy. If there were no friction between the cabs and air and between the cabs and the track, then the roller coaster ride would continue forever. But the roller coaster owner depends on this friction to convert your kinetic energy into heat. The successive hills must therefore get shorter and shorter, until a short final hill just before the ride ends. If you are a roller coaster enthusiast, then all other things being equal, the roller coaster with the single highest hill will also be the longest and the fastest in the world.
Sunlight is, perhaps, the most pervasive form of energy on Earth. Nearly every form of energy that one encounters on Earth can be traced back to the Sun. A car that runs on roof-top solar panels is, in principle, no different from a car that runs on potatoes. Both use energy derived from the Sun. Wood for your fireplace (or wood in general) can burn because it contains a lifetime of energy that a tree absorbed from the Sun. From the point of view of energy, sitting before a toasty fireplace is no different from sitting before a hearth of sunlight, except that burning logs pollute the atmosphere. Hydroelectric plants derive their energy from falling water, usually through ducts in a dam. They exploit the extra gravitational potential energy that water in the dammed lake has over water in the valley below. But how did the water get from sea level up to the lake in the first place? It is the Sun’s energy that helps to evaporate ocean waters, while convection in the atmosphere, which is also caused by the Sun, brings this moisture inland, where it falls out of the sky as rain—hydroelectric energy is really a form of solar energy.
We can also attribute the complexity of life, itself, to solar energy. There are countless organic and inorganic chemical reactions on Earth that thrive in the presence of the Sun’s abundant energy. How else do you think an acorn becomes an oak tree? If the Sun were to disappear tomorrow, then all flora and fauna would eventually “wind down” until the chemical reactions that sustain life ceased. In addition, all motion would stop as mechanical energy irreversibly converts to heat energy. With the Sun as a rather impressive source of external energy, however, almost anything is possible. And the self-organization of complex forms of matter is expected.
For similar reasons, there can never be an isolated “perpetual motion machine,” unless you feed it energy, in which case it would be simply be a battery operated “temporary motion machine.” This is not a statement of inadequate engineering, it is a fundamental axiom of the physics of systems that do not tap an external source of energy.
Calories are a direct measure of heat energy. This simple fact seemed to elude the makers of a well known peanut-filled candy bar in the mid 1980s. The print on the wrapper featured the following absurd claim, “High in energy, Low in calories!” An equally absurd statement might be, “High in weight, Low in pounds!” The human body uses calories derived from food as a means to maintain body temperature and as a source of mechanical energy to do things such as walk, talk, run, circulate blood, and climb stairs. For example, if you just ate a T-bone steak, then the calories you consumed came from the loin of somebody’s cud-chewing cow, and the cow was assembled from farm-feed such as grass and grain, which was grown with the Sun as a source of energy. Credit the Sun, once again.
An under-appreciated aspect of eating cold food is that its net calorie content is always less that what is advertised on the label. Do you want to lose a fast forty calories? Just drink a liter of ice water. Water is often advertised to have zero calories, but by the time it emerges from your body it will have been heated to your body temperature at the expense of your own stored energy. The cost? About forty calories. You get to subtract even more calories for treats such as frozen desserts. Ice cream, for example, is commonly consumed at temperatures well-below freezing. Its calorie correction would be quite large. The only disadvantage is that unlike a liter of water, a tub of premium ice cream packs two or three thousand calories. For this reason, we should not expect the “ice cream diet” to emerge as the latest fad.
Insight to the correspondence between mechanical energy and heat energy was obtained experimentally by the 19th century British physicist James Joule. He revealed that only a small change in temperature results from the dissipation of an enormous amount of mechanical energy. A similar correspondence exists between the food calories that the body consumes and the mechanical energy that is derived from them. In a now famous experiment, Joule stirred a jar of water by the action of falling weights. The gravitational energy of the weights was transferred into the water. Joule describes the experiment:
The paddle moved with great resistance in the can of water, so that the weights (each of four pounds) descended at the slow rate of about one foot per second. The height of the pulleys from the ground was twelve yards, and consequently, when the weights had descended through that distance, they had to be wound up again in order to renew the motion of the paddle. After this operation had been repeated sixteen times, the increase of the temperature of the water was ascertained by means of a very sensible and accurate thermometer…
I may therefore conclude that the existence of an equivalent relation between heat and the ordinary forms of mechanical power is proved … If my views are correct, the temperature of the river Niagara will be raised about one fifth of a degree by its fall of 160 feet.3
In a possibly more relevant example than the Niagara Falls, the calorie content from the stored chemical energy in a single McIntosh apple is more than enough for a 150 pound person to climb, against gravity, every step from the ground to the top floor of the tallest building in the world. In over-fed nations such as the United States, “calorie” is often taken to be a bad word. However you choose to view it, “calorie” still means energy, even when your body stores excess quantities of it as layers of fat on your tummy.
