Spatial variations of the atmospheric temperature are associated with changes in the atmospheric density (the number of air molecules in a given volume). When a volume of denser air is adjacent to a dilute region, there will be a net flow of air from the high-to low-density spaces until the density in each volume element is equal. This flow of air can be understood simply on the basis of the entropy argument discussed in the previous chapter. If there is a constant input of energy, keeping one region at a lower density than another, then this flow of air—or wind—will persist. The wind can, in turn, move cloud cover, changing the spatial pattern of sunlight absorption, which changes the airflow trajectories that influence the cloud cover, and so on. Of course, the Earth’s rotation determines the global direction of air circulation.
The ability to accurately predict the weather is therefore limited by the precision with which one knows, at some specified time, the air speeds and temperatures everywhere in space. Furthermore, changes in temperature lead to airflow that in turn changes the absorbed sunlight, leading to new airflow patterns. There is a nonlinear feedback in place, such that any small uncertainty in our knowledge of the initial conditions quickly becomes magnified. In a linear system a small change in the input results in a corresponding small variation in the output, while for nonlinear systems, such as the weather, a small change could lead to a very large variation in the output. This has become popularly known as “the butterfly effect,” whereby the beating of a butterfly’s wings in Cleveland may, several weeks later, produce tornado-like conditions in Chile. Meteorologists do an excellent job of predicting the weather in the short term, but anything beyond a few weeks is intrinsically unreliable, regardless of the quality of the measurement systems.
A physically plausible explanation for Storm’s ability to control the weather is that she is able to alter atmospheric temperature variations in space and time at will. The wind that allows Storm to fly, as illustrated in fig. 24, is created by a temperature gradient beneath her. Storm presumably uses her mutant power to make the region of air under her hotter than that above her. The temperature of the air is a measure of its average kinetic energy, so air at a very low temperature is moving much slower than warmer air. This cooler air is denser, and it will fall toward the ground. The faster-moving, less dense “hot” air molecules will occupy the space left vacant by the falling “cold” air molecules, simply because if they are zipping around at great speeds, colliding with one another, there are many more ways they can scatter into unoccupied regions than if they collide and always manage to stay near the ground. The average kinetic energy of the hot air molecules is large; consequently, the gravitational potential energy is only a small addition to its total energy. Once the hot air molecules are near the cold upper region, and the cold air molecules are near the ground, the lower molecules will gain energy from collisions with the heated ground, and the hot air will lose energy following collisions with the cool air above it. There will once again be a situation where hot air is on the ground and cold air is above it, and the cycle will continue.
This process is termed “convection” and such thermal convection rolls are an extremely efficient way to transfer energy from a hot source to a cold one through the thermal link of the air in the room.
Fig. 24. Scene from X-Men # 145, where the mutant Storm employs her ability to generate controlled thermal gradients to warp wind patterns, carrying her aloft on convection cells.
The fraction of air that is composed of water vapor depends on the average kinetic energy (ambient temperature) and pressure of the atmospheric molecules. Colder air is denser and has less room to accommodate the water molecules. If Storm is indeed able to control the local temperature, then she can also vary the barometric pressure and humidity at will. It is not unreasonable that she would be able to cause localized rain- or snowstorms, or even generate lightning strikes, though her ability to control the exact position of the strike would be hampered by factors (such as the local charge buildup on the ground) outside of her control. All told, if Stan Lee was not bothered by his creation of Iceman, a mutant who could lower his own body temperature to below 32 degrees Fahrenheit and also project localized regions of lower temperature in his immediate vicinity, then a mutant such as Storm, who can control not her own temperature but that of the surrounding atmosphere, should not have been too great a stretch.
A final thought about a connection between genetic mutation and thermodynamics. According to Stan Lee, mutants, particularly those with dramatic superpowers, comprise an entirely new species, Homo superior, and are distinct from most comic-book readers, Homo sapiens. The process of speciation, by which new species develop, was put forth by Charles Darwin and independently by Alfred Wallace in the 1850s. In Darwin’s original formulation of the theory of evolution, he proposed that speciation was a slow, gradual process and that several hundred million years were necessary to account for the current biological diversity. The only problem was that the physics of the time estimated that the Earth was only roughly twenty-million years old.
One of the foremost scientists of the nineteenth century, William Thomson (later honored as Lord Kelvin for his efforts in developing transatlantic telegraph cables) performed a thermal conductivity calculation that challenged Darwin’s hypothesis. Thermal conductivity is a basic property of all matter, and it reflects the rate that heat is transferred in response to a given temperature difference. Metals have a very high thermal conductivity, such that they are able to carry away heat very efficiently for a particular temperature difference (for example a wet tongue at 98.6 degrees Fahrenheit and a metal lamppost below 32 degrees Fahrenheit in winter), while wood is a fairly poor thermal conductor. Making reasonable assumptions that the Earth was a sphere of molten rock at 7,000 degrees Fahrenheit when it initially formed, and knowing the thermal conductivity of rock, Lord Kelvin was able to determine how long it would take the Earth to cool to its present temperature. His conclusion, that the Earth was at least ten times too young to provide sufficient time for evolution’s effects, was considered to be a near-fatal flaw in Darwin’s arguments. Kelvin’s understanding of thermodynamics was so highly regarded that the absolute temperature scale mentioned in the previous chapter, in which zero kinetic energy is recorded as zero degrees absolute, is named in his honor (and is now referred to as “degrees Kelvin”). There was nothing wrong with his calculation.
