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Clapeyron and Ehrenfest equations and hyperfree energy for partly open systems

Identifikátory výsledku

  • Kód výsledku v IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60461373%3A22310%2F18%3A43915518" target="_blank" >RIV/60461373:22310/18:43915518 - isvavai.cz</a>

  • Nalezeny alternativní kódy

    RIV/60461373:22810/18:43915518

  • Výsledek na webu

    <a href="https://link.springer.com/chapter/10.1007/978-3-319-45899-1_7" target="_blank" >https://link.springer.com/chapter/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" target="_blank" >10.1007/978-3-319-45899-1</a>

Alternativní jazyky

  • Jazyk výsledku

    angličtina

  • Název v původním jazyce

    Clapeyron and Ehrenfest equations and hyperfree energy for partly open systems

  • Popis výsledku v původním jazyce

    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, a f) in the reservoir. Hence, in addition to P-T diagrams, the phase relations can be represented in T–a f, P–a f, and a f–a g 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

  • Název v anglickém jazyce

    Clapeyron and Ehrenfest equations and hyperfree energy for partly open systems

  • Popis výsledku anglicky

    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, a f) in the reservoir. Hence, in addition to P-T diagrams, the phase relations can be represented in T–a f, P–a f, and a f–a g 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

Klasifikace

  • Druh

    C - Kapitola v odborné knize

  • CEP obor

  • OECD FORD obor

    10403 - Physical chemistry

Návaznosti výsledku

  • Projekt

  • Návaznosti

    N - Vyzkumna aktivita podporovana z neverejnych zdroju

Ostatní

  • Rok uplatnění

    2018

  • Kód důvěrnosti údajů

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

Údaje specifické pro druh výsledku

  • Název knihy nebo sborníku

    Thermal Physics and Thermal Analysis: From Micro to Macro

  • ISBN

    978-3-319-45899-1

  • Počet stran výsledku

    17

  • Strana od-do

    159-175

  • Počet stran knihy

    585

  • Název nakladatele

    Springer International Publishing Switzerland

  • Místo vydání

    Cham

  • Kód UT WoS kapitoly