introduction to thermodynamic geomodeling · phase - component ρ 2, t 2 ρ 1, t 1 Σ ρ 3, t 3 12...

Introduction to thermodynamic geomodelingViktoriya YarushinaPGPfall semester 2009

Open system: matter and energy exchangeClosed system: energy exchengeIsolated system: no exchange

Thermodynamic system– system in thermodynamicequilibrium, i.e. all parameters areconst in time, d/dt = 0, d/dx = 0, no fluxes

Nonequilibrium system –d/dt ≠ 0 or d/dx ≠ 0

m, VΣ

m, VΣ

3

Homogeneous system –f(x) – continuousGas mixturesLiquid and solid solutions

Heterogeneous systemf(x) – discontinuous Partially molten rock Melting iceOil-gas mixture

Phase - Component

ρ2, T2 ρ1, T1

ρ3, T3Σ12

Σ13

Component is a chemically distinct constituent of a system. Their concentrations may be varied independently in the various phases.

Internal – External parameters

p = constp - external

V p

V = constV - external

ρ, p, V, e

but

x, v

x1

x2

v t2

t1

Thermodynamic parameters (internal)

Extensive Intensive

Mass TemperatureVolume DensityEnergy Pressure

V1 V2 V1+V2+ = T1 T2 T1+T2+?=

Energy

What is the energy?

Energy

Kinetic Potential InternalE = K + Epot + U

System as a whole, K = mv2

In external force fields, Epot = mghEverything else,

U = U(ai,T), ai – external parameters

Thermodynamics deals only with internal energy with some exceptions

WorkOne of the means of energy exchange when external parameters change

W = ∫F ds

dW is not a perfect differential∫dW depends on the path

W is not a state variable

dW = -p dVdW = V0∑σikdeik

A

B

dW ≠ WB-WA

Heat

One of the means of energy exchange when external parameters DO NOT change

dQ is not a perfect differential∫dQ depends on the path

Q is not a state variable

A

B

dQ ≠ QB-QA

12

The First Law or Energy Balance

For isolated systems: dE = 0

For closed systems: dU = dQ + dW

For open systems: ?

dU = dQ + ∑Aidaiai – external parameters U is perfect differentialAi – conjugate forces

Perpetuum mobile of the 1st kind is impossible: any device which indefinitely produces the work without consuming the energy is forbidden

A

B

dU=UB-UA

The Second Law or Entropy and absolute temperature

∫dQ/T = dS = SB-SA

Entropy S is a state variableT is thermodynamic (absolute) temperature (K)

dQ = TdSdS≥0

No process is possible whose sole effect is to transfer heat from cold body to a hot body

Perpetuum mobile of the 2nd kind is impossible: An engine that produces work by extracting heat from its surroundings is impossible

A

B

dS=SB-SA

Entropy

What is the entropy?

S = S1+S2

Gibb’s equation

dU = dW + dQ+

dQ = ?dW = ?

=?

Matter exchange – open systemsVariations in composition – chemical reactions

dU = dW + dQ+

dQ = ?dW = ?

=?

Thermodynamic processes

Isothermal: T = const, dU = -pdV + TdSIsochoric: V = const, dU = -pdV + TdSIsobaric: p = const, dU = -pdV + TdS

Adiabatic: Q = const, dU = -pdV + TdS

Thermodynamic potentialsGibbs energy G = U – TS: U=U(Ai,T)

Enthalpy H = U + pV: U=U(Ai,S)Helmholtz energy F = U – TS: U=U(ai,T)