Chemical Education Today
Commentary In Defense of Thermodynamics—An Animate Analogy Sture Nordholm Department of Physical Chemistry, Göteborg University, S-41296 Göteborg, Sweden Thesis Thermodynamics is inescapable in its generality. In its purest form it has been seen by generations of intrepid scientists in the inanimate realm of chemistry and physics, but if we grasp its essence we see the concepts and the principles at work in our daily lives and they become clearer by standing out in the great confusion of human behavior. The Argument Thermodynamics is a key theory of chemistry, physics, and all natural sciences. This statement would generally be accepted as a fact. However, thermodynamics is a littleloved part of the science curriculum. The theory is abstract, perhaps to the point of being forbidding to some, and thought to be applicable only to inanimate matter. Its claimed applicability to engines and refrigerators appeals mainly to the technically oriented student. Its great generality and power remains hidden by layers of abstraction and axiomatic rigor. Must this be so? Could we not gain much by loosening the strictures and bringing the main point home by more qualitative applications of thermodynamics to the widest range of everyday experiences? An attempt, at the same time loose and seriously meant, follows. I will argue that given the proper translation of terms and concepts from the inanimate to the animate world the laws of thermodynamics can be seen at work in our everyday lives. No proofs will be offered and we should not be surprised that human behavior will remain richer and more complex than our simple analogy could possibly explain. Even in their usual habitat the laws of thermodynamics were never more than idealized limiting laws. In the animate applications the ifs and buts will not be fewer but the telltale signs of thermodynamic laws at work may be more impressive. The work we do to recognize these laws so far from their home may clarify their meaning also in their normal applications and persuade us that such power and generality is worth the effort to learn and use. In order to illustrate the deepest roots of thermodynamics and its great power and generality I shall apply it to human behavior from an economic point of view. Many economists and marketing executives would like to know what drives human behavior in the so-called marketplace. Thermodynamics explains what “drives” inanimate behavior, that is, which processes will spontaneously occur and towards what equilibrium conditions they strive. Thus we might apply this theory also to economic behavior of humans. In thermodynamics the two quantities of greatest interest are the energy and the entropy. Energy is a property of all physical systems that is conserved in total but transferrable among subsystems. The availability of energy is a precondition for states to occur. Thus the transfer of energy is directly connected with the possibility that the system change its state. Perhaps the first and simplest, but imperfect, observation associated with thermodynamics is that
usually the surroundings seek to minimize the energy of any given subsystem (the small part of the universe you are focusing on). Thus energy minimization seems to be a driving force of nature. Its effects are most clearly seen in the preference of molecules for their lowest energy electronic states, in the fact that stones tend to roll down hill and rolling cars stop unless pushed on by an engine. While the tendency of nature (the surroundings) to minimize subsystem energy is readily accepted it becomes less obvious upon further thought. In the form of heat, energy often flows the other way—from the surroundings to the subsystem. Apparently the spontaneous energy redistribution observed in nature is related to a more fundamental driving force. The initially more subtle but in the longer term more obvious rule of thermodynamics is that nature seeks to maximize the number of available states. This rule applies also to the case of a closed system wherein all states have the same energy. One can now understand that the first rule, that energy is minimized, is a consequence of the second rule, that the number of states is to be maximized. The transfer of energy from the subsystem (i.e., the energy minimization) makes energy available to the rest of the system (the universe) so that it can increase the number of states available to it. Let us call “the number of available states” W. Then the entropy is defined as entropy = S = k B ln W where kB is the Boltzmann constant, a positive constant, and ln denotes the natural logarithm. Since S grows logarithmically (i.e., monotonically) with W we can see that maximizing W is the same as maximizing S. Thus we can state the fundamental rule of thermodynamics as Nature seeks to maximize the entropy.
For a closed system that does not exchange energy with its surroundings this rule alone determines whether a process is spontaneous. Thus it applies also to the universe as a whole. More commonly we consider a small subsystem of fixed volume exchanging energy with its surroundings acting as a thermal reservoir. The fundamental rule leads to a corollary for this case: Nature seeks to minimize the free energy E – TS of a subsystem.
This result follows from the fact that entropy increases with energy E for both the subsystem and its surroundings. T is the inverse of the rate of increase of the entropy of the reservoir with increasing energy. We call T the temperature. It determines the direction of energy flow, that is, from high towards low temperature. From the point of view of the subsystem the energy minimization or the entropy maximization may predominate depending on whether T is high or low. From the point of view of the universe only the entropy maximization applies. Now we turn to human behavior. It is incredibly complex so we shall have to be satisfied with gross simplifica-
Vol. 74 No. 3 March 1997 • Journal of Chemical Education
273
Chemical Education Today tions, but perhaps we can still grasp the essence of the phenomena we wish to describe. I will now propose the following identifications: •
energy = wealth kinetic energy = cash potential energy = property
•
entropy = freedom
Will this mapping of thermodynamics onto human behavior have any merit? Note that the tendency towards energy minimization then corresponds to the observation that the natural action of the environment on an individual is to make him or her poor. This is believable and the reason is that the other humans want themselves to become rich, so they want to transfer money or value from you to themselves. The entropy rule corresponds to the fundamental rule of human behavior: Humans seek to maximize their freedom.
