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Transcript
Historical burdens on physics 112 Thermal energy Subject: From a school book: “The thermal energy is a part of the internal energy and essentially determined by the temperature. Since in many cases one can presuppose the constancy of the other components, one often only considers the thermal energy… Heat tells us how much thermal energy is transferred from one system to another.… The following relation holds between transferred heat and energy change: Q = ΔEthermal .” From another school book: “The potential and the kinetic energy of the particles taken together is called thermal energy.” From a third school book: “The total energy of a thermodynamic system, which consists of thermal energy (potential and kinetic energy of the particles), of chemical energy and nuclear energy is the internal energy U.” Deficiencies: The intention of these definitions of thermal energy is clear: The authors of the statements try to define a quantity which measures the “heat content” of a system and which has the following properties: 1. It should be a state variable, i.e. it should have a well-defined value for a system in a given state. 2. It should be an energetic quantity, i.e. a quantity that is measured in Joule. 3. It should be a part of the internal energy. Another part would be the chemical energy. 4. Differences of it should be equal to the process quantity Q, which in physics is called heat. The problem is that a quantity that meets these requirements does not exist and cannot be defined. It is not possible to distinguish the potential and kinetic energy of particles from a part which might be called chemical energy. Any temperature increase is related to electronic excitations, to oscillations, to excitations of the spin system, to the dissociation of molecules, to a rearrangement of atoms, i.e. chemical reactions, and finally to nuclear reactions. There is no possibility to decompose the energy that is engaged in these processes in an unambiguous way into a thermal and a chemical component. If such a decomposition were possible, it would manifest itself in the fact that one summand (the thermal energy) would depend only on temperature and not on the chemical potential and another summand only on the chemical potential and not on temperature. But such a decomposition is not possible. Origin: Physics, chemistry and technical thermodynamics need a measure for the heat content of a system. Common sense suggests that it should be possible to define it, since we intuitively operate successfully with such a quantity. However, when trying to define a measure for heat in the 19th century, a mistake was made: It was supposed that such a quantity should be an energetic quantity. However, a definition of an energetic quantity with the desired properties could not work. As a result several surrogates appeared, each of which satisfies some of the requirements and others not. The quantity Q, which was called heat, is one of them. The problem is that Q is not a physical quantity in the usual sense of the word. One says that it is a “process quantity” since it makes no sense to ask for its values for a given system in a given state. Chemists prefer to manage with another “surrogate” quantity, the enthalpy. This quantity behaves like a heat content, but only as long as one restricts to processes at constant pressure – for the physicist an unacceptable restriction. None of the quantities Q and H meets the justified expectation towards a measure of a heat content. So, why not define a quantity that better suits to our needs, the thermal energy? It is interesting that the concept “thermal energy” can only be found in school books, but not in University texts. Do we have to reproach to the school text book authors for inventing untenable concepts, due to their ignorance of thermodynamics? Yes and no. Yes, because the definition does not work. No, because they are not to blame for the fact that thermodynamics is so unfamiliar and so unpopular. It is the University that is to blame. Here, what students learn about thermal phenomena: Relations between four quantities that change their values simultaneously, interlaced partial derivatives, changes of variables, unintuitive quantities like enthalpy, free energy, and Gibbs’ free energy are the requisites of the chamber of horror. For the simple explanation of the compression of the gas in a Diesel engine the so-called adiabatic index is used, which is defined as the quotient of two partial derivatives, which are distinguished by the fact that in one of them one variable is kept constant in the other another variable. It is not to expect that the students get a non-tensed relation to thermal phenomena in this way. But how can he or she, later as a teacher, present thermal facts to beginners? It is understandable that the school teachers and school book authors try to construct a thermodynamics that does not offend common sense. Disposal: It is much simpler than one might believe. It is sufficient to abstain from demanding that a measure of heat must be an energetic quantity. All the difficulties disappear when introducing entropy as the measure for a heat content. Friedrich Herrmann, Karlsruhe Institute of Technology Georg Job, University of Hamburg