Ch 05 Thermodynamics.ppt download to score an a

thermodynamics notes

1. Thermodynamics
a system:
Some portion of the universe that you wish to study
The surroundings:
The adjacent part of the universe outside the
system
Changesin a system are associated with the transfer of
energy
Natural systems tend toward states of minimum energy

2. Energy States
Unstable: falling or rolling
Stable: at rest in lowest
energy state
Metastable: in low-energy
perch
Figure 5.1. Stability states. Winter (2001) An Introduction to
Igneous and Metamorphic Petrology. Prentice Hall.

3. Gibbs Free Energy
Gibbs free energy is a measure of chemicalenergy
All chemical systems tend naturally toward states
of minimum Gibbs free energy
G = H -TS
Where:
G = Gibbs Free Energy
H = Enthalpy (heat content)
T = Temperature in Kelvins
S = Entropy (can think of as randomness)

4. Thermodynamics
aPhase:a mechanically separable portion of a system
Mineral
Liquid
Vapor
a Reaction: some change in the nature or types of phases
in a system
reactions are written in the form:
reactants = products

5. Thermodynamics
The change in some property, such as G for a
reaction of the type:
2 A + 3 B = C + 4 D
DG = S(n G)
products-S(n G)
reactants
= G
C+ 4G
D-2G
A-3G
B

6. Thermodynamics
For a phasewe can determine V, T, P, etc., but not G or H
We can only determine changesin G or H as we change
some other parameters of the system
Example: measure DH for a reaction by calorimetry -the heat
given off or absorbed as a reaction proceeds
Arbitraryreference stateand assign an equally arbitrary
value of H to it:
Choose298.15 K and 0.1 MPa(lab conditions)
...and assignH = 0 for pure elements(in their natural
state -gas, liquid, solid) at that reference

7. Thermodynamics
In our calorimeter we can then determine DH for the reaction:
Si (metal) + O
2(gas) = SiO
2 DH = -910,648 J/mol
= molar enthalpy of formationof quartz (at 298, 0.1)
It serves quite well for a standard value of H for the phase
Entropyhas a more universal reference state: entropy of every
substance = 0 at 0K, so we use that (and adjust for temperature)
Then we can use G = H -TSto determine G of quartz
= -856,288 J/mol

8. Thermodynamics
For other temperatures and pressures we can use the
equation:
dG = VdP –SdT(ignoring DX for now)
where V = volume and S = entropy (both molar)
We can use this equation to calculate G for any phase at
any T and P by integrating
zzG G VdP SdT
TP TP
T
T
P
P
2 11
1
2
1
2
2
- = -

9. Thermodynamics
If V and S are constants, our equation reduces to:
G
T
2
P
2
-G
T
1
P
1
= V(P
2-P
1) -S (T
2-T
1)
which ain’t bad!

10. Thermodynamics
In Worked Example 1 we used
G
T
2
P
2
-G
T
1
P
1
= V(P
2-P
1) -S (T
2-T
1)
and G
298, 0.1= -856,288 J/mol to calculate G for quartz at several
temperatures and pressures
Low quartz Eq. 1 SUPCRT
P (MPa) T (C)G (J) eq. 1G(J) V (cm3)S (J/K)
0.1 25 -856,288-856,64822.69 41.36
500 25 -844,946-845,36222.44 40.73
0.1 500 -875,982-890,60123.26 96.99
500 500 -864,640-879,01423.07 96.36
Agreement is quite good
(< 2% for change of 500
o
and 500 MPa or 17 km)

11. Thermodynamics
Summary thus far:
G is a measure of relative chemical stability for a phase
We can determine G for any phase by measuring H and S for
the reaction creating the phase from the elements
We can then determine G at any T and P mathematically
Most accurate if know how V and S vary with P and T
•dV/dP is the coefficient of isothermal compressibility
•dS/dT is the heat capacity (Cp)
Use?
If we know G for various phases, we can determine which is
most stable
Why is melt more stable than solids at high T?
Is diamond or graphite stable at 150 km depth?
What will be the effect of increased P on melting?

12. Does the liquid or
solid have the larger
volume?
High pressure favors
low volume, so which
phase should be stable
at high P?
Does liquid or solid have a
higher entropy?
High temperature favors
randomness, so which
phase should be stable at
higher T?
We can thus predict that the slope
of solid-liquid equilibrium should
be positive and that increased
pressure raises the melting point.
Figure 5.2.Schematic P-T phase diagram of a melting reaction.
Winter (2001) An Introduction to Igneous and Metamorphic
Petrology. Prentice Hall.

13. Does the liquid or solid
have the lowest G at
point A?
What about at pointB?
The phase assemblage with the lowest G under a specific set of
conditions is the most stable
Figure 5-2. Schematic P-T phase diagram of a melting reaction.
Winter (2001) An Introduction to Igneous and Metamorphic
Petrology. Prentice Hall.

14. Free Energy vs. Temperature
dG = VdP -SdT at constant pressure:dG/dT = -S
Because S must be (+)G for a phase decreases as T
increases
Would the slope for the
liquid be steeper or
shallower than that for
the solid?
Figure 5.3. Relationship between Gibbs free energy and temperature
for a solid at constant pressure. T
eq
is the equilibrium temperature.
Winter (2001) An Introduction to Igneous and Metamorphic
Petrology. Prentice Hall.

15. Free Energy vs. Temperature
Slope of G
Liq> G
sol since
S
solid< S
liquid
A:Solid more stable than
liquid (low T)
B:Liquid more stable than
solid (high T)
Slope dP/dT = -S
Slope S < Slope L
Equilibriumat T
eq
G
Liq= G
Sol
Figure 5.3. Relationship between Gibbs free energy and temperature
for the solid and liquid forms of a substance at constant pressure. T
eq
is the equilibrium temperature. Winter (2001) An Introduction to
Igneous and Metamorphic Petrology. Prentice Hall.

16. Now consider a reaction, we can then use the equation:
dDG = DVdP -DSdT (again ignoring DX)
For a reaction of melting (like ice water)
DV is the volume change involved in the reaction (V
water-V
ice)
similarly DS and DG are the entropy and free energy changes
dDG is then the change in DG as T and P are varied
DG is (+) for S L at point A (G
S< G
L)
DG is (-) for S L at point B (G
S> G
L)
DG = 0 for S L at point x (G
S= G
L)
DG for any reaction = 0 at equilibrium

17. Pick any two points on the equilibrium curve
DG = ? at each
Therefore dDG from point X to point Y = 0 -0 = 0
dDG = 0 = DVdP -DSdT
X
Y
dP
dT
DS
=
DV

18. Figures I don’t use in class
Figure 5.4. Relationship between Gibbs free energy and pressure for
the solid and liquid forms of a substance at constant temperature.
P
eq
is the equilibrium pressure. Winter (2001) An Introduction to
Igneous and Metamorphic Petrology. Prentice Hall.

19. Figures I don’t use in class
Figure 5.5. Piston-and-cylinder apparatus to compress a gas. Winter
(2001) An Introduction to Igneous and Metamorphic Petrology. Prentice
Hall.