On the Teaching of Thermodvnamics I
J
F. G. BRICICWEDDE National Bureau of Standards, Washington, D. C., and University of Maryland, College Park, Maryland
1 . .
N recent years the status of thermodynamics in the phys~cscurriculum has become uncertain. Some typical statements of others will make this clearer: An outstanding authority in physical chemistry in one of our large universities made the statement that it was chemists and not physicists who really knew thermodynamics. The head of a graduate department of physics remarked that in giving a course in thermodynamics he felt as though he were teaching physical chemistry. A teacher of advanced physics in another large university expressed the opinion that physics departments, in general, rated thermodynamics as a subject of minor importance for physics, and left instruction in i t to chemistry departments. If these statements were true a thermodynamics course in the physics curriculum would be of little value to chemistry students. The majority of physicists will dispute these statements. Nevertheless, they cast doubts on the teaching of thermodynamics by physicists and make it necessary to review here the purposes of physics teaching in general and thermodynamics teaching in particular. The utilitarian purpose of advanced physics teaching is the training of students to solve original and practical problems arising in fields regarded as part of physics. The solution of these problems may call for laboratory
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Presented jointly before theDivisionsof Chemical Education and Physical and Inorganic Chemistry of the American Chemical Society, 108th meeting, New York City, September 11, 1944.
work, for paper and pencil work, or a combination of both. In the course of instruction leading to a degree, the average student can be taught only a few of the many types of physical problems that may arise after graduation. Hence, the training of the student must be such that he is enabled to solve unfamiliar types of problems. This training is based on-givingthe student a knowledge of important experimental phenomena, facility in the use of the mathematical tools of physicists, and a broad and deep understanding of the fundamental concepts of the diierent branches of physics. The education of a physicist does not end with the conferring of a degree, but it is expected that by graduation the student shall have made great progress in the development of the ability to analyze physical problems, to make clear and understanding statements of them, and to solve them with the help of all the available books and journal articles, and discussions with experts. The principal divisions of classical physics are generally given as mechanics, heat, sound, light, and electricity and magnetism. Active interest in different branches of physics changes with time. Thus, while sound is still an important branch of physics, active interest in i t on the part of teachers of advanced physics is in general far less than in electricity or optics. The pra$ical importance of a branch of physics must not be judged the placed Won it in the physics curriculum because teachers of physics must
emphasize those branches that give the student the best training in the solution of a broad range of problems covering the whole field of physics. Conversely, the importance of a branch of physics in the training of physicists in a university cannot be determined from its practical importance. Our concern is with the teaching of physics. The phenomena of heat, of energy changes, and of equilibria, and the laws covering them are important for the training of both physicists and chemists. In view of the doubts that have been expressed concerning the importance of thermodynamics in the physics curriculum it is necessary to demonstrate this importance for physicists, and for chemists who might be interested in taking a thermodynamics course in a physics department. This may be done by directing attention to phases of thermodynamics not ordinarily covered in courses in the chemistry curriculum. In the first place, all the temperature-dependent properties of bodies, whose changes are associated with the doing of work, excepting coefficients of friction, are amenable to thermodynamic treatment. Thus, if X is such a property and y is its generalized force such that ydX is the work done by a body or system when its property X changes, the first law of thermodynamics states that AO=dU+pdV+ydX
(1)
and for a reversible change the second law yields TdS=dU+pdV+ydX
