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On Existence of Reversible Adiabatic Surfaces
Author(s) -
Dutta M.
Publication year - 1969
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19694770702
Subject(s) - disjoint sets , adiabatic process , equivalence relation , hausdorff space , mathematics , pure mathematics , manifold (fluid mechanics) , space (punctuation) , equivalence (formal languages) , closed set , physics , mathematical analysis , quantum mechanics , computer science , mechanical engineering , engineering , operating system
From the notion of equivalence relation and classes induced by them, the sets of points related by reversible processes restricted suitably are shown to be disjoint. By definition, each of thr above sets is arcwise‐connected and so connected by HAUSDORFF'S theorem. Adiabatic processes are defined to be those in which, changes of states of a system are entirely by changing the deformation coordinates. First and second laws of thermodynamics are introduced just after CARATHÉODORY. Then by arguments of abstract mathematics every points in an r. a. set in an ( n + 1)‐dimensional space has been shown to gave a neighbourhood homeomorphics to a n ‐dimensional sphere, i. e., an r. a. set is an n ‐dimensional manifold having one‐to‐one correspondence with the deformation space. Thus, the existance of reversible adiabatic surfaces has been established.