Bevezetés II A kőzettan termodinamikai alapjai

Átírás

1 Bevezetés II A kőzettan termodinamikai alapjai Felhasznált anyagok: Miron G. Best 2002: Igneous and Metamorphic Petrology 2nd Edition, Wiley Blackwell, 758 p. ( GNEOUS_AND_METHAMORPHIC_PETROLOGY.PDF) Juraj Majzlan 2016: Introduction into thermodynamics (Solid state thermodynamics); TAI 2016, Balatonfüred (Irodalom c. könyvtárban) geol.ucsb.edu

2 Miért fontos a kőzettanban a termodinamika? 1. What are the basic concepts of thermodynamics and why is thermodynamics important in petrology? 2. How can the flows of matter and energy in changing rock forming systems be predicted and interpreted using thermodynamic models? 3. How do phase diagrams reflect the thermodynamic stability of different states of matter?

3 Mi mozgatja a kőzettani folyamatokat, hogyan kvantifikálhatók? rock forming processes in changing geologic systems tend toward a state of stable equilibrium in which the energy is the lowest possible. (Best 2002, p. 51) Thermodynamics is a set of mathematical models and concepts that describe the way how changes in T, P, and chemical composition affect states of stable equilibrium in rockforming systems. (Best 2002, p. 52)

4 A Gibbs féle szabadenergia Termodinamikai potenciális ( elérhető, hozzáférhető, rendelkezésre álló szabad) energia Univerzális függvény, ami: Lehetővé teszi egy rendszer viselkedésének leírását, változó (változtatható) P, T, X körülmények között rock forming processes in changing geologic systems tend toward a state of stable equilibrium in which the energy is the lowest possible. (Best 2002, p. 51)

5 Alapfogalmak I. System : A part of the universe we consider. For example, water in the bottle, a piece of rock. Surrounding : Everything outside of the system. Equilibrium : A state of a system in which none of the properties of the system change with time. Phase : A mechanically separable part of a system. Minerals are phases ; water is also a phase. Sodium chloride dissolved in water is not a phase because it cannot be mechanically separated (for example, by titration) from the water. Component : An algebraic operator. The composition of any phase in the system must be expressed as a linear combination of the components. One should try to select the smallest number of components. Example. A system is made of K feldspar (KAlSi3O8), sillimanite (Al2SiO5), and quartz (SiO2). Components for this system are K2O, Al2O3, and SiO2. Each phase can be expressed as a linear combination of these components.

6 Alapfogalmak II. Rendszerek: Nyílt Zárt Izolált Adiabatikus

7 Alapfogalmak III. Állapot jellemzők (state variables) Intenzív (belső) változók are independent of the amount of material present; they have a definite value at each point within the system, such as T, P, and concentration of a particular chemical species Extenzív (külső) változók they depend on the amount of material, such as the mass and volume of some chemicals constituting a system /Származtatott változók/

8 Alapfogalmak IV. A termodinamikai folyamatok lehetnek: Irreverzibilisek (visszafordíthatatlanok): Átalakulás egy kezdeti metastabilis állapotból egy végső, stabil állapotba (kisebb energia) Példa: The conversion of metastable volcanic glass into more stable crystals a process called devitrification under near atmospheric conditions is one example of an irreversible process. The energy trough in which metastable glass is stuck has to be surmounted, overcoming the activation energy, before it can move to a lower energy state. The atomic bonds in the glass must be broken or reformed into more stable crystalline structures. Devitrification of glass occurs spontaneously in the direction of diminishing energy, never in reverse

9 Reverzibilisek (visszafordíthatók): két egyenértékű, stabil állapot között játszódik le A reversible process is never actually realized in nature; it is a hypothetical concept that is used to make the mathematical models of thermodynamics work

10 A termodinamika I. főtétele (energiamegmaradás) Suppose that a change in the internal energy, de i of a rock system, such as a mineral grain, is produced by adding some amount of heat to it, dq. As a result of absorbing heat, the mineral grain expands by an increment in volume, dv, doing an increment of PV work, dw = PdV, on the surrounding mineral grains. According to the first law of thermodynamics, or law of conservation of energy, the increase in internal energy due to heat absorbed is diminished by the amount of work done on the surroundings,

11 Izobár rendszerben (dp = 0): Entalpia

12 Entalpia változással járó folyamatok 1. Chemical reactions, such as the reaction of quartz plus calcite creating wollastonite + CO A change in state, such as crystals melting to liquid, that occurs at a fixed T once that T is reached in heating a system. 3. A change in T of the system where no change in state occurs, such as simply heating crystals below their melting T.

