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Entropy Principles

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Principles of Continuum Mechanics

Part of the book series: Nečas Center Series ((NECES))

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Abstract

The constitutive theory of materials cannot be complete without thermodynamic considerations. In thermodynamics, two concepts are essential: energy and entropy.

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Notes

  1. 1.

    This postulate is acceptable for a one-component body; in mixtures, a more general form of the entropy flux is necessary. For instance, an additional term is added to (7.2)1 such that the entropy flux and heat flux are not collinear vectors.

  2. 2.

    A thermodynamic process during which the entropy remains constant is called an isentropic process.

  3. 3.

    A principal submatrix of a square matrix A is the matrix obtained by deleting any k rows and the corresponding k columns. The determinant of a principal submatrix is called the principal minor of A.

  4. 4.

    This assumption is modified for a multicomponent system by the existence of semipermeable membranes.

  5. 5.

    To give an example of T(θ), let the Celsius scale be considered the measure of empirical temperature. Choosing

    we obtain the Kelvin scale as a measure of the absolute temperature, which can be used to replace the empirical temperature θ with the absolute temperature T.

  6. 6.

    Liu (2002, Section 7.4) proved the collinearity of \(\vec q\) and \(\vec s\) without assuming the relation (7.116).

References

  • Hutter, K., & Jöhnk, K. (2004). Continuum methods of physical modeling. Continuum mechanics, dimensional analysis, turbulence. Berlin: Springer.

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  • Liu, I.-S. (1972). Method of Lagrange multipliers for exploitation of the entropy principle. Archive for Rational Mechanics and Analysis, 46, 131–148.

    Article  MathSciNet  Google Scholar 

  • Liu, I.-S. (2002). Continuum mechanics. Berlin: Springer.

    Book  Google Scholar 

  • Müller, I. (1967). On the entropy inequality. Archive for Rational Mechanics and Analysis, 26, 118–141.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University in Prague, Prague, Czech Republic

    Zdeněk Martinec

  2. Dublin Institute for Advanced Studies Geophysics Section, Dublin, Ireland

    Zdeněk Martinec

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  1. Zdeněk Martinec
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Martinec, Z. (2019). Entropy Principles. In: Principles of Continuum Mechanics. Nečas Center Series. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-05390-1_7

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