Thermodynamics培训课件.ppt.ppt

ThermodynamicsBegin with a brief review of Chapter 5Natural systems tend toward states of minimum energyEnergy States Unstable: falling or rollinglStable: at rest in lowest energy statelMetastable: in low-energy perchFigure 5.1. Stability states. Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Gibbs Free EnergyGibbs free energy is a measure of chemical energyGibbs free energy for a phase:G = H - TSWhere:G = Gibbs Free EnergyH = Enthalpy (heat content)T = Temperature in KelvinsS = Entropy (can think of as randomness)ThermodynamicsDG for a reaction of the type:2 A + 3 B = C + 4 DDG = S (n G)products - S(n G)reactants = GC + 4GD - 2GA - 3GBThe side of the reaction with lower G will be more stableThermodynamicsFor 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 integratingzzGGVdPSdTT PT PTTPP21112122-=-If V and S are constants, our equation reduces to:GT2 P2 - GT1 P1 = V(P2 - P1) - S (T2 - T1)Now consider a reaction, we can then use the equation:dDG = DVdP - DSdT(again ignoring DX)D DG for any reaction = 0 at equilibriumWorked Problem #2 used: dDG = DVdP - DSdT and G, S, V values for albite, jadeite and quartz to calculate the conditions for which DG of the reaction: Ab + Jd = Q is equal to 0lfrom G values for each phase at 298K and 0.1 MPa calculate DG298, 0.1 for the reaction, do the same for DV and DSlDG at equilibrium = 0, so we can calculate an isobaric change in T that would be required to bring DG298, 0.1 to 00 - DG298, 0.1 = -DS (Teq - 298)(at constant P)lSimilarly we could calculate an isothermal change0 - DG298, 0.1 = -DV (Peq - 0.1)(at constant T)MineralS(J)G (J)V (cm3/mol) Low Albite207.25-3,710,085100.07 Jadeite133.53-2,844,15760.04 Quartz41.36-856,64822.688From Helgeson et al. (1978).Table 27-1. Thermodynamic Data at 298K and0.1 MPa from the SUPCRT DatabaseMethod:NaAlSi3O8 = NaAlSi2O6 + SiO2P - T phase diagram of the equilibrium curveHow do you know which side has which phases?Figure 27.1. Temperature-pressure phase diagram for the reaction: Albite = Jadeite + Quartz calculated using the program TWQ of Berman (1988, 1990, 1991). Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. pick any two points on the equilibrium curvedDG = 0 = DVdP - DSdTThusdPdTSV=DDFigure 27.1. Temperature-pressure phase diagram for the reaction: Albite = Jadeite + Quartz calculated using the program TWQ of Berman (1988, 1990, 1991). Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Return to dG = VdP - SdT, for an isothermal process:GGVdPPPPP2112-=zFor solids it was fine to ignore V as f(P)For gases this assumption is shittyYou can imagine how a gas compresses as P increasesHow can we define the relationship between V and P for a gas?Gas Pressure-Volume RelationshipsIdeal Gas As P increases V decreases PV=nRT Ideal Gas Law P = pressure V = volume T = temperature n = # of moles of gas R = gas constant = 8.3144 J mol-1 K-1P x V is a constant at constant TFigure 5.5. Piston-and-cylinder apparatus to compress a gas. Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Gas Pressure-Volume RelationshipsSince we can substitute RT/P for V (for a single mole of gas), thus:and, since R and T are certainly independent of P:GGVdPPPPP2112-=zGGRTPdPPPPP2112-=zzGGRTPdPPPPP2112-=1Gas Pressure-Volume RelationshipsAnd sinceGP2 - GP1 = RT ln P2 - ln P1 = RT ln (P2/P1)Thus the free energy of a gas phase at a specific P and T, when referenced to a standard atate of 0.1 MPa becomes: GP, T - GT = RT ln (P/Po)G of a gas at some P and T = G in the reference state (same T and 0.1 MPa) + a pressure term1xdxx=zlnoGas Pressure-Volume RelationshipsThe form of this equation is very useful GP, T - GT = RT ln (P/Po)For a non-ideal gas (more geologically appropriate) the same form is used, but we substitute fugacity ( f ) for Pwhere f = gPg is the fugacity coefficientTables of fugacity coefficients for common gases are availableAt low pressures most gases are ideal, but at high P they are notoDehydration Reactions Mu + Q = Kspar + Sillimanite + H2O We can treat the solids and gases separatelyGP, T - GT = DVsolids (P - 0.1) + RT ln (P/0.1) (isothermal) The treatment is then quite similar to solid-solid reactions, but you have to solve for the equilibrium P by iterationDehydration Reactions (qualitative analysis)dPdTSV=DDFigure 27.2. Pressure-temperature phase diagram for the reaction muscovite + quartz = Al2SiO5 + K-feldspar + H2O, calculated using SUPCRT (Helgeson et al., 1978). Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Solutions: T-X relationshipsAb = Jd + Q was calculated for pure phasesWhen solid solution results in impure phases the activity of each phase is reducedUse the same form as for gases (RT ln P or ln f)Instead of fug