The calorie content of an apple is not nearly as impressive as the heat content of the world’s oceans. The ocean may feel cold when you swim in it, but if you were to add up the vibration energy of every water molecule, then you would get an enormous total quantity of heat. In household example, a standard five gallon fish tank at room temperature contains over 60 times the total heat energy that is found in an eight ounce cup of hot tea. Yes, the cup of tea is hotter, but it contains many fewer water molecules. The tremendous capacity for oceans to store heat energy and influence the local climate it is what keeps the England from becoming a major cross country ski resort; the entire nation is located farther north than the northern tip of the state of Maine. The warm North Atlantic Drift current of the Atlantic Ocean encircles the British Isles, warms the air, and ensures a relatively temperate climate throughout the year.
Photons of all varieties are also a form of energy. The energy created in the core of the Sun emerges as photons from the solar surface. These photons, however, do not come from chemical energy, or gravitational energy. They are the by-products of thermonuclear fusion, which converts raw matter into energy. Four hydrogen atoms assemble under high pressure and temperature to become a single helium atom. The mass of the helium atom is slightly less than the combined mass of the four hydrogen atoms. The lost mass transforms to energy as described by Albert Einstein’s famous formula,
Energy = mass × (speed of light)²
which may be more recognizable when written with its familiar symbols
where c stands for the speed of light, which we learned from Chapter 3 to be a very large number. A small amount of lost mass, after being multiplied by the square of the speed of light, becomes an enormous amount of energy. For example, just one ounce of matter, converted to energy, could power a 100 watt light bulb for over 800,000 years. This simple and profound fact is why tiny humble atoms can serve as the energy source for nuclear power plants, nuclear bombs, and for every living star in the universe.
There are three ways that heat energy can move from one place to another. One is through conduction, which is what happens when you hold the fireplace poker too long with the tip embedded among the burning embers. Heat from the fireplace induces faster vibration in the poker’s atoms. These vibrations are communicated systematically up the poker from atom to atom until the top of the poker burns your unsuspecting hand. Conduction is the primary way that solid objects transfer heat.
Another method of heat transfer is radiation, which simply means energy is transferred directly by photons. Quite independent of your burning hand on the fireplace poker, infrared photons that are emitted from the fire will strike you directly. The human body senses this infrared energy as heat, which is why your exposed skin feels warm when you turn toward a raging fire, yet your skin immediately feels cooler when somebody blocks your view. Photons also travel by radiation from the Sun to Earth along a 500 second journey through interplanetary space. If you had a melt-proof 93 million mile long fireplace poker, then you could poke the Sun and tap solar energy by conduction if you felt so inclined, but it is much simpler to wait for the Sun’s photons to arrive.
A third method of heat transfer is convection. This is how a gaseous or liquid fluid manages to move heat when conduction is ineffective. Returning to our fireplace, the air nearest the burning embers is at a much higher temperature than the air anywhere else in the room. Much of this hot air convects up the chimney as it is replaced with cooler air along the floor of the room. Unfortunately, the frigid outside air then seeps into your home to replace the hot air that went up the chimney. There is no doubt that a fireplace is a toasty addition to any domicile because of the direct infrared photons it provides. Convection, however, insures that it does a poor job of raising a room’s air temperature.
A pot of water on the stove that is being heated to boil normally sits atop a very high flame or a very hot electrical coil. Rather than communicate this high heat through slow conduction from the bottom of the water to the surface, blobs of steam and pockets of water physically move from the bottom to the top. If this were all that happened, then the water would jump out of the pot and float to the ceiling, which would be in conflict with culinary experience. In fact, blobs of water at the surface descend to the bottom to replace the volume that was previously occupied by the rising blobs. When water behaves this way, it is common to say that the water is “boiling.” Raisins make excellent tracers of convecting blobs. Just toss one into a pot of boiling water, and you can entertain yourself for hours as you watch it circulate up and down. If you could toss a flame-proof raisin into the Sun, you would discover that convection is the major means by which energy traverses the outer gaseous layers before it is released as photons from the surface.
A few thoughts about these precious solar photons might possibly help you through the work-day without caffeine. The next time your energy level is low, or the next time the elevator is broken and you must walk up the steps to your destination, remember that you possess stored chemical energy from the food you have eaten, and that the energy content of the food owes its origin to sunlight. You thus have permission to declare to yourself that you are (indirectly) powered by thermonuclear fusion.
- 1 From Dear America: Letters Home from Vietnam, 1985, ed. Bernard Edelman (W. W. Norton: New York), pp. 64–65.
- 2 From Merlin’s Tour of the Universe, 1989, Neil deGrasse Tyson (Columbia University Press: New York), p 230. Used with permission of the author.
- 3 From a letter to the editor of Philosophical Magazine (1845) vol. 27, p 205, reprinted in Great Experiments in Physics, ed. Morris H. Shamos. (1959) (Dover: New York), p 170.