An axiomatic basis for classical thermodynamics

Abstract

In 1908, Caratheodory [I, 21 proposed a deductive theory of therrnodynamics. The special features of his theory are less important than the fact that he set standards for rigorous thinking in the subject. Hence it is not necessary to emphasize this aspect of the present approach. Physically speaking, the present objective is to build the theory on the concepts of thermometry and calorimetry, taking temperature and heatgeneration as the primary concepts, and to show how entropy and absolute temperature arise as derivative concepts. By not having work production as a primary concept, we obtain a purely thermal theory to which the first law and internal energy need not be attached, unless desired. This more traditional approach is in contrast with Caratheodory’s (see also refs. 3,4, and 5). We do not use an axiom about inaccessible states, as Carat&odor-y does, because such an axiom tends to obscure the fact that the “thermodynamic relations” which are the practical objectives of the subject are statements about reversible processes. (Irreversible processes take one out of the space of equilibrium states.) Our form of the second law is based on a semi-Carnot cycle which consists of heat generation (or absorption) at one temperature only, plus an adiabatic return to the initial state. Our axiom says that in this case, the total heat generated is zero. The compelling inductive proof of the second law based on the impossibility of perpetual motion of the second kind applies directly to support this axiom, because if positive total heat were generated in such a cycle then that heat, all absorbed at one temperature, could be converted into work indefinitely by reversing the cycle. Here, because we want a deductive theory, we cannot wait until, say, the concept of absolute temperature arises, and then inject the physical observation that this cannot be zero. We have somehow to make such specifications on our primary concepts (which are: the space of states, the temperature