Geol 2312 Igneous and Metamorphic PetrologyThermodynamics is the study of the relationships between heat, work, and energyStates of Energy Natural systems tend toward states of minimum energyGibbs Free Energy measure of the energy content of a chemical systemEquilibrium of a Chemical ReactionGibbs Free Energy of a Phase at its Reference StateMolar Gibbs Free Energy of FormationDetermining the G of a Phase at another Temperature and PressureGibbs Free Energy for a Reaction Solid LiquidTemperature Effect on Free EnergySlide 11Pressure Effect on Free EnergyPhase diagram portray the Lowest Free Energy Surfaces Projected on to T-P spaceMELTS Determines Phase Equilibrium based on Thermodynamic MeasurementsGEOL 2312 IGNEOUS AND METAMORPHIC PETROLOGYLecture 5Introduction to Thermodynamics Feb. 2, 2009THERMODYNAMICS IS THE STUDY OF THE RELATIONSHIPS BETWEEN HEAT, WORK, AND ENERGYSYSTEM- Some portion of the universe that we wish to studySURROUNDINGS - The adjacent part of the universe outside the systemChanges 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 GravitationalSTATES 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 stateGOOD THING FOR GEOLOGY!Winter (2001), fig. 5-1GIBBS FREE ENERGYMEASURE OF THE ENERGY CONTENT OF A CHEMICAL SYSTEMAll chemical systems tend naturally toward states of minimum Gibbs free energy (G)G = H - TSG = H - TSWhere:Where:G = Gibbs Free EnergyG = Gibbs Free EnergyH = 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 REACTIONPhase - 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 + 2ETo 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 =  (nG)products - (nG)reactants = 3GD + 2GE - 2GA - GB - GCIf G is positive, the reactants are favored; if negative, the products are more stableGIBBS 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/molDETERMINING THE G OF A PHASE AT ANOTHER TEMPERATURE AND PRESSUREThe 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 pressuresLow quartz Eq. 1 SUPCRTP (MPa) T (C) G (J) eq. 1 G(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 96.36GIBBS 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 – SddTTWe can portray the equilibrium states of this reaction with a phase diagramWhat 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 individuallyTEMPERATURE EFFECT ON FREE ENERGYdG = VdP - SdT at constant pressure: dG/dT = -SBecause S must be (+) G for a phase decreases as T increasesWould the slope for the liquid be steeper or shallower than that for the solid?TEMPERATURE EFFECT ON FREE ENERGYSlope of GLiq > Gsol since Ssolid < SliquidA: Solid more stable than liquid (low T)B: Liquid more stable than solid (high T)Slope P/T = -SSlope S < Slope LEquilibrium at TeqGLiq = GSolPRESSURE EFFECT ON FREE ENERGYdG = VdP - SdT at constant temperature: dG/dP = VNote that Slopes are +Why is slope greater for liquid?PHASE DIAGRAM PORTRAY THE LOWEST FREE ENERGY SURFACES PROJECTED ON TO T-P SPACEFrom Philpotts (1990), Fig. 8-2MELTS DETERMINES PHASE EQUILIBRIUM BASED ON THERMODYNAMIC