While Darwin could not refute Kelvin’s result, he remained convinced of the validity of the theory of evolution, as it was able to account for too many biological phenomena to be completely wrong, despite Kelvin’s objection. Darwin passed away in 1882. A few years later, radioactivity was discovered, and it was realized that there was an additional internal heat source within the Earth that Kelvin had not taken into account, simply because he (like the rest of the world) was unaware of its existence. This extra heat within the Earth would lengthen the time needed for the planet to cool to its present temperature. When Kelvin redid his calculation in 1905, now incorporating the energy provided by radioactive decay, he arrived at a minimum estimate of the Earth’s age of several hundred million years, closer to Darwin’s original proposal. The current determination of the age of the Earth is 4.5 billion years, easily old enough to provide a landscape for evolution to operate. Darwin went to his grave not knowing that Kelvin was mistaken, yet nevertheless maintained his belief in the correctness of his theory of evolution.
There are critics of evolutionary theory today who point out particular biological phenomena that the theory cannot currently explain, but this does not necessarily invalidate a scientific theory. For example, the motion of three masses interacting through their mutual gravitational attraction turns out to be so complicated as to defy analytical calculation, but this does not indicate that the theory of gravity is wrong. There are always gaps in our knowledge and many things we do not presently understand, but the only way we will change this situation is through critical thinking and the experimental testing of evide
nce. If you find the scientific method lacking in one aspect of science, then honesty would indicate that you should refrain from using its results in other parts of your life, which will certainly save you some money on doctor and electricity bills.
15
HOW THE MONSTROUS MENACE OF THE MYSTERIOUS MELTER MAKES DINNER PREPARATION A BREEZE—PHASE TRANSITIONS
NOT EVERY SUPERHERO possesses powers and abilities far beyond those of mortal men. Some, such as Batman and Wildcat, bravely face down supervillains armed with nothing more than a good right hook and the courage to appear in public wearing their underwear on the outside of their clothes. Of course, Batman would try to even the odds somewhat by using his analytical brain, as highly trained as his body, to produce a fabulous array of crime-fighting weapons that he stored within his utility belt. Over at Marvel Comics, the engineer as superhero reached its apogee in Tales of Suspense # 39, featuring the debut of the invincible Iron Man. When electrical engineering genius and weapons manufacturer Tony Stark dons his flexible suit of red-and-golden armor, he has the strength of a hundred men, is able to fly using jets built into the soles of his boots, and can fire concussive “repulsor rays” from the palms of his gloves.
We will have much, much more to say about Tony and his Golden Avenger alter-ego when we get to Chapter 24, which is devoted to a discussion of solid-state physics. Right now I want to consider one of the charter members of the gallery of superpowered villains who would bedevil Iron Man time and again. This villain was one of the first to actually strike fear into Tony’s shrapnel-damaged heart.49 For if you are wearing a suit of iron, and your only superpower stems from this armor, then one of your worst nightmares would involve a villain possessing a “melting ray,” capable of dissolving iron like butter on a stovetop. Unfortunately for Iron Man, Bruno Horgan possessed just such a melting gun, and as the costumed criminal the Melter, he was only too willing to use it. When the Melter first appeared back in 1963, the notion of a melting ray seemed suitable only for comic books. As we’ll now discuss, science and engineering have advanced to the point where such devices are commonplace. You probably have one in your home right now (you no doubt refer to it as a “microwave oven”).
Before we can answer why solids melt when they become very hot, we need to address a more basic question: Why do atoms combine to become solids in the first place? It all comes down to energy and entropy. Under certain circumstances, two atoms may have a lower total energy when they are close enough to each other that their electrons’ “orbits” overlap. When this happens, a chemical bond forms between the two atoms. This lowering of energy is not always very significant. If the two atoms are moving very fast when they are brought together, then their individual kinetic energies can be much greater than any lowering of energy resulting from the formation of a chemical union, and no chemical bond will form. It’s easier to hook up a trailer to a towing hitch on the back of a truck if you slowly back onto the hitch, rather than smash into it at 100 mph. The slower the atoms are moving, the greater the chance that the resulting lowering of energy will prevail when they overlap, and they will remain linked, bonding to form a molecule.
What is true for two atoms will also hold for two hundred, or two trillion trillion, atoms. As the temperature of a gas is lowered, the average kinetic energy of each atom decreases and the greater the chance that the atoms, when they collide, will condense into a new phase of matter—a liquid. Adding thermal energy—heat—to the liquid reverses the process, and the fluid will boil and return to the vapor phase. Similarly, upon lowering the temperature of a liquid, a point is reached at which the atoms cannot glide past one another, and they become locked into a rigid, solid network. Pressure also plays a role in phase transitions. If I squeeze on the collection of atoms, I force them to remain closer to one another than they would ordinarily, changing the temperature at which a phase transition will occur.
