determined exclusively by the temperatures of the bodies between which, at the end of the process, the passage of caloric has taken place." (Carnot, pp. 76-77) This seminal principle had a guiding role both in the development of the concept of entropy and also in the burgeoning process of producing more efficient steam engines. Since it presupposed the concept of temperature it could not of itself supply a non-circular basis for defining 'temperature'. After considerable confusion Thomson finally defined temperature as T = J/, where J is the mechanical equivalent of heat and can be defined in terms of the work done by an ideal engine in a reversible cycle. Though neither J nor was determined with sufficient accuracy to use Thomson's formula as a practical basis for measuring temperature, it supplied a basis for a concept of temperature independent of the properties of any particular substance. (See Cropper, 1987). As Gillispie (1959, p. 367) has noted, the idea of a reversible reaction played a role in the nineteenth century similar to that of inertia two centuries earlier. Just as no real bodies ever persevere in rectilinear motion indefinitely, so no real reaction is completely reversible. Both idealizations supplied concepts which could be readily expressed mathematically. Both the first (energy conservation) and second (entropy) laws of thermodynamics rely on idealized concepts of matter and processes.
Thermodynamics could have been developed as a replacement for caloric theory with energy conservation replacing and broadening caloric conservation and assumptions about molecular motions replacing assumptions about short range attractive and repulsive forces. Clausius deliberately rejected this in favor of a sharp distinction between thermodynamics, developed as a phenomenological science, and kinetic theory:
Before writing my first memoir on heat, which was published in 1850, and in which heat was assumed to be a form of motion, I had already formed for myself a distinct conception of the nature of this motion, and had even employed the same in several investigations and calculations. In my former memoirs I intentionally avoided mentioning this conception, because I wished to separate the conclusion which are deducible from certain general principles from those which presuppose a particular kind of motion. . . (citation from Brush, 1976, p. 112).
Except for Rankine, the leading developers of thermodynamics, Helmholtz, Thomson, Maxwell, and Tait followed Clausius's lead in basing thermodynamics on its own principles, rather than on ontological considerations. In labeling this 'phenomenological' physics I am following the practice of physics, rather than philosophy. The term 'phenomenological' was prominently reintroduced into discussion of physics in the mid-nineteenth century by Whewell (adapting Newton's usage) and Helmholtz (adapting Kant's usage) (Olson, 1975, chapt. 5). The net result was that thermodynamics was an idealized science where the basic idealizations were the following:
The state of a system can change continuously. One can, accordingly, use differential equations to express infinitesimal changes.
Reversible changes can be defined in a way that does not depend on the nature of the working substance.
Because thermodynamics is geared to equilibrium conditions, processes can be treated in terms of an infinite number of quasi-static states.
The differential formulation of thermodynamic laws signals an end to the question of whether the laws treat the heat in a body or transferred from a body. Since the