SECTION 2
ENERGY-HEAT AND LIGHT
12
THE CENTRAL CITY DIET PLAN—CONSERVATION OF ENERGY
THE FLASH MAY BE ABLE to run across the ocean and pluck bullets from the air, but a more pressing question is: How frequently does he need to eat?
The short answer is, a lot! Before we determine exactly what his caloric intake must be as he rounds up his rogue’s gallery of supervillains in Central City, we address the more basic question: Why does he need to eat? What exactly does food contain that is essential for any activity, whether running, walking, or just breathing while sitting still? And why do we only obtain these qualities from organic matter, and not from rocks or metal or plastic?
The Flash eats for the same reason we all do: to provide raw materials for cell growth and regeneration, and to provide energy for metabolic functioning. At birth, your body contains a certain quantity of atoms that was insufficient to accommodate all of the growth that will occur during your lifetime. As you grew and matured, you needed more atoms, typically provided in the form of complex molecules that your body would break down and convert into the building blocks necessary for cell replacement and growth. As noted in our discussion of the explosion of Krypton, all of the atoms in the universe—including in the food we ingest—were synthesized via nuclear reactions in a now long-dead star where hydrogen atoms were squeezed together to form helium atoms, helium fused to form carbon, and so on. An additional by-product of these fusion reactions in our sun provides the second essential component of the food we eat. Matter- Eater Lad of the Legion of Super-Heroes may be able to subsist by consuming inert objects such as metal or stone, and the cosmic menace Galactus must consume the life-energy of planets, but for us, for the most part, the food we eat must have been previously alive. Only such foodstuffs provide the necessary component for life, as mysterious as its name is mundane: energy.
The use of the word “energy” is so common that it is unnerving to realize how difficult it is to define without using the word “energy,” “heat,” or “work” in the explanation. The simplest non-mathematical definition is that “energy” is a measure of the ability to cause motion. If an object is already moving, we say it possesses “kinetic energy,” and it can cause motion if it collides with something else. Even if it is not moving, an object can possess energy, such as when it is pulled by an external force (for example, gravity) but is restrained from accelerating (say, by being physically held above the ground). Since the object will move once it is let go, it is said to possess “potential energy.”
All energy is either kinetic or potential, though depending on the circumstances, a mass can have both kinetic and potential energy, such as when Gwen Stacy fell from the top of the bridge in Chapter 3. When she was on the top of the bridge, she had a large potential energy, as gravity could act on her over a long distance, from the top of the tower to the river below. But her motion was constrained, as the bridge was holding her up. When she was knocked off the tower, this constraint was removed, and the force acting on her (gravity) then began her acceleration. As she plummeted, she had a shorter and shorter distance over which to continue falling, so her potential energy decreased. This energy didn’t disappear, but rather her large potential energy at the top of the bridge was converted to ever-increasing kinetic energy as she fell faster and faster. At any given point in her fall, the amount of kinetic energy she gained was exactly equal to the amount of potential energy she lost (ignoring the energy expended in overcoming air resistance). If she had struck the water at the base of the bridge, her potential energy relative to the ground would have been zero (once at the base of the tower she has no more potential to fall), while her speed and, hence, kinetic energy would have been at its greatest. In fact (again ignoring air drag) her kinetic energy at the base would have been exactly equal to her large potential energy at the top of the bridge when she started to fall. This kinetic energy is then transferred to the water, which supplies a large force that changes her high velocity to zero, with a similar dire result as when she was caught in Spider-Man’s webbing, as described in Chapter 3.
Or imagine Spider-Man swinging back and forth on his webbing, like a pendulum. At the top of his arc, he is not moving (which, again, is why it’s the highest point of his swing), but he is high off the ground, and has a large potential energy. His potential energy at the bottom of his swing is a minimum, and if he had started at this point, he would not move. Starting at a higher point, his earlier potential energy changes to kinetic energy, and at the lowest point in his arc, his loss of potential energy is exactly equal to his gain in kinetic energy. The only force acting upon him at this lowest point is gravity (straight down) and the tension in the webbing (straight up). Neither of them acts in the horizontal direction of his swing at this point. But he is already moving, and an object in motion will remain in motion unless acted upon by an external force. As he overshoots this lowest point and starts to rise again, his kinetic energy changes back to potential energy. If no one pushes him, he can never have more total energy than what he started off with (where would it come from?), and so the final point of his swing cannot be higher than his initial starting height. In fact, some of his kinetic energy is used up in pushing the air out of his way (air drag), so on each swing he will rise to a lower height than his previous swing, never returning to the high point.
This accounting of how much energy is potential and how much is kinetic leads to one of the most profound ideas in all of physics: Energy can neither be created nor destroyed—it can only be transformed from one form to another. This concept goes by the fancy title of the Principle of Conservation of Energy. We have never been able to catch nature in a slipup where the energy at the start of a process does not exactly equal the energy at the end. Never.
