
Thermodynamics  
C http://ijolite.geology.uiuc.edu/08SprgClass/geo436/lectures.html
http://ijolite.geology.uiuc.edu/08SprgClass/geo436/436%20lectures/L4Thermo.html
A. Def: Thermodynamics study of energy (work and energy)
For geology, thermo is applied to chemical energy
Thermo data available for many minerals
B. Laws  expressed mathematically, but can be understood by experience
First law: energy can be changed from one form to another, but it can''t be destroyed
Second law: natural processes are directional
Mathematical statements used to calculate equilibrium conditions for a reaction
C. Terminology
System = isolated part of the world.
Systems evolve to a condition of minimum energy = stable state
A system not at minimum energy = unstable
System not at minimum energy but not evolving = metastable
System that is not changing = at equilibrium
System in the process of change = in disequilibrium
A property that is dependent only on the state of the system and not on the path = variable of state (e.g., T and P)
Closed and opened systems
II. State Variables
A. From the first law, internal energy E includes heat and work. Then E + PV = H = enthalpy = a state variable describing heat content of a system
In practice, we calculate dH, not absolute value of H
dH of a reaction = heat withdrawn from surroundings at constant P
Exothermic reaction gives off heat, so dH is negative
Endothermic reaction absorbs heat, so dH is positive
B. From the second law comes another state variable S = entropy where dS = dQrev / T (Q represents heat exchanged between a system and its surroundings
C.
But a reversible process is only a concept; all natural processes are irreversible.
Thus the general form is dS= dQ / T, or dS > dQ / T (= for a reversible process, > for irreversible)
S represents the disorder in a system
Consider an isolated system => dQ = 0, so dS > 0 for a real reaction, i.e., entropy increases. S increases until equilibrium is attained, then dS = 0 and S = a maximum.
C. Third law: S of a pure, perfectly crystalline substance at absolute zero is zero.
From this, S at temperature T = the integral of Cp / T dT , evaluated from 0 to T, where Cp = heat capacity = amount of heat required to raise the temperature of a unit mass of a substance 1o at constant P
Cp varies with T: this variation can be modeled by a + b T  c/T^2 where a, b, c are constants determined experimentally.
III. Gibbs Equation
A. Thermodynamic relations
First law gives relation between various forms of energy
Second law gives the direction of reactions by introducing entropy
Third law gives absolute values of S
B. These can be combined to give a general relation that controls reactions and equilibrium
Gibbs Free Energy = G = H  T S or dG for a reaqction = dH  T dS
For a reaction to occur,  dG > 0, i.e., free energy must decrease
At equilibrium, dG = 0 => dH = T dS => Teq = dH / dS
C. Variation with T and P
Thermodynamic data is generally available only for T = 298 K, P = 10^5 Pa => we must know how T and P affect dG.
In a closed system, dG = f (T, P) only, thus d dG = (partial derivative of dG with respect to T at constant P) dT
+ (partial derivative of dnG with respect to P at constant T) dP
If the only work done by the system is expansion, then dG =  dS dT + dnV dP =>
(partial derivative of dG with respect to T at constant P) =  dS
And (partial derivative of dnG with respect to P at constant T) = dV
D. Clapeyron equation
Return to dG =  dS dT + dV dP. At equilibrium, dG = 0 => dS dT = dV dP or
dP / dT = dV / dS
Clapeyron Eqn gives slope of equilibrium line in P vs T diagram
