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Clapeyron and Ehrenfest Equations and Hyper-free Energy for Partly Open Systems

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23640%2F17%3A43950599" target="_blank" >RIV/49777513:23640/17:43950599 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.1007/978-3-319-45899-1_7" target="_blank" >http://dx.doi.org/10.1007/978-3-319-45899-1_7</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/978-3-319-45899-1_7" target="_blank" >10.1007/978-3-319-45899-1_7</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Clapeyron and Ehrenfest Equations and Hyper-free Energy for Partly Open Systems

  • Original language description

    Following the approach applied by Clapeyron to describe sharp phase transitions in P-T diagrams of unary systems as well as that used by Ehrenfest for so-called second-order phase transitions, we derived a set of analogous equations for partly open binary and higher-order systems. These systems share one or more components with the surroundings (reservoir), and thus, their content in the system is given by their chemical potentials (activities, af) in the reservoir. Hence, in addition to P-T diagrams, the phase relations can be represented in T–af, P–af, and af–ag phase diagrams and three additional Clapeyronian equations describe the corresponding borderlines delimiting the different phase fields. Moreover, it is shown that Ehrenfest equations cannot be applied for λ-transitions; however, their applicability is demonstrated for so-called partial phase transitions such as liquidus curves in closed binary systems. For partly open systems, 28 new Ehrenfestian equations are derived for partial phase transitions which involve, apart from the changes of heat capacity, thermal expansion and compressibility appearing in the original three Ehrenfest equations, the changes of newly defined quantities such as thermal, pressure, proper, and mutual plutabilities. The Clapeyronian and Ehrenfestian equations derived in this chapter can be useful for equilibrium studies and construction of thermodynamic models of nonstoichiometric phases as well as for the construction of simple phase diagrams reflecting the equilibrium phase relations under a given controlled atmosphere.

  • Czech name

  • Czech description

Classification

  • Type

    C - Chapter in a specialist book

  • CEP classification

  • OECD FORD branch

    20303 - Thermodynamics

Result continuities

  • Project

    <a href="/en/project/LO1402" target="_blank" >LO1402: CENTEM+</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2017

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Book/collection name

    Thermal Physics and Thermal Analysis

  • ISBN

    978-3-319-45897-7

  • Number of pages of the result

    17

  • Pages from-to

    159-175

  • Number of pages of the book

    567

  • Publisher name

    Springer International Publishing A

  • Place of publication

    Cham, Switzerland

  • UT code for WoS chapter