Joule-Thomson coefficient in systems with multiple chemical equilibria (Q1381416)

The Joule-Thomson coefficient \(\mu\) is the change of temperature caused by the change of pressure at constant enthalpy, \(\mu=(\partial T/ \partial P)_H\). It plays a distinguished role in chemical thermodynamics. (Recall that among the 336 possible first partial derivatives involving the eight common thermodynamic variables, viz., \(P,V,T,U,H,S,A\) and \(G\), only \(\mu\) has been named after scientists.) In view of this we examined the behavior of \(\mu\) in systems with multiple chemical equilibria. Throughout this paper it is assumed that the system considered is at thermodynamic equilibrium. Recently the concept of response equilibria in chemical thermodynamics was shown to be useful when considering the sensitivity of the equilibrium state of general reacting systems with respect to different parameters influencing the position of the equilibrium. It appears that within the stoichiometric formulation of the equilibrium conditions, the system's response may be presented as a sum of contributions associated with so-called Hessian and non-Hessian response equilibria (HEQs and NHEQs), and pairs thereof. For ideal systems the response is given as a sum of contributions originating solely from response equilibria (i.e., without contributions from pairs of HEQs and/or NHEQs). So far, systems at constant temperature and pressure \((T,P=\)const.) have been considered. We extend our approach to systems constrained by constant enthalpy and pressure \((H,P=\)const.), with emphasis on the Joule-Thomson coefficient.