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Carnot and the fields formulation of elementary thermodynamics

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Thermodynamics centres on the fact that work and heat are not functions of state yet the natural formalism to capture this fact was denied to thermodynamics by its historical pre-dating of vector field notation. One reason for re-examining this omission is provided by the work of Sadi Carnot who initiated thermodynamics. His results, which he derived from his grand principle, were not obtained by what is now called the second law of thermodynamics or by the first law of thermodynamics. His results were obtained a (co)vector formula, albeit expressed in words not symbols. Carnots formula allowed him to obtain several standard results of thermodynamics, including the Clausius-Clapeyron equation. The formula also implies the Maxwell relations.

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