Criteria for equilibrium and spontaneous transformation

If a system is in equilibrium with its surroundings, every possible infinitesimal transformation is reversible. Hence, a necessary condition for equilibrium is that Eq. (2.20b) holds for all infinitesimal transformations that is, the sum of the entropy of the system and its surroundings is constant. This is the most general criterion for a system to be in equilibrium. Similarly, the most general criterion for a spontaneous transformation is given by Eq. (2.20c) that is, the transformation must result in an increase in the sum of the entropy of the system and its surroundings. However, these criteria are difficult to apply in practice because they involve the system and its surroundings, rather than the system alone. 

To develop criteria for equilibrium and spontaneous transformations that involve only the system, we introduce a new function of state, called the Gibbs free energy (G, or g for unit mass) which is defined by 

If we now confine ourselves to transformations at constant temperature and pressure (which are common conditions for chemical reactions) 

Expressed in terms of finite changes in molar quantities for a chemical reaction, Eq. (2.28) becomes 

For a system at constant pressure and temperature, we have from Eqs. (2.16) and (2.28) 

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