Chemical Education Today
Commentary
“Mysteries” of the First and Second Laws of Thermodynamics by Rubin Battino
Over the years the subject of thermodynamics has taken on an aura of difficulty, subtlety, and mystery. Most often it is the concept of the entropy function (as ensconced in the Second Law) that is considered to be mysterious in the sense that it is a universal descriptor of Nature that always increases. Attempts to answer why have been many, and continue to proliferate. I maintain that the First Law is equally mysterious in its incredible combination of two inexact differentials (the work and heat effects) to yield an exact differential (the energy function).1 The distinction between exact and inexact differentials, functions and effects, is crucial in applying thermodynamics to real world problems. General chemistry texts blithely ignore this distinction in their haste to keep up with other texts and incorporate as much of thermodynamics as they possibly can in their mistaken notion that their students can understand and use this subject without a knowledge of the calculus. (I have written about this many years ago to no avail (1).) It would be helpful for the reader to know at this point that I am an unabashed classic macroscopic thermodynamicist. By that I mean that all of the useful relationships in thermodynamics can be developed and used without any knowledge of the existence of atoms and molecules. Macroscopic thermodynamics is concerned with chunks of matter that you can see and hold and manipulate. It is nice to know (since there is much evidence for this) that matter can actually be subdivided into molecules and atoms. Dalton made a good case for this based on experimental evidence almost two hundred years ago. There has thus been a great temptation to explain thermodynamic concepts, particularly the entropy function, using atoms and molecules and probability as manifested in statistical mechanics. Yet, if we were really interested in simplicity, we would not need these extra postulates of the existence of atoms and molecules and their probabilistic distributions. Instead, we could just state that here are the laws of thermodynamics that we have obtained from careful observation of natural phenomena. We raise these observations to the status of laws because they accurately describe the world around us, and no one has ever observed a contravention to these codifications of observation. Another way of saying this is that it is not Nature that obeys these laws, but that we believe these laws are valid because they continue to accurately describe Nature. In the remainder of this essay I will discuss the First and Second Laws separately with respect to this mystery business, and then make some concluding comments. The First Law of Thermodynamics We admit of two ways of bringing about energy changes, and they are by heat and work effects. Both of these effects can be defined operationally, that is, in terms of a set of operations (experiments) that anyone can carry out. For heat effects we use the Bunsen ice calorimeter and variants involvwww.JCE.DivCHED.org
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ing other substances besides water, and at a variety of pressures to cover all temperatures. In essence, a heat effect occurring inside the calorimeter is converted to a volume change of a fluid. In addition, for heat effects, we need to be able to measure the temperature. Thermometers and related temperature scales can also be defined operationally. The work effect is a force times a displacement, and both force and displacement can be operationally defined. This means that the central components required to measure heat and work effects can be carefully defined with respect to macroscopically observable and experimental phenomena. When heat and work effects are determined for a particular change of state like melting a solid or carrying out a chemical reaction at constant temperature and pressure, it is observed that the magnitude of these effects depends on how the change of state occurs. That is, the heat and work effects are dependent on the path between the two states. Mathematically, this means that the integral of the differential of work or heat not only depends on the initial and final states, but also the path connecting them. In other words, DW and DQ are inexact differentials. (Lower case d is used for exact differentials, and upper case D for inexact ones.) Yet, for a given change of state the sum of these two inexact differentials (both energies) is an exact differential, the energy function. This is summarized in the equation of the First Law of Thermodynamics which is dU = DQ + DW (or ⌬U = Q + W )
(1)
where U is the energy function. The mystery, the “miracle” if you will, is that somehow in our universe the sum of two inexact differentials results in an exact differential. The integral of an exact differential is independent of the path between the initial and final states, that is, its value depends only on the initial and final states. We therefore call it a state function. How is it possible that simply adding two inexact differentials results in an exact one? We could perhaps cite many reasons for this from Creationism to statistical mechanics, or we can simply accept that this is the way our universe is, and be happy that enough experiments have been carried out to validate the observations summarized in eq 1. Scientists observe and record and then describe those observations in the shorthand of mathematics. Isn’t it sufficient that we have been able to compress into one equation such a universality? Why the sum of heat and work effects results in a state function is a marvel that might be explained by stating that eq 1 is a mathematical representation of the Law of Conservation of Energy. Okay. This law is also the result of observation and many non-contravened experiments. What an interesting universe we live in—there are so many simple descriptions we can make about natural phenomena! Is there a mystery here or something to acknowledge and appreciate? The energy function, U, is frequently and inappropriately called the internal energy. This language has its origins
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Chemical Education Today
Commentary in the days when it was simplistically thought that heat (energy) was a substance (calor) which could be added to or removed from an object. This mistaken notion also led to writing about latent heats. Recall that the caloric theory of heat was disproved over two centuries ago. It is certainly time to banish the term internal energy. (Also, consider the implication that if there is an internal energy, there must also be an external energy, and what could that possibly be?) The Second Law of Thermodynamics Perhaps more nonsense has been written in attempting to explain the second law to students than anything else I have ever come across in the literature. These explanations are apparently needed due to the extent that thermodynamics has inappropriately penetrated general chemistry courses. The subject should rightly be left for physical chemistry courses where the calculus is a prerequisite. General chemistry students rarely know calculus, and are mostly concrete operational thinkers (á la Piaget) so the seemingly abstract concepts of thermodynamics really become a challenge. This is especially the case with the entropy function since there are no entropy meters, and the definition involves determining heat effects for reversible changes