Kinetic and potential energy in the first law of thermodynamics

Kinetic and potential energy are included in the first law of thermodynamics in quite a contradictory way. Whereas in thermodynamics the total energy is understood as the sum of internal, kinetic and potential energy, the total energy in continuum mechanics incorporates only internal and kinetic energy, the potential energy being part of the work. The Gibbs ' fundamental equation is also occasionally extendend to contain a term for the potential energy. Some serious contradictions may result from this. As is first shown, kinetic and potential energy do not have any influence on the internal energy as long as relativistic effects are excluded. The Gibbs' fundamental equation therefore describes exchange processes between the “internal variables? of a system and its surroundings. Proceeding from this result one obtains a general definition of heat in open systems, including electromagnetic reactions, surfaceeffects and variable mole numbers. Exchange processes between the “external variables? of a system and its surroundings and hence also the influence of kinetic and potential energy are described by another independent equation, i.e. the energy equation of mechanics. Addition of both equations leads to the heat definition which is usually but under some further neglects given in textbooks. This definition has considerable disadvantages compared to the one derived before. In particular it is no longer possible to realize how mechanical and thermal energy are transformed into each other, which may give rise to errors.