The Physics of Superheroes: Spectacular Second Edition (26 page)

13

THE CASE OF THE MISSING WORK—
THE THREE LAWS OF THERMODYNAMICS

UNLIKE HENRY PYM
,
who found that he could reverse the polarity of “Pym particles” and enlarge himself into Giant-Man, and the actress Rita Farr (Elasti-Girl) of the Doom Patrol who, after breathing mysterious vapors from a previously undiscovered volcanic vent during an African movie shoot, was able to either grow to the size of a five-story building or shrink to the size of an insect, the DC Comics hero the Atom could only change his size in one direction: down.

The Atom is one of my favorite comic-book superheroes, for in his secret identity he is Ray Palmer, physics professor.
Showcase # 34
introduced us to Professor Palmer as he was fruitlessly trying to develop a shrinking ray, motivated by the economic benefits of such a device. As he records in his audio journal after Experiment # 145 fails (well, actually, Experiment # 145 succeeded in reducing the size of a kitchen chair to only a few inches, but the chair subsequently exploded, just as every other object that had been shrunken), “compression of matter [ . . .] would enable farmers to grow a thousand times more than they do, on the same land! A single freight car could transport the goods of a hundred freight trains.” Of course, the exploding part would make maintaining inventory difficult.

Palmer found the solution to his shrinking- ray problems one night when, on a nighttime drive, he spied a chunk of a white-dwarf star falling near him. This extraterrestrial material would turn out to be the one key missing ingredient
⁴²
that enabled Palmer to safely reduce objects without subsequent explosion. Presumably because this stellar remnant has the word “dwarf” in its name, it possesses miniaturization properties previously unsuspected by physicists. We’ll have more to say about the Atom’s origin and the white-dwarf meteor at the end of the book. Suffice it to say that the mechanism for how Ray Palmer was able to reduce his height to six inches (his typical crime-busting size) and much further, all the way down to smaller than an electron, makes about as much physical sense as inhaling strange underground vapors or Pym particles.

What is significant about the Atom was that unlike Ant Man or Elasti-Girl, he was not restricted to a constant-density reduction. That is, the Atom could independently control both his size and his mass. Apparently, white-dwarf matter provides two “miracle exceptions” for the price of one.

At normal height, Ray Palmer was six feet tall and weighed approximately 180 pounds, equivalent to a mass of 82 kilograms. When reduced to a height of six inches, he is twelve times smaller than normal. His width and breadth will decrease also by a factor of twelve—that is, if he wants to avoid looking like his reflection in a fun-house mirror. His volume therefore decreases by a multiple of 12 × 12 × 12, or a factor of 1,728. If he were to shrink at a constant density, then his mass would also have to be reduced by this same factor of 1,728, leading to the Atom having a mass of only 47 grams, or 1.66 ounces. This is pretty light, and it is hard to see how such an ephemeral crime-fighter could tangle with the likes of Chronos the Time Thief or Doctor Light. Fortunately for those of us on the side of Good, the Atom could maintain his diminutive stature and increase his body weight up to his full-grown 180 pounds with just a click of his “size and weight controls” that he kept in his costume’s belt buckle (later he added controls to his gloves as well). As shown in fig. 20, at his lighter weight, he could use a pink rubber eraser as a trampoline, propelling himself into the face of a crook, and at the moment of impact increase his weight to 180 pounds. The resulting blow landing on the crook’s chin would have the same force as when the Tiny Titan was his full height.
⁴³

Fig. 20.
Image from the cover of
Atom # 4,
where the Mighty Mite demonstrates his mastery of both his size and mass. Decreasing his density so that he is lightweight enough to use a pink rubber eraser as a trampoline brings him to within striking distance of a crook’s chin. At this point he increases his mass dramatically, so that his punch kayos the “innocent thief.”

Another trick the Atom would employ was, while only a few inches tall, to grab hold of the necktie that a criminal wore and then increase his weight to 180 pounds. The crook’s head would be violently jerked downward and would crash on a tabletop or some other hard surface, knocking him out cold. This is undoubtedly why criminals in the late 1960s were in the fashion avant garde in adopting a more “casual Friday” approach to their work clothes when breaking the law.

Being able to control his mass (but only when his size was reduced from his normal height), the Atom could ride air currents generated by the wind or thermal gradients to get from place to place. (He would also make use of the fact that he could reduce himself to the size of an electron and telephone himself to distant locations—we will discuss the physics underlying this trick in Chapter 26.) The Atom would often be shown, as in fig. 21, gracefully gliding along air currents. In this panel, from
Atom # 2,
the Atom needs to get to the top of a barn that is on fire. He shrinks down to less than an inch and adjusts his density so that he is “lighter than a feather”—at which point he is then pushed aloft by the “hot air currents to the roof.” In reality, he should suffer a much more disorienting and punishing trip, and would, via direct, firsthand experience, verify the statistical mechanical underpin nings of the branch of physics called thermodynamics.

