GEOL 2312
IGNEOUS AND METAMORPHIC
PETROLOGY
Lecture 5
Introduction to Thermodynamics
Feb. 2, 2009
THERMODYNAMICS IS THE STUDY OF THE
RELATIONSHIPS BETWEEN HEAT, WORK, AND ENERGY
SYSTEM- Some portion of the universe that we wish to study
SURROUNDINGS - The adjacent part of the universe outside the
system
Changes in a system are associated with the transfer of energy from
one form to another
Energy of a system can be lost or gained from its surroundings, but
collectively energy is conserved.
Types of Energy include:
Potential
Kinetic
Thermal
Gravitational
Chemical
Mechanical
STATES OF ENERGY
NATURAL SYSTEMS TEND TOWARD STATES
OF MINIMUM ENERGY
Stable – at minimum
energy state
 Unstable – energy
state in flux
(disequilibrium)
 Metastable –
temporary energy
state that is not
lowest, but requires
energy to push it to
lower energy state
GOOD THING FOR
GEOLOGY!

Winter (2001), fig. 5-1
GIBBS FREE ENERGY
MEASURE OF THE ENERGY CONTENT OF
A CHEMICAL SYSTEM
All chemical systems tend naturally toward states of
minimum Gibbs free energy (G)
G = H - TS
Where:
G = Gibbs Free Energy
H = Enthalpy (heat content)
T = Temperature in Kelvins (=oC + 273)
S = Entropy (randomness)
Basically, Gibbs free energy parameter allows us to predict the
equilibrium phases of a chemical system under particular
conditions of pressure (P), temperature (T), and composition (X)
EQUILIBRIUM OF A CHEMICAL REACTION
Phase - a mechanically separable portion of a system
(e.g., Mineral, Liquid, Vapor)
Reaction - some change in the nature or types of phases
in a system. Written in the form:
Reactants
Products
e.g. 2A + B + C = 3D + 2E
To know whether the products or reactants will be favored (under
particular conditions of T, P, and X, we need to know the Gibbs free energy
of the product phases and the reaction phases at those conditions
DG = S (n*G)products - S(n*G)reactants
= 3GD + 2GE - 2GA - GB - GC
If DG is positive, the reactants are favored;
if negative, the products are more stable
GIBBS FREE ENERGY OF A PHASE
AT ITS REFERENCE STATE

It is not possible to measure the absolute chemical
energy of a phase. We can measure changes in the
energy state of a phase as conditions (T,P,X) change.
Therefore, we must define a reference state against
which we compare other states.
The most common reference state is to consider the
stable form of pure elements at “room conditions”
(T=25oC (298oK) and P = 1 atm (0.1 MPa)) as having
G=0 joules.
 Because G and H are extensive variables (i.e.
dependent on the volume of material present), we
express the G of any phase as based on a quantity of
1 mole (called the molar Gibbs free energy).

MOLAR GIBBS FREE ENERGY OF FORMATION
With a calorimeter, we can then determine the enthalpy (Hheat content) for the reaction:
Si (metal) + O2 (gas) = SiO2
DH = -910,648 J/mol
Since the Enthalpy of Si metal and O2 is 0 at the reference state, the value
for DH of this reaction measures is the molar enthalpy of formation of
quartz at 298 K, 0.1MPa.
Entropy (S) has a more universal reference state: entropy of every
substance = 0 at 0 oK, so we use that (and adjust for temperature)
Then we can use G = H - TS to determine molar Gibbs
free energy of formation of quartz at it reference state
DGof = -856,288 J/mol
DETERMINING THE G OF A PHASE
AT ANOTHER TEMPERATURE AND PRESSURE
The differential equation for this is:
dG = VdP – SdT
V/dP – isothermal compressibility
S = Cp/T, Cp – heat capacity
(heat required to raise 1 mole of substance 1°C)
Assuming V and S do not change much in a solid over the T and P of interest,
this can be reduced to an algebraic expression:
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. 1
G(J)
V (cm3)
S (J/K)
0.1
25
-856,288
-856,648
22.69
41.36
500
25
-844,946
-845,362
22.44
40.73
0.1
500
-875,982
-890,601
23.26
96.99
500
500
-864,640
-879,014
23.07
96.36
GIBBS FREE ENERGY FOR A REACTION
SOLID
LIQUID
Here, X is constant (one comp)
so we just have to consider
affects of T and P on G
dG = VdP – SdT
We can portray the equilibrium
states of this reaction with a
phase diagram
What does this say about the DG of
the reaction at Points A, X, and B?
High temperature favors
randomness, so which phase
should be stable at higher T?
High pressure favors low volume,
so which phase should be stable at
high P?
Let’s look at the effects of P and T
on G individually
TEMPERATURE EFFECT ON FREE ENERGY
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?
TEMPERATURE EFFECT ON FREE ENERGY
Slope of GLiq > Gsol since Ssolid < Sliquid
A: Solid more stable than liquid (low T)
B: Liquid more stable than solid (high T)
Slope dP/dT = -S
 Slope S < Slope L

Equilibrium at Teq
GLiq = Gsol
= crystallization/melting
temperature
PRESSURE EFFECT ON FREE ENERGY
dG = VdP - SdT
at constant temperature: dG/dP = V
Note that Slopes are +
Why is slope greater for liquid?
PHASE DIAGRAM PORTRAYS THE LOWEST FREE
ENERGY SURFACES PROJECTED ON TO T-P SPACE
From Philpotts (1990), Fig. 8-2
MELTS
DETERMINES PHASE EQUILIBRIUM BASED ON
THERMODYNAMIC MEASUREMENTS
PELE – MELT FOR PC USE
A. BOUDREAU 2002