If the atoms or molecules lower their energy when they link up and form a collective state as either a liquid or a solid, then it follows that one has to add energy to remove atoms. It takes quite a bit of energy to enable a water molecule to leave the liquid state. This energy comes from its surroundings, either the rest of the liquid, or the surface on which the water is in contact. In either case, when the water molecule leaves the liquid state and returns to the vapor state, that is, during evaporation, it leaves its surroundings with less energy. The average energy per atom, characterized by the temperature, is lowered when a water molecule evaporates from the liquid state. In this way, water molecules undergoing a phase transition from the liquid state to vapor cool the remaining cup of coffee, or the skin on which perspiration is drying.
What determines the exact temperature and pressure at which a phase transition takes place depends on the details of how the individual atoms link up when their electronic clouds overlap. To determine the temperature at which a phase transition such as melting or boiling occurs, we must do more than simply count up the energy needed to break each chemical bond that holds a solid or liquid together. We also have to take into account the large change in the randomness of the atoms—that is, their entropy. For a given internal energy, systems tend to increase their entropy, because all other things being equal, there are generally more ways to be in disordered configurations than in neat, ordered piles. The competition between lowering energy and increasing entropy leads to a fascinating collective phenomenon in which all of the atoms in a solid decide to melt at the same temperature. By the way, the bubbling we associate with boiling water in a pot arises from small irregularities in heating at the bottom of a typical saucepan. Individual points on the pan’s bottom will be hotter than neighboring regions, and the liquid-to-vapor transition occurs first at these locations. The underwater vapor forms a buoyant bubble that rises to the surface.
To initiate the melting process, we must add energy to the solid. We can do this the slow, conventional way, by placing the solid in an oven, or the quick way, à la Bruno Horgan and his melting ray. In a conventional oven, the heating elements—either gas-flame jets or electrical coils—cause the average temperature inside the oven to rise. A solid placed in the oven, such as a nice roast, will come to the temperature of the oven as air molecules collide with the walls of the oven, pick up some extra kinetic energy, and then make their way to the roast. Striking the surface of the roast, these fast moving air molecules transfer their energy to the meat. With a conduction oven, one must wait for the hot air molecules to randomly make their way from the hot walls to the cooler roast, while with a convection oven a fan generates circulation cells from hot to cold and back again (as in our discussion about Storm of the X-Men in the previous chapter). In either case, the surface of the roast warms up first, and one must wait, sometimes several hours, for the center of the meat to reach a higher temperature. As the internal temperature of the meat increases, the atoms shake more and more violently about their equilibrium positions. At a given temperature, the shaking of the connecting fibers and deposits of fat in the roast is sufficiently pronounced that these fibers undergo a phase transition and melt.50 Since these were the tough, stringy tissues binding the muscle cells in the roast, melting them makes the meat more tender and easier to eat. This is the same principle utilized by the Flash when escaping from the solid blocks of ice in which Captain Cold would routinely entomb him.51
If you’re in a rush but unable to vibrate at superspeed, there is another technique you can use. This involves grabbing hold of every single atom in the solid at the same time and shaking them back and forth very rapidly, using internal friction to cook all parts of the roast simultaneously. This is what a microwave oven—and the Melter’s deadly ray gun—does.
Every atom in a solid is electrically neutral, with exactly as many positively charged protons in the nucleus as there are negatively charged electrons swarming about it. But the electrons are not always distributed around the nucleus in a perfectly symmetrical manner. Due to the vagaries of the probability clouds an
d the nature of the chemical bonds holding the atoms together, one side of the atom may have a little more electric charge than the other. In this case, the atom will be a bit more negative on one side and a bit more positive on the other, just as a bar magnet will have one end with a North magnetic pole and the other end will be the South magnetic pole. This charge imbalance is not very great, but it gives an applied electric field something to grab onto. Even molecules with perfectly symmetrical charge distributions can be polarized by an external electric field.
If a large enough electric field is applied across the solid, the imbalanced atoms line up with the field, just as the needle of a compass will rotate and point in the direction of an external magnetic field. If I now suddenly reverse the direction of the electric field, all the atoms will flip 180 degrees and point in the opposite direction. Changing the electric field back to its original orientation, the atoms will have to rotate once again. If I flip the direction of the electric field back and forth several billion times a second, the atoms are going to do some serious rotating. This energy of vibration will very quickly raise the average internal energy of each atom in the material and, in so doing, raise its temperature. As the external electric field penetrates deeper within the material (with a few exceptions), more atoms will move back and forth due to the oscillating electric field at the same time, not just those on the surface. This process is many times more efficient than waiting for the transfer of kinetic energy by the impact of hot air molecules. The frequency of oscillation of the alternating electric field is in the microwave portion of the electromagnetic spectrum, hence, this type of cooking device is called a microwave oven.
The Physics of Superheroes: Spectacular Second Edition Page 21