We have considered Newton’s three laws of motion; now we take up the three laws of thermodynamics. The field of thermodynamics, the study of the flow of heat, was empirically developed by scientists in the nineteenth century, well before a proper understanding of the atomic nature of matter. As such, they came slowly to these laws, struggling with such problems as the connection between useful work and heat, a quantitative concept of temperature, the nature of phase transitions, and the intrinsic inefficiency of any mechanical process. Our consideration of this topic will hopefully be less painful, as we already know that matter is composed of atoms. We’ll begin by elucidating the First Law of Thermodynamics with the simple question of why there is a net upward force on the Atom (fig. 21) as he rides the air currents created by the burning barn.

Fig. 21.
Panel from
Atom # 2,
wherein the Tiny Titan utilizes his ability to reduce both his size and his weight to ride the thermal air currents from a burning building.

Back in the 1800s, scientists believed that matter contained a separate fluid termed “caloric” (previously named “phlogiston”). When mechanically deformed, objects would release their caloric fluid, and thus would feel warm to the touch. The caloric fluid was alleged to be “self repelling” (which accounted for why objects expanded when heated). It may sound silly today, but if you did not know that matter is composed of atoms, the caloric model seemed a reasonable way to account for these and other observations. The mystery of the true nature of heat was solved by Joule, Benjamin Thompson, and others, who demonstrated that mechanical work could be directly converted to heat without the release of any special fluid. The term “heat” describes any exchange of energy without the system performing work (defined in the previous chapter as a force multiplied by a distance). That any change in the energy of an object can only come about by either a transfer of heat or the performance of work is the essence of the First Law of Thermodynamics.

When an object is “hot,” the kinetic energy of its constituent atoms is large, while when an object is “cold,” the kinetic energy of the atoms is lower. The “temperature” of an object is therefore just a useful bookkeeping device to keep track of the average energy per atom of the object. We say something has a high temperature when the atoms contain a larger amount of kinetic energy compared with another object with a lower kinetic energy per atom, which we call “cold.”

In our earlier discussion of friction and the Flash in Chapter 4, we noted that when two objects are rubbed or dragged against each other, this process can be viewed at the atomic level as the scraping of one atomic mountain range across the other. The kinetic energy of the dragged objects is converted into the shaking of the constituent atoms in each surface. The transfer of kinetic energy per atom is referred to as “heat flow,” and the temperature of the respective objects is raised, without a caloric fluid being present.

From Chapter 12 we know that energy comes in only two flavors: potential or kinetic. The energy of the air molecules in your room is essentially all kinetic. As the mass of any given air molecule is very small, the variation of the gravitational potential energy (given by the weight of the air molecule multiplied by its distance above the floor) across the height of the room is so tiny that we make only a very small error by ignoring it. The following discussion does not depend on the exact chemical composition of the atmosphere, so we’ll refer to generic “air” molecules. The hot air underneath the Atom in fig. 21 has a greater kinetic energy than the colder air above him. Of course, this last statement is unscientific, for there is no such thing as “hot air” or “cold air,” just air that is hot compared with some other object or cold compared with another reference, which for the sake of argument we’ll take to be the Atom’s body temperature.

The hot air beneath the Atom in fig. 21 warms and lifts him. When a speeding car collides with a stationary or slowly moving vehicle, the faster car will usually slow down and the slower car will speed up. Similarly, air molecules that have a higher kinetic energy than those in the Atom’s body will, upon colliding with him, transfer some of their kinetic energy, on average, to the atoms in his costume, causing them to shake more violently than before. Since energy is conserved in the process, the kinetic energy (that is, the temperature) of the air will decrease following the collisions, while the temperature of the Mighty Mite will increase. The atomic nature of matter makes clear why, when two objects are in thermal contact, the net flow of heat is always from the higher-temperature object to the lower-temperature object, and never in the other direction. Similarly, when exposed to cold air, the atoms in the Tiny Titan’s costume will be moving back and forth much faster than the air molecules that they collide with, so after the collision, the air will be moving faster at the expense of the atoms in his costume, cooling the Atom down.

When the Atom is lightweight enough to float on air currents (as illustrated in fig. 21), and if all of the air surrounding him is the same temperature, he is being bombarded in all directions with roughly equal force. In this case, no matter how small his mass, gravity will eventually pull him down to the ground. The thermal draft that keeps the Atom aloft arises from the hotter air molecules below the Atom that are moving faster than the cooler molecules above him. There are therefore more collisions per second beneath the Atom that push him upward than collisions above him that direct him toward the ground. Furthermore, the force needed to reverse the direction of a faster-moving molecule is larger than compared with slower-moving molecules. Forces come in pairs, so the force the Atom exerts on the air molecules, changing their direction, also pushes back on the Atom. There will therefore be a net unbalanced force on the Atom due to the fact that there are more collisions underneath him pushing him upward than above him driving him down. Of course, this force will not be smooth and uniform, but will in fact be discontinuous and noisy, and occasional statistical fluctuations will lead to him being pushed down rather than up. But over time, the average force from the thermal gradient will be to push him away from the hot source and toward the cooler region.

The Atom in fig. 21, therefore, gains both kinetic and potential energy. He warms up slightly (that is, the kinetic energy of the atoms in his body increase) due to the flow of heat from the hot-air current. He will also be raised to a greater altitude, increasing his gravitational potential energy, thanks to the work done on him by the net force exerted by the hotter air molecules. The First Law of Thermodynamics states that the net change in the Atom’s total energy is the sum of the heat flow and the work done on him.