## 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*/*N*_{A} - 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**S*j =*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!