Delicate Balance of Thermodynamic Laws Through Structural Phase Transitions Illustrates the Nature of Entropy and Third Law

In 1865, Clausius—and, some decades later, Planck—established the second law of thermody- namics, which was defined up to an additive constant, without identifying entropy as a measure of disorder. Here, I consider the two important laws of thermodynamics and phase transitions to discuss some important thermodynamic parameters. I use this combined thermodynamic laws to discuss the absolute entropy at 0 K, despite the physical inaccessibility of this limit expressed by the unattainability principle. In Planck’s treatment of gas mixtures, the pdV contribution accounts for entropy changes associated with expansion and links to the entropy of mixing. For the solids considered here, volume changes are negligible, so this term can be omitted; yet another additive constant remains in general formula. Planck fixed the additive entropy constant by choosing a zero- entropy limit for chemically homogeneous substances, while retaining a nonzero mixing contribution at 0 K in his extension to solutions. I demonstrate here that the material-dependent additive con- stant must be considered when comparing the free energies of competing phases through structural phase transitions. I therefore investigate whether the material-dependent additive constant in the entropy can also be explained meaningfully through the analysis of phase transitions. Overall, the entire content of this paper is to address the following: first, grasp the first law; then the second law becomes readable, and finally, the third law, established by Nernst in 1906, can be better ex- amined. Based on the thermodynamic principles established by Clausius and Planck, together with Nernst’s original heat theorem, whose fundamental significance was transparently acknowledged by Planck, the present framework provides a more general ground for understanding phase stability and designing materials with enhanced thermal stability.