# Special Relativity and the Transformation of Temperature

Amazingly, the question of how temperature is transformed in the special theory of relativity is still controversial in the literature: What is the value *T' * ja relativistic observer should ascribe to the temperature of a quantity of gas when it has the value *T j*in the rest frame? Do consistent transformations exist at all for those thermodynamic state variables? One of the first to take up this question was none other than Max Planck with his doctoral candidates Kurd von Mosengeil and Max von Laue.

First we will only discuss the ransformations of pressure, volume, temperature and entropy. We will cautiously assume that such transformations do exist and show how little wiggle room there is for these transformations, given a few elementary results of the special theory of relativity. Within this narrow scope, we opt for one of two possible solutions which will actually amount to a deeper definition of the concept of temperature. We justify the choice in detail and then show that the second choice would have led to exactly the same results as for Planck et al. The proposals of many other authors however, including such famous persons as Eddington, are not logically consistent.

In a second part "STR and Heat" we will discuss the transformations of heat, internal energy, enthalpy and total energy. This discussion is completely independent of the first part. Connecting the results of both discussions will end in a great 'finale'.

Planck himself is perhaps a bit to blame that this discussion was not settled long ago. In 1907 he provided a 'proof' that the entropy *S* jmust be relativistically invariant. Even the clever Pauli accepted this result uncritically in his famous encyclopedia article of 1920. We show that Planck assumes in his proof what indeed was to be proved, and thus makes the classic mistake of begging the question. Neither the entropy *S* jnor the Boltzmann constant *k* must necessarily be relativistically invariant.

Translated to the Latin of our days by Rick Sermersheim in July 2013

Current version 2.0 released 29 / 5 / 2014