# 22: Helmholtz and Gibbs Energies

- Page ID
- 62256

- 22.1: Helmholtz Energy
- Above we have answered the question: what is entropy really, but we still do not have a general criterion for spontaneity, just one that works in an isolated system. Let's fix that now. It leads to two new state functions that prove to be most useful ones of thermodynamics.

- 22.3: The Maxwell Relations
- To fully exploit the power of the state functions we need to develop some mathematical machinery by considering a number of partial derivatives.

- 22.4: The Enthalpy of an Ideal Gas
- The enthalpy of an ideal Gas Is independent of pressure.

- 22.5: Thermodynamic Functions have Natural Variables
- The fundamental thermodynamic equations follow from five primary thermodynamic definitions and describe internal energy, enthalpy, Helmholtz energy, and Gibbs energy in terms of their natural variables. Here they will be presented in their differential forms.

- 22.7: The Gibbs-Helmholtz Equation
- The first order partial on G versus P is the volume V; this allows us to find the dependence of G on P by simply integrating over the volume V from one pressure to the other.