Even when physicists thought that energy was not being conserved, it eventually turned out that it was. Studies of the decay of radioactive nuclei in the 1920s and 1930s found that the final energies of the emitted electrons and resultant nuclei was less than the starting energy of the initial nuclei. Faced with the possibility that energy was not being conserved in the decay reaction, Wolfgang Pauli instead suggested that the missing energy was being carried away by a mysterious “ghost particle” that was invisible to their detectors. Eventually, devices were constructed to observe these “ghost particles.” They turned out to be real, and did in fact account for the energy imbalance in the radioactive decay. In fact, neutrinos (as these mystery particles were named, somewhat whimsically, by Enrico Fermi, describing them in Italian as “little neutral ones”) are some of the most prevalent forms of matter in the universe.
In more mundane circumstances, one must still be careful in accounting for all of the energy in any process. Consider driving a nail into a wooden board. The potential energy of the hammer, held over a carpenter’s head, is converted to kinetic energy as she swings. When the hammer strikes the nail, the hammer’s kinetic energy causes the motion of the nail (hopefully deep into the board of wood) and, as a side effect, also causes the atoms in the head of the nail to shake more violently, warming up the nail. The partitioning of the incident kinetic energy of the hammer into additional vibrations of the atoms in the nail head, the forward motion of the nail itself, and the breaking of molecular bonds in the wood (necessary if the nail is to occupy space previously claimed by the board) can be summarized by describing the “efficiency” of the hammering process. If one carefully adds up all of the small and large bits of kinetic energy in the nail, wood, and even the air (the “bang” one hears upon striking the nail results from a pressure wave—sound—induced in the surrounding atmosphere), the net result will exactly equal the initial kinetic energy of the hammer right before it strikes the nail head. However, warming the nail and creating a sound effect are “waste energies” from the point of view of the carpenter, and count against the efficiency of the hammering process.
Sometimes this waste energy is not so insignificant. An a
utomobile traveling along a level road has a certain amount of kinetic energy. This energy arises from a chemical reaction during the combustion of gasoline vapor with oxygen, ignited by an electrical jolt from the spark plug. The gases resulting from this small explosive reaction are moving at great speeds, so that they may displace a piston. The piston’s up/down motion is translated via an ingenious system into the rotation of the car’s tires. Of course, not all the energy of this chemical reaction goes into the displacement of the auto’s pistons—much of it heats up the engine, which is useless from the point of view of locomotion. In addition, as the car travels down the highway, energy is also needed to push the air out of the way of the car. An automobile’s efficiency is limited in large part by the effort it must expend displacing air from the immediate volume it intends to occupy—over six tons of air for every mile traveled by an average-size car! The larger the profile of a car or truck, the greater the volume of air that must be displaced, and the more energy must be devoted to this task, in addition to propelling the car forward. This same principle also explains why it is easier to run underwater through a swimming pool with your hands flat at your sides than if you hold them out away from your body. The smaller the surface area, the greater the fuel efficiency for comparable-mass vehicles (assuming the vehicles have the same engine).
The Green Goblin expended energy carrying Gwen Stacy to the top of the George Washington Bridge. This increase in her potential energy was stored as she lay atop one of the towers. The increase in her potential energy came from the chemical energy in the fuel in the Goblin’s glider, and so on. Taken to its logical conclusion, the Principle of Conservation of Energy states that, if one can never create new energy or destroy current energy, but simply convert it from one form to another, then all of the energy and matter currently in the universe was present at the moment of the Big Bang that heralded the universe’s creation. At this primordial instant, the entire universe was compressed within an inconceivably small volume. As the universe expanded, the total energy and mass content remained unchanged but was now spread over an ever increasing volume.
“Energy density” is the energy per volume. Consequently, if the amount of energy remains the same but the volume increases, the energy density will decrease. Energy and matter are able to interconvert through a process represented by Einstein’s famous equation E = mc2. Ordinarily, when photons collide and form matter, an equal amount of matter and antimatter is created. Within a fraction of a second after the Big Bang, as the universe expanded and cooled down, protons and neutrons started forming from a “quark-gluon plasma.” Through a process that remains poorly understood, slightly more protons and neutrons formed in the early universe than anti-protons and anti-neutrons. This formation of matter occurred only once—early in the universe’s history the energy density was high enough to allow matter to condense into existence. At later times (such as now) when the energy density is below the E = mc2 threshold, there is not enough background energy in outer space to spontaneously form matter.35 The protons, neutrons, and electrons created in the early moments of the universe came together to form hydrogen and helium nuclei. Gravity pulled some of these atoms together to form large clumps that became stars. In the centers of these stars, held together by gravitational potential energy, a nuclear reaction transforms these hydrogen atoms into heavier elements and kinetic energy.
Now, it is all well and good to say that all of the energy (and consequently all of the matter) found in the universe today was present at the moment of the Big Bang. But this only leads to two deeper questions about energy: What is it really? And where did it originally come from? Science provides the same answer to both questions: Nobody knows.
FAST FOOD
In order to figure out how much the Flash must eat to be able to run at superspeed, we need to calculate his kinetic energy. Physicists are always looking to conserve energy—consequently, we’ll recycle the math from Chapter 1 so we won’t have to do any more work. Speaking of work, in order to change the kinetic energy of an object by either speeding it up or slowing it down, one must do Work. “Work” is capitalized here, because in physics the term has a very specific meaning that is slightly different from its common usage.
