Thermodynamics, Systems, Equilibrium & Energy

1. Thermodynamics, Systems, Equilibrium & Energy Lecture 1

2. Plan of the Course • The geochemical toolbox • Thermodynamics • Kinetics • Aquatic systems • Trace elements & magmatic systems • Isotopes • Radiogenic • Stable • The Big Picture: Cosmochemistry • Formation of the elements • Formation of the Earth and the Solar System • Chemistry of the Earth

3. Thermodynamics • Thermodynamics is the study of energy & its transformations. • Chemical changes involve energy; by “following the energy” we can predict the ‘equilibrium state of a system and therefore the outcome of reactions. • For example, we can predict the minerals that will crystallize from a cooling magma. • We can predict that as the concentration of atmospheric CO2 increases, ocean pH will decrease and calcium carbonate skeletons of coral will become more soluble. • Thermodynamics uses a macroscopic approach. • We can use it without knowledge of atoms or molecules. • We will occasionally consider the microscopic viewpoint using statistical mechanics when our understanding can be enhanced by doing so.

4. Thermodynamics and Kinetics • The equilibrium state of a system is independent of any previous state. So, for example, if we do a partial melting experiment with rock, it should not matter is we start with a solid and partially melt it or with a melt and partially crystallize it. • Kinetics is the study of rates and mechanisms of reaction. Kinetics concerns itself with the pathway to equilibrium; thermodynamics does not. Very often, equilibrium in the Earth is not achieved, or achieved only very slowly, which naturally limits the usefulness of thermodynamics.

5. ‘The System’ • A thermodynamic system is the part of the universe we are considering. Everything else is referred to as the surroundings. • We are free to define the ‘system’ anyway we chose. However, how we define it may determine whether we can successfully apply thermodynamics. • Four kinds of ‘systems’

6. Equilibrium • The equilibrium state is the one toward which a system will change in the absence of constraints. • It is time invariant on the macroscopic scale, but not necessarily on the microscopic one.

7. Equilibium & Thermodynamics • Conundrum: strictly speaking, we can apply thermodynamics only to the equilibrium state. If a reaction is proceeding, then the system is out of equilibrium and thermodynamic analysis cannot be applied! • Solution: we imagine reversible processes in which systems are only infinitesimally out of equilibrium. In contrast, natural processes can proceed only in one direction and are irreversible. • We might also imagine local equilibrium where even if the whole system (e.g. the ocean, magma and crystals) is out of equilibrium, we can imagine a part of it is (rim of the crystal).

8. Fundamental Variables • Pressure: P • Force/unit area • Volume; V • Work: W • we are mainly concerned with P-V work: pressure integrated over volume change • Work done by a system is negative • Heat: Q • Energy: U • Temperature: T • Entropy: S – more on that in next lecture

9. State Variables and Equations of State • State variables depend only on the state of the system, not on the path taken. Not all the variables listed above are state variables. • Extensive vs. Intensive variables. We can convert extensive variables to intensive ones. • Equations of state express the relationship between state variables, e.g. PV=NRT • Tells us, for a given number of moles, now temperature, volume, and pressure of an ideal gas relate to each other; i.e., if we heat the gas, what happens to volume and pressure? • Van der Waals Equation and Ideality

10. General Equation of State • Obviously, there is no one solution to the ideal gas law, but we can imagine a couple of special cases. • Isothermal compressibility (β): change in volume with change in pressure at constant temperatureper unit volume: 1/V(∂V/∂P)T • Coefficient of thermal expansion (α): change in volume with change in temperature at constant pressure per unit volume 1/V(∂V/∂T)P. • We can write a general equation relating V, T & P: dV= ∂V/∂T)PdT + (∂V/∂P)TdP dV = VαdT + VβdP

11. Temperature • Temperature is a measure of the average kinetic energy of a system. • How do we measure it? • Volume of an ideal gas • We can arbitrarily define a scale such that • V = V0(1+γτ) • If so, we might have negative τ. • But note V cannot be negative, so there must be an absolute minimum to temperature. • The absolute minimum of T occurs where the volume of an ideal gas is 0. • Use the absolute scale (K) in all thermodynamic calculations.

12. ZerothLaw • Two bodies in thermal equilibrium have the same temperature. • Two bodies in equilibrium with a third body are in equilibrium with each other.

13. The First Law • Energy is conserved in all transformations • Heat and work are equivalent (the sum of the two is always the same). • Change in energy of a system is independent of the path taken. • Mathematically: ΔU = Q +W • Energy change is path independent and thus is a state variable. Heat and work are not. • State variables have exact differentials (heat and work do not). • (we are mainly concerned with energy changes, not absolute amounts). • SI units of energy are Joules (kg-m2/s2). Calorie is another metric unit of energy, but not SI.

14. State Functions & Path Independence • State functions are path independent and have exact differentials. • Think about an internal combustion engine. Chemical energy is released by burning gas. Some of that energy goes into heat and some to work. There is no fixed rule about how much goes to each – it depends on your engine design (engineers work to increase the amount going to work). • Therefore, heat and work cannot be state functions. • However, no matter how you design the engine, the sum of heat and work for a given amount of (fully) combusted gasoline is the same. • Energy is path independent and a state function.

15. State Functions & Exact Differentials • State functions have exact differentials. • (These are not new, they are the kind you have learned about in calculus). • This means we can obtain (in principle anyway) an exact solution if we differentiate them (or integrate the differentials). • Exact differentials have the property that the cross differentials are equal (in other words, if we differentiate by two separate variables, the order doesn’t matter). • Again, this is what you learn in calculus. • Consider dV= (∂V/∂T)PdT + (∂V/∂P)TdP • If V is a state function, then (∂V2/∂T∂P)= (∂V2/∂P∂T) • This is not true of non-state functions like work and heat.

16. Work • Work is not a state function • dW= -PdV • For an ideal gas: