On the concepts of mass and linear momentum in Galilean thermodynamics

Abstract

The paper presents a systematic treatment of the consequences of the first law of thermodynamics and of the Galilean principle of relativity for continuous bodies. It is shown that these two principles, when combined, imply not only the existence of energy, but also the existence of linear momentum. Both these quantities are represented by extensive state functions satisfying the equations of balance of energy and linear momentum, respectively. The linear momentum doesnot generally have the usual classical Newtonian form (“mass times velocity”). If, additionally, an assumption is made that the linear momentum is a function of velocity only, then the classical expression is recovered. The general equation of balance of linear momentum reduces then to Cauchy's equations of motion of continuum mechanics. But even without this additional assumption the concept of mass emerges as a derived concept in the theory: it figures in the transformation law for linear momentum under Galilean transformations.