Lecture 4: Thermodynamics continued Flashcards
How would you find the mole fraction of a component B in a B+L phase?
lever rule
In a plot of ΔGmix vs. composition, how would you find the chemical potentials @ at specific composition for single phase (alpha)?
- draw a tangent line where the comp meets alpha
- the intercepts at 0 and 1 comp are the chemical potentials of compo
Does chemical potential change with composition?
yes
What is the notation for chemical potential?
𝜇
sub - component
exponent - phase its in
In a plot of ΔGmix vs. composition 2, how would you find the chemical potentials for the phases (for two phase equilibrium)?
draw the common tangent line between the two phases and extended it to the ends
at 0,
a. μ 1α = μ 1β
b. μ 2α = μ 2β
**so the chem potentials of the same COMPONENT (not phase) are equal
For single phase ΔGmix, how many chemical potentials are there?
2
if phase is alpha–
𝜇 sub 1 ^alpha
𝜇 sub 2 ^alpha
What are four conditions of two-phase equilibrium?
- thermal equilibrium T α = T β
- mechanical equilibrium P α = P β
- chemical equilibrium
a. μ 1α = μ 1β
b. μ 2α = μ 2β - the system energy in α +β region is the common tangent segment (red line)
For an ideal solution phase diagram, explain how to draw the gibbs free energy at temperatures 1 2 and 3
think about putting the phase present at each composition on the bottom on the CURRENT Point of the gibbs diagram
How are gibbs free energy and phase diagrams related?
the system with lowest free energy will be adopted
What is a eutectic phase diagram?
phase diagram where there’s a point where a L transforms into to two solid phases
Which lines are the liquidous, solidus, and solvus?
What is the lowest melting temp at any comp on a eutectic phase diagram?
eutectic temp
What coexists at a eutectic point?
3 phases
What is the degrees of freedom for binary phase diagram?
f = c - p +1 (usually it’s 2),
this is because P is fixed at 1 atm
What are the degrees of freedom at a Eutectic point? Can this change?
f = 2-3+1 = 0
No, it’s fixed for the sysem
At any point in the alpha + beta region of a eutectic phase diagram, what is the composition of each phase?
it’s the same as the solvus boundary @ the temp (the composition of phases are unique and a property of the phase itself, nothing overall)
What happens to the compositions of alpha and beta if your X2 is between the two solvus lines?
The COMPOSITIONS of alpha and beta don’t individually change, but the OVERALL composition changes (phase fraction)
What rule do you use to determine phase fractions?
Lever Rule
How do you find the total Gibb’s free energy at P (a point on a phase diagram @ a temperature T)? How is this denoted?
A weighted sum of the two phases (their phase fractions and individual Gibbs free energies of mixing)
Where is the total Gibbs Free energy at P located?
on the common tangent line
How do you find the phase fractions of alpha and beta?
What does the lever rule determine?
The relative amounts of two phases when the coexist in equlibrium
What is the composition at P denoted by?
What would the material drawing (box with alpha and beta background or circles) look like when P is close to A?
beta circles in alpha background – since the phase fraction of alpha is bigger
