Properties of the Gibbs function

For the change of a system between states 1 and 2 we have from (2 3) 

Consider the special case (a) that the only heat transferred to the system is from a reservoir which remains at the constant temperature 

T (5) that the initial and final temperatures, andJTa of the system are equal, and are equal to the temperature T of the reservoir (c) apart from the system, the only other body which has undergone a change of volume at the end of the process is at a constant pressure p (e.g. a surrounding fluid such as the atmosphere) d) the initial and final pressures, and p, are equal, and are equal to p. 

Substituting in (2 18) and putting T2=Ti=T, and also p%=Pi= p, we obtain after rearrangement 

The term p(V — Fj) is the work done by the system in displacing its environment at the steady pressure p. This is not necessarily the whole of the work, —u , done by the system, and therefore we define an additional work time —by the relation 

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In our exposition of the properties of the Gibbs function G (Chapter 7), we examined systems with constraints on them in addition to the ambient pressure. We found that changes in Gibbs function are related to the maximum work obtainable from an isothermal transformation. In particular, for a reversible transformation at constant pressure and temperature [Equation (7.79)],... 

Given that classical equilibrium thermodynamics has had unparalleled success as a theory in chemistry and materials science for over a hundred and fifty years and continues to be successful, can we claim it to be above falsification We could claim that, as a mathematical structure developed by Gibbs, equilibrium theory is beyond falsification. For instance, equations 15 and 16 follow directly from the anal3ftical properties of the Gibbs function. Mathematical truths, however, only lead to other mathematical truths through valid arguments. They are not falsifiable by experiment. The connection to the empirical world comes because equations. 15 and 16 contain observable quantities. These equations connect one set of experimental observations to another. Hence they can be useful or useless, but cannot be false. 

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