## Learning Objectives

After mastering the material presented in this chapter, one will be able to:

- Define the free energy functions \(A\) and \(G\), and relate changes in these functions to the spontaneity of a given process and constant volume and pressure respectively.
- Use the definitions of entropy and reversible work of expansion to write an equation that combines the first and second laws of thermodynamics.
- Utilize the combined first and second law relationship to derive Maxwell Relations stemming from the definitions of \(U\), \(H\), \(A\), and \(G\).
- Utilize the Maxwell Relations to derive expressions that govern changes in thermodynamic variable as systems move along specified pathways (such as constant temperature, pressure, volume, or adiabatic pathways.)
- Derive and utilize an expression describing the volume dependence of \(A\).
- Derive and utilize an expression describing the pressure dependence of \(G\).
- Derive and utilize expressions that describe the temperature, dependence of \(A\) and \(G\).
- Derive an expression for, and evaluate the difference between \(C_p\) and \(C_V\) for any substance, in terms of \(T\), \(V\), \(\alpha\), and \(\kappa_T\).