Thermodynamics as a theory of measurement

Some Features of the Modified Solid-Liquid-Vapor Equation of State

“…Description of real gas thermodynamics in terms of differential geometry has been suggested in [4]. It was shown that the thermodynamic states of real gas are the Legendrian or the Lagrangian manifolds in the corresponding contact or symplectic spaces.…”

“…The differential geometry approach is continuing to expand nowadays. Lychagin [4] introduced a Riemannian structure on the Lagrangian and Legendrian manifolds as well as higher-order symmetric differential forms, introduced for the description of higher-order phase transitions.…”

“…The thermic EoS represents pressure as a function of the volume and the temperature, while the caloric EoS expresses the internal energy in terms of the volume and the temperature. Moreover, these coordinates on the manifolds define the thermodynamic potential, from which other potentials and equations of state are derived [4].…”