### Publications in the European Journal of Physics

A hydrauic energy flow within the moving earth

F. HERRMANN and M. POHLIG

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.

A relativistic paradox and its resolution or who drives the entropy current between two bodies in relative motion?

F. HERRMANN and M. POHLIG

Eur. J. Phys. 42 (2020) 015607

Abstract: The 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.

The geodynamo for non-geophysicists

F. HERRMANN and T. VORBACH

Eur. J. Phys. 41 (2020) 045803

Abstract: The geodynamo usually appears as a somewhat intimidating subject. Its understanding seems to require the intricate theory of magnetohydrodynamics. The solution of the corresponding equations can only be achieved numerically. It seems to be a subject for the specialist. We show that one can understand the basics of the functioning of the geodynamo solely by using the well-known laws of electrodynamics. The topic is not only important for geophysicists. The same physics is the cause for the magnetic fields of sun-like stars, of the very strong fields of neutron stars, and also of the cosmic magnetic fields.

The absorption refrigerator as a thermal transformer

F. HERRMANN

Eur. J. Phys. 30 (2009) 331-336

preprint arXiv: 0809.2348v3 pdf

Abstract: The absorption refrigerator can be considered a thermal transformer, that is, a device that is analogous to the electric transformer. The analogy is based on the correspondence between the extensive quantities entropy and electric charge and the intensive variables temperature and electric potential.

Chemical potential – a quantity in search of recognition

G. JOB and F. HERRMANN

Eur. J. Phys. 27, 353-371 (2006)

Abstract: The chemical potential is a quantity for which students hardly have an intuitive feeling in contrast to other intensive quantities like pressure or temperature. Some students may believe that this is not really an insufficiency because the chemical potential seems to be essentially a quantity for chemists. We will try to show that the chemical potential does not merit its reputation as a difficult to understand quantity. Not only is it easy to grasp, it is a particularly intelligible quantity for which even the layman can develop a feeling. Moreover, this quantity is not only important for chemists. It is just as useful for describing physical phenomena and processes, such as phase transitions, the stratification of gases in a gravitational field and electric currents in semi-conductor junctions and nuclear reactions, to mention just a few.

F. HERRMANN

Eur. J. Phys. 22, L1-L2 (2001)

Abstract: I reply to some of the questions appearing in a Comment concerning the Karlsruhe physics course raised by J Strnad (2000 Eur. J. Phys. 21 L33 36).

Momentum flow diagrams for just-rigid static structures

M. GRABOIS and F. HERRMANN

Eur. J. Phys. 21, 591-601 (2000)

Abstract: Flow diagrams are a powerful tool for visualizing the current distribution in networks of well defined channels. They can often be interpreted at a single glance. The procedure is common for substance, energy, heat and electric currents. However, it can also be applied to the flow of momentum. We show by means of examples from the statics of plane trusses that such diagrams are easy to draw and to interpret.

The Karlsruhe Physics Course

F. HERRMANN

Eur. J. Phys. 21, 49-58 (2000)

Abstract: The Karlsruhe Physics Course is an attempt to modernize the physics syllabus by eliminating obsolete concepts, by restructuring the contents and by extensively applying a new model, the substance model. The course has been used, tested and improved for several years and we believe that the time has come to make it known to a greater public. We introduce the structure which is underlying the course and discuss some consequences for the teaching of various subfields of physics.

The historical burden on scientific knowledge

F. HERRMANN and G. JOB

Eur. J. Phys. 17, 159-163 (1996)

Abstract: The development of scientific knowledge is compared with the evolution of biological systems. Just as every biological system inevitably contains fossils our physics syllabus contains obsolete concepts and methods. It is argued that the potential for simplifying the teaching of science by eliminating these historical burden is high. Several examples for obsolete concepts in physics are given.

Color charge and perceptible color a suitable analogy?

A GRUTSCH and F. HERRMANN

Eur. J. Phys. 16, 271-274 (1995)

Abstract: Elementary texts about the strong interaction between elementary particles suggest that the space of the color charge is three-dimensional. We discuss what should be understood by the term ³dimension of a physical quantity² and show that the space of the color charge is two-dimensional.

Comment on "Electromagnetic or electromagnetic induction?"

F. HERRMANN

Eur. J. Phys. 8, 217-218 (1987)

Momentum flow in the gravitational field

G. HEIDUCK, F. HERRMANN, G. BRUNO SCHMID

Eur. J. Phys. 8, 41-43 (1987)

Abstract: In gravitation an action-at a distance description of the interaction between two bodies is still in use. However, the momentum current picture presents a local-causes description of this interaction. The suggested approach allows for an easy way to visualise and quantitatively sketch the stress distribution in a weak static gravitational field by means of momentum current density field lines. Computer sketches of such streamlines in the common field of the earth and the moon are presented. It is shown that two massive bodies are 'pushed together' by their common gravitational field.

Is an energy current energy in motion?

F. HERRMANN

Eur. J. Phys. 7, 198-204 (1986)

Abstract: It is an old question whether an energy current can be imaged as energy moving with a well-defined velocity. It is shown that in two important systems, namely in the electromagnetic field and in moving matter under stress, the energy current can be decomposed into two parts of opposite directions. Each part can be imaged as energy moving with the velocity of light or with the velocity of sound, respectively.

Simple examples of the theorem of minimum entropy production

F. HERRMANN

Eur. J. Phys. 7, 130-131 (1986)

Abstract: The theorem of minimum entropy production governs the distribution of a voltage on two resistors connected in series and the distribution of an electric current on two resistors connected in parallel. It is suggested that this important theorem be used in introductory physics courses.

An analogy between information and energy

F. HERRMANN, G. BRUNO SCHMID

Eur. J. Phys. 7, 174-176 (1986)

Abstract: The total entropy of an information storage system can be decomposed into independent terms, i.e. into functions which have no independent variables in common. One of these terms represents the information (=entropy) in which the user of a computer is interested. This decomposition corresponds to a break up of the entire system into non-interacting subsystems and is analogous to the decomposition of the total energy of a system into independent terms commonly referred to as energy forms. In both dccompositions, the term usually of interest is many orders of magnitude smaller than the rest.

Analogy between mechanics and electricity

F. HERRMANN, G. BRUNO SCHMID

Eur. J. Phys. 6, 16-21 (1985)

Abstract: The dissipative transport of energy is described in the momentum current picture. This picture provides a local-causes approach to mechanics whereby forces are considered as momentum currents. In this approach, friction, i. e. mechanical heat production, appears when a momentum current flows between two bodies of different velocities. The treatment of the transport and dissipation of energy follows the same rules in mechanics as in electricity. An 'Ohm's Law of momentum currents' is introduced in analogy to Ohm's Law in electricity. Newton's Third Law reduces to a simple statement about momentum conservation.

Entropy, a resurrection of caloric a look at the history of thermodynamics

G. FALK

Eur. J. Phys. 6, 108-115 (1985)

Abstract: The entropy introduced into physics by Clausius was, contrary to general belief, not a new physical quantity but the reconstruction of the 'quantity of heat' conceived about one hundred years earlier by the Scottish chemist Black. The same quantity was also used under the name 'calorique' by Carnot in his work which laid the foundations of thermodynamics. That entropy and Black's 'quantity of heat' are only two names for the same physical quantity is not only of historical interest but is of significance to the teaching of thermodynamics as well. It asserts that entropy can be visualised as a kind of substance which obeys 'half a conservation theorem': it can be created but not destroyed.