The Triple Product Rule and the Subtleties of the Mathematical Tools Used in Thermodynamics

Abstract

We have clarified several formulas from mathematics and physics. Specifically, we have shown that several standard concepts from thermodynamics, which have been recently investigated and rejected in some papers, continue to be valid. Thus, we have studied the triple product rule, the first law of thermodynamics, Mayer's relation, work, function of state, the relationship between the coefficient of thermal expansion, coefficient of isothermal compressibility and thermal coefficient of pressure. We have used multivariable calculus and properties of Jacobians and other mathematical tools. Likewise, we have provided several didactic examples concerning the interpretation of thermodynamical and mathematical formulas. We have concluded that the basement of several thermodynamical formulas is correct but full of subtleties. Thus, those formulas continue to be valid despite some claims in the recent literature.