This paper addresses a number of points, some subtle and some not so subtle, that are important for the careful student of chemical thermodynamics. They range from distinctions between equilibrium and non-equilibrium functions and between functions as such and specified values thereof (without which not even the usual statement delta U = q + w of the First Law is valid) to the recognition that the global pressure and temperature (i.e., the pressure and temperature of fluid surroundings) are sufficient to specify the eqilibrium of a system, even an inhomogeneous system that includes stressed solids. Our most important point is that, especially for systems featuring a flexible container, it is the Gibbs function of the total system, encompassing container and all, that is essentially the sole guardian of the usual thermodynamic equality and inequality criteria. The simple Gibbs function G = U - TS + PV, with T and P the global temperature and pressure, applies to complex systems just as it does to simple fluid systems, its form being the inevitable consequence of two facts, true for both kinds of system: partial derivative of q = T(surr)dS and partial derivative of w = -P(surr)dV. Examples are given.
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