31   The Equation  dQ i= T · dS  is form-invariant

 
Following sections 8 and 12 of the first part of this treatise, the product T · dS jnecessarily transforms the same way as T · k , that is by multiplication by the root factor. In 26 and 27 we established  dQ'  =  dQ · √   and hence the relation

T ·  dS j =  dQ        or      d=  dQ / T

is form-invariant too, independant of our option in favour of temperature or entropy to be relativistically invariant. This result has been announced in section 14 .

We did not suppose the invariance of this relation. The invariance is the result of our investigations on the transformations of  k · T  and heat quantities Q . In section 34 we will present some further relations between T and dS jincluding the notion of molar heat capacities.