Relativistic Mechanics and Thermodynamics. IV. Thermodynamic processes

Abstract Two thermodynamic processes, an adiabatic gas compression and an isothermal gas compression, taking place in a moving lab are analysed using a four-vector fundamental equation, ${\rm d} E^\mu = \delta W^\mu + \delta Q^\mu$, a relativistic generalization of the first law of thermodynamics ${\rm d}E=\delta W+ \delta Q$. These processes are first described in frame S, with the lab at rest, and then in frame ${\bar {\rm S}}$, moving with constant velocity relative to S. This formalism shows that Lorentz transformation preserves the principle of relativity in thermodynamics. The physical meaning of the norm of a four-vector is analysed, and Clausius definition of entropy variation is generalised to relativity. The classical description of the process is obtained in a moving lab by taking the low-speed limit in the four-vector fundamental equation. The formalism naturally incorporates the role of the laws of mechanics when analysing processes that are typically considered as purely thermodynamic.