Phase Transitions and Chemical Reactions

Abstract

We now want to return to the important problem of how many state variables are actually necessary to uniquely determine the state of a system. To this end, we start from an isolated system which contains K different particle species (chemical components) and P different phases (solid, liquid, gaseous,…). Each phase can be understood as a partial system of the total system and one can formulate the first law for each phase, where we denote quantities of the i^th phase by superscript i = 1,…, P. For reversible changes of state we have

$$ d{U^{\left( i \right)}} = {T^{\left( i \right)}}d{s^{\left( i \right)}} - {p^{\left( i \right)}}d{V^{\left( i \right)}} + \sum\limits_{l = 1}^k \mu _l^{\left( i \right)}dN_L^{\left( I \right)}dN_l^{\left( i \right)},i = 1,2,...P$$

(3.1)