Relativistic mechanics and thermodynamics: part I. A linear-translation four-vector formalism

Abstract

Einstein’s special theory of relativity is presented in a Minkowski four-vector formalism integrating mechanics and thermodynamics at a sophomore level, allowing the solution of undergraduate exercises in linear translation requiring both. This relativistic formalism directly incorporates the mechanics (Newton’s second law) and the thermodynamics (first law of thermodynamics) of a process in a four-vector fundamental matrix equation. This four-vector formalism is used to analyse two processes: a block descending an inclined plane with friction (a mechanical energy dissipation process increasing the entropy of the universe—if frictionless, a mechanical energy conservation process), and a cannonball ascending an incline, moved by a force exerted by a chemical reaction (a mechanical energy production process), with Gibbs’ free enthalpy function decreasing.