Thermodynamics MOC

Thermodynamic potential

A thermodynamic potential is an extensive quantity which is naturally¹ a function of the natural² independent variables and whose minimization or maximization follows from the ^P4 when these independent variables are held constant.

Equations of state

To show that a quantity 𝑀 is naturally a function of parameters (𝑥𝑖)𝑛𝑖=1, one takes the Exterior derivative 𝑑𝑀 and shows 𝑑𝑀 =∑𝑛𝑖=1𝑓𝑖𝑑𝑥𝑖, where 𝑓𝑖 are 0-forms. One then arrives at the equations of state

𝜕𝑀𝜕𝑥𝑖=𝑓𝑖

Examples

• Entropy
• Helmholtz free energy
• Gibbs free energy
• Enthalpy
• Landau free energy

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tidy | en | SemBr

Footnotes

1. i.e. by the First law of thermodynamics. ↩

2. a natural choice of variables for the situation at hand, i.e. the intensive or extensive parameters that can be controlled directly. ↩