Thermodynamics培训课件.ppt.ppt

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1、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 Metamorp

2、hic 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:

3、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 u

4、se 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

5、 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 s

6、ame 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/m

7、ol) 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 h

8、as 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 curvedD

9、G = 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

10、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=

11、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 Pr

12、essure-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 en

13、ergy 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

14、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 a

15、re 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 R

16、eactions (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