A Margules' Power Series Formula: Deriving Coefficients

AI Thread Summary
Margules proposed a power series formula to describe the activity composition variation in binary systems, represented by lnγ1 and lnγ2 equations. The derivation involves applying the Gibbs-Duhem equation while neglecting higher-order coefficients, leading to specific relationships among the coefficients, such as α1=β1=0 and β2=α2+α3. The discussion seeks clarification on the derivation of these relationships and the implications of ignoring coefficients beyond i=4. Participants also request references for Margules' original work and explanations of the terms used in the formulas. Understanding these concepts is crucial for accurately applying the Margules power series in thermodynamic calculations.
jinayb
Messages
1
Reaction score
0
Margules suggested a power series formula for expressing the activity composition variation of a binary system.
lnγ1=α1x2+(1/2)α2x2^2+(1/3)α3x2^3+...
lnγ2=β1x1+(1/2)β2x1^2+(1/3)β3x1^3+...
Applying the Gibbs-Duhem equation with ignoring coefficients αi's and βi's higher than i=3, we can obtain α1=β1=0, β2=α2+α3, β3=-α3

I don't know how that relationship between coefficients is derived.
Also, what would be the relationship when higher than i=4 is ignored?
Please help!
 
Mathematics news on Phys.org
Could you elaborate a bit? E.g.

a) "Margules suggested ..." where? Reference?
b) Here is explained how you can type formulas on PF: https://www.physicsforums.com/help/latexhelp/
c) "the activity composition variation of a binary system" means what? Forces? Number system?
 
Last edited:

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Hot Threads

Recent Insights

Back
Top