Relationship Between Free Energy and Work

Under certain p, V, T conditions we can relate the Helmholtz free energy and the Gibbs free energy to work done in the process. To find the relationship between dA and 6u, we write 

1 Errors can become especially large when derivatives of equations of state are involved, as is the case in this derivation. 

in an isothermal reversible process, dA equals the reversible work. Note that 5vr in equation (3.92) is the total work. It includes pressure-volume work and any other forms, if present. 1 

A relationship between dG and work can also be obtained. To do so we divide the work for a reversible process into pressure-volume work (—p dV) and 8w, the work other than pressure-volume work that may occur, and write 

in a reversible process that is both isothermal and isobaric, dG equals the work other than pressure-volume work that occurs in the process. Equation (3.96) is important in chemistry, since chemical processes such as chemical reactions or phase changes, occur at constant temperature and constant pressure. Equation (3.96) enables one to calculate work, other than pressure-volume work, for these processes. Conversely, it provides a method for incorporating the variables used to calculate these forms of work into the thermodynamic equations. 

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