Three chances for entropy Michael Pohlig1, Joel Rosenberg2 1Didaktik der Physik, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany. 2Lawrence Hall of Science, U.C. Berkeley, Centennial Drive, Berkeley, CA, 94703, USA. E-mail: [email protected], [email protected] (Received 25 July 2011; accepted 37 October 2011) Abstract Entropy is known to be one of the most difficult physical quantities. The difficulties arise from the way it is currently introduced, which is due to Clausius. Clausius showed that the ratio of the process quantity heat and the absolute temperature is the differential of a state variable, which he called entropy. About 50 years later, in 1911, H. L. Callendar, at that time the president of the Physical Society of London, showed that entropy is basically what had already been introduced by Carnot and had been called caloric, and that the properties of entropy coincide almost perfectly with the layman’s concept of heat. Taking profit of this idea could simplify the teaching of thermodynamics substantially. Entropy could be introduced in a way “which every schoolboy could understand”. However, in 1911 thermodynamics was already well-established and Callendar’s ideas remained almost unnoticed by the physics community. This fact should not be an excuse for ignoring Callendar’s idea. On the contrary, this idea should be established, especially since entropy plays an important part not only in Thermodynamics but in the whole of physics. A two-man play is included in the appendix to this paper, written to introduce this history to teachers to encourage them to consider this useful complementary model. Keywords: Thermodynamics, history of science, entropy. Resumen La entropía es conocida por ser una de las magnitudes físicas más difíciles. Las dificultades se derivan de la forma en que actualmente se la introduce, lo que se debe a Clausius. Clausius mostró que el cociente de la cantidad de proceso “calor” y la temperatura absoluta es el diferencial de una variable de estado, a la que llamó entropía. Unos 50 años más tarde, en 1911, H. L. Callendar, en ese momento el presidente de la Sociedad de Física de Londres, demostró que la entropía es básicamente lo que ya había sido introducido por Carnot y había sido llamado calórico, y que las propiedades de la entropía coinciden casi perfectamente con el concepto de calor del lenguaje común. Teniendo en cuenta esta idea podría simplificar la enseñanza de la termodinámica considerablemente. La entropía podría ser introducida de una manera "que un niño pueda entender". Sin embargo, en 1911 la termodinámica ya estaba bien establecida y las ideas de Callendar permanecían casi inadvertidas por la comunidad científica. Este hecho no debe ser una excusa para ignorar la idea de Callendar. Por el contrario, esta idea debería ser establecida, sobre todo porque la entropía juega un papel importante no sólo en la termodinámica, sino en la física entera. Una pieza de teatro para dos actores está incluido en el anexo del presente documento, escrito para presentar esta historia a los maestros para animarlos a considerar este modelo . Palabras clave: Termodinámica, historia de la ciencia, entropía. PACS: 05.70.-a, 01.65.+g, 07.20.Pe, 01.40.-d ISSN 1870-9095 I. INTRODUCTION anything". [1] What could be in greater contradiction with this sentence than Callendar’s idea that entropy can be Not many ideas get more than one chance to be accepted, introduced in a way “which every schoolboy could but the idea that entropy can be visualized as a kind of understand?” [2]. substance has had more than one chance. However, this idea has been almost unnoticed by the physics community. This perhaps explains why it took about 300 years for a II. FIRST CHANCE — BLACK AND THE great number of renowned scientists to develop ‘QUANTITY OF HEAT’ thermodynamics. For the teaching of physics, it has been mostly a disaster. Today no one is surprised that the For about 150 years (ca. 1600–1750), scientists had been majority of physics teachers believe that entropy is difficult essentially engaged in the measurement of temperature. to teach. In one American cartoon a scientist says to another Joseph Black (1728–1799) was the first to assert that two scientist: "If you can live with entropy you can live with physical quantities are needed to describe thermal Lat. Am. J. Phys. Educ. Vol. 6, Suppl. I, August 2012 49 http://www.lajpe.org Pohlig, Rosenberg phenomena. Black, a Scottish physicist and chemist, psychological barrier was probably too high, and the discovered the latent heat, specific heat, carbon dioxide and production of the 'quantity of heat' could not be accepted. magnesium. He was professor for chemistry and medicine Only one small step was missing to