Abstract
In the preceding chapter of this book on Continuum Physics we have discussed the notion of material points. They are infinitely small from a macroscopic point of view and infinitely large from a microscopic point of view. Just think of the temperature field T = T(t, x). The material point at location x at time t is large enough for obeying the rules of infinitely large systems, such as the ideal gas law, for example. On the other hand, it is small enough so that it approaches thermodynamic equilibrium practically immediately. The state of the material point is always an equilibrium, or Gibbs state which is characterized by parameters such as temperature or chemical potentials.
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Notes
- 1.
The article on Reaction and diffusion is an exception
- 2.
As contrasted with a solid medium.
- 3.
The region which is afflicted by weather phenomena, roughly the first 15 km. It contains 75% of the air mass and more than 98% of water vapor.
- 4.
One mole of the isotope { 12}C has a mass of exactly 0.012 kg, by definition.
- 5.
R = 8. 314 { J} { K} − 1 { mol} − 1.
- 6.
. 02897 { kg} { mol} − 1 for dry air.
- 7.
Recall \({G}_{jj} = {\partial }_{j}{v}_{j}\).
- 8.
By the way, one speaks of the ideal gas because B 1 = 1 holds true for all kinds of molecules.
- 9.
Per unit mass.
- 10.
Recall that specific refers to unit mass.
- 11.
λ stands for the external parameters.
- 12.
The number of particles within the system is not fixed.
- 13.
Quantized lattice vibrations. Phonons are quasi-particles because they cannot live in free space.
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Hertel, P. (2012). Material Equations. In: Continuum Physics. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29500-3_2
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DOI: https://doi.org/10.1007/978-3-642-29500-3_2
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