"Availability, Entropy, and the Laws of Thermodynamics"
Excerpt from Paul R. Ehrlich, Anne H. Ehrlich, and John P. Holdren "Ecoscience"
(W. H. Freeman and Company, 1977)
"Availability, Entropy, and the Laws of Thermodynamics"
Excerpt from Paul R. Ehrlich, Anne H. Ehrlich, and John P. Holdren "Ecoscience"
(W. H. Freeman and Company, 1977)
"Many processes in nature and in technology involve the transformation of energy from one form into others. For example, light from the sun is transformed, upon striking a meadow, into thermal energy in the warmed soil, rocks, and plants; into latent heat of vaporization as water evaporates from the soil and through the surface of the plants; and into chemical energy captured in the plants by photosynthesis. Some of the thermal energy, in turn, is transformed into infrared electromagnetic radiation heading skyward. The imposing science of thermodynamics is just the set of principles governing the bookkeeping by which one keeps track of energy as it moves through such transformations. A grasp of these principles of bookkeeping is essential to an understanding of many problems in environmental sciences and energy technology.
The essence of the accounting is embodied in two concepts known as the first and second laws of thermodynamics. No exception to either one has ever been observed. The first law, also known as the law of conservation of energy, says that energy can neither be created nor destroyed. If energy in one form or one place disappears, the same amount must show up in another form or another place. In other words, although transformations can alter the distribution of amounts of energy among its different forms, the total amount of energy, when all forms are taken into account, remains the same. The term energy consumption, therefore, is a misnomer: energy is used, but it is not really consumed. One can speak of fuel consumption, because fuel, as such, does get used up. But when we burn gasoline, the amounts of energy that appear as mechanical energy, thermal energy, electromagnetic radiation, and other forms are exactly equal all together to the amount of chemical potential energy that disappears. The accounts must always balance; apparent exceptions have invariably turned out to stem from measurement errors or from overlooking categories. The immediate relevance of the first law for human affairs is often stated succinctly as. "You can't get something for nothing."
Yet, if energy is stored work it might seem that the first law is also saying, "You can't lose!" (by saying that the total amount of stored work in all forms never changes). If the amount of stored work never diminishes, how can we become worse off? One obvious answer is that we can become worse off if energy flows to places where we can no longer get at it - for example, infrared radiation escaping from Earth into space. Then the stored work is no longer accessible to us, although it still exists. A far more fundamental point, however, is that different kinds of stored work are not equally convertible into useful, applied work. We can therefore become worse off if energy is transformed from a more convertible form to a less convertible one, even though no energy is destroyed and even if the energy has not moved to an inaccessible place. The degree of convertibility of energy - stored work into applied work is often called availability.
Energy in forms having high availability (that is, in which a relatively large fraction of the stored work can be converted into applied work) is often called high-grade energy. Correspondingly, energy of which only a small fraction can be converted to applied work is called low-grade energy, and energy that moves from the former category to the latter is said to have been degraded. Electricity and the chemical energy stored in gasoline are examples of high-grade energy; the infrared radiation from a light bulb and the thermal energy in an automobile exhaust are corresponding examples of lower-grade energy. The quantitative measure of the availability of thermal energy is temperature. More specifically, the larger the temperature difference between a substance and its environment, the more convertible into applied work is the thermal energy the substance contains; in other words, the greater the temperature difference, the greater the availability. A small pan of water boiling at 100° C in surroundings that are at 20° C represents considerable available energy because of the temperature difference; the water in a swimming pool at the same 20° C temperature as the surroundings contains far more total thermal energy than the water in the pan, but the availability of the thermal energy in the swimming pool is zero, because there is no temperature difference between it and its surroundings.
With this background, one can state succinctly the subtle and overwhelmingly important message of the second law of thermodynamics: all physical processes, natural and technological, proceed in such a way that the availability of the energy involved decreases. (Idealized processes can be constructed theoretically in which the availability of the energy involved stays constant, rather than decreasing, but in all real processes there is some decrease. The second law says that an increase is not possible, even in an ideal process.) As with the first law, apparent violations of the second law often stem from leaving something out of the accounting. In many processes, for example, the availability of energy in some part of the affected system increases, but the decrease of availability elsewhere in the system is always large enough to result in a net decrease in availability of energy overall. What is consumed when we use energy, then, is not energy itself but its availability for doing useful work.
The statement of the second law given above is deceptively simple; whole books have been written about equivalent formulations of the law and about its implications. Among the most important of these formulations and implications are the following:
1. In any transformation of energy, some of the energy is degraded.
2. No process is possible whose sole result is the conversion of a given quantity of heat (thermal energy) into an equal amount of useful work.
