The reason that 1kg-m eter2/sec2 is equal to 0.24 calories is that in the mid-nineteenth century, physicists were confused about energy, a situation that has not greatly improved in the intervening years. A calorie was originally defined as a unit of heat, as heat was thought to be a separate quantity distinct from work and energy. Hence, one system of measurement for heat was developed, while a different unit was employed to measure kinetic and potential energy. The physicist who recognized that heat was simply another form of energy, and that mechanical work could be directly transformed into heat, was James Prescott Joule, in whose honor a standard unit of energy (1 Joule = 1 kg-meter2/sec2 = 0.24 calories) is named. While physicists use Joules when quantifying kinetic or potential energy, we’ll stick with the more cumbersome kg-meter2/ sec2 in order to emphasize the different factors that enter into any determination of energy.38
It should be noted that a physicist’s calorie is not the same as a nutritionist’s calorie. To a physicist, one calorie is defined as the amount of energy needed to raise the temperature of one gram of water by one degree Celsius. This is a perfectly valid, if arbitrary, way of defining energy in a laboratory setting. But this definition leads to the observation that a single soda cracker contains enough energy to raise the temperature of 24,000 grams of water by one degree. In other words, to a physicist, the energy content of one plain cracker is 24,000 calories! In order to avoid always dealing with these very large numbers, a food calorie is defined to be equal to 1,000 of these “physics calories.” Therefore the twenty-four food calories in a single cracker are actually equivalent to 24,000 calories using the physics laboratory definition of the term. Just as well—it’s bad enough to think of the roughly 500 food calories in a cheeseburger, but if we considered that it actually contained 500,000 physics calories, we might never eat anything ever again!
To convert the Flash’s kinetic energy of 75 trillion calories into food calories, we should divide his energy by 1,000. This helps, but he still expends 75 billion food calories running at 1 percent the speed of light. Put another way, he would need to eat 150 million cheeseburgers in order to run this fast (assuming 100 percent of the food’s energy is converted into kinetic energy).38 If he stops, his kinetic energy goes to zero, and in order to run this fast again, he needs to eat another 150 million burgers. At one point in Flash comics (during the mid 1980s) it was briefly acknowledged that he would need to eat nearly constantly (even chewing at superspeed) in order to sustain his high velocities. In the Golden Age, the Silver Age, and now in the Modern Age, conservation of energy is conveniently ignored. Nowadays the Flash’s kinetic energy is ascribed to his being able to tap into and extract velocity from the “Speed Force,” which is a fancy way of saying: Relax, it’s only a comic book.
CHEESEBURGERS AND H-BOMBS
The next in a seemingly never-ending series of questions we ask is: Why does a cheeseburger, or any food, provide energy for the Flash? It’s easy to identify kinetic energy when something is moving, and the potential energy due to gravity is also pretty straightforward, but there are many other forms of energy that require some thought as to which category—potential or kinetic—they belong. The energy the Flash gains by eating is not due to the kinetic energy of atoms shaking in his food (a hot meal has the same number of calories as a cold one) but from the potential energy locked in the chemical bonds in his food. As energy can never be created or destroyed, but only transformed from one state to another, let us follow the chain backward, to see where the stored potential energy in a cheeseburger comes from.39
In order to understand the potential energy stored in food, we have to consider some basic chemistry. When two atoms are brought close to each other, and the conditions are right, they will form a chemical bond, and a new unit, termed a “molecule” will be created. A molecule can be as small as two oxygen atoms linked together, becoming an oxygen molecule (O2), or it can be as long and complex as the DNA that lies within every cell of your body. The question of whether and when two or more atoms will form a chemical bond, and the elucidation of these conditions, is the basis of all chemistry. All atoms have a positively charged nucleus around which a swarm of electrons hover. The chemical properties of an element are determined by the number of electrons it possesses, and how they manage to balance their mutual repulsion (as they are all negatively charged) with their attraction toward the positively charged nucleus. When an atom is brought very close to another atom, the most likely locations of the electrons from the two atoms overlap and, depending on their detailed nature, there will be either an attractive or repulsive force between the two atoms. If the force is attractive, the electrons create a chemical bond and the atoms form a molecule. If the force is repulsive, then we say that the two atoms do not chemically react. In order to determine whether the force is attractive or not involves sophisticated quantum mechanical calculations. (We’ll have much more to say about quantum mechanics in Section 3.) If the force is attractive, and one restrains the two atoms to keep them physically apart, then there is a potential energy between the atoms, since once this restraint is removed, the two atoms form a molecule. In this way, we say that the two atoms, once chemically joined, are in a lower-energy state, just as a brick’s gravitational potential energy is lower when placed on the ground. Work has to be done to lift the brick to a height h, just as energy has to be supplied to the molecule to break it apart into its constituent atoms.
