Geol 2312 Igneous and Metamorphic Petrology

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 Chemical Mechanical Thermal Gravitational

STATES OF ENERGYNATURAL 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 ENERGYMEASURE OF THE ENERGY

CONTENT OF A CHEMICAL SYSTEM

All chemical systems tend naturally toward states of minimum Gibbs free energy (G)

G = H - TSG = H - TSWhere:Where:

G = Gibbs Free EnergyG = Gibbs Free Energy

H = Enthalpy (heat content)H = Enthalpy (heat content)

T = Temperature in Kelvins (=T = Temperature in Kelvins (=ooC + 273)C + 273)

S = Entropy (randomness)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

G = (nG)products - (nG)reactants

= 3GD + 2GE - 2GA - GB - GC

If G 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 FORMATIONWith a calorimeter, we can then determine the enthalpy (H-

heat content) for the reaction:

Si (metal) + O2 (gas) = SiO2 H = -910,648 J/molSince the Enthalpy of Si metal and O2 is 0 at the reference state, the value

for H 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

Gof = -856,288 J/mol

DETERMINING THE G OF A PHASE AT ANOTHER TEMPERATURE AND PRESSURE

The differential equation for this is:

ddG = VG = VddP – SP – SddTTAssuming 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:

GGT2 P2T2 P2 - G - GT1 P1T1 P1 = V(P = V(P22 - P - P11) - S (T) - S (T22 - T - T11))

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 REACTIONSOLID LIQUID

Here, X is constant (one comp) so we just have to consider affects of T and P on GddG = VG = VddP – SP – SddTT

We can portray the equilibrium states of this reaction with a phase diagram

What does this say about the G 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 Let’s look at the effects of P and T on G individually 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 P/T = -S Slope S < Slope L

Equilibrium at Teq

GLiq = GSol

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 PORTRAY 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