8 - Thermodynamic potentials

Abstract

To understand the behavior of a thermodynamic system when one or more of its intensive parameters are held constant requires forms of the fundamental equation in which one or more of the extensive parameters are replaced by the conjugate intense parameter without loss of information. If these forms of the fundamental equation are derived in the energy representation, they are referred as “alternative thermodynamic potentials.” An alternative thermodynamic potential is a fundamental equation containing one or more intensive parameters as canonical variables. Such a fundamental equation cannot be obtained simply by replacing an extensive parameter by its conjugate intensive parameter. A simple replacement does not turn a fundamental equation into another one. Instead, it produces an equation of state, with an attendant loss of information. This chapter discusses these thermodynamic potentials, their derivation through the use of the Legendre transformation, and their properties. The chapter concludes with a discussion on the Gibbs–Duhem equation and the degrees of freedom of a thermodynamic system.