ABSTRACT
This chapter constructs thermodynamic potentials that are suited for systems that exchange energy with their surroundings, building on the second law and the Clausius inequality. Of particular importance, the Gibbs free energy will be developed as a transform of the Clausius inequality, and will be shown to serve as the thermodynamic potential when pressure and temperature are held constant. Systems at constant temperature and pressure are common in the laboratory, and in much of biology. The chapter modifies our entropy potential so that it implicitly keeps track of exchanges with the surroundings, while directly focusing on the variables of the system. It illustrates the internal energy potential by deriving an expression for the internal energy of a monatomic ideal gas in terms of S and V. The chapter develops a formalism that represents the thermodynamic contributions of each component, and combines each of these contributions to give the thermodynamics of the whole system.
