# 6: Putting the Second Law to Work

- Page ID
- 84329

- 6.1: Free Energy Functions
- In the previous chapter, we saw that for a spontaneous process, ΔS for the universe > 0. While this is a useful criterion for determining whether or not a process is spontaneous, it is rather cumbersome, as it requires one to calculate not only the entropy change for the system, but also that of the surroundings. It would be much more convenient if there was a single criterion that would do the job and focus only on the system. As it turns out, there is by introducing Free Energies.

- 6.2: Combining the First and Second Laws - Maxwell's Relations
- Modeling the dependence of the Gibbs and Helmholtz functions behave with varying temperature, pressure, and volume is fundamentally useful. But in order to do that, a little bit more development is necessary.

- 6.3: ΔA, ΔG, and Maximum Work
- The functions A and G are oftentimes referred to as free energy functions. The reason for this is that they are a measure of the maximum work (in the case of ΔA ) or non p-V work (in the case of ΔG ) that is available from a process.

- 6.4: Volume Dependence of Helmholtz Energy
- The Helmholtz function changes with changing volume at constant temperature.

- 6.5: Pressure Dependence of Gibbs Energy
- The pressure and temperature dependence of G is also easy to describe. Specifically the pressure dependence of G is given by the pressure derivative at constant temperature.

- 6.6: Temperature Dependence of A and G
- The Gibbs-Helmholtz equation can be used to determine how ΔG and ΔA change with changing temperatures.

- 6.7: When Two Variables Change at Once
- So far, we have derived a number of expressions and developed methods for evaluating how thermodynamic variables change as one variable changes while holding the rest constant. But real systems are seldom this accommodating. If the change in a thermodynamic variable (such as G) is needed, contributions from both changes are required to be taken into account. We’ve already seen how to express this in terms of a total differential.

- 6.8: The Difference between Cp and Cv
- Constant volume and constant pressure heat capacities are very important in the calculation of many changes. The ratio Cp/CV=γ appears in many expressions as well (such as the relationship between pressure and volume along an adiabatic expansion.) It would be useful to derive an expression for the difference Cp–CV as well. As it turns out, this difference is expressible in terms of measureable physical properties of a substance.

- 6.E: Putting the Second Law to Work (Exercises)
- Exercises for Chapter 6 "Putting the Second Law to Work" in Fleming's Physical Chemistry Textmap.

- 6.S: Putting the Second Law to Work (Summary)
- Summary for Chapter 6 "Putting the Second Law to Work" in Fleming's Physical Chemistry Textmap.

## Contributors and Attributions

Patrick E. Fleming (Department of Chemistry and Biochemistry; California State University, East Bay)