Using reversible processes to define the entropy

The existenee of reversible adiabatic surfaces is the justification for defining a new state function S, the entropy. S is specified to have the same value everywhere on one of these surfaces, and a different, unique value on each different surface. In other words, the reversible adiabatic surfaces are surfaees of constant entropy in the A-dimensional space. The fact that the surfaces fill this spaee without intersecting ensures that 5 is a state function for equilibrium states, because any point in this space represents an equilibrium state and also lies on a single reversible adiabatic surface with a definite value of S. 

We know the entropy function must exist, because the reversible adiabatic surfaces exist. For instance. Fig. 4.9 on the next page shows a family of these surfaces for a closed system of a pure substance in a single phase. In this system, A is equal to 2, and the surfaces 

How can we assign a unique value of S to each reversible adiabatic surface We can order the values by letting a reversible process with positive one-way heat, which moves the point for the state to a new surface, correspond to an increase in the value of S. Negative one-way heat will then correspond to decreasing S. We can assign an arbitrary value to the entropy on one particular reversible adiabatic surface. (The third law of thermodynamics is used for this purpose—see Sec. 6.1.) Then all that is needed to assign a value of S to each equilibrium state is a formula for evaluating the difference in the entropies of any two surfaces. 

Suppose the same experimental system undergoes a second reversible process, not necessarily with one-way heat, along a different path connecting the same pair of reversible adiabatic surfaces. This could be path C D in Fig. 4.10(a). The net heat entering the 

Thermodynamics and Chemistry, second edition, version 3 2011 by Howard DeVoe. Latest version www.chem.umd.edu/thermobook 

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