Mass - and volume - speci ̄ c views on thermodynamics for open systems

A general framework for the thermodynamics of open systems is presented. The theory is fundamentally based on the generalized balance of mass, which is enhanced by additional surface-°ux and volume-source terms. The presentation highlights the in°uence of the enhanced mass balance on the remaining balance equations. To clarify the impact of the variable reference density, we introduce the notions of volumespeci ̄c and mass-speci ̄c formats. Particular attention is drawn to the fact that the mass-speci ̄c balance equations are free from explicit open-system contributions. They resemble the classical balance equations and can thus be evaluated in complete analogy to the closed-system case. Restrictions for the constitutive equations follow from the second law of thermodynamics, as illustrated for the particular model problem of thermo-hyperelasticity.