(2)
The free energy becomes F=H-TS=
U+@V+yX-TS
(3)
Applying the rules for diierentiation ordinarily used in thermodynamics one obtains equations relating changes in X with changes in T , p, V , and y, as for instance
and
As an example of a property X in equations (1) to (5) may be cited the intensity of magnetization of a paramagnetic body or the electric polarization of a dielectric. The symbol y becomes the magnetic or electric field intensity. From thermodynamics, therefore, are obtained relations connecting the intensity of magnetization and the electrical polarization with temperature, volume, pressure, and intensity of the magnetic or electric field. Equation (4) becomes a fundamental relation for electro- and magneto-striction, telling one that the volume rates of change of the intensity of magnetization and electric polarization at constant temperature and field intensity are equal to the rates of change of the pressure necessary to maintain constant volume a t constant temperature
when the field intensity is changed. The third law of thermodynamics and equation (5) show that the temperature coefficients of intensity of magnetization and electric polarization, ( d X / d T ) , fall to zero as the temperature O°K. is approached. Equations (4) and ( 5 ) are only typical of numerous other relations that may be derived for X and y. Surface tension may be cited as an example of a property of the type y in equations ( 1 ) to (3). X becomes the area of the surface. The application of the mathematical methods of thermodynamics leads to equations for: (1) capillary rise of a liquid in a tube; (2) the curvature of a liquid meniscus; (3) dependence upon particle size of solubility, of vapor pressure, and of equilibrium properties between different phases in general; (4) changes in concentration of a solute a t a surface; and (5) changes of surface tension with changes in concentration of a solute. Thermodynamics has an explanation for the much greater changes in surface tension produced by solutes lowering the surface tension than by solutes raising the surface tension. There is another type of physical problem amenable to thermodynamic treatment. This type is concerned primarily with energy or changes in energy form. Energy, the direction of change of mechanical systems, and the conditions for mechanical equilibrium are important considerations for the science of mechanics. But mechanics is not adequate for the handling of problems that involve a generation or flow of heat. A good illustration of the point in hand may be taken from electrodynamics. By the application of the energy principle of mechanics to an electromagnetic field in free space i t is shown that the energy density of the HZ). If the field in Gaussian units is (1/8rr) (E' same mechanical principles are applied to an isotropic dielectric with magnetic permeability fi and dielectric constant K one obtains (1/8r) (KE2 pH2) which expression is often incorrectly given for the field energy in a dielectric. If K and p are temperature dependent, as is true for dielectrics in general, changes of E and H in the dielectric will be accompanied by changes in temperature and a flow of heat. Mechanics is not able to handle this problem. Thermodynamics is necessary and yields for the energy density in a dielectric
+
+
Temperature radiation and the thermocouple may be cited as examples of other problems involving changes in the form of energy and involving heat. The application of thermodynamics to the radiation field yields Kirchhoff's Law for the ratio of the emissive and absorptive powers of a surface, the Stefan-Boltzman T 4 Law, and the Wien Displacement Law Ex = (1IA6)f (AT). The existence of Thomson electromotive forces in a conductor in which there is a temperature gradient is most easily demonstrated through the application of thermodynamics to a thermocouple circuit.
,
The electromotive force of a thermocouple is
This is a statement of conservation of energy in which slzis the rate of ahscrption of heat a t the junction of metals 1 and 2 a t the temperature T when unit current flows from metal 1 to 2, ?r12' is for the junction at the temperature T', and al and a? are the rates of ahsorption of heat in the wires 1 and 2 of the thermocouple for unit current and unit temperature difference between the ends of the wires. T and a are the socalled Peltier and Thomson coefficients. Only through the use of thermodynamics can equations (7) and (8) for separating the Peltier and Thomson coefficients be derived.
