Zusammenfassung: Wärme Q und Entropie S sind zwei zentrale Größen der Wärmelehre. Die eine, nämlich Q, scheint die einfachere, anschau-
lichere Größe zu sein, die andere ist bekannt dafür, schwierig zu sein. Wir zeigen, dass dieser Eindruck die Sache nicht trifft: die Wärme Q ist eine außerordentlich tückische Größe. Die Entropie dagegen hat ihren schlechten Ruf zu Unrecht. Hat man einmal verstanden, dass die Entropie nahezu perfekt das beschreibt, was man umgangssprachlich unter Wärme versteht, so entdeckt man, dass sie eine der anschaulichsten physikalischen Größen überhaupt ist.
When relativistic physics is lectured on, interest is focused on the behavior of mechanical and electromagnetic quantities during a reference frame change. However, not only mechanical and electromagnetic quantities transform during a reference frame change; thermodynamic and chemical quantities do too. We will study the transformations of temperature and chemical potential, show how to obtain the corresponding transformation equations with little effort, and exploit the fact that the energy conjugate extensive quantities, namely entropy and amount of substance, are Lorentz-invariant.
Abstract: It is shown that upon a reference frame change, the chemical potential transforms in the same way as temperature and electric potential. Consequently, during a reference frame change, a chemical equilibrium remains a chemical equilibrium.
Zusammenfassung: Der Begriff Bezugssystem begegnet uns im Physikunterricht an verschiedenen Stellen. Bezugssystemwechsel sind ein wichtiges Werkzeug der Physik. Wir wollen das Thema hier kritisch beleuchten.
Zum einen schlagen wir vor, Bezugssystemwechsel nicht nur im Zusammenhang mit der Mechanik zu behandeln. Zum zweiten empfehlen wir, den Begriff der Scheinkraft nicht einzuführen, und die Erscheinungen, bei denen sie auftreten, auf eine andere Art zu deuten. Schließlich plädieren wir dafür, das Thema Bezugssystemwechsel nicht zum Hauptthema der speziellen Relativitätstheorie zu machen.
In diesem Beitrag, der auf einem Vortrag beim MNU-Bundeskongress 2023 beruht, geht es um die Lokalisierung der potenziellen Energie. Wenn man einen Körper anhebt, nimmt die potenzielle Energie zu. Aber wo genau steckt diese Energie? Das ist eine vernünftige und naheliegende Frage. Die Lehrbücher gehen unterschiedlich mit ihr um. Manche sagen, die Energie stecke in dem Körper, den man angehoben hat. Andere sagen, sie stecke in dem System Erde-Körper. Eine bessere Antwort ist: Sie steckt im Gravitationsfeld. Wir schlagen vor, wie man im Unterricht mit der „potenziellen“ Energie sprachlich umgeht.
Abstract: In the context of teaching relativity, one encounters two situations in which two observers age at different rates. Usually, these effects are treated as if they were independent of each other. Often one is referred to as special-relativistic, the other as general-relativistic. We show that both are special cases of an effect which follows naturally from the fact that space and time form a unity. They exist in a flat space-time and therefore neither of them deserves the label general relativistic.
Abstract: We consider the Earth moving through empty space at 30 km/s (in the sun's frame of reference). Associated with this motion is a convective flow of kinetic and internal energy. Since there is high pressure inside the earth, and since the earth is moving, there is yet another "hydraulic" energy flow. This latter is what this article is about. Although this energy flow is huge, it is not addressed in the textbooks. The reason is that for the explanation one needs a concept which is not introduced in traditional presentations of classical gravitation: the gravitomagnetic field. The corresponding theory, gravitoelectromagnetism, was formulated in 1893 by Heaviside in analogy to Maxwell's theory of electromagnetism. We discuss the question of what are the sources and sinks of this hydraulic, non-convective energy flow. To answer the question, we need to study the energy flow density distribution within the gravitational field. In doing so, we will make some interesting observations. The energy flow within the field is twice as large as it should be to transfer the field energy from one side of the Earth to the other. The excess flow goes back through the matter of the Earth. Since our readers may not be familiar with Heaviside's theory, we first treat the electromagnetic analogue of our problem and then translate the results to the gravitational situation.
