Introductory remarks

In the last two chapters, we have stated and developed the second law of thermodynamics along traditional lines. The statements of the law asserted the impossibility of certain processes which are easily visualized and readily believed. However, to arrive at the real substance of the matter, we had to equip ourselves with the paraphernalia of idealized heat engines and wade through lengthy arguments about efficiencies and cyclic processes. Only then did we discover that we had arrived, as if by good fortune, at a new function of state, the entropy, on which depends all the subsequent development of the subject. In fact, the essential function of the second law is to enable us to define this quantity and to derive its properties. It seems desirable, therefore, to adopt a formulation of the law which achieves this end with greater economy. That put forward early this century by Caratheodory does precisely that (see Caratheodory, 1909 and 1925).

One may well enquire why, if it has this advantage, Carathéodory's statement of the second law is not more widely used. There are two reasons for this. In the first place, any formulation which makes it possible to avoid the use of cycles and heat engines in the basic development must necessarily be framed in somewhat more abstract terms than the Kelvin or Clausius statements which refer to specific processes.