The thermogalvanic effectsassociated with the names Ettinghausen, Righi-Leduc, and Nernst are also amenable to thermodynamics. Attention has been directed to types of problems involving thermodynamics since, as has been pointed out, i t is a purpose of advanced physics teaching to instruct students in the solution of type problems. There are applications of thermodynamics to numerous special subjects as heat and refrigerating machines, phase changes of the second kind, superconductivity, liquid He 11, and the production of low temperatures by adiabatic demagnetization. For a physicist the properties of the thermodynamic scale of temperature are of fundamental importance. Physicists should know that fundamentally a thermodynamic scale is independent of the properties of any particular piece or kind of matter, even the properties of the ideal gas; that the nonexistence of temperatures below O°K. is a consequence of something more fundamental than the vanishing of the pressure or the volume of the ideal gas at O°K.; and that there are thermodynamic reasons why the temperature O°K. is theoretically as well as practically unattainable. In citing only subjects outside the field of specialized interests of chemists, the aim has been to show that a good course in chemical thermodynamics does not adequately meet the needs of the physics major. Subjects of interest to both physicists and chemists such as solutions, p-V-T properties of state, and equilibrium of phases (phase rule) need not be elaborated upon here. It has been said that thermodynamics is essentially a practical science. This being so, chemists emphasize applications to chemistry and physicists applications to physics. Indeed much chemistry and physics may he learned from thermodynamics courses. For this reason both physics and chemistry departments should, and in general do, offer thermodynamics courses emphasizing applications in their respective fields.
There are other differences between thermodynamics courses in chemistry and in physics departments hesides the difference in the fields of application. Physics'courses are much concerned with the development of students' concepts of fundamental physical quantities and properties. This is considered necessary for the training of students to tackle the unfamiliar problems that will arise in connection with original research, and industrial and engineering work. In line with the development of concepts emphasis is placed upon physical rigor, that is, upon a logical presentation of methods of measurement, upon empirical phenomena, and upon basic assumptions of the mathematical theory, as well as upon a correct application of mathematical methods. Now a rigorously logical development of a science appeals to the aesthetic sense of most scientists, and given the time it would he required of every science. But student days are limited and the knowledge to be acquired is very great. Hence in one's education it is necessary, for lack of time, to forgo rigor in some fields of science in order to extend one's knowledge in other fields. But in a thermodynamics coume, physics teachers are less justified in forgoing rigor than chemistry teachers and are obliged to give more attention to the development of concepts because there is a greater variety of applications of thermodynamics in physics than in chemistry and hence a greater prohability that after graduation a physicist will he called upon to solve an unfamiliar problem calling for thermodynamics. There is, in general, a difference in the level of mathematical difficulty of thermodynamics courses given in chemistry and physics departments. Mathematics is an important tool of the physicist. He needs it for the study of physical theory and for the solutionof problems. Hence, physics majors have more extensive training in mathematics than chemistry majors. This is reflected in the thermodynamics courses. Assuming that thermodynamics as an important course in the physics curriculum is justified, let us turn our attention to the development of thermodynamics in the physics department. In Table 1, in which the principal divisions of instruction in the science of heat are listed, it will be seen that thermodynamics is classified as one of the divisions of the theory of heat. As with other branches of physics, the TABLE 1
D~vrsrolrsOP lasrrtnrnm IN r m S c r e ~ OP ~ gHBIT I.
II.
Thermal phenomeoa-Laboratory and class study of empirical phenomena covering: thermometry, calorimetry, properties Of state (0-V-T data), phase changer, and equilibria in single- and multicomponent systems, solutions, and chemical changes. Theory 1. Thermal conduction 2. Thermodynamics 3. Statistical mechanics and kinetic theories of matter
elementary course in heat is planned to present the student, through laboratory and classroom work, with the important empirical phenomena, in particular the
