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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Clapeyron and Ehrenfest Equations and Hyper-free 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, 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.

Název v anglickém jazyce

Clapeyron and Ehrenfest Equations and Hyper-free 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, 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.

Druh

C - Kapitola v odborné knize

CEP obor

—

OECD FORD obor

20303 - Thermodynamics

Projekt

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

Návaznosti

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

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název knihy nebo sborníku

Thermal Physics and Thermal Analysis

ISBN

978-3-319-45897-7

Počet stran výsledku

17

Strana od-do

159-175

Počet stran knihy

567

Název nakladatele

Springer International Publishing A

Místo vydání

Cham, Switzerland

Kód UT WoS kapitoly

—