The Physics of Superheroes: Spectacular Second Edition

by Kakalios, James

  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.

  Another example: When a hot gas pushes against a piston in an automobile cylinder, lifting the piston and thereby, through a series of cams and shafts, causing the wheels to rotate, the energy of the hot gas that goes into moving the piston is termed “Work.” The Industrial Revolution came about when scientists and engineers realized that during the transfer of energy through the flow of heat from hot to cold, productive work, meaning a force applied across a given distance, could be extracted. Prior to this, the development of simple machines such as levers and pulleys to amplify forces required the energy stored within humans, draft animals, wind, or waterfalls. The work supplied by humans or animals is converted from the stored chemical energy in the foodstuffs ingested. The potential energy in the food has to accomplish many other tasks, from maintaining body temperature to continuing metabolic functions, and so on. Consequently, the amount of energy available for pushing down on a lever is only a small fraction of that stored within the food. In contrast, releasing the stored potential chemical energy by burning coal or oil enables a more direct conversion into work. While not 100-percent efficient, it is far more advantageous than using living beings.

  The First Law of Thermodynamics tells us that in a best-case scenario, with all losses and external noise removed, the total amount of work we can get out of any device is exactly equal to the heat flow (change in kinetic energy) that drives the machine. By the Principle of Conservation of Energy, it is impossible to extract more work than is available from the heat flow from a hot-to-cold source. The heading of this section alludes to the fact that the universe ensures that you can never win (that is, get more out than you put in).

  Well, if winning is ruled out, why is breaking even so difficult? We can certainly convert all of our work into heat—when we rub our hands together. We do work, applying a force against friction over a distance, and the result is that our hands warm up. Why couldn’t we make a perfect machine that extracts all possible heat and converts it to work, without waste? We’ll see in a moment that the random motion of the gas atoms during the transfer of heat places strict limits on the amount of usable work we can obtain from any machine, no matter how cleverly designed.

  THE SECOND LAW-YOU CAN’T EVEN BREAK EVEN

  There is nothing in the Principle of Conservation of Energy, which underlies the First Law of Thermodynamics, that prevents or forbids the construction of a 100-percent-efficient machine, where the work created by the device exactly equals the heat energy put into it. In fact, if all we had to go on was the First Law of Thermodynamics, we would reasonably expect that machines must be 100-percent efficient, for we know that energy can never be gained or lost, but only transformed from one form into another. In order to understand what limits the conversion of heat into work, we must introduce a new concept that is complementary to, but as important as, energy. This concept, called “entropy,” is intimately connected to heat flow, and will give the Atom a very bumpy ride, even when he isn’t floating along thermal drafts.

  Whenever there is an explosion in the Justice League of America’s satellite headquarters orbiting in outer space, or on the quin-jet spaceship used by the Avengers, there is a violent outpouring of air into the low-pressure surroundings. Why? What compels the air to rush out of the opening in the JLA satellite? A common metaphor invoked to explain why air races into any region that is at a lower pressure is that “nature abhors a vacuum.” And yet there would be no violation of Newton’s laws of motion if all the air were to remain inside the JLA’s satellite, even with the door left open, though admittedly such a situation is extremely unlikely. It is the random motion of the air associated with the air molecules’ kinetic energy that underlies the explosive decompression on the satellite.

  Imagine that the room next door to the one you are sitting in has had all of its air removed. As long as the door connecting the two rooms is kept hermetically sealed, you would never know that a perfect vacuum was waiting in the next room. The air molecules in your room are at a certain temperature and pressure, and are buzzing merrily along. This peaceful, stable scenario changes when the door from your room swings open into the vacuum room.

  Instead of asking why the air would rush out of your room into the vacuum room once the door was opened, the better question is, why wouldn’t it? Those air molecules that were moving toward the door, and would have bounced off of it had it remained closed, will now continue moving in a straight line into the vacuum room (per Newton’s first law). However, only a small fraction of the air molecules in your room would have been heading toward the door right before it was opened. Some of the air molecules would be moving away from the door, where they would collide with other air molecules moving in different directions. It is conceivable, though implausible, that aside from those air molecules initially heading toward the now-open doorway, all of the remaining air molecules would continue to collide with one another, with no more passing into the second room. This is as likely as, with the door remaining closed, all of the air molecules, through random collisions, managing to always avoid the region right next to the door. You would not have to worry about suffocating if you sat next to the door, because a fairly constant fraction of the air is always heading toward you at any given moment. The air molecules occupy all regions available to them—there is no reason for them not to. Any particular air molecule may spend most of its time in one particular corner of the room, but on average, every volume is just as likely to have air in it as any other, just as in a well-shuffled deck of cards, any one of the fifty-two cards is as likely to be turned up at the top of the deck as any other.

