4: State Functions in Thermodynamics
- Page ID
- 453429
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- 4.1: 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.
- 4.2: 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.
- 4.3: Gibbs Energy Determines the Direction of Spontaneity at Constant Pressure and Temperature
- Gibbs energy is the maximum amount of non-\(PV\) work that can be extracted from a thermodynamically closed system. At constant temperature and pressure, Gibbs energy determines the direction of spontaneous processes, such as chemical reactions.
- 4.4: 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.
- 4.5: Volume Dependence of Helmholtz Energy
- The Helmholtz function changes with changing volume at constant temperature.
- 4.6: 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.
- 4.7: Temperature Dependence of A and G
- The Gibbs-Helmholtz equation can be used to determine how ΔG and ΔA change with changing temperatures.
- 4.8: The Enthalpy of an Ideal Gas is Independent of Pressure
- Ideal gases do not interact with each other (no intermolecular forces), so the enthalpy of an ideal gas is independent of pressure.
- 4.9: 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.