Online course and simulator for engineering thermodynamics

The RTM(E) Model

Articulations of scientific knowledge: The RTM(E) Model

When a teacher wants to define the content of his teaching, having an adequate typology to describe the knowledge to be transmitted seems to us as essential as specifying the educational objectives.

To tackle this subject, didactics emphasizes the today classic distinction between knowledge and know-how. Develay specifies that "declarative knowledge is of the order of discourse and knowledge, while procedural knowledge is of the order of action and know-how". This distinction is obviously essential, but it is too global for our purpose.

As we have not found in the literature a model which fully meets our expectations, we propose one, called RTM(E), in which the knowledge to be transmitted is grouped into four main interconnected categories, called Reality, Theory, Methods (and Examples).

The study of Reality (or even facts, nature, terrain, the world, technology ...) by observation, analysis and experimentation, allows one to develop or refine the Theory, that is to say an explanatory scheme highlighting the similarities of the different observations of Reality, and explaining them in a way that is both coherent and as simple and generic as possible. The Theory on the one hand thus constitutes a grid for reading Reality, and on the other hand serves as a guide for the development of Methods (and/or operational tools) for problem solving, calling if necessary on specific concepts.

This typology very fruitfully structures knowledge relating to a scientific discipline, especially if it is supplemented by the main application Examples, which illustrate very concretely how to solve (thanks to Methods and within the framework of a Theory) a class of problems relating to a particular aspect (of Reality).

Learning a scientific discipline thus supposes the acquisition of both declarative knowledge for Reality and Theory, and procedural knowledge for Methods, which essentially correspond to know-how. When studying Examples, learners acquire knowledge of Reality on the one hand, and the practice of Methods on the other. It is on this occasion that they see how the theory can be applied to the real world, according to rules which, although possibly specific to an example, all fall within the same theoretical framework.

When presenting the Examples, it is essential that the teachers spend the time necessary to make the link between the description of the technologies and the modeling hypotheses made in the Methods. For example, it is necessary to carefully explain why a compressor or a turbine can most often be considered adiabatic, why a heat exchanger or a combustion chamber operating in an open system are a first isobaric approximation...

As the Examples play a fundamental role in learning, it is imperative that they be realistic, failing which the learners' perception of the discipline will be wrong: they will have the impression that it does not solve the real problems. This last remark is a charge against the classic method of teaching thermodynamics: putting too much emphasis (for supposedly simplifying things) on perfect gas models, learners end up thinking that the discipline ability to problem resolution is limited.

Reality, Theory, Methods and Examples constitute an essential part of what Kuhn, in the afterword of the 2nd French edition of The Structure of Scientific Revolutions, calls the disciplinary matrix, which represents what a group of scientists has in common (at instead of Reality, he speaks of nature, instead of Theory, of symbolic generalizations, but the meaning is the same, and he strongly insists on the one hand on the objective of "normal science" which is to solve enigmas, which requires the development of Methods, and on the other hand on the key role played by the Examples). The importance of the disciplinary matrix stems from the fact that it is characteristic of the group's identity and that its content is an integral part of learner training, due to the fundamental role it plays in structuring the schemes.. This is in line with a remark by Develay, who indicates that "the knowledge to be taught constitutes the heritage that one generation wishes to bequeath to the next".

By retaining these four categories, we can break down the contents of a course on energy powered systems in the following manner.


The study of Reality covers that of facts, nature, terrain, the world, technology...

The content of the teaching here is not particularly controversial. It is necessary to present on the one hand the different technologies and their uses, on the other hand the properties of the matter, at least on the qualitative level, and finally the typology of the problems raised. For this, the most used educational methods are visits, lectures, slide presentations, film screenings, readings, disassembly/reassembly of devices, practical work... Let us also note that Reality represents a very important part of the 'teaching, the initial knowledge of the learners on this subject being very limited, at least in initial training.

In our opinion the following points should be addressed:

  • the contextual, particularly environmental, issues

  • the types of problems posed (design - dimensioning, audit - improvement, regulation)

  • the architecture of the various technologies

  • the description of the technologies, with presentation of the main constructive constraints, in particular with regard to the materials used

  • the history of technologies, industrial achievements, manufacturers

  • the technical documentation, constructive orders of magnitude

  • the qualitative presentation of the properties of fluids


The theory of thermodynamics covers a very wide field (hypotheses, equations, models of fluids...). Therefore choices must be made in what is exposed. In terms of Theory, the learners generally have some initial knowledge, unfortunately often fragile and fragmented, which must be taken up, most often by lectures and tutorials. It is undoubtedly at this level that the debates are today the strongest, in particular on the question of the equations to be presented.

The other topics to be taught on theory are generally:

  • Carnot's cycle, which constitutes a reference for numerous cyles.

  • The thermodynamics of simple components (compression, expansion, combustion ...) at least on a qualitative way.

  • The theory of heat-exchangers.


The Methods make it possible to pass from theory to applications, and in particular to the resolution of the problems posed in the context of Examples. This passage corresponds to the act of modeling and the acquisition of know-how. By reversing the perspective, we can say that the theory represents abstractions of the different methods of resolution.

To clarify what we mean by this, consider the expression of the first law for an open system in which the kinetic energy can be neglected. The practical calculation (Method) of a heat exchanger is written Delta h = Q, that of a compressor or a turbine Delta h = tau, and that of an expansion valve without work Delta h = 0. These are three forms of the same abstraction (Theory), the first law, which is written Delta h = tau + Q.

The knowledge of the Methods which the learners have is most of the time embryonic, because decoupled from the applications. As we have seen, teaching here can greatly benefit from the study of Solved Basic Examples and from the practice of exercises intended to make learners operational. It is essentially at this level that simulators are of interest as supports for innovative pedagogies.

The knowledge concerned is in our view (and we do not think there is any particular controversy here either) the following:

  • The use of state functions and of usual physical quantities (h, Q, tau ...).

  • The use of charts

  • Building up the conservative and entropy balances.

  • The methodology for calculating simple components (compression, expansion, combustion ...).

  • The characteristic curves of the components.

  • The practical calculation of heat-exchangers (LMTD, NTU).

  • The principles of modeling complex systems.


It is around Examples that the links that exist between the three reference poles (Reality, Theory, Methods) are most clearly explained.

Hence their fundamental importance when learning the discipline. For the reasons mentioned above, it is in particular essential that these examples be realistic and that they show by which methods the theories are applied.

Presentations are generally focused on:

  • The four basic examples : refrigeration machines, steam power plants, gas turbines and reciprocating internal combustion engines.

  • Their variants.


Develay, M. , De l'apprentissage à l'enseignement, ESF, 1992

Kuhn, T.S. , postface to "The Structure of the scientific revolutions", Flammarion, 1972

copyright R. Gicquel v2022.1

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