13 Példa: 2, 3

14 Az előző dia magyarázata Enthalpy T relations for CaMgSi2O6 at 1 atm. (Weill DF, Hon R, and Navrotsky A, The igneous system CaMgSi2O6 CaAl2Si2O8 NaAlSi3O8) As diopside crystals absorb heat up to their melting point, (3., above), T increases proportionally with the heat capacity, Cp. The slope of this line is (dh/dt)p = Cp. At the melting T absorbed heat does not increase T, but is consumed in breaking the atomic bonds of the crystalline structure to produce the more random liquid array. This relatively large amount of absorbed heat at the constant T of melting, (2., above), is the latent heat of melting, or enthalpy of melting, Hm.

15 A termodinamika II. főtétele second law of thermodynamics is that spontaneous natural processes tend to even out the concentration of some form of energy, smoothing the energy gradient. Example: hot lava flow extruded from a lofty volcano cools to atmospheric T as it descends down slope, thereby reducing differences in thermal and gravitational potential energy between initial and final states in accordance with the second law. The measure of the uniformity in concentration of energy in a system is called the entropy, S. The more uniform the concentration of some form of energy, the greater the entropy.

16 Az entrópia mindig nő! Entropy increases in a spontaneous, irreversible process in an isolated system. Bottom left, a hypothetical isolated system a box filled with atoms of two gases (black and white balls) separated by an impermeable wall. Bottom right, the wall has been removed in the box, and the atoms of the two gases have mixed spontaneously and irreversibly as a result of their motion (kinetic energy). An increase in disorder or randomness of the atoms in the system and an increase in entropy, S = 0. No change in energy has occurred.

17 Entrópia a kőzettanban S = T1 T2 (C P /T) dt For example, the entropy of graphite at 1 atm = 5.7 J/mol K; the entropy of diamond at 1 atm = 2.4 J/mol K; thus, at any given T, graphite has a lower (more negative) entropic energy than diamond; with increasing T, therefore, graphite has a lower free energy than diamond and is the polymorph favored by increasing T.

18 A termodinamika III. főtétele The third law of thermodynamics states that at absolute zero, where the Kelvin temperature is zero (0K = C), crystals are perfectly ordered and all atoms are fixed in space so that the entropy is zero. A convenient way to think of relative entropies is that a gas made of high speed molecules in random trajectories has a greater entropy than the compositionally equivalent liquid array, which, though still somewhat disordered, has linked atoms. The compositionally equivalent crystalline solid has still lower entropy, because its atoms form an ordered array.

19 A Gibbs féle szabadenergia (G) G = H TS G = Ei + PV TS dg = dei + PdV + VdP TdS SdT dq = TdS dg = VdP SdT The above equation is a useful thermodynamic expression that allows us to make powerful statements regarding the direction of changes in geologic systems as the independent intensive variables of state, T and P, change.

20 Gibbs free energy decreases in a spontaneous change in a closed system where the initial and final states are at the same P and T. In this example, the energy of diamond is greater than that of graphite at the same P and T, or G diamond > G graphite, so the change in energy, G P,T, in the spontaneous process is negative, or G diamond G graphite = G P,T < 0. Note the activation energy barrier, Ea, that must be surmounted in order for the change to occur.

21 Fázisdiagramok, P T A phase diagram shows which phase, or assemblage of two or more phases, is more stable as a function of P, T, or other variables. dg = VdP SdT

22 Fázisdiagramok, P T

23 A fázisok közötti felület (egyenes, görbe) kvantitatív meghatározása Amit ismerni kell: Moláris térfogat Entrópia Kalorimetria

24 A komponensek moláris aránya X A A komponens moláris aránya n A az a komponens mennyisége mólban az adott fázisban, vagy rendszerben N B a b komponens

25 Parciális moláris térfogat egy jó analógia Mennyivel nő meg a fázis térfogata, ha az adott komponensből infidezimálisan keveset hozzáadunk

26 Egy példa: A víz parciális moláris térfogata tiszta víz és víz + albit olvadék esetén The volume increase that results from the addition of an infinitesimally small amount of one component water, in this case to a solution of that component plus NaAlSi3O8 is the partial molar volume of water in the melt.

27 Parciális moláris Gibbs féle szabadenergia a kémiai potenciál (μ)

28 Diagramon ábrázolva G Commonly tabulated for pure phases at atmospheric conditions of 25 C (298.15K) and 1 bar

29 Mitől függ az adott fázis stabilitása? Az elérhető energiát befolyásoló faktorok: Moláris térfogat, ami a nyomás függvénye Entrópia, ami a hőmérséklet függvénye Kémiai potenciál, ami a koncentráció függvénye now have a general thermodynamic tool that is applicable to all systems, not just those whose phases are of fixed composition, to which the restricted equation 3.9* applies. * dg = VdP SdT