Geoscience Reference
In-Depth Information
closed system of constant composition and without nonexpansion work, one can
write
dw
rev
¼
PdV
:
ð
2
:
5
Þ
Then, for a reversible change in a closed system, substitution of Eqs. (
2.5
) and
(
2.3
) (written for dq
rev
) into Eq. (
2.1
) yields
dU ¼ T dS
PdV
:
ð
2
:
6
Þ
Equation (
2.6
) is called a fundamental equation and because dU is an exact
differential, its value is independent of path. Hence, Eq. (
2.6
) applies to any
change—reversible or irreversible—of a closed system that does no additional
work (Atkins and de Paula
2002
).
Given that, in the subsurface, we are dealing with an open system, the funda-
mental equation may be applied only when the macroscopic system is decoupled
in isolated, well-defined systems. As an example, we can consider that an adiabatic
''zone'' of the subsurface solid phase is in contact with an aqueous solution
through a rigid barrier, surrounded by an insulating wall.
Gibbs free energy (G) is probably the most frequently used quantity in ther-
modynamics; it measures spontaneity of a reaction or energy available to do work
in a system. Free energy is a state function because it is defined formally only in
terms of the state functions enthalpy and entropy and the state variable tempera-
ture. The Gibbs free energy is defined as
G ¼ H
TS
:
ð
2
:
7
Þ
At constant temperature and pressure, chemical reactions are spontaneous in the
direction of decreasing Gibbs free energy. Some reactions are spontaneous because
they give off energy in the form of heat (DH\ 0). Other reactions are spontaneous
because they lead to an increase in the disorder of the system (DS[0). Calculations
of DH and DS can be used to probe the driving force behind a particular reaction.
2.1.2 Equilibrium
A system is in equilibrium when all acting influences are canceled by others,
resulting in a stable, balanced, or unchanging system in relation to its surround-
ings. In the subsurface, equilibrium can be defined in terms of thermal, chemical,
or mechanical equilibrium. Usually, in the subsurface, changes occur slowly over
geological time scales, so that a state of equilibrium is never reached. However, in
the subsurface, when mainly anthropogenic-induced effects are involved, various
changes do occur over ''observable'' time scales, ranging from seconds to years.
Under these conditions, an apparent equilibrium may be reached. The concept of
equilibrium in subsurface systems is discussed in classical topics of geochemistry,
