Legendre Transformation (Thermodynamic Potentials)

Given two variables, we can convert a function depending on one variable into another function that depends on another variable using a so called Legendre transformation, and the two variables which are known as conjugate variables. For a function \(f\) of a single variable \(x\) this can be shown to be

\[g(y) = f(x) - x y,\]

where \(y\) is conjugate to \(x\) and g is the Legendre transformation of f.

Links:

1. Wikipedia — Legendre transformation — Thermodynamics

2. Wikipedia — Conjugate variables (thermodynamics)

Contents:

• Enthalpy via Gibbs energy
  • enthalpy
  • temperature
  • pressure
  • gibbs_energy
  • law
• Internal energy via Helmholtz free energy
  • internal_energy
  • temperature
  • volume
  • free_energy
  • law