An individual acts to maximize his or her own personal freedom but against this tendency stands the same driving force acting on the other humans in the society to which the individual belongs. Thus we should understand the desire of someone to be rich as a desire to become free and the desire of a salesman to have his customers’ money as an attempt to optimize freedom somewhere else in society. The richer among us are more free in the sense that they can place their money in many different investments, which can be changed with time. Ultimately, what we want to buy with money is freedom. This word “freedom” is perhaps hard to define precisely, let alone maximize, but I claim that it is a fair translation of the concept of “entropy” from thermodynamics of inanimate matter to thermodynamics of human life. It is also a most positive concept almost synonymous with life itself. Who could then doubt the need for a concept of entropy or deny its claim to be central to the theory of change be it inanimate or animate? The thought that the dry and forbidding discipline of thermodynamics could be applied to that most theory-defying of all applications, human behavior, may be staggering, and perhaps heresy to some. After all, the purity and precision of thermodynamics has been maintained on the strength of its validity only as a collection of limiting laws for infinitely large systems undergoing infinitely slow changes. However, the interest in thermodynamics has always been based on the great relevance for finite real systems undergoing changes that are fast on our everyday time scale and slow only on the microscopic time scale of atomic motion. Thus we are merely extending the beam of insight from the lifeless behaviors of inanimate matter to the vivid complexities of human behavior. In the final analysis this far-reaching analogy rests on the fact that the basic elements of the description of atoms, molecules, and matter can be scaled up to the realm of living organisms without changes other than in the complexity of the systems and their behavior. In its most elementary form the thermodynamical view of reality can be summarized as follows:
by trade. It recognizes that the ultimate driving force of all human behavior is the search for greater freedom, which simply means that we have within us an urge to explore reality in all its dimensions, shapes, and forms. When Sir Edmund Hillary was asked to explain why he had taken all the trouble to climb Mount Everest he is purported to have answered “Because it is there”. Exercises, Questions, and Points of Discussion 1. Discuss the human driving forces that brought down the Berlin wall. Comment: Was it not a search for freedom acting like an osmotic pressure that brought down the wall? 2. Which physical property most directly influences the relative importance of energy minimization and entropy maximization in an inanimate physical system? Can you think of an equivalent property applicable to human behavior? Comment: Temperature establishes the balance between energy and entropy in inanimate thermodynamics. Would “standard of living” similarly describe the balance between wealth (or poverty) and freedom? 3. Discuss the political systems dictatorship and democracy from the point of view of the proposed rules of human behavior. Which system of government is most in tune with animate thermodynamics? How might the level of education in a society influence the choice of system of government? Comment: Is not democracy a form of government in tune with the thermodynamics of animate behavior? It generates freedom (entropy) by spreading decision making among all people. Clearly, the individual rights granted all citizens are also balanced against restrictive laws with the general intent of maximizing total freedom in society. Dictatorship, on the other hand, attempts to put a straightjacket on freedom by a combination of threats and promise of material reward. This runs counter to the basic law of “animate thermodynamics”. A high level of education simply speeds up the irresistible tendency to maximize freedom by making people aware of more alternatives and better equipped to explore them. 4. In many texts disorder is associated with high entropy. Give a critical analysis of the relevance of this analogy within first inanimate then animate thermodynamics. Is it true that anarchy maximizes freedom for individuals? How is the need for law and order related to the population density in society? Is there an inanimate analogy for this aspect of government of humans?
Reality is described by a set of states and various forms of dynamics that cause changes of states. There is a quantity called energy which is conserved in the dynamics of an isolated part of reality and thereby constrains the states available to the dynamics. All forms of dynamics tend to explore all parts of reality.
Our animate analogy claims that reality can still be described by a set of states even though the dynamics is of indescribable complexity. It proposes that money is a commodity invented by humans to play the role of kinetic energy to allow the dynamics to more rapidly explore reality
274
Journal of Chemical Education • Vol. 74 No. 3 March 1997
Comments: Disorder is, at best, a very construed synonym of freedom. When used in texts on thermodynamics it is surely clear to the authors that disorder in an ideal gas increases with the volume; but to most uninitiated, disorder is a more qualitative concept. A gas may then appear to be as disordered in a small volume as in a large volume. In the animate realm, youthful observers may think that anarchy is the ultimate freedom but the older and wiser know that the constraints of the law, personal discipline, and morality actually increase freedom when summed over all members of society. The closer contact we have with the rest of humanity the more we need laws, discipline and morality. In inanimate thermodynamics it is known that the hard sphere fluid, the structure of which is only determined by the principle of maximal entropy, becomes ordered at high density.
