Exergy of an open continuous medium

Exergy is a very important thermodynamic quantity in several fields such as economy, engineering, and ecology and yet it has attracted little attention in pure physics. One of the main problems of the currently used definition of exergy is its dependence on an arbitrarily chosen reference state, which is the thermodynamic state of a reservoir the system is supposedly in contact with. In this paper, starting from a very general definition of exergy, a formula is derived for the exergy balance of a general open continuous medium without any reference to an external environment. A formula is also derived for the most suitable thermodynamic parameters of the Earth atmosphere when seen as an external environment in the usual exergy applications.

Figure 1

Energy-entropy diagram of an isolated system with fixed volume $V$. The allowed states lie in the region above the equilibrium curve $U\left(S\right)$. The exergy is the difference between the actual energy and the energy $U\left(S\right)$ at constant entropy. The irreversible evolution drives the system from the initial state $(E,S)$ to the equilibrium point $(E,S_{\mathrm{eq}})$, entailing a decrease of exergy until it vanishes.

Figure 2

Two systems in contact at temperature $T_1$ and $T_2$ can be used to extract useful work by means of an auxiliary body (depicted as circular double arrow) making infinitesimal cyclic transformations.

Figure 3

A small system $A$ in a thermal bath of the reservoir $R$ with temperature $T_R$, pressure $p_R$ and chemical potentials ${\mu }_R$.

Figure 4

The reference frame for the atmosphere. The coordinate $z$ is the height, where the plane $z=0$ being the Earth surface is the lower boundary.