On suggested simplifications of Carathéodory's thermodynamics

Scientific article / Phys. Status Solidi, 1961, Vol. 1, No 2, p. 120–126.The geometrical approach to thermodynamics which was initiated by carathéodory has recently been more widely accepted. In fact, in the last few years a number of attempts have been made aimed at simplifying it with a view to developing an elementary approach. An attempt has also been made to replace the geometrical by an algebraic procedure. In this paper these suggestions are examined for geometrical by an algebraic procedure. In this paper these suggestions are examined for implicit assumptions, and attention is drawn to problems which they leave unsolved. It is pointed out that carathéodory's original derivation of the increasing property of the entropy involves also some implicit continuity assumptions concerning non-static adiabatic changes. An elementary approach is here understood to have the following properties:
— It appeals only to mathematical theorems familiar to most physicists (i. e. it does not involve carathéodory's theorem or similar technicalities), and
— it leads to a full specification of the content of the second law of thermodynamics as normally understood.