Chemical Education Today 5. Is it true that spontaneous processes observable to us appear to be driven mainly by energy minimization? Why might this be so? Comment: Energy minimization appears to rule when the observed subsystem is at a higher temperature (has more energy per degree of freedom) than the environment. Observable processes around us often arise when macroscopic objects have been given large (superthermal) amounts of energy which are then in time dissipated out to microscopic objects in the environment. We can see the macroscopic but generally not the microscopic degrees of freedom. We can impart energy to a few objects of our own dimensions but we cannot see the many atomic and molecular motions that receive the energy lost from the few macroscopic degrees of freedom by dissipation. 6. In inanimate thermodynamics energy is usually conserved in the total system considered. However, in the world of human behavior, wealth is created and consumed by each individual to a varying extent. Consider the implications of this difference. Does it invalidate the analogy? Comment: Clearly wealth is an immensely multifaceted quantity that will be hard to fit into the mold of inanimate energy. However, is this not a problem more of practice than of principle? There would appear to be many cases of, e.g., economic behavior of humans where the practice of “thermodynamics” is comparatively straightforward. In other cases the implementation of thermodynamics may involve unfathomable difficulty. 7. Is human behavior more complicated than the behavior of inanimate matter? Consider this question and give supporting arguments for your conclusion. Comment: The intuitive answer is “yes”, but try to justify it by considering what factors make an inanimate problem hard and apply the same criteria to the animate problem. 8. Thermodynamics is often applied to the evolution of life-forms on earth. Critics have opposed such applications, arguing that thermodynamics only becomes applicable when, for example, an animal dies. Which side of this argument do you favor? Why? Comment: The very definition of life in distinction from lifeless existence seems capable of generating interminable argument. Perhaps the scale is continuous and divided into life and lifeless only by personal predilection. Where on such a continuous scale would thermodynamics cease to be relevant?
Epilogue Here we leave our open-ended excursion into animate thermodynamics and return to the most pressing need at hand—to convey the edifice of thermodynamics to present and future students. From our analogy above we should be able to gain: • • •
an antidote for the boredom, confusion or lack of interest many captive students of thermodynamics feel; a new word to associate with entropy—freedom; a clear and compelling illustration of the content of the second law of thermodynamics.
The power of the limiting laws of thermodynamics is not their splendid purity but their ability to remain relevant in the confusion of reality. Students live in the confusion of reality. The animate analogy is an attempt to find them there and bring to them the benefits of the purity of the limiting laws of thermodynamics.
The Information Column Journal of Chemical Education • Subscription Fulfillment: new, gift, renewal, change of address: see Reader Inquiry Card • A Guide for Submissions: see page 1246 of December 1996; also available from the Editorial Office by fax, email, or World Wide Web (JCE: Online) • JCE Online: http://jchemed.chem.wisc.edu/ • Books and Other Publications: see A200 of September 1996 • JCE: Software orders, information: see page 346 of March 1997, call 1-800/991-5534, send email to
[email protected], or visit JCE Online.
ACS Division of Chemical Education, Inc. • Membership Information, Officers, or Newsletter: Jerry L. Sarquis, CHED Secretary, Department of Chemistry, Miami University, Oxford, OH 45056; 513/529-2819; 513/529-5715 (fax);
[email protected]; http://divched.chem.wisc/ed/divched/#top
Examinations Institute • ACS DivCHED Standardized Tests, Test Item Banks: Examinations Institute, 223 Brackett Hall, Clemson University, Clemson, SC 29634 864-656-1249; 864/656-1250 (fax);
[email protected]; http://tigerched.clemson.edu
Safety Guidelines • Minimum Safety Guidelines for Chemical Demonstrations: Jerry L. Sarquis, see above.
Lists of Available Textbooks and Other Classroom Materials • Book Buyer's Guide: a print resource in each September Journal; updates each March. • Chemical Education Resource Shelf: an online resource (http://www.umsl.edu/~chemist/books/ index.html) of JCE Internet, includes Index to Chemistry Textbooks in Print; has hyperlinks to publisher's sites; lists publisher’s addresses.
Organizations • American Chemical Society: 1155 Sixteenth Street NW, Washington, DC 20036; 202/872-4600; http://www.acs.org/ • AAAS: American Association for the Advancement of Science, 1200 New York Avenue, NW, Washington, DC 20005; 202/326-6640; 202/371-9526 (fax); http://www.aaas.org/ • NSTA: 1840 Wilson Boulevard, Arlington, VA 222013000; 800/722-NSTA; http://www.nsta.org/ • National Science Foundation: 4201 Wilson Blvd., Arlington, VA 22230; 703/306-1234; http://www.nsf.gov/ • U.S. Department of Education: Washington, DC 20202; 800/872-5327; http://www.ed.gov/
Vol. 74 No. 3 March 1997 • Journal of Chemical Education
275
