The Use of the Legendre Transform in Chemical Thermodynamics: A Powerful Tool

This article highlights the importance of the Legendre transform (LT) in thermodynamics, demonstrating its role in replacing nonmeasurable variables, such as entropy, with experimentally accessible coordinates. Despite its essential nature, the LT is rarely covered in Physical Chemistry textbooks, a gap noted in the literature as well. The article clarifies the LT, applies it in detail to Thermodynamics, discusses its connection to the extensiveness of internal energy, and proposes a mnemonic rule for obtaining the differential forms of thermodynamic potentials from the Gibbs equation. It is also shown that the total LT of an extensive function is zero, which leads to Euler's relation and reinforces the relevance of including the topic in teaching materials.