6.S: Putting the Second Law to Work (Summary)
- Page ID
- 84510
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)
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 \(\kappa_T\).
Vocabulary and Concepts
- free energy
- Gibbs Free Energy
- Gibbs function
- Gibbs-Helmholtz equation
- Helmholtz function
- maximum work
- Maxwell Relation
- standard free energy of formation (\(\Delta G_f^Oo\)