Introduction to
thermodynamic
geomodeling
Viktoriya Yarushina
PGP
fall semester 2009
Thermodynamic system
– system in thermodynamic
equilibrium, i.e. all parameters are
const in time, d/dt = 0, d/dx = 0,
no fluxes
„
„
„
Open system: matter and energy exchange
Closed system: energy exchenge
Isolated system: no exchange
Nonequilibrium system –
d/dt ≠ 0 or d/dx ≠ 0
Σ
m, V
Σ
m, V
Homogeneous system –
f(x) – continuous
Gas mixtures
Liquid and solid solutions
Heterogeneous system
f(x) – discontinuous
Partially molten rock
Melting ice
Oil-gas mixture
3
Phase - Component
Σ13
ρ3, T3
Σ12
ρ2, T2
ρ1, T1
Component is a chemically distinct constituent
of a system. Their concentrations may be varied
independently in the various phases.
Internal – External
parameters
x, v
ρ, p, V, e
but
x2
v
V
p = const
p - external
p
V = const
V - external
t2
t1
x1
Thermodynamic parameters
(internal)
Extensive
Intensive
Mass
Volume
Energy
V1
+
V2
=
V1+V2
Temperature
Density
Pressure
T1
+
T2
?
= T1+T2
Energy
What is the energy?
Energy
Kinetic
Potential Internal
E = K + Epot + U
System as a whole, K = mv2
In external force fields, Epot = mgh
Everything else,
U = U(ai,T),
ai – external parameters
Thermodynamics deals only with internal energy with some exceptions
Work
One 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 dV
dW = V0∑σikdeik
B
A
dW ≠ WB-WA
Heat
One of the means of energy exchange
when external parameters DO NOT
change
B
1
dQ is not a perfect differential
∫dQ depends on the path
Q is not a state variable
2
A
dQ ≠ QB-QA
The First Law or Energy Balance
For isolated systems: dE = 0
For closed systems: dU = dQ + dW
B
For open systems: ?
dU = dQ + ∑Aidai
ai – external parameters
Ai – conjugate forces
A
dU=UB-UA
U is perfect differential
Perpetuum mobile of the 1st kind is impossible: any device which
indefinitely produces the work without consuming the energy is forbidden
The Second Law or
Entropy and absolute temperature
∫dQ/T = dS = SB-SA
B
Entropy S is a state variable
T is thermodynamic (absolute) temperature (K)
dQ = TdS
dS≥0
A
dS=SB-SA
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
Entropy
S = S1+S2
What is the entropy?
Gibb’s equation
dU = dW + dQ
+
dQ = ?
dW = ?
=
?
Matter exchange – open systems
Variations in composition – chemical reactions
dU = dW + dQ
+
dQ = ?
dW = ?
=
?
Thermodynamic processes
Isothermal: T = const, dU = -pdV + TdS
Isochoric: V = const, dU = -pdV + TdS
Isobaric: p = const, dU = -pdV + TdS
Adiabatic: Q = const, dU = -pdV + TdS
Thermodynamic potentials
Gibbs 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)