dorsal/arxiv
View SchemaNotes on the Third Law of Thermodynamics.I
| Authors | F. Belgiorno |
|---|---|
| Categories | |
| ArXiv ID | physics/0210037 |
| URL | https://arxiv.org/abs/physics/0210037 |
| DOI | 10.1088/0305-4470/36/30/301 |
Abstract
We analyze some aspects of the third law of thermodynamics. We first review both the entropic version (N) and the unattainability version (U) and the relation occurring between them. Then, we heuristically interpret (N) as a continuity boundary condition for thermodynamics at the boundary T=0 of the thermodynamic domain. On a rigorous mathematical footing, we discuss the third law both in Carath\'eodory's approach and in Gibbs' one. Carath\'eodory's approach is fundamental in order to understand the nature of the surface T=0. In fact, in this approach, under suitable mathematical conditions, T=0 appears as a leaf of the foliation of the thermodynamic manifold associated with the non-singular integrable Pfaffian form $\delta Q_{rev}$. Being a leaf, it cannot intersect any other leaf $S=$ const. of the foliation. We show that (N) is equivalent to the requirement that T=0 is a leaf. In Gibbs' approach, the peculiar nature of T=0 appears to be less evident because the existence of the entropy is a postulate; nevertheless, it is still possible to conclude that the lowest value of the entropy has to belong to the boundary of the convex set where the function is defined.
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"abstract": "We analyze some aspects of the third law of thermodynamics. We first review\nboth the entropic version (N) and the unattainability version (U) and the\nrelation occurring between them. Then, we heuristically interpret (N) as a\ncontinuity boundary condition for thermodynamics at the boundary T=0 of the\nthermodynamic domain. On a rigorous mathematical footing, we discuss the third\nlaw both in Carath\\\u0027eodory\u0027s approach and in Gibbs\u0027 one. Carath\\\u0027eodory\u0027s\napproach is fundamental in order to understand the nature of the surface T=0.\nIn fact, in this approach, under suitable mathematical conditions, T=0 appears\nas a leaf of the foliation of the thermodynamic manifold associated with the\nnon-singular integrable Pfaffian form $\\delta Q_{rev}$. Being a leaf, it cannot\nintersect any other leaf $S=$ const. of the foliation. We show that (N) is\nequivalent to the requirement that T=0 is a leaf. In Gibbs\u0027 approach, the\npeculiar nature of T=0 appears to be less evident because the existence of the\nentropy is a postulate; nevertheless, it is still possible to conclude that the\nlowest value of the entropy has to belong to the boundary of the convex set\nwhere the function is defined.",
"arxiv_id": "physics/0210037",
"authors": [
"F. Belgiorno"
],
"categories": [
"physics.gen-ph"
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"doi": "10.1088/0305-4470/36/30/301",
"title": "Notes on the Third Law of Thermodynamics.I",
"url": "https://arxiv.org/abs/physics/0210037"
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