When a force acts on an object over a given distance, we say that the force does Work on the object and, depending on the force’s direction, will either increase or decrease the object’s kinetic energy. In this way Work is just another term for energy, and they will have the same units. For a falling mass m, the force acting on it is its weight due to gravity F = mg, and the distance the force acts upon the object is just the height h that it falls. So Work = (Force) × (distance) = (mg) × (h) = mgh. This turns out to be the potential energy that the object had at a height h, so in this example, Work can be viewed as the energy needed to increase an object’s potential energy.
Consider the falling Gwen Stacy from Chapter 3 or the leaping Superman from Chapter 1. In either case the Work that gravity does is given by Work = mgh. For Gwen, the force pulls her down in the direction of her motion, so the Work increases her kinetic energy, and for the Man of Steel, the force is still downward, but is opposite to the direction of his leap, so the Work decreases his kinetic energy. Gwen starts with no kinetic energy, but the gravitational force acting over a distance (the height of the bridge tower) provides her with quite a large final velocity right before striking the water. The connection between her final speed v and the distance she fell h was given by v2 = 2gh, where g is the acceleration due to gravity. This is a true statement, and according to our Rule of Algebra (see Preface), we can multiply and divide both sides of a true statement by the same quantity, and it remains a true statement. So if both the left- and right-h and sides of v2 = 2gh are divided by 2, the result is v2/2 = gh. If we now multiply both the left- and right-h and sides by Gwen’s mass m, we obtain ½ mv2 = mgh. The right-h and side is the Work that gravity does on Gwen. The left-hand side must therefore describe her change in kinetic energy—that is, her final kinetic energy minus her initial kinetic energy. Since she started with no kinetic energy (no motion, no kinetic energy, though she had plenty of potential energy), her final kinetic energy is stated as Kinetic Energy = ½ mv2. Congratulations—you’ve just done another physics calculation.36
When the Flash stops running, the Work of changing the Scarlet Speedster’s kinetic energy is done by friction between his boots and the ground. From time to time, the acceleration or deceleration that the Flash must experience is (more or less) realistically addressed, and we see the consequences of these decelerations. In Flash # 106, the Flash needed to stop suddenly while chasing an object that was traveling at 500 mph. The comic shows him gouging giant ruts in the ground with his feet as he attempts to quickly bring himself to rest. Here, the forces that would accompany his rapid deceleration—friction in particular—are represented accurately. In bringing himself to rest from a speed of 500 mph, the large change in kinetic energy requires a correspondingly large Work. The comic panel (fig. 19) shows the Flash stopping in approximately fifteen feet, so the distance is relatively short, and since Work = (Force) × (distance), the force that his feet exert on the ground must be correspondingly very large. In fact, to change his velocity of 500 mph in a distance of fifteen feet requires a force of more than 80,000 pounds!
Similarly, in Flash Comics Vol. 2, Issue # 25 (April 1989), Wally West37 runs so fast that, in his attempt to stop suddenly, he leaves mile-long gashes across North America. From the length of the skid marks, the scientists who are tracking Wally are able to determine both how fast he was going and his probable stopping point, using the same techniques that the police employ when reconstructing an automobile accident from the length of the tire skid marks. Realistically, one should always know where the Flash has been from the deep gouges his feet excavate every time he suddenly starts or stops running. Fortunately for the Central City Department of Roads and Transportation, this physically accurate portrayal of the Flash’s powers only occurre
d occasionally.
Returning now to the Flash’s eating habits, if kinetic energy KE is written mathematically as KE = (½) mv2, then the Flash’s caloric intake requirements increase quadratically the faster he runs. If he runs twice as fast, his kinetic energy increases by a factor of four, and thus he needs to eat four times more in order to achieve this higher speed. Back in the Silver Age (late 1950s to 1960s), artist Carmine Infantino would draw Barry Allen as fairly slender and not as a hulking mass of muscle, since he was, after all, a runner (the Flash, that is, not Carmine). If the Flash weighed 155 pounds on Earth, then his mass would be 70 kilograms. When running at 1 percent of the speed of light (nowhere near the Flash’s top speed), his speed would be v = 1,860 miles/sec, or 3 million meters/sec. In this case his Kinetic Energy KE is (½) × (70 kg)×(3,000,000 meters/sec)2 = 315 trillion kg-meter2/sec2 = 75 trillion calories. Energy is so frequently used in physics that it has several units of measurement, one of which is termed the “calorie,” and is defined as 0.24 calories = 1 kg-meter2/ sec2. That is, roughly one quarter of a calorie is equal to the Work resulting from applying a force of 1 kg-meter/sec2 over a distance of one meter.
Fig. 19. A rare example from Flash # 106 of the realistic effects of the Flash’s sudden deceleration. The shorter the stopping distance, the greater the force his boots must exert on the ground when braking.
The Physics of Superheroes: Spectacular Second Edition Page 16
