Lecture 2/3: Phases Equilibria Thermodynamics (Phase and Stability)

Question 1

What is a system (thermo)?

Answer 1

a material with one or more phases (ex: Fe-C alloy)

Question 2

What is a phase (thermo)?

Answer 2

portion of the system whose properties are homogenous (typically atomic structure is the same, such as fcc, bcc, solid/liquid/vapor)

Question 3

what is a component (thermo)?

Answer 3

chemical elements or compounds which make up the system (ex: Fe and C in the Fe-C system)

Question 4

what is a composition (thermo)?

Answer 4

concentration of components in a phase (ex: 99.5 at %Fe and 0.5 %C or wt%)

Question 5

What is U?

Answer 5

U-internal energy

includes both kinetic and potential energy

Question 6

What is H?

Answer 6

H - enthalpy

note the heat absorbed or released under constant pressure is the change of enthalpy

Question 7

What is S?

Answer 7

S- entropy

A measure of the “disorder” of a system. For example, S (gas) > S(liquid) > S (solid) for the same material

Question 8

What is G?

Answer 8

G - gibbs free energy

At constant P and T, the equilibrium state has the lowest G

G = H - TS

Question 9

What must be required with G for a spontaneous change? what is the driving force?

Answer 9

the change of G from the initial state to the final state the change must be negative (initial greater),

change of G is the “driving force”

Question 10

What does a graph of G vs. system configurations look like?

Answer 10

Question 11

According to G = H-TS, what do you need to have the lowest G? Why would you want it?

Answer 11

small H (enthalpy) and high S (entropy)

highest stability

Question 12

How can you calculate G?

Answer 12

calculate H and S from Cp

Question 13

What is the 3rd law of thermodynamics?

Answer 13

S is zero for single element in its perfect stable form at 0K (e: FCC Cu)

Question 14

What reference condition do we use for H and G and why?

Answer 14

they don’t have an absolute 0 value so we need a reference, usually standard condition

298 K
1 atm

Question 15

At constant T & P, which phase is the most stable?

Answer 15

phase with the lowest G

Question 16

How does G behave at transition temperatures?

Answer 16

it’s continuous bc ΔH = TΔS

so they cancel out at the transition temperatures

Question 17

What is the Gibbs Phase Rule?

Answer 17

Question 18

In Gibbs Phase Rule, what does f stand for?

Answer 18

degrees of freedom

Question 19

In Gibbs Phase Rule, what does c stand for

Answer 19

components

Question 20

In Gibbs Phase Rule, what does p stand for?

Answer 20

of phases

Question 21

In Gibbs Phase Rule, what does the 2 represent

Answer 21

P and T

Question 22

At any one point in a one-phase area, what is f?

Answer 22

Question 23

At a point along a two-phase coexistence line, what is f?

Answer 23

Question 24

At a triple point (3-point coexistence), what is f?

Answer 24

Question 25

what is a critical point (f=0)?

Answer 25

beyond which liquid and gas are indistinguishable

Question 26

What is a multi-component system?

Answer 26

related to mixing several components together

Question 27

If mixed completely, what is the product of a multi-component system?

Answer 27

a solution (solid or liquid solution, gas mixture)

Question 28

Can you determine solution properties from the pure components?

Answer 28

NO. they are NOT the sum of the pure components

Question 29

What is G sub i? what is it called?

Answer 29

"the effective Gibbs free energy per mole" the partial molar gibbs free energy of component i called the "chemical potential"

Question 30

What does the bar represent?

Answer 30

a partial molar property

Question 31

How do you calculate the new Gibbs free energy after mixing?

Answer 31

the weighted sum of the partial molar Gibbs free energy/chemical potentials

Question 32

what is ai for pure materials?

Answer 32

ai = 1

Question 33

what is ai for ideal solution?

Answer 33

ai = Xi

Question 34

what is ai for non-ideal solution?

Answer 34

ai = yi*Xi (yi is the activity coefficient)

Question 35

How would you find the total Gibbs after mixing?

Answer 35

adding G unmix + G mix

Question 36

what is the gibbs free energy before mixing

Answer 36

weighted sum of pure components

Question 37

what is the gibbs free energy of mixing?

Answer 37

additional energy due to mixing

Question 38

How would you find the enthalpy of mixing?

Answer 38

delta H is enthalpy of mixing

Question 39

What does it mean if ΔH = 0? ΔH < 0? ΔH >0?

Answer 39

ΔH = 0 - ideal solution - spontaneous random mixing bc ΔG mix <0 ΔH < 0 - non-ideal solution - non-random mixing bc ΔGmix<0 ΔH >0 - non-ideal solution - phase separation below a certain T

Question 40

For an ideal solution, do enthalpy and volume change after mixing?

Answer 40

no. ΔH mix = 0, ΔV mix =0

Question 41

What is mixing driven by for an ideal solution? spontaneous or not?

Answer 41

driven by entropy of mixing it is spontaneous

Question 42

What is the entropy of mixing for an ideal solution? Independent of dependent of T?

Answer 42

independent of T

Question 43

What is the Gibbs free energy of mixing? Independent or dependent of T?

Answer 43

dependent of T

Question 44

What do the graphs of ΔSmix, ΔGmix, ΔVmix, and ΔHmix look like for an ideal solution?

Answer 44

Question 45

What does the phase diagram look like for an ideal solution (ex: Ni-Cu binary system)?

Answer 45

Question 46

Determine the ΔGmix & phase boundaries at T1, T2, and T3.

Answer 46

*closer is more stable = lower * middle is split

Question 47

What is the eutectic temperature?

Answer 47

the lowest melting temperature at any composition -- lower than both pure components

Question 48

At the eutectic point, what happens?

Answer 48

3 phrases coexist f = 0 (for binary system), so it's fixed for the system

Question 49

What doe a eutectic phase diagram look like? where are the liquidus, solidus, and solvus lines?

Answer 49