Constitutive relations of energy storage in a gas in preferred integral causality

This paper deals with the derivation and use of the preferred integral causal form of the constitutive relations describing a three-port capacitor (C-element) that represents the energy storage in a gas that can be considered either an ideal gas (Boyle Gay-Lussac) or a Van-der-Waals gas. It is shown under which conditions this derivation is possible and under which conditions other forms of state equations can be analytically converted to the desired form. A comparison is made between simulations in which the thermal port has integral causality and implicit simulations in which this causality is derivative.