Abstract: Mass is usually introduced as a measure of the inertia of a body. But what do we mean by inertia anyway? We introduce a measure of inertia. It turns out that for high, relativistic velocities neither the rest mass nor the relativistic mass fulfills the requirements for a meaningfully defined measure of inertia. But how are we going to talk about inertia in the physics lesson? How can we use students' everyday language and still arrive at a clear conceptualization? We will try to give an answer to these questions.
Abstract: We learn and teach classical mechanics essentially as it was developed by Newton. The theory is more than 300 years old, but still useful for many purposes. However, even in contexts where it produces correct results, it has a flaw: it uses actions at a distance. In addition, it is not able to describe the transport and storage of energy in the gravitational field locally. The general theory of relativity not only eliminated the actions at a distance of Newtonian mechanics, but also predicted phenomena which the Newtonian theory of gravitation could not explain. However, for solving many problems and for an introduction of gravitation in a standard lecture, general relativity is too complicated, mainly because of the tensor calculus. To bridge the gap between these two theories we propose to use Heaviside’s theory of gravitoelectromagnetism. This theory has the same structure as Maxwell’s electromagnetism. It has the advantage that it does not describe forces as actions at a distance and that it allows to establish a local energy balance. We discuss the limits of applicability of Heaviside’s theory. It turns out that besides the well-known condition low field/slow motion, another condition must be satisfied. The theory is only applicable to quasi-stationary processes. In particular, it cannot describe gravitational waves. Nevertheless, it is useful for teaching, because some major shortcomings of the Newtonian theory are avoided.
Gravitation is still taught largely in a way that suggests the existence of action-at-a-distance. A theory without such shortcomings, gravitoelectromagnetism, was proposed by Heaviside in 1893, but it did not become well-established because many effects it describes are very small and the later emergence of general relativity seemed to make a theory of gravitoelectromagnetism superfluous. We argue that gravitoelectromagnetism still retains relevance in the physics curriculum because it by no means describes only tiny effects and does not demand the mathematical level of general relativity.
Im Zusammenhang mit der Relativitätstheorie begegnen uns in Schulbüchern zwei Situationen, in denen zwei Beobachter unterschiedlich schnell altern. Es scheint sich um zwei voneinander unabhängige Effekte zu handeln. Oft wird der eine als speziell-, der andere als allgemein-relativistisch bezeichnet. Tatsächlich handelt es sich beide Male um ein und denselben Effekt, beschrieben in zwei verschiedenen Bezugssystemen.
Abstract: Mathematical derivations alone do not necessarily lead to physical understanding. Tools that can replace the mathematical treatment of a physical process and at the same time increase the physical understanding are computer-aided modeling programs, also called system dynamics software. Examples of such software are Stella, Berkeley Madonna, Wensim, Dynasys, Powersim or COACH 7. They solve differential equations and systems of differential equations with numerical methods. One works with a graphical user interface. We want to show how such a software can be used to get from a non relativistic model to a relativistic model with only minimal modifications. Equating mass and energy alone, ensures that the model provides essential statements of relativistic dynamics: the existence of a terminal velocity for all physical motions, the relativistic dependence of the velocity of a body on its momentum, the relativistic relation between momentum and energy of a body.
Abstract: This chapter describes the main features of an introductory course about relativity at high-school level that focuses on relativistic dynamics. It is intended for readers who are interested in a novel approach to relativity that avoids the topic of changing reference frames, which students often find difficult. The chapter describes the basics of a course on special and general relativity. The laws of special theory of relativity, or special relativity for short, are derived from those of classical mechanics along with one extra postulate. In the Karlsruhe Physics Course , the extensive quantities, such as energy, momentum, electric charge, and entropy are introduced as basic quantities. The twin paradox plays a major role in the teaching of special relativity and is part of every textbook or course on special relativity. The development of a teaching concept for the school, in our case for the secondary school, is a balancing act.
