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Calorimetric test of purity I

Analysis of descriptions of the melting curve dH/dT vs. T

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Abstract

Relationships of various levels for the thermodynamical description of two-component eutectic systems have been investigated. It has been established that the van't Hoff relationship describes the melting curve dH vs. T with satisfactory accuracy, but for its practical application a modification of the mathematical character, maintaining the physical content of the equation, is needed. The interpretation and the mode of application of the modified equation are given.

Résumé

On a examiné diverses corrélations pour décrire des systèmes eutectiques à deux composants. On a établi que la relation de van't Hoff décrit la courbe de fusion dH/dTT avec une exactitude satisfaisante. Cependant, son application pratique exige une modification de caractère mathématique mais celle-ci ne porte pas sur le contenu physique de l'équation. On donne l'interprétation et le mode d'application de l'équation modifiée.

Zusammenfassung

Verschiedene Zusammenhänge zur thermodynamischen Beschreibung eutektischer Zweikomponentensysteme wurden untersucht. Es wurde festgestellt, daß der van't Hoff-sche Zusammenhang die Schmelzkurve dH/dTT mit befriedigender Genauigkeit beschreibt, daß jedoch ihre praktische Anwendung eine Abänderung mathematischen Charakters benötigt, wobei der physikalische Inhalt der Gleichung erhalten bleibt. Deutung und Anwendungsmethode der modifizierten Gleichung werden angegeben.

Резюме

Исследованы взаимос вязи различного уров ня для термодинамическ ого описания двухкомпонентных эв тектических систем. У становлено, что соотношение Вант –Гоффа с удовлетворительно й точностью описывае т кривую плавления dH/dTT, но для практического приме нения требуется видо изменение его математического характера, сохраняя при этом физ ическое содержание у равнения. Представлена интерп ретация и метод применения это го видоизмененного у равнения.

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Abbreviations

1:

Index, symbol of the main component

2:

Index, symbol of the impurity

R :

Gas constant, J/mol K

T :

Equilibrium temperature of the system, K

Ti:

Melting point of thei-th pure component, K

ΔHi:

Change in enthalpy of fusion of thei-th pure component, J/mol

ΔH i 0 :

Change in enthalpy of fusion of thei-th pure component at the melt in point, J/mol

ΔC i 0 :

Difference of specific heat in the solid and molten states of thei-th pure component at the melting point, J/mol K

x i :

Molar fraction of thei-th component in the melt phase

¯x i :

Total molar fraction of thei-th component in the system

f i :

Activity coefficient of thei-th component in the melt phase

F :

Molten fraction, mol/mol

W :

Interaction energy between the two components J/mol

Δh :

Change in enthalpy of fusion of the sample investigated up to temperatureT, J

n :

Quantity of sample investigated, mol

References

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Kiss, G., Seybold, K. & Meisel, T. Calorimetric test of purity I. Journal of Thermal Analysis 21, 49–56 (1981). https://doi.org/10.1007/BF01913699

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