  Air molecules have no free will, and if they are going to collide and head toward the door when it is closed, they will do so when the door is open. The only difference, and it is a big difference, is that once the air molecules move into the vacuum room, there are initially no other air molecules for them to collide with. There are many, many more ways for the atoms in the first room to move into the vacuum room than there are for them to bounce off one another and never pass into the second room. “Entropy” is the term used to describe the number of different ways a given system can arrange itself. A brand-new deck of cards with all the cards arranged in numerical order by suit has low entropy (I always know what the top card will be), while the entropy is at a maximum once the deck has been thoroughly shuffled (I have a one in fifty-two chance of correctly predicting the top card). It is hard to be dealt four aces in a row from a well-shuffled deck, just as it is harder to know where a particular air molecule is if it can possibly be in two rooms rather than just one.

  When physicists say that systems tend toward maximum entropy, all they are saying is that the most probable situations will be the ones observed. When Peter Parker pulls his socks out of the dryer after they have been tumbling for some time, it is possible that he will extract them two at a time in perfectly matched pairs, but don’t count on it. There is only one way that could happen, but many more ways in which the socks can be mismatched. The dryer randomizes the socks, so every sock has an opportunity of pairing with any other sock. Issues concerning entropy only apply to such fully randomized situations, and there are obviously many examples of externally imposing order on a system (such as Aunt May manually sorting the socks).

  When the door between rooms is opened and the atoms move into the second, initially vacant room, we say that the entropy of the air molecules increases, but what this basically means is that if something can happen, it will happen. There are many more ways for
the air molecules in the room to be spread out uniformly, each sharing a nearly equal portion of the total kinetic energy of the room, than for any other scenario, such as one molecule having all the kinetic energy of the atmosphere and the rest of the molecules having none. Those things that are observed most often are those most likely to occur. Wanda Maximoff, the mutant Scarlet Witch, who was originally a villain in Magneto’s Brotherhood of Evil Mutants in Marvel Comics’ X-Men and later rehabilitated as a hero in the Avengers, had a “hex power,” whereby she could gesture at an object and something untoward would occur. It was suggested in West Coast Avengers # 42 that her power consisted of the ability to alter probabilities, so that a highly unlikely event would actually have a near-certain probability of happening. The above would suggest that her mutant talent involves the power to alter the entropy of a system, bringing about rare configurations (such as all the air moving over to one side of a room) much sooner than would reasonably be expected.44

  In order to get useful work out of the compressed gas in a car cylinder or the steam in a boiler, it typically must expand from a confined region to a more spacious configuration. Think about the air molecules in the room, separated from the vacuum room. It would be nice if they could be arranged to push the door open on their own, without your having to do so manually. If we unlock the door between the two rooms, then there are many air molecules striking the door on one side, and none counteracting on the other, so that there will indeed be a net force on the door that could push it open. This is the same unbalanced force that pushes the Justice League members out of their satellite headquarters when there is a hull breach. This unbalanced force arises quickly—the time between collisions for air molecules at room temperature is less than a nanosecond (one billionth of a second).

  Once the air has moved into the vacuum room, it has a higher degree of disorder, that is, its entropy has increased. Closing the door, the air will not again push the door open, unless I scoop all the air out of the second room, repeating the original configuration (one room at atmospheric pressure, the other room under vacuum). This takes effort, and when I count up all the energy expended in returning the system to its original state, I wind up using more energy than I gained when the door was pushed open. No matter how cleverly I arrange things, I can never convert all the energy of a system into useful work—there will always be some part that goes into increasing the entropy, which is not useful.

  When the mixture of gasoline and oxygen is ignited in your automobile engine, it undergoes a chemical reaction, releasing heat (that is, the reactant products are moving faster than they had been before the explosive reaction). Only those faster-m oving molecules that are heading in the right direction will displace the piston in the engine, leading to rotation of the tires. It would be much more useful, from the driver’s point of view, if all of the molecules following the explosive combustion of gasoline and air were moving in a direct path toward the piston head, so that they all contribute to the lifting force that leads to tire rotation. But there is essentially only one way that the gas molecules can arrange themselves to be all moving in the same direction, while there are many, many more ways they can be moving in all possible directions, with only a fraction of them heading toward the piston head. Those molecules that are heading away from the piston are wasted, from the point of view of getting something useful out of the chemical reaction. Not only can you not get more energy out of a process than you put in, but the entropy constraint means that you will always get out less useful work than you used to set the system up.

  This is the heart of the Second Law of Thermodynamics. No process can be 100-percent efficient (defined as all of the heat being converted into useful work), and in fact, most motors and engines rarely convert more than a third of their available energy into useful work. The Second Law of Thermodynamics is a harsh mistress, but there doesn’t seem to be any way around it. Or is there?