We are finally (and I can almost hear you saying: Thank goodness!) in a position to answer the question of why the Flash needs to eat, or rather, why food provides the energy he needs to maintain his kinetic energy. When the Flash runs, he expends energy at the cellular level in order to flex his leg muscles. This cellular energy, in turn, came from the breakfast that Barry Allen ate. From where did the energy in the food arise? From plants, either directly consumed or through an intermediate processing step (such as when plants are eaten by animals and those animals are eaten by humans). This stored energy in food is simply potential energy on a molecular scale. Plants take several smaller molecular “building blocks” and process them, stacking them up into a subcellular “tower of blocks.” This molecular tower of complex sugars, once constructed, is fairly stable. The process of lifting and arranging a group of blocks into a tall tower raises all of the blocks’ potential energy (except for the bottom block).
Similarly, plants do Work when constructing sugars from simpler molecules, raising the potential energy of the final, synthesized molecule. The potential energy remains locked within the sugars until the mitochondria within our cells construct adenosine triphosphate (called ATP for short) and release the saved energy, just as the Work in building a tower of blocks is stored as the potential energy of the top blocks until the tower is knocked down, converting their potential energy into kinetic energy. The amount of energy released by the ATP in the Flash’s leg-muscle cells is greater than the energy needed to “knock the complex-sugar tower down,” though the gain to the Flash is much less than the plant cell’s effort in raising the tower in the first place.
Where did the plant cell obtain this energy? Through photosynthesis, whereby the energy in sunlight is absorbed by the plant cell and employed in complex-sugar construction. The light comes from the sun (don’t worry, we’re nearly at the end of the line), where it is generated as a by-product of the nuclear-fusion process, in which hydrogen nuclei are fused together through gravitational pressure to create helium nuclei. Ultimately, all of the chemical energy in food is transformed sunlight that was generated by the same nuclear-fusion process in the center of the sun that occurs during the detonation of a hydrogen bomb. In this way, the majority of energy on Earth is solar energy at its source, just as all the atoms on Earth, from the ATP molecules throughout the Flash’s body to the ring in which he stores his costume, were created in a solar crucible (in the massive star that preceded our own sun).
Ultimately, all of life is possible because the mass of a helium nucleus (containing two prot
ons and two neutrons) is slightly less than that of two deuterium nuclei (deuterium is an isotope of hydrogen in which the single nuclear proton is joined by a neutron) combined in the center of a star. And by slightly less, I mean that the mass of a helium nucleus is 99.3 percent of two deuterium nuclei. This small mass difference leads to a large outpouring of energy, since from E = mc2 the change in mass is multiplied by the speed of light squared.
And 99.3 percent really is the magic number. If the mass difference were 99.4 percent, then deuterium nuclei would not form, and hence fusion of helium could not proceed. In this case, stars would shine too dimly to synthesize elements, and no violent supernova explosions would occur to both generate heavier elements and expel them into the void, where they might form planets and people. On the other hand, if the mass difference were 99.2 percent, then too much energy would be given off from the fusion reaction. In this case, too many protons would combine directly to form helium nuclei in the early universe, and no nuclear fuel would remain when stars formed. The source of this amazing fine-tuning of the basic properties of nature is the subject of current investigation.
POWER IS WORK OVER TIME!
