Relativistic thermodynamics on conveyor belt

Abstract

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.

Relativistic mechanics and thermodynamics: IV. Thermodynamic processes

“…ensuring the cylinder constant speed V during the process. This conveyor belt effect [20] holds true in classical physics, with W F Vt ex c ex c 0 = ¯. Entropy variation.…”

“…The internal energy of n ξ moles of a self-contained extended body is obtained by adding over its (r) elementary particles, considering interaction energies [i.e. nuclear (N), atomic (A), molecular (M) (no zero-point energy has been considered)] and its temperature-dependent internal energy, as [20]…”

“…To keep things simple, throughout this work the gravitational interaction will be considered as a conservative force from a phenomenological point of view, to avoid adding unnecessary complexity to the thermodynamic processes (see, e.g. [20].) Considering the Earth-ball gravitational interaction, with g = ( − g, 0, 0) the gravitational field (Earth-gas gravitational interaction will not be considered), the Earth's on-ball force g F , 0, 0…”

“…A strategy to solve a problem in frame S ¯is to describe the process first in frame S, i.e. the lab frame where the effect of forces applied on the system-linear impulse exerted and work performed on it-can be described with reliability, obtaining the process' four-vector fundamental equation, and then transform this four-vector equation in S to those in frame S ¯ [20].…”

Landauer Bound in the Context of Minimal Physical Principles: Meaning, Experimental Verification, Controversies and Perspectives

“…It should be emphasized that understanding the relativistic extension of the Landauer bound remains an open problem due to the fact that the construction of a relativistic thermodynamics theory is still controversial after more than 110 years of its development. In particular, the problem of the relativistic transformation for temperature remains unsolved [98][99][100][101][102].…”