ABSTRACT
This chapter shows that different fundamental functions and extremum principles are required to define the state of equilibrium, depending on what quantities are known or controlled at the boundaries. Often we can control temperature T, rather than energy U, so the condition for equilibrium is that the free energy is at a minimum. This chapter considers a process inside a test tube, sealed so that it has constant volume V and no interchange of its N particles with the surroundings. A heat bath holds the test tube at constant temperature T. It might vary in rate from a quasi-static process to an explosion. The enthalpy H is a function of the natural variables S, p, and N. Enthalpy is seldom used as an extremum principle, because it is not usually convenient to control the entropy. Heat capacities, which are measurable quantities, can be used to obtain energies, enthalpies, and entropies, which in turn help to predict free energies.