Frequently, the constraint in performing a task is not how much energy is required, but how fast that energy can be supplied and used. Consider the Flash in fig. 19, stopping in roughly fifteen feet from a speed of 500 miles per hour. The Work needed to decrease his large kinetic energy to zero was a little over a million pound-feet, which called for a force of more than eighty thousand pounds. If the Scarlet Speedster were to stop over a longer distance, say a mile rather than fifteen feet, then the force needed would be under 230 pounds, and it is doubtful that he would leave such deep ruts and scarring in the ground. Put another way, it requires less force to change his kinetic energy if he has a longer time to do so.
Power is defined in physics as the rate at which the energy of a system is changed (technically, by “changed,” I mean transformed from one form to another, such as the kinetic energy of the Flash being converted to mechanical work done by his boots on the ground). If I do Work on my automobile, pushing it from rest until it is moving at 60 mph, its final kinetic energy is the same if this process takes six seconds or six hours. The rate of change of the car’s kinetic energy is obviously much higher in the first case, and if you have a motor capable of accelerating an auto from 0 to 60 mph in six seconds, we say your car’s engine has more power than the engine that takes six hours. As Work, “kinetic energy” and “heat” are just different expressions for energy, the rate of change of energy, measured in units of kg-meter2/sec2 per second, is defined as a Watt (after James Watt, an early pioneer of the study of thermodynamics). We often need a lot of energy in a short period of time, so one convenient unit is one thousand Watts, which is termed a kiloWatt. A Watt is a unit of power—that is, the rate at which energy is used. To keep track of how much energy one uses in, say an hour, we multiply the rate of usage by the time—the resulting expression is referred to as kiloWatt-hours and is how the electric company keeps track of how much electrical energy you have used. Large power plants have to supply electrical energy to a great many homes at any given moment. A plant that can provide a kiloWatt of power (which a typical residential house requires) for one million homes is rated as capable of producing a gigaWatt of power.
It’s the power and not the energy that determines why we don’t have flying cars, despite the fact that we are presently well within the “far future” as imagined by Silver Age comic books of the 1950s and 1960s. Consider Nite Owl’s flying “Owlship” from the 1986 graphic novel Watchmen. Nite Owl (technically Nite Owl II), in the novel by Alan Moore and Dave Gibbons, is a knockoff of the Charleton Comics superhero Blue Beetle, who in turn was a knockoff of the DC Comics hero Batman. Dan Dreiberg in Watchmen used his inheritance from his banker father to outfit himself with a brownstone with a large basement in which he stored an array of gadgets, specialized superhero costumes (for fighting evildoers in such extreme environments as underwater, in the Arctic, and in a radioactive hot zone), a collection of trophies and mementos from memorable cases, and a large flying airship called Archimedes (or Archie for short). The airship, a large, rounded transport about the size of a minivan, is modeled on the Blue Beetle’s flying beetle airship—and uses the same mechanism to achieve flight: imagination.
Archie in Watchmen has no visible means of levitation or thrust, and can hover in the air during a daring rescue of stranded citizens trapped in a tenement fire, or fly from New York City to Antarctica. It takes a lot of power to accomplish this. Earlier we considered the potential energy of an object raised a distance h above the ground. We determined that the potential energy (say, of Gwen Stacy on the top of the George Washington Bridge) is described by the expression mgh, where m is the mass and g is the acceleration due to gravity. The larger the weight of an object, the more Work one must do to raise it against gravity to a height h.