develop a concept of at the University of Edinburgh and he became a friend and entropy that even a layman could understand. mentor of his assistant James Watt. Black distinguished between the intensive quantity temperature and the extensive ‘quantity of heat’: III. SECOND CHANCE — CARNOT’S “If, for example, we have one pound of water in a PRINCIPLE vessel, and two pounds of water in another, and these two quantities of water are equally hot, as examined by a Sadi Carnot (1796-1832) asked, “Is there a fundamental thermometer, it is evident, that the two pounds must contain limit for the improvement of heat engines?” and “How can twice the ‘quantity of heat’ that is contained in one pound” the limit be specified?” These led to his principle: [3]. FIGURE 2. Nicolas Léonard Sadi Carnot. FIGURE 1. Joseph Black. “La production de la puissance motrice est donc due, …, non à une consommation réelle du calorique, mais à son Black’s idea leads to the conclusion that a temperature transport d’un corps chaud à un corps froid,…” [6]. difference is the driving force for a flow of the ‘quantity of (The production of motive power has its cause not in a heat’. Moreover, the ‘quantity of heat’ can be visualized as real consumption of heat (caloric) but in a transport from a a kind of substance. It was a general conviction that hot to a cold body.) something that can be visualized as a kind of substance will automatically obey a conservation law. A “creatio ex nihilo” -- a quasi divine act of creation -- was unthinkable at that time. Today, one could believe that Black’s ‘quantity of heat’ is energy. However, his ‘quantity of heat’ is a state variable and thus it must not be confused with heat as a form of energy. Due to this, one can find in recent books about thermodynamics sentences like: “It is correct, then, to say that a system has a large amount of internal energy, but it is not correct to say that a system has a large amount of heat or a large amount of work. Heat is not something that is contained in a system. Rather, it is a measure of energy that flows from one system to another because of a difference in temperature” [4]. Today we know that Black's concept of ‘quantity of heat’ coincides perfectly with what we call entropy [5]. Count Rumford's experiment using a boring machine with a blunt tool succeeded in raising cold water to the boiling point by means of friction, questioning whether Black's quantity of heat could be a substance. It should not be a FIGURE 3. Heat engine flow diagram (above) demonstrating surprise to modern readers that the 'quantity of heat' obeys Carnot's principle and water wheel analogy flow diagram (below). only half a conservation theorem. Back then, the Lat. Am. J. Phys. Educ. Vol. 6, Suppl. I, August 2012 50 http://www.lajpe.org Three chances for entropy Fig. 3 illustrates the meaning of Carnot's principle (top) and V. THE INTRODUCTION OF ENTROPY describes analogically a water wheel (more exactly mass engines [7]) (bottom). Each machine needs two reservoirs. Clausius (1822-1888) introduced the quantity entropy by an Heat (caloric) can realize work (motive power) when it is equation relating the change in entropy of the system to the transferred from a reservoir of higher temperature (T2) to a change in heat (form of energy) of the system: reservoir of lower temperature (T1). Mass can realize work when it is transferred from a reservoir of higher Q gravitational potential (gh ) to a reservoir of lower S S . (1) 2 0 gravitational potential (gh1). At given temperatures and T gravitational potentials both machines realize a maximum of work when they work reversibly. To ensure reversibility, where Q is the amount of heat (form of energy) absorbed Carnot uses cycles. That means that all physical quantities in a reversible process in which the system changes from have the same value at the beginning and at the end of the one state to another. According to this definition one cannot cycle. From today's perspective, Carnot’s experiments are see that entropy has a density, that entropy can flow and correctly described, if we equate heat (caloric) with that entropy can be stored. Entropy has become one of the entropy. The amount of realized work can then be written most difficult physical quantities, which provokes people to as W = ΔE = ΔS (T2 – T1) and W = ΔE = Δm (gh2 – gh1) make pointed remarks like: respectively. Here ΔS is the amount of entropy that is “The concept of entropy is anyway one of the most transported from the reservoir with higher to the other with occult concepts in physics” [8]. lower temperature. And Δm is the mass that is transported “Such a definition appeals to the mathematician only” from a place of higher to place of lower gravitational [2].