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Thermodynamik, Diffusion

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Mathematische Modellierung

Part of the book series: Mathematik Kompakt ((MAKO))

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Zusammenfassung

Die Thermodynamik beschäftigt sich mit den Gesetzmäßigkeiten, die bei der Umwandlung von einer Energieform, zum Beispiel Wärme, in eine andere auftreten. Diese Gesetzmäßigkeiten sind in den Hauptsätzen der Thermodynamik formuliert. Jedes thermodynamische System muss ihnen genügen. In der Modellbildung sind insbesondere nur solche konstitutiven Gesetze zu den Erhaltungsgleichungen zulässig, die diese Forderung erfüllen.

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Notes

  1. 1.

    Historische Formulierung des 0. Hauptsatzes [8]: „There exists for every thermodynamic system in equilibrium a property called temperature. Equality of temperature is a necessary and sufficient condition for thermal equilibrium.

  2. 2.

    Historische Formulierung des 1. Hauptsatzes [8]: „There exists for every thermodynamic system a property called the energy. The change of energy of a system is equal to the mechanical work done on the system in an adiabatic process. In a non-adiabatic process, the change in energy is equal to the heat added to the system minus the mechanical work done by the system.

  3. 3.

    Historische Formulierung des 2. Hauptsatzes [8]: „There exists for every thermodynamic system in equilibrium an extensive scalar property called the entropy, S , such that in an infinitesimal reversible change of state of the system, dS  =  dQ T , where T is the absolute temperature and dQ is the amount of heat received by the system. The entropy of a thermally insulated system cannot decrease and is constant if and only if all processes are reversible.

  4. 4.

    Die Temperatur T ist hierbei eine Verschiebung zur absoluten Temperatur θ, d. h. T = θ − θ 0 mit einem festen θ 0.

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Correspondence to Gabriele Witterstein or Gabriele Witterstein .

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Hoffmann, KH., Witterstein, G. (2014). Thermodynamik, Diffusion. In: Mathematische Modellierung. Mathematik Kompakt. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0346-0650-9_5

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