of state. I wrote “seemingly abstract” above because students typically find the subject difficult despite the fact that it is the most practical discipline in chemistry. After all, for example, everyday devices like automobile engines, refrigerators, and chemical plants are all exemplars of applied thermodynamics. If you really feel compelled to include some mention of thermodynamics in general chemistry, then please confine it to easily understandable things like Hess’s Law and thermochemistry. The Law of Mass Action and equilibria can simply be approached empirically, that is, this is the way that chemical reactions work. The Gibbs function need never be mentioned! And, the Second Law can have a few words said about it with respect to knowing that there is a direction for the occurrence of phenomena in Nature, and that there is a quantitative measure of this called the entropy function (which they can learn about in detail in a later course). This will free up lecture time to talk about chemistry, the properties and reactivities of chemical substances. Why load up general chemistry with quantum mechanics and thermodynamics when there is all of that fascinating material about chemicals that can be discussed and demonstrated? How can the entropy function compete with the seemingly magical transformation of a reaction between a silvery active metal (sodium) and a noxious gas (chlorine) to produce an essential component of life (salt, NaCl)? And, did you know that with a magnifying glass you can see the cubic structure of NaCl crystals?2 Let me return to this mysterious entropy function. Its rigorous definition is: dS = DQrev/T
(2)
Somehow, dividing a reversible heat effect by the Kelvin temperature results in a state function. dS is an exact differential and the integral of dS (which is ⌬S) depends only on the initial and final states for any change of state. Please note that changes in the value of the entropy function can only be 754
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measured along reversible paths—that is an essential part of the definition. (Please note that changes in the Gibbs function and the Helmholtz function, since they are defined in terms of the entropy function, must also be determined along reversible paths. This constraint is frequently ignored, but it is essential when calculating changes in the value of these functions. Also, IUPAC banished the ambiguous term “free energy” decades ago.) The concept of reversibility can be difficult to explain, and is best left to physical chemistry. Despite there being no entropy meters, changes in the entropy function can be determined—see any physical chemistry or chemical thermodynamics text. Temperature and reversible heat effects can be defined operationally. This is all practical material as calorimeters for measuring heat effects are readily available. The mystery for many appears to be that changes in the entropy function are an indicator of direction in chemical reactions and processes and changes of state. Students will readily recognize that Nature has a direction, that is, certain changes are likely, and other changes are never observed. A glass of water does not spontaneously have the liquid water get warmer while ice is formed. Gas mixtures do not un-mix by themselves, it has never been noted that you can completely convert a quantity of energy to work without some of the heat being delivered to a low temperature reservoir, balls do not roll uphill by themselves, heat is never transferred spontaneously from a cold to a warm reservoir, etc. Students have a naive experiential knowledge of direction for phenomena. Again, they can simply be told that changes in the entropy function are related to direction.3 There is a strong caveat here that is rarely emphasized when discussing the entropy function in general chemistry. That is, when you sum up all of the entropy changes in an isolated system, the entropy change is either zero or positive. The zero applies to a state of equilibrium between all of the subsystems in the isolated system, and the positive change applies when any natural or spontaneous or irreversible change occurs in that isolated system. It is only for entropy changes in isolated systems that entropy changes can be used to predict the possibility of a change of state. Recall that time is not a thermodynamic coordinate, and that thermodynamics deals with equilibrium states. You may need to wait a very long time for the prediction to be realized! The prime example here is that if diamond and graphite were in equilibrium, you would have mostly graphite. Unless a lecturer is willing to spend sufficient time to discuss exact and inexact differentials, reversibility, heat and work effects, changes of state, temperature measurement, and the nature of an isolated system, then it is a waste of time in my judgment to discuss the entropy function in general chemistry. It should be sufficient to just accept the notion that there is a descriptor of natural phenomena that is connected to the direction of changes in Nature. This is not a mystery, it is an observation! Concluding Comments Since general chemistry text authors inappropriately introduce the Gibbs function wherever they can, it is impor-
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Chemical Education Today
tant to drop this concept from general chemistry courses. What would be so radical about teaching about chemistry, period? As the conservation of energy law the First Law is conceptually easy to understand as ⌬U = Q + W. Thermochemistry does not require the calculus, so why not stop there? But, when you use the First Law in the differential form of dU = DQ + DW, it is imperative to discuss the distinctions between exact and inexact differentials. It is remarkable that there is a measurable quantity that is related to the direction of changes in Nature. The Second Law of Thermodynamics and the entropy function provide that measure via experiment. For atomists, the why of this is given by probability and statistical mechanics. For the experimentalist, the why is given by the observation that the results of calculating changes in the entropy function (with all of the constraints mentioned above) have turned out to be an accurate descriptor of natural phenomena. Please do not clutter up the minds of general chemistry students with concepts they are not mathematically prepared to understand when there is so much real chemistry they can experience and be taught.
Why load up general chemistry with quantum mechanics and thermodynamics when there is all of that fascinating material about chemicals that can be discussed and demonstrated?
tials whose values depend on the path between two states, and are described as effects. 2. Photographs of salt crystals taken through a microscope appeared in this Journal. See Ramette, R. W. J. Chem. Educ. 2007, 84, 16–19. 3. A silent movie on DVD about the Second Law is available from the author for a nominal fee.
Literature Cited 1. Battino, R. J. Chem. Educ. 1979, 56, 520.
Note 1. All thermodynamic functions are exact differentials whose changes are independent of the path between two states, and are described as functions. Heat and work effects are inexact differen-
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Rubin Battino, an emeritus member of the Chemistry Department at Wright State University, resides at 440 Fairfield Pike, Yellow Springs, OH 45387;
[email protected] Vol. 84 No. 5 May 2007
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