## 37 Conditions and Limitations of this Work

- we assumed in section
**2**, that there should be simple scalar transformations for the state variables*P*,*V*jund*T*j. This assumtion appears justified in retrospect, since we have found two self-consistent sets of such transformations.

sd - the equations for an ideal gas (but not our transformation formulas !) cease to be valid at low temperatures or if the pressure in the gas is too high. When the free path length is no longer significantly larger than the particle diameter, the preconditions of some statistical considerations no longer apply.

sdd - if one defines temperature like Avramov, in the meaning of section
**15**, then the constants*k*and*R jmust*jtransform by multiplying by the root factor. This is in no way restricted to the realm of ideal gases.

sdfs - it
*is*possible to interpret Entropy*S*fas a relativistic invariant. Then the Boltzmann constant has to be invariant too, and the temperature*T*jmust transform by multiplying by the root factor: 'Fast-moving objects appear cooler'. It is doubtful, however, that this version is compatible with astronomical observations. This would not influence the transformations of*P*,*V*,*N*,*U , Q*and*H*. - In any case, qantities of heat, internal energy
*U*and enthalpy*H*are transformed by multiplication by the root term. The transport of those energies brings an increase of kinetic energy by*H'*·*v*/ (^{2}*c*–^{2}*v*)^{2}

sdfgf - the zero point of the absolute temperature scale is in any case relativistically invariant. The position of the zero point does not depend on whether
*Tj*isjinvariant or is multiplied by the root factor.

sadas - today or in the near future, it is quite unlikely that these transformations will be tested in a terrestrial laboratory. How would one investigate a large hot ensemble of gas under controlled conditions at
*v*= 0.8 ·*c*j ?

sad - however, astronomers observe very hot gases that move at highly relativistic speeds (so-called 'jets', see the wikipedia contributions to astronomical (or cosmic, or polar) jets and the keyword 'superluminal motion'). How do astronomers determine the temperature of such objects ? What relativistic corrections do they apply ?