The full-scale model of the Owlship constructed for the Warner Bros. 2009 film Watchmen weighed an impressive four tons (the imaginary airship has to be strong to withstand the guards’ gunfire as they break Rorschach out of prison). Lifting such a heavy object one eighth of a mile, so that it could fly above the towers of New York, raises its potential energy by more than seven million kg-meter2/sec2. That’s a lot of energy, but more importantly, since the Owlship is just suspended in thin air, we must expend this amount of energy every second to keep it levitated. The rate at which the Owlship uses energy when simply hovering in the air, 200 meters above the ground, is 7,200 kiloWatts, or 7.2 megaWatts (where a megaWatt is a million Watts). If we wish to fly the Archimedes to some other location, then we need to provide kinetic energy as well, and this will add to our power needs. At a uniform cruising speed of 700 miles per hour, for long distance travel at 30,000 feet, the total power needed to fly Archie is over 500 megaWatts. A trip from New York to Antarctica would therefore require more than 180,000 gallons of gasoline!40 The Watchmen graphic novel required a significant suspension of disbelief when it came to the superpowered Dr. Manhattan, but perhaps the biggest miracle exception from the laws of nature involved the energy supply for Nite Owl’s flying ship.
The Owlship as drawn by Dave Gibbons in the 1986 graphic novel displays no visible signs of a propulsion system. The airship in the 2009 film version has some jet thrusters added underneath and to the rear of the transport, to acknowledge some mechanism by which it flies. Personally, if I had designed and constructed a flying ship that could hover and fly for more than thirteen hours at the speed of sound using a novel lightweight and highly efficient energy source, I would not be sitting naked in my underground Owl Cave, moping about my former crime-fighting career. Rather I’d be too busy counting the kajillion dollars a day I would earn by licensing this process.
DEEP BREATHING EXERCISES
In order to run, the Flash needs the energy stored in food, which is locked up in complex molecules. We have described this energy as similar to the potential energy of a tower of blocks that plants stack, expending Work. We transform this stored energy—after first consuming the plants—into kinetic energy when the tower is knocked over. But what is the trigger to topple this tower? How does the tower know when the cell needs the energy to be released? There’s a lot of biochemistry that goes into the release of energy by the mitochondria in a body’s cells, but the essential step involves a chemical reaction of oxygen going in and carbon dioxide coming out. Without oxygen intake, the stored energy in the cell cannot be unlocked, and there’s no point in eating. The faster the Flash runs, the more kinetic energy he manifests, the more potential energy stored in his cells he needs to release, and the more oxygen he needs to breathe. We’ve already discussed the fact that he would need to eat a staggering amount of food in order to account for the kinetic energy he routinely displays. What about his oxygen intake? Would the Flash use up all of the Earth’s atmosphere as he ran?
To answer this question, we first need to know how muc
h O2 the Flash uses when he runs a mile. The volume of oxygen used by a runner will depend on his or her mass, and has been measured to be about 70 cubic centimeters of O2 per kilogram of runner per minute, for elite athletes at a pace of a six minute mile. Taking the Flash’s mass to be 70 kg, he then uses nearly 30 liters of O2 for every mile he runs (a liter is one thousand cubic centimeters, a little under a quart). Let’s assume that this rate of O2 use remains the same even for much higher speeds. Thirty liters of O2 contains under a trillion trillion oxygen molecules, and at a speed of ten miles per second, this means that the Flash inhales about a trillion trillion O2 molecules every second. That sounds like a lot, but fortunately there are many more O2 molecules in our atmosphere than that. A lot more. In fact, very roughly, the Earth’s atmosphere contains more than ten million trillion trillion trillion O2 molecules. So even at a rate of consumption of one trillion trillion molecules per second, he would have to run this fast (10 miles/sec) and breathe at this rate continuously for more than 100 billion years before he exhausted our oxygen supply. The faster he ran, the quicker he would use up our air, but even running at nearly the speed of light (which he is capable of, but doesn’t do very often) it would take him more than two million years of continuous running and breathing at this rate to exhaust the atmosphere. So, at least regarding this aspect of his superspeed, we can breathe easier.
The Earth’s atmosphere may be safe, but of course this assumes that the Flash is able to breathe at all while he runs—at several hundred miles per hour, would he be able to even draw a deep breath? Fortunately for the Scarlet Speedster, he carries a reservoir of air with him whenever he runs. In Flash # 167, this region of stationary air (relative to the Flash) is described as his “aura,” while in fluid mechanics it is termed the “no-slip zone.” Whatever you call it, it’s the reason golf balls have dimples.
The Physics of Superheroes: Spectacular Second Edition Page 17
