 | Thermodynamics |
C http://ijolite.geology.uiuc.edu/08SprgClass/geo436/lectures.html
http://ijolite.geology.uiuc.edu/08SprgClass/geo436/436%20lectures/L4-Thermo.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-dH of a reaction = heat withdrawn from surroundings at constant P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