18 Summary of the First Part
If one defines temperature as a fundamental unit of physics, as in section 15 of this paper, then the following values are relativistically invariant:
- temperature T j( and temperature changes )
- pressure P j( and pressure changes )
- particle number N j and amount of substance n j=j N / NA
- thermodynamic efficiency
The following values are transformed by multiplying by the root factor:
- volume V j( and volume changes )
- the Boltzmann constant k nand the universal gas constant R
- entropy S j( and their changes )
The following value is transformed by dividing by the root factor:
- density of particles
Taking into account these transformations, the essential relationships of thermodynamics remain valid.
The following relationships are form invariant:
- the second law of thermodynamics mmmm ∆S j≥j 0 mm in a closed system
- for ideal gases mmmm P · V j= jn · R · T j= jN · k · T
- the entropy is mmmym Sj =j k · ln(Ω)
It should be noted that we have not assumed the validity of these relationships for a fast-moving observer in order to derive the transformation rules! We only assumed that such transformations exist, and in addition we have defined temperature within the limits of k' · T' n= k · T · √ so that it is relativistically invariant.
Planck, Einstein, Hasenöhrl and von Mosengeil made no errors (unlike many others) in the derivation of their results. They just decided that jS' j= S should apply, and then they derived their other results in a logically correct way.
Avramov, however, made the better choice!