Abstract: “What is heat?” was the title of a 1954 article by Freeman J. Dyson, published in Scientific American. Apparently, it was appropriate to ask this question at that time. The answer is given in the very first sentence of the article: heat is disordered energy. We will ask the same question again, but with a different expectation for its answer. Let us imagine that all the thermodynamic knowledge is already available: both the theory of phenomenological thermodynamics and that of statistical thermodynamics, including quantum statistics, but that the term “heat” has not yet been attributed to any of the variables of the theory. With the question “What is heat?” we now mean: which of the physical quantities deserves this name? There are several candidates: the quantities Q, H, Etherm and S. We can then formulate a desideratum, or a profile: What properties should such a measure of the quantity or amount of heat ideally have? Then, we evaluate all the candidates for their suitability. It turns out that the winner is the quantity S, which we know by the name of entropy. In the second part of the paper, we examine why entropy has not succeeded in establishing itself as a measure for the amount of heat, and we show that there is a real chance today to make up for what was missed.
Abstract: At school and university, gravity is taught essentially in the Newtonian way. Newtonian mechanics originated at a time when there were no fields, when energy did not exist as a physical quantity, and when one still had to be satisfied with the concept of actions at a distance. A theory without such shortcomings, Maxwell’s electromagnetism, came into being about 150 years later. It could have served as a model for a modern theory of gravitation. In fact, such a theory of gravitation, gravitoelectromagnetism, was proposed by Heaviside. However, it did not establish itself, because, firstly, many effects it describes are very, very small, secondly, it makes certain statements that seemed unacceptable to some researchers, and thirdly, shortly thereafter, General Relativity was born, which removed the old deficiencies and seemed to make a classical field theory of gravity superfluous. We argue that the subject of gravitoelectromagnetism has its legitimacy in teaching at school and university even now.
On the one hand, general relativity is impractical for many applications because the mathematical effort is high, and on the other hand, the theory of gravitoelectromagnetism by no means describes only tiny effects. Rather, it solves a problem that is deliberately ignored in the traditional teaching of Newtonian mechanics: To which system do we assign the so-called potential energy? Where is the “potential” energy located? We also encounter some peculiarities of gravitoelectromagnetism, the cause of which is the fact that compressive and tensile stresses within the gravitational field, are swapped against each other in comparison with the electromagnetic field.
Abstract: We discuss a paradox from the field of relativistic thermodynamics: two heat reservoirs of the same proper temperature move against each other. One is at rest in the inertial reference frame SA, the other in SB. For an observer, no matter in which of the two reference frames he is at rest, the temperatures of the two reservoirs are different. One might, therefore, conclude that a thermal engine can be operated between the reservoirs. However, the observers in SA and SB do not agree upon the direction of the entropy flow: from SA to SB, or from SB to SA. The resolution of the paradox is obtained by taking into account that the 'drive' of an entropy current is not simply a temperature difference, but the difference of a quantity that depends on both temperature and velocity.
Zusammenfassung: Die Masse wird gewöhnlich eingeführt als Maß für die Trägheit eines Körpers. Aber was will man überhaupt unter Trägheit verstehen? Wir führen ein Maß für die Trägheit ein. Es stellt sich heraus, dass für hohe, relativistische Geschwindigkeiten weder die Ruhemasse, noch die relativistische Masse die Anforderungen an ein sinnvoll defi niertes Trägheitsmaß erfüllt. Wie wollen wir aber im Physikunterricht über Trägheit sprechen? Wie kann man die Alltagssprache der Schüler/innen nutzen und trotzdem zu einer soliden Begriffsbildung gelangen? Auf diese Fragen versuchen wir eine Antwort zu geben.
