Relativistic thermodynamics on conveyor belt


 Two thermodynamic processes are analysed by using a relativistic four-vector fundamental equation formalism: the launching of a projectile by forces produced by chemical reactions inside a cannon (equivalent to a person launching a ball) placed on a moving platform, a mechanical energy production process, and the Joule-Kelvin process implemented on a conveyor belt. Each process is first studied in frame S, in which the device -- the cannon or the porous plug --, is at rest, obtaining its four-vector fundamental equation ${\rm d} E^\mu = \delta W^\mu + \delta Q^\mu$. Using the Lorentz transformation, the corresponding four-vector equation in frame ${\bar {\rm S}}$ -- in which the processes are carried out on a moving platform or a conveyor belt -- ${\rm d} {\bar E}^\mu = \delta {\bar W}^\mu + \delta {\bar Q}^\mu$, is obtained, obeying Einstein's principle of relativity. For the relativistic description to be coherent, one has to assign linear momentum to the non-mechanical energies and consider their variations in the corresponding Newton's second law equation and the relativistic non-simultaneity and conveyor belt effects. In relativistic thermodynamics, Newton's second law and the first law of thermodynamics are not independent equations. It is shown that entropy variations and fuel consumption are frame independent magnitudes.