On the Quantification of Non-equilibrium Exergy for Thermodynamic Systems Evolving According to Cattaneo’s Equation

This paper is a follow-up of previous work aimed at the identification and quantification of the exergy of macroscopic non-equilibrium systems. Assuming that both energy and exergy are a priori concepts, it is possible to show that a system in an initial non-equilibrium state relaxes to equilibrium releasing (or absorbing) an additional amount of exergy, called non-equilibrium exergy, which is fundamentally different from Gibbs’ Available Energy and depends on both the initial state and the imposed boundary conditions. The existence of such a quantity implies that all iso-energetic non-equilibrium states can be ranked in terms of their non-equilibrium exergy content, any point of the Gibbs plane corresponding therefore to a possible initial distribution, each one with its own exergy-decay history. The non-equilibrium exergy is always larger than its equilibrium counterpart and constitutes the “real” total exergy content of the system, i.e., the real maximum work extractable (or absorbable) from the system. The application of the method to heat conduction problems led to the calculation of a “relaxation curve”, i.e., to the determination of the time-history of the relaxation towards equilibrium that takes place in finite rather than infinite time interval. In our previous works, use was made of the Fourier heat diffusion equation. In this study, the Cattaneo heat transfer equation is used instead, in an attempt to extend the validation range of the procedure. Cattaneo introduced in 1948 a second time derivative term that renders the diffusion equation hyperbolic and avoids an infinite speed of propagation. A finite propagation velocity of thermal disturbances affects the value of the non-equilibrium exergy: this paper presents the new results and offers a discussion of the implications