Abstract：The Karlsruhe Physics Course (KPC) is a novel approach to the teaching of physics at the secondary school. The KPC text books have since been used in a certain, slightly increasing number of German schools. Simultaneously, ideas of the KPC have found their way into the mainstream textbooks. The basic ideas of the course had been published in the European Journal of Physics, the American Journal of Physics and other scientific reviews. Several selected chapters had been presented on previous GIREP-Meetings. Only recently, the German Physical Society (DPG) got aware of the course. In their opinion the KPC represents a danger to the teaching of physics at school and University. Therefore, the DPG nominated an „expert group“ with the assignment of finding scientific errors in the KPK. The group believed to have found such errors. Thereupon the DPG has initiated a campaign with the objective of eliminating not only the KPC textbooks from the market but to eradicate any other manifestation of ideas that might have originated in the KPC work. DPG did so not only in Germany but worldwide. So, among other things, DPG alerted the European Physical Society and the Chinese Physical Society. As a result of these measures, a discussion of unusual fierceness arose, first in Germany, but then spreading to other countries. Thereby the physics community got more and more polarized. A chronicle of an eventful year and a brief evaluation will be given from the perspective of the author.
Aus dem Vorwort des Themenhefts: Wir sind daran gewöhnt, in Physik und Technik mit Strömen zu operieren: elektrische Ströme, Energie- ströme, Massenströme, Stoffströme, Datenströme. Es ist für uns so normal, dass wir uns die Frage nach der Berechtigung dieses Vorgehens gar nicht mehr stellen. Dabei sind Ströme physikalischer Größen keine Selbstverständlichkeit. Man hat sie nicht in der Natur vorgefunden, sondern sie sind Konstruktionen der Naturwissenschaft. Und sie sind eine recht moderne Vorstellung. Zu Newtons Zeit gab es noch keine elektrische Ladung und keine Energie, und natürlich auch nicht die entsprechenden Ströme….
Aus dem Prolog: ,“Das Konzept der Entropie ist ohne Zweifel eines der okkultesten Konzepte der Physik" Heuser spricht mit diesem Satz, der in seinem Duktus jeden Widerspruch undenkbar erscheinen lässt, einer großen Menge von Physiklehrerinnen und Physiklehrern aus dem Herzen und treibt, einen amerikanischen Cartoonisten zitierend die Polemik auf die Spitze:“lf you can live with entropy, you can live with anything“. Dagegen steht H.L. Collendars (1863- 1930) Überzeugung, Entropie könne auf eine Weise verständlich gemacht werden, “which any schoolboy could understond“. …
Aus dem Vorwort des Themenhefts: Die Entwicklungen in der Physik- und der Chemiedidaktik verfolgen bisweilen divergierende Pfade: Während aktuelle Lehrwerke für den Physikunterricht nahezu vollständig auf den Begriff Arbeit verzichten und stattdessen konsequent Energie verwenden, findet diese Entwicklung in chemiedidaktischen Beiträgen und Lehrwerken kein nennenswertes Echo. Neben der Energie wird verbreitet auch mit mechanischer und elektrischer Arbeit, mit Wärme sowie Enthalpie, freier Energie und freier Enthalpie argumentiert. Es haben sich in der Physik und Chemie Gewohnheiten etabliert, die eine fächerübergreifende Betrachtungsweise behindern. …
Zusammenfassung:Legt man sich nicht auf den traditionellen Weg fest, so kann man mit einfachen Mitteln schnell zu den wichtigen Ergebnissen der speziellen Relativitätstheorie gelangen. Man verwendet Kenntnisse, die man bereits auf anderen Gebieten der Physik gewonnen hat. Der Aufsatz zeigt diesen Weg auf und begründet ihn.
Zusammenfassung: Es wird gezeigt, wie ein Physikunterricht, der in der Wärmelehre die Entropie neben der Temperatur als zentrale Begriffe vermittelt und, unterstützt durch ein Modellbildung wie POWERSIM™, physikalische Sachverhalte vermitteln kann, deren unterrichtliche Behandlung ohne ein computerunterstütztes Modellbildungssystem zu schwierig sind, obwohl sie der täglichen Erfahrung einer Schülerin /eines Schülers sehr nahe kommen. Die vorgestellte Aufsatz geht von den elementaren Modellen des Heizens und Abkühlens von Körpern aus, macht Fließgleichgewichte verständlich und zeigt schließlich ein einfaches Modell für eine globale Erwärmung der Erde. (Anmerkung: Die Modelle lassen sich einfach auch in andere Softwaremodelle (z.B. Coach 7 etc.) übertragen.)
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