Ch 05 Thermodynamics
Transcript of Ch 05 Thermodynamics
ThermodynamicsThermodynamics a system:
Some portion of the universe that you wish to study
The surroundings:The adjacent part of the universe outside the system
Changes in a system are associated with the transfer of energy
Natural systems tend toward states of minimum energy
Energy StatesEnergy 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.
Gibbs Free EnergyGibbs Free EnergyGibbs free energy is a measure of chemical energy
All chemical systems tend naturally toward states of minimum Gibbs free energy
G = H - TSWhere:
G = Gibbs Free EnergyH = Enthalpy (heat content)T = Temperature in KelvinsS = Entropy (can think of as randomness)
ThermodynamicsThermodynamicsa Phase: 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
ThermodynamicsThermodynamicsThe change in some property, such as G for a reaction of the type:
2 A + 3 B = C + 4 DG = (n G)products - (n G)reactants
= GC + 4GD - 2GA - 3GB
ThermodynamicsThermodynamicsFor a phase we can determine V, T, P, etc., but not G or H
We can only determine changes in G or H as we change some other parameters of the systemExample: measure H for a reaction by
calorimetry - the heat given off or absorbed as a reaction proceeds
Arbitrary reference state and assign an equally arbitrary value of H to it: Choose 298.15 K and 0.1 MPa (lab conditions)
...and assign H = 0 for pure elements (in their natural state - gas, liquid, solid) at that reference
ThermodynamicsThermodynamicsIn our calorimeter we can then determine H for the reaction:
Si (metal) + O2 (gas) = SiO2 H = -910,648 J/mol
= molar enthalpy of formation of quartz (at 298, 0.1)
It serves quite well for a standard value of H for the phaseEntropy has 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 - TS to determine G of quartz
= -856,288 J/mol
ThermodynamicsThermodynamicsFor other temperatures and pressures we can use the equation:
dG = VdP – SdT (ignoring X 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 SdTT P T P T
T
P
P
2 1 11
2
1
2
2
ThermodynamicsThermodynamicsIf V and S are constants, our equation reduces to:
GT2 P2 - GT1 P1 = V(P2 - P1) - S (T2 - T1)
which ain’t bad!
ThermodynamicsThermodynamicsIn Worked Example 1 we used
GT2 P2 - GT1 P1 = V(P2 - P1) - S (T2 - T1)and G298, 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 -856,648 22.69 41.36500 25 -844,946 -845,362 22.44 40.730.1 500 -875,982 -890,601 23.26 96.99500 500 -864,640 -879,014 23.07 96.36
Agreement is quite good (< 2% for change of 500o and 500 MPa or 17 km)
ThermodynamicsThermodynamicsSummary 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?
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.
Does the liquid or solid have the lowest G at point A?
What about at point B?
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.
Free Energy vs. Free Energy vs. TemperatureTemperature
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. Teq is the equilibrium temperature. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Free Energy vs. Free Energy vs. TemperatureTemperature
Slope of GLiq > Gsol
since Ssolid < Sliquid
A: Solid more stable than liquid (low T)
B: Liquid more stable than solid (high T) Slope P/T = -S Slope S < Slope L
Equilibrium at Teq GLiq = GSol
Figure 5.3. Relationship between Gibbs free energy and temperature for the solid and liquid forms of a substance at constant pressure. Teq is the equilibrium temperature. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Now consider a reaction, we can then use the equation:
dG = VdP - SdT(again ignoring X)For a reaction of melting (like ice water)
V is the volume change involved in the reaction (Vwater - Vice)
similarly S and G are the entropy and free energy changesdG is then the change in G as T and P are
varied G is (+) for S L at point A (GS < GL) G is (-) for S L at point B (GS > GL) G = 0 for S L at point x (GS = GL)
G for any reaction = 0 at equilibrium
Pick any two points on the equilibrium curve G = ? at each Therefore dG from point X to point Y = 0 - 0 = 0
dG = 0 = VdP - SdT
X
Y
dPdT
SV
Figures I don’t use in Figures I don’t use in classclass
Figure 5.4. Relationship between Gibbs free energy and pressure for the solid and liquid forms of a substance at constant temperature. Peq is the equilibrium pressure. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.