Publisher Summary This chapter discusses equilibrium in ideal system in which several components co-exist in one or more phases. It proceeds gradually from the simple equilibrium condition to more complex cases, underlying that if equilibrium is to prevail, the system must be a subject to constraints, all of which are ultimately based on Gibb's criterion. In Gibb's criterion, the chemical potential of a given species must be the same in all phases at equilibrium. It examines the stringent constraints that arise when two or more distinct phases are to be maintained in equilibrium. Apart from uniformity of temperature and pressure, it requires that the chemical potential “μi” for each of the “c” components be the same throughout all the “p” phases. The basic problem in thermodynamics consists of determining the final equilibrium state that an isolated system reaches after starting out from a given set of initial conditions and constraints. In this matter, it is guided by two corollaries of the First and Second Laws namely, that in an isolated system subjected to any change, the entropy cannot decrease, and that its energy remain constant.