Thermodynamics in a Carnot Equation



Because of the nonconservative nature of thermodynamic fields, exterior differential forms seem like the natural formulation of thermodynamics. The so-called covectors of heat and work, \(\mathcal{H}\) and \(\mathcal{F}\), are not gradients of any scalar functions. Information can be had by studying their “curls,” which are nonvanishing and measuring the deviations of these functions from “gradients,” which would lead to state functions that are path independent. These equations can be considered as being analogous to the first and second laws of circuitation in electrodynamics (Heaviside 1893).

A great simplification is that the usual state space of thermodynamics is the plane in which the “cross product” or “wedge product,” ^, of covectors in the state plane can be interpreted as a vector pointing in the direction “perpendicular” to the plane (Hannay 2006). The resulting “covector,” which is not an arrow vector because directions and distances are not defined in thermodynamics, is “perpendicular” to the state plane, which can be treated, therefore, like a scalar quantity.


Entropy Furnace Enthalpy Compressibility 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Università CamerinoCamerinoItaly

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