3. No process is possible whose sole result is the flow of heat from a colder body to a hotter one.
4. The availability of a given quantity of energy can only be used once; that is, the property of convertibility into useful work cannot be "recycled."
5. In spontaneous processes, concentrations (of anything) tend to disperse, structure tends to disappear, order becomes disorder.
That Statements 1 through 4 are equivalent to or follow from our original formulation is readily verified. To see that statement 5 is related to the other statements, however, requires establishing a formal connection between order and availability of energy. This connection has been established in thermodynamics through the concept of entropy, a well defined measure of disorder that can be shown to be a measure of unavailability of energy, as well. A statement of the second law that contains or is equivalent to all the others is: all physical processes proceed in such a way that the entropy of the universe increases. (Not only can't we win - we can't break even, and we can't get out of the game!)
Consider some everyday examples of various aspects of the second law. If a partitioned container is filled with hot water on one side and cold water on the other and is left to itself, the hot water cools and the cold water warms - heat flows from hotter to colder. Note that the opposite process (the hot water getting hotter and the cold getting colder) does not violate the first law, conservation of energy. That it does not occur illustrates the second law. Indeed, many processes can be imagined that satisfy the first law but violate the second and therefore are not expected to occur. As another example, consider adding a drop of dye to a glass of water. Intuition and the second law dictate that the dye will spread, eventually coloring all the water - concentrations disperse, order (the dye/no dye arrangement) disappears. The opposite process, the spontaneous concentration of dispersed dye, is consistent with conservation of energy but not with the second law.
A more complicated situation is that of the refrigerator, a device that certainly causes heat to flow from cold objects (the contents of the refrigerator - say, beer - which are made colder) to a hot one (the room, which the refrigerator makes warmer). But this heat flow is not the sole result of the operation of the refrigerator: energy must be supplied to the refrigeration cycle from an external source, and this energy is converted to heat and discharged to the room, along with the heat removed from the interior of the refrigerator. Overall, availability of energy has decreased, and entropy has increased.
One illustration of the power of the laws of thermodynamics is that in many situations they can be used to predict the maximum efficiency that could be achieved by a perfect machine, without specifying any details of the machine! (Efficiency may he defined, in this situation, as the ratio of useful work to total energy flow.) Thus, one can specify, for example, what minimum amount of energy is necessary to separate salt from sea water. to separate metals from their ores, and to separate pollutants from auto exhaust without knowing any details about future inventions that might be devised for these purposes. Similarly, if one is told the temperature of a source of thermal energy - say, the hot rock deep in Earth's crust - one can calculate rather easily the maximum efficiency with which this thermal energy can be converted to applied work, regardless of the cleverness of future inventors. In other words, there are some fixed limits to technological innovation, placed there by fundamental laws of nature...
More generally, the laws of thermodynamics explain why we need a continual input of energy to maintain ourselves, why we must eat much more than a pound of food in order to gain a pound of weight, and why the total energy flow through plants will always be much greater than that through plant-eaters, which in turn will always be much greater than that through flesh-eaters. They also make it clear that all the energy used on the face of the Earth, whether of solar or nuclear origin, will ultimately be degraded to heat. Here the laws catch us both coming and going, for they put limits on the efficiency with which we can manipulate this heat. Hence, they pose the danger... that human society may make this planet uncomfortably warm with degraded energy long before it runs out of high-grade energy to consume.
Occasionally it is suggested erroneously that the process of biological evolution represents a violation of the second law of thermodynamics. After all, the development of complicated living organisms from primordial chemical precursors, and the growing structure and complexity of the biosphere over the eons, do appear to be the sort of spontaneous increases in order excluded by the second law. The catch is that Earth is not an isolated system; the process of evolution has been powered by the sun, and the decrease in entropy on Earth represented by the growing structure of the biosphere is more than counterbalanced by the increase in the entropy of the sun...
It is often asked whether a revolutionary development in physics, such as Einstein's theory of relativity, might not open the way to circumvention of the laws of thermodynamics. Perhaps it would be imprudent to declare that in no distant corner of the universe or hitherto-unexplored compartment of subatomic matter will any exception ever turn up, even though our intrepid astrophysicists and particle physicists have not yet found a single one. But to wait for the laws of thermodynamics to be overturned as descriptions of everyday experiences on this planet is, literally, to wait for the day when beer refrigerates itself in hot weather and squashed cats on the freeway spontaneously reassemble themselves and trot away."
