Response to the comments by Prof. Swendsen on “Concepts against mathematics: self-inconsistency in thermodynamic evaluations”

Abstract

The Comments declare that ‘‘Thermodynamics is mathematically rigorous and its predictions are unique’’. Such a statement must be supported by rigorous mathematic operations. Surprisingly, the mathematical transformations in the ‘‘Comments’’ are incorrect and the comments on the transformations more damage thermodynamics than defend it. To explain the damage and mathematical tricks in the ‘‘Comments’’, we have to remind basic equations of thermodynamics. Thermodynamics operates with four energies (U is the internal energy, H is the enthalpy, G is the Gibbs energy, and F is the Helmholtz energy) and four variables (T is the temperature, S is the entropy, P is the pressure, and V is the volume). The functions relate with one another according to equations U 1⁄4 F þ TS ð1aÞ H 1⁄4 U þ PV ð1bÞ G 1⁄4 H TS ð1cÞ F 1⁄4 G PV : ð1dÞ