brought quantitative precision to thermal studies through the distinction between temperature and heat, the introduction of specific heats, the distinction between overt and latent heat, and the contention that measurements concerned heat transfer, rather than the heat in a body. Lavoisier's adaption of caloric theory systematized these results by assuming virtually massless caloric atoms that repel each other, but are differentially attracted to atoms of gross matter. This supplied a qualitative account of the transition from solid to liquid to gaseous states and, through the assumption of caloric conservation, a basis for calculating the thermal outcome of mixtures of different substances at different temperatures. In spite of a limited success, the assumption of caloric atoms became increasingly suspect due to Rumford's criticisms, the acceptance of the wave theory of light, and the phenomenological thermodynamics introduced by Fourier.13
The concept 'energy' stemmed from Leibniz's vis viva and Mme. Du Châtelet's demonstration that earlier experiments showing that weights dropped onto a clay floor had impact depths proportional to the square of the velocity supported conservation of vis viva rather than momentum It achieved a pivotal role through the establishment of energy conservation by Mayer and Helmholtz and Joule's demonstration of the interconvertability of mechanical and thermal energy. . As Harman summarized it:
By the middle of the nineteenth century the concept of energy was being employed to provide the science of physics with a new and unifying conceptual framework, which brought the phenomena of physics within the mechanical view of nature, embracing heat, light and electricity together with mechanics in a single conceptual structure. The establishment of the mechanical view of nature, which supposed that matter in motion was the basis for physical conceptualization, as the program of physical theory, and of the concept of energy and the law of the conservation of energy as principles unifying all physical phenomena, was the distinctive feature of the conceptual structure of nineteenth‑century physics. (Harman, 1982a, p. 106)
Though thermodynamics was related to mechanism, it featured three distinctively non-mechanical concepts: 'temperature', 'state of a system' and 'entropy'. The concept 'temperature', was originally based on expansive properties of particular substances: air, water, alcohol, or mercury. This involved both practical difficulties, such as changes of state and non-uniform expansion, and conceptual inconsistencies. The accepted principle that bodies in equilibrium are at the same temperature, aka the zeroth law of thermodynamics, deprives any particular substance of a privileged status in defining temperature Independently Gay-Lussac and Dalton proposed basing the concept of temperature on the coefficient of expansion of gases. By the middle of the nineteenth century, it was realized that this coefficient, 0.00366 per degree, strictly applied only to ideal gases. The theoretical resolution depended on the second distinctive thermodynamic concept.
Carnot's originally neglected treatise on the motive power of heat contained two novel concepts: 'state of a system' and 'reversible cycle'. In an ideal reversible cycle the system returns to its original state. By a qualitative use of caloric theory and an analogy between the relative efficiency of water falling on a paddle wheel and caloric dropping to a reservoir, Carnot reached the conclusion: "The motive power of heat is independent of the working substances that are used to develop it. The quantity is
13 For a general survey see Brush, 1976.