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Thermodynamic stability criterion for pure substances and mixtures
Author(s) -
Beegle Bruce L.,
Modell Michael,
Reid Robert C.
Publication year - 1974
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690200621
Subject(s) - simple (philosophy) , limit (mathematics) , stability (learning theory) , mathematics , thermodynamics , legendre transformation , function (biology) , legendre polynomials , partial derivative , derivative (finance) , mathematical analysis , physics , computer science , philosophy , epistemology , machine learning , evolutionary biology , biology , financial economics , economics
Criteria are derived to specify the limit of stability for pure material and multicomponent thermodynamic systems. Through the use of Legendre transforms, the criteria may be expressed in a very simple form that only involves the determination of positiveness of a single second‐order partial derivative of a potential function. Alternate and equivalent criteria are shown to result from a simple reordering of the independent variables in the Fundamental Equation of Gibbs. Certain criteria that are often stated as necessary conditions of stability (for example, C v > 0 ) are shown to be insufficient for specifying the limit of stability; that is, a system will always become unstable for other reasons before C b can attain a negative value.