Learning Objectives and Fundamental Questions• What is thermodynamics and how are its conceptsused in geochemistry?• How can heat and mass flux be predicted orinterpreted using thermodynamic models?• How do we use phase diagrams to visualizethermodynamic stability of minerals and aqueoussolutions?• How do kinetic effects affect our interpretationsfrom thermodynamic models? - We will addressthis later in the class.What is Thermodynamics?• Thermodynamics: A set of of mathematicalmodels and concepts that allow us to describe theway changes in the system state (temperature,pressure, and composition) affect equilibrium.– Can be used to predict how geological systems (e.g.melts-minerals; solutes in aqueous solutions) willrespond to changes in state– Invert observed chemical compositions of minerals andmelts to infer the pressure and temperature conditionsor originDefinitions of Stability vs. EquilibriumThermodynamic Systems - DefinitionsIsolated System: No matteror energy cross systemboundaries. No work can bedone on the system.Open System: Free exchangeacross system boundaries.Closed System: Energy can beexchanged but matter cannot.Adiabatic System: Special casewhere no heat can be exchangedbut work can be done on thesystem (e.g. PV work).Thermodynamic State Properties• Extensive: These variables or propertiesdepend on the amount of material present(e.g. mass or volume).• Intensive: These variables or properties DONOT depend on the amount of material(e.g. density, pressure, and temperature).Idealized Thermodynamic Processes• Irreversible: Initial system state is unstable ormetastable and spontaneous change in the systemyields a system with a lower-energy final state.• Reversible: Both initial and final states are stableequilibrium states and the path between them is acontinuous sequence of equilibrium states. NOTACTUALLY REALIZED IN NATURE, BUTCAN BE APPROXIMATED IN LABORATORY.Spontaneous Reaction DirectionEnergy and Work• Energy: commonly defined as the capacity to do work (i.e.by system on its surroundings); comes in many forms• Work: defined as the product of a force (F) times times adisplacement acting over a distance (d) in the directionparallel to the forcework = Force x distanceExample: Pressure-Volume work in volcanic systems.Pressure = Force/Area; Volume=Area x distance;PV =( F/A)(A*d) = F*d = wForms of Energy• Chemical energy: energy bound up withinchemical bonds; can be released through chemicalreactions• Thermal energy: related to the kinetic energy ofthe atomic particles within a body (solid, liquid, orgas). Motion of particles increases with highertemperature.• Heat is transferred thermal energy that results because of adifference in temperature between bodies. Heat flows fromhigher T to lower T and will always result in the temperaturesbecoming equal at equilibrium.Heat Capacity DefinedAn increment of heat, Δq, transferred into a body produces aproportional incremental rise in temperature, ΔT, given byΔq = Cp * ΔT where Cp is called the molar heat capacity of J/mol-degreeat constant pressure; similar to specific heat, which is basedon mass (J/g-degree).1 calorie = 4.184 J and is equivalent to the energy necessaryto raise 1 gram of of water 1 degree centigrade. Specific heat of water is 1 cal /g °C, where rocks are ~0.3 cal / g °C.First Law of ThermodynamicsThe increase in internal energy as a result ofheat absorbed is diminished by the amount ofwork done on the surroundings:dEi = dq - dw = dq - PdVBy convention, heat added to the system, dq,is positive and work done by the system, dw, on its surroundings is negative.This is also called the Law of Conservation of EnergyDefinition of EnthalpyWe can define a new state variable (one where the path to its current state does not affect its value) called enthalpy:H = Ei + PVEnthalpy = Internal Energy + PVUpon differentiation and combining with our earlier definitionfor internal energy:dH = dEi + PdV + VdPdEi = dq - PdVdH = dq + VdPReaction DeltasThermodynamics uses well established formalism. Oneof the most widespread shorthands is the reaction delta.the example below is for molar volume change, but itcan be extended to other molar properties and state variables.Reaction Notation: ΔV = Vfinal - VinitialaA + bB + … = mM + nN + …Δ rV = mM + nN + … - aA - bB - …Δ rV = VAl2O3*3H2O - VAl2O3 - 3VH2ONote that the r subscriptis added to show thatthe Δ rV correspondsto a chemical reaction.The ° superscript isadded to show that thethermodynamic data are for standard state conditions.!rV°= VAl 2O 3"3H 2O°# VAl 2O 3°# 3VH 2O°We will do an example on the board.Additivity of State VariablesState variables may be added or subtracted in order tocalculate the value for a particular reaction, mineral, etc. C + O2 = CO2 !rH°= "393.509 kJmol-1 CO + 12O2 = CO2 !rH°= "282.984 kJmol-1Subtracting the reactions - this means reverse the2nd reaction and change the sign of !rH°, we get C + 12O2 = CO !rH°= "110.525 kJmol-1This allows us to calculate the enthalpy of formationfor CO from C and O2, a reaction that is impossible tocomplete in the lab. The method is extensible to otherstate variables and molar properties.This of course is appropriate because the thermodynamic state variable’s value, for example the enthalpy of formation ONLY depends on the “state” of the system and not the “path” to reach some specific state.Enthalpy, Melting, and HeatFor isobaric (constant pressure) systems, dP = 0 and then thechange in enthalpy is equal to the change in heat:dHp = dqpThree possible changes in a system may occur:1) Chemical reactions (heterogeneous)2) Change in state (e.g. melting)3) Change in T with no state changeCp = (dH/dT)pHeat capacity is defined by the amount of heat that may be absorbedas a result of temperature change at constant pressure:More on Heat CapacitiesHeat capacity is definedby the amount of heatthat may be absorbedas a result oftemperature change atconstant pressure.The conceptcan be extended toenthalpies of formation,reaction, etc.dHdT!"#$%&P= Cp BASIC FORMAL DEFINITIONd'HdT!"#$%&P= 'Cp DELTA RULES APPLYd'rH°dT!"#$%&P= 'rCp° STANDARD STATE RXNMAIER-KELLY EQUATION - T dependence of CpCp= a + bT ( cT(2'rCp°= 'ra + 'rbT ( 'rcT(2Enthalpy of Melting580°CTemperature Dependence of Enthalpyd!rH°dT"#$%&'P= !rCp° STANDARD STATE RXNWHAT IF WE WANT TO EVALUATE AT ANOTHER T? d!rH°=TrT(!rCp°dTTrT(!rHT°) !rHTr°= !rCp°dTTrT(= (!ra + !rbT )