more obvious and fundamental ones. I n the highschool physics course, which is intended to acquaint the student with the physical world about him, he begins the development of his concepts of temperature and heat, and though he is not instructed in entropy or the second law of thermodynamics he does learn about the degradation for useful work of energy converted into heat, and that heat always flows from a higher to a lower temperature. In the laboratory he learns thermometry and calorimetry and makes measurements of change in state and p-V-T relations of gases. The sophomore college course in physics goes beyond the high-school course but still emphasis is upon thermal phenomena and the solution of mathematical exercises illustrating applications of empirical laws. While the sophomore student may have heard of entropy he has no working concept of it. Further, calculus is not taught until the sophomore year in most colleges. Consequently, any study of thermodynamics as a mathematical science has to be postponed until the junior or senior year. The usual practice is to offer the junior or senior studeut a one-semester or twoquarter course in heat covering thermodynamics, thermal conduction, and Emetic theories of matter. Such a course acquaints the studeut with entropy but his knowledge of thermodynamics is necessarily limited as the time devoted to its study is short. A fuU-semester or two-quarter term devoted just to thermodynamics and its applications in the field of physics is recommended for the undergraduate physics curriculum with additional time in the undergraduate curriculum for the theory of thermal conduction and kinetic theories of matter. Undergraduate physics and chemistry majors in their junior year are qualified to handle the mathematics of thermodynamic theory, and the covering of parts of other branches of physics in discussions of radiation, thermoelectricity, surface tension, and electric and magnetic polarization in a thermodynamics course justifies this additional time. An important feature of the junior or senior course in heat is the advanced laboratory in beat measurements. This is, in general, the last opportunity afforded the student for laboratory work in heat unless he assists in testing or original work in a laboratory devoted to heat measurements, or himself undertakes original work in this field for a thesis. The study of thermodynamics emphasizing basic concepts and applications to radiation, magnetic, electric, and surface tension phenomena is usually placed in the graduate curriculum. Graduate physics courses in thermodynamics are often, and in fact should be, followed by a course in statistical mechanics and kinetic theories of matter. Statistical mechanics helps to make the physical natures of temperature and entropy clearer and provides the physical bases for the three fundamental laws of thermodynamics. It accounts for the fluctuations in density responsible for the molecular scattering of light (Rayleigh scattering), for the opalescence of gases in the region of their critical state, and the opalescence of two-phase liquid solu-
tions in the region of the critical solution state. Kinetic theories of matter acquaint the student with the structural and molecular properties of matter that determine the thermodynamic properties. The field of heat of greatest active interest a t present is the calculation of thermodynamic properties from spectroscopic and molecular structure data, using the methods of quantum statistics. Statistical mechanics and thermodynamic functions are being used for the calculation of rates of chemical reactions and liquid viscosities. It is evident that a course in statistical mechanics and kinetic theories of matter greatly enhances the value of a course in thermodynamics. In conclusion, it is recommended that students majoring in physical chemistry take the undergraduate and graduate courses in heat and thermodynamics offered by the physics department in addition to the course in thermodynamics in the chemistry department. Likewise, it is recommended that physics majors, not specializing in such applied fields as electronics and hydraulics, take the undergraduate course in physical chemistry and the graduate course in chemical thermodynamics offered by the chemistxy department. It is well recognized that training in physics is an asset for a chemist. The converse, that training in chemistry, especially physical chemistry, is an asset for a physicist is also true, hut unfortunately not so well appreciated. Of all the branches of classical physics, heat, including thermodynamics, is of greatest utility to the chemist, and the mathematics involved is the least difficult. Thermodynamics courses in the chemistry and physics departments do not duplicate each other. There is a further reason for chemists' acquiring training in physics and for physicists' acquiring training in chemistry. There are differences in the points of view of the average chemist and the average physicist, and a difference in the way they tackle problems. Given a problem, the chemist is likely to begin laboratory work very soon, trying something to obtain some information as soon as possible. On the other hand the physicist will likely start by analyzing the problem and planning a program of work before starting any laboratory work. The problem may be complicated and analysis so difficult that the physicist is overcome a t the start, whereas the chemist with his probing experiments may uncover a lead to the solution of the problem. However, i t does not always work out this way. Sometimes the results of the chemist's probing experiments are too difficult to interpret because of incomplete control of all the variables or because the essentials of the problem are not understood. A combmation of the two points of view and methods of attack is likely to be the most effective for a great range of both chemical and physical problems. Undergraduate courses in physical chemistry and heat, and graduate courses in thermodynamics offer students an opportunity of becoming acquainted with the point of view and method of attack of their allied science.
