Thermal Equilibrium - Theoretical Foundations

Theoretical Foundations

It is scientifically permissible, and perhaps unavoidably necessary, to start a project of reasoning with several mutually coherent and dependent primitive presupposed concepts. The concept of thermal equilibrium is thus coherent with the concepts of temperature and of heat transfer. These three concepts hardly make physical sense without each other. They were considered coordinately before and during and after the developments of calorimetry and of thermodynamics, for example by Maxwell and by Planck.

Instead of relying on this triple of jointly defined physical concepts, some writers, motivated by a desire for axiomatic parsimony and precision or mathematical elegance, prefer to define thermal equilibrium by relying on a presupposed notion of thermodynamic equilibrium, in which all mechanically measurable properties of a body have become stationary, and one infers that consequently the otherwise undefined thermal properties also are stationary. Carathéodory is an example of such writers, as seen in his 1909 article. This approach leaves one at the mercy of the questions of what is meant physically by "all mechanically measurable properties" and what is meant by saying that they "have become stationary", and still relying on some concept that allows bodies not 'thermally connected' to be put into 'thermal connection'. It also leaves a person, who does not know in advance the notions of heat transfer and temperature, reliant on the assumptions, such as conservation of energy, and on the mathematical development, of the theory of thermodynamics.