Learning Objectives and Fundamental Questions

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Daisy Rice
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1 Learning Objectives and Fundamental Questions What is thermodynamics and how are its concepts used in geochemistry? How can heat and mass flux be predicted or interpreted using thermodynamic models? How do we use phase diagrams to visualize thermodynamic stability of minerals and aqueous solutions? How do kinetic effects affect our interpretations from thermodynamic models? - We will address this later in the class.

2 What is Thermodynamics? Thermodynamics: A set of of mathematical models and concepts that allow us to describe the way 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) will respond to changes in state Invert observed chemical compositions of minerals and melts to infer the pressure and temperature conditions or origin

3 Definitions of Stability vs. Equilibrium

4 Thermodynamic Systems - Definitions Isolated System: No matter or energy cross system boundaries. No work can be done on the system. Open System: Free exchange across system boundaries. Closed System: Energy can be exchanged but matter cannot. Adiabatic System: Special case where no heat can be exchanged but work can be done on the system (e.g. PV work).

5 Thermodynamic State Properties Extensive: These variables or properties depend on the amount of material present (e.g. mass or volume). Intensive: These variables or properties DO NOT depend on the amount of material (e.g. density, pressure, and temperature).

6 Idealized Thermodynamic Processes Irreversible: Initial system state is unstable or metastable and spontaneous change in the system yields a system with a lower-energy final state. Reversible: Both initial and final states are stable equilibrium states and the path between them is a continuous sequence of equilibrium states. NOT ACTUALLY REALIZED IN NATURE, BUT CAN BE APPROXIMATED IN LABORATORY.

7 Spontaneous Reaction Direction

8 Energy 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 a displacement acting over a distance (d) in the direction parallel to the force work = Force x distance Example: Pressure-Volume work in volcanic systems. Pressure = Force/Area; Volume=Area x distance; PV =( F/A)(A*d) = F*d = w

9 Forms of Energy Chemical energy: energy bound up within chemical bonds; can be released through chemical reactions Thermal energy: related to the kinetic energy of the atomic particles within a body (solid, liquid, or gas). Motion of particles increases with higher temperature. Heat is transferred thermal energy that results because of a difference in temperature between bodies. Heat flows from higher T to lower T and will always result in the temperatures becoming equal at equilibrium.

10 Heat Capacity Defined An increment of heat, Δq, transferred into a body produces a proportional incremental rise in temperature, ΔT, given by Δq = Cp * ΔT where Cp is called the molar heat capacity of J/mol-degree at constant pressure; similar to specific heat, which is based on mass (J/g-degree). 1 calorie = J and is equivalent to the energy necessary to 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.

11 First Law of Thermodynamics The increase in internal energy as a result of heat absorbed is diminished by the amount of work done on the surroundings: de i = dq - dw = dq - PdV By 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 Energy

12 Definition of Enthalpy We can define a new state variable (one where the path to its current state does not affect its value) called enthalpy: H = E i + PV Enthalpy = Internal Energy + PV Upon differentiation and combining with our earlier definition for internal energy: dh = de i + PdV + VdP de i = dq - PdV dh = dq + VdP

13 Reaction Deltas Thermodynamics uses well established formalism. One of the most widespread shorthands is the reaction delta. the example below is for molar volume change, but it can be extended to other molar properties and state variables. Reaction Notation: ΔV = V final - V initial aa + bb + = mm + nn + Δ r V = mm + nn + - aa - bb - Note that the r subscript is added to show that the Δ r V corresponds to a chemical reaction. Δ r V = V Al2O3*3H2O - V Al2O3-3V H2O! r V = V Al 2O 3"3H 2O # V Al 2O 3 # 3V H 2O We will do an example on the board. The superscript is added to show that the thermodynamic data are for standard state conditions.

14 Additivity of State Variables State variables may be added or subtracted in order to calculate the value for a particular reaction, mineral, etc. C + O 2 = CO 2! r H = " kjmol -1 CO + 1 O 2 = CO 2! r H = " kjmol -1 2 Subtracting the reactions - this means reverse the 2nd reaction and change the sign of! r H, we get C + 1 O 2 = CO! r H = " kjmol -1 2 This allows us to calculate the enthalpy of formation for CO from C and O 2, a reaction that is impossible to complete in the lab. The method is extensible to other state 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.

15 Enthalpy, Melting, and Heat For isobaric (constant pressure) systems, dp = 0 and then the change in enthalpy is equal to the change in heat: dh p = dq p Three 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 change Heat capacity is defined by the amount of heat that may be absorbed as a result of temperature change at constant pressure: C p = (dh/dt) p

16 More on Heat Capacities! " #! " # dh$ dt % & P d'h $ dt % & = C p BASIC FORMAL DEFINITION P! d' r H $ " # dt % & = 'C p DELTA RULES APPLY P = ' r C p STANDARD STATE RXN MAIER-KELLY EQUATION - T dependence of C p C p = a + bt ( ct (2 Heat capacity is defined by the amount of heat that may be absorbed as a result of temperature change at constant pressure. The concept can be extended to enthalpies of formation, reaction, etc. ' r C p = ' r a + ' r bt ( ' r ct (2

17 Enthalpy of Melting 580 C

18 Temperature Dependence of Enthalpy " # $ d! r H % dt & ' P =! r C p STANDARD STATE RXN WHAT IF WE WANT TO EVALUATE AT ANOTHER T? T ( d! r H = (! r C p dt T r! r H T )! r H T r! r H T )! r H T r T T r T = (! r C p dt = ( (! r a +! r bt )! r ct )2 )dt T r T T r =! r a(t ) T r ) +! rb 2 (T " 2 ) T 2 r ) +! r c 1 T ) 1 # $ T r Where! r H T is the standard enthalpy of reaction at temperature, T, and! r H T is the standard enthalpy of r reaction at the reference temperature, T r, normally K % & '

Hence. The second law describes the direction of energy transfer in spontaneous processes

Hence. The second law describes the direction of energy transfer in spontaneous processes * Heat and Work The first law of thermodynamics states that: Although energy has many forms, the total quantity of energy is constant. When energy disappears in one form, it appears simultaneously in other