  Could I use the talents of the Atom to try to beat the Second Law of Thermodynamics? The air molecules in your room are characterized by a certain temperature, which measures the average energy of the air. The key word is “average”—not every single air molecule in the room has exactly the same kinetic energy. Some are moving a little faster than average, while some poke along a little slower. The steam coming off a fresh cup of coffee is a reflection of the fact that not every molecule in a cup has exactly the same energy. Those water molecules in the coffee energetic enough to escape from the liquid state (more on such phase transitions in Chapter 15) form the clouds hovering over the coffee. The hotter the coffee is initially, the greater the steam forming over the liquid surface, as there are more water molecules at the high end of the kinetic-energy distribution. When you blow on your coffee to cool it off, you do not reduce the temperature of the coffee, because your breath is a frosty 98.6 degrees Fahrenheit. True—your breath is cooler than the hot coffee, but not enough to effect significant refrigeration. Rather, what you do is disturb the steam, pushing the most energetic water molecules away so that they are unable to be deflected back into the coffee. Once they are permanently removed from the coffee/steam system, the average energy (that is, temperature) of the remaining coffee decreases. This physical process is called “evaporation cooling”—it is the physics underlying the operation of refrigerators and is the reason why sweating is more effective in cooling you down if there is a strong breeze to carry the perspiration away.

  The idea of the Atom getting around the Second Law of Thermodynamics is a variation on the concept of evaporation cooling. We’ll start by having the Atom shrink down so that he is only several times bigger than an air molecule. He’ll have a box with him, with a small, hinged door. In this example the Atom assumes the identity of “Maxwell’s Demon,” proposed by James Clerk Maxwell to test the Second Law of Thermodynamics. All the air molecules in the room are at the same temperature, which means that they cannot be used to generate a heat flow to power a machine. But now the Atom makes use of the fact that the temperature is an average measurement, and starts sorting out the air molecules, based upon their kinetic energy. Those air molecules coming toward him that are moving faster than the average he collects by opening the door of his box and trapping them inside (it’s a thermally insulated box, so those molecules retain their kinetic energy once secured inside). Those that are moving slower than average, he ignores. Before long he has acquired a large number of air molecules that have a kinetic energy larger than the corresponding initial average value. Furthermore, by removing these faster-m oving molecules, the average energy of the remaining air molecules decreases, just as when you blow on your steaming coffee. The Atom can now take these hotter-than-average molecules and, bringing them into thermal contact with some colder molecules, allow the net heat flow between them to power an engine, thereby getting useful work out of air that was initially at one average temperature.

  Or he would, if we didn’t have to worry about the Atom himself. He expends energy in opening and closing his box to sort and trap the energetic molecules. This energy must be included in any balancing of the total energy added to and extracted from a process. To neglect his expenditure of energy would be equivalent to saying that you are able to drive your car for just pennies a day, if you ignore the cost of the gasoline. When the heat and work contributions of the Atom’s sorting of the air molecules are carefully accounted for, we find that by collecting the faster molecules, the Atom himself contributes energy to the remaining atmosphere, increasing its average kinetic energy, so that in the end there has been no net temperature differential. If you blow on your coffee and remove the steam but replace it with other molecules that are just as hot, you have not cooled your drink.

  No matter how hard you try (and believe me, many have tried), there is only one way, discussed below, around the no-win scenario presented by the Second Law of Thermodynamics. Unfortunately, even that option is not available to us.

  THE THIRD LAW- YOU CAN NEVER GET OUT OF THE GAME

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p; If entropy considerations limit the amount of useful work we can extract from any process, whether it’s a V-8 engine, a gas turbine, or the chemical reactions in your cells’ mitochondria, then couldn’t we just get around this problem by dealing with systems with no entropy? After all, it is conceivable, no matter how difficult it may be in practice, to have a system where all the atoms are in a precise, uniform configuration, so that there is no uncertainty regarding the location of any single element within it. Why can’t I arrange my two systems that generate the heat flow that powers my engine to have no entropy, so that I don’t have to worry about the Second Law?

  The reason why this won’t work is that the entropy of a substance and its internal energy (which could be available for heat transfer) are related, such that we can’t change one without affecting the other. The entropy of the air molecules in the room is a measure of their random motion. If I lower the air’s kinetic energy, eventually the gas condenses into a liquid. The entropy of the liquid is lower than that of the same molecules in their vapor state, because there is less uncertainty as to where any given molecule might be (they’re in the puddle on the floor, as opposed to spread out throughout the room). But there are still chaotic fluctuations in position and velocity of the molecules in the liquid state. Lower the temperature of the liquid further, and eventually the average kinetic energy of the molecules is insufficient to overcome the attractive bonding between molecules, and the material freezes into a solid. The chemical bonds between the molecules have preferred orientations, so the natural configuration of the solid will be a particular crystalline arrangement, with all of the atoms or molecules lined up in a certain way. At very low temperatures, all of the atoms will be in their ideal crystalline spots, and we will know the location of any given atom.