Abstract
In this chapter we discuss physical quantities like mass, electric charge, energy and so on. If two systems are joined, these quantities add. The quantities in question are bound to particles, atoms or molecules. If they move, they take their properties with them. Therefore the quantities under discussion are transportable.
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Notes
- 1.
Pressure 1, 013 hPa, 0\({}^{\circ }\)C temperature.
- 2.
\({k}_{\textrm{ B}} =\)1. 380649 × 10 − 23 { J} { K} − 1.
- 3.
Einstein’s summation convention.
- 4.
A well-known example is the expression for the Poynting vector \(\mathbf{\mathit{j}}({E}^{\textrm{ em}}) = \mathbf{\mathit{S}} = \mathbf{\mathit{E}} \times \mathbf{\mathit{H}}\) for the energy \({E}^{\textrm{ em}}\) of an electromagnetic field. Many alternative forms have been proposed such that the energy current density is restricted to regions where electric charge flows. However, none of the alternatives is compatible with the notion that field energy is transported by streams of photons.
- 5.
As opposed to charge, where there may be a charge current density while the charge density vanishes.
- 6.
At least in non-relativistic approximation.
- 7.
A balance equation with vanishing production term is a continuity equation.
- 8.
We always have a Cartesian system of coordinates in mind.
- 9.
\(\mbox{ $\Omega $}\) describes the direction and the angular velocity of the rotation.
- 10.
We do not discuss radiation in this book. Adding a mass independent term for black body radiation of temperature T or any other contribution of energy not bound to mass is an easy exercise.
- 11.
A star denotes the time reversed quantity, in this context.
- 12.
Heat and hot are related words in ordinary English, just as Wärme and warm in everyday German, or calor and calido in Spanish.
- 13.
If magnetic effects are ignored.
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Hertel, P. (2012). Balance Equations. In: Continuum Physics. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29500-3_1
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DOI: https://doi.org/10.1007/978-3-642-29500-3_1
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