# Special Relativity and the Transformation of Heat

Amazingly, the question of how temperature or heat 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.

The second part of this treatise is about *heat* and *energy*: What are the transformations for Internal energy *Ui*, thermodynamic work *P·V* , enthalpy *H* and total energy *E i*in STR ? We will show that the transformations of Planck, von Mosengeil and Pauli are correct, and we will show why it is erroneos to transform heat energy by *dividing* through the root term. The arguments do not depend on *T* jor *S* jbeing chosen for relativististic invariant. Epstein diagrams give a clear illustration on which part of the energy added to the system has to be interpreted as increase in kinetic energy and which part may be interpreted as increase in enthalpy.

Finally the results of both parts are brought together. We will find that all of the laws of thermodynamics are form-invariant regarding the transformations derived in this treatise.

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

Current version 2.0 released 29 / 6 / 2014