2.6 The Second Law and Stability
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provides the relevant condition for irreversible processes occurring under
isothermal–isochoric conditions.
A similar line of reasoning for irreversible processes occurring at constant T and
P , brings the Gibbs energy, G, into play as the relevant thermodynamic potential.
Thus, with dG given by
dG = −SdT + V dP − δQ
,
(2.6.5a)
we obtain the condition
δQ
= −dG > 0 ,
(2.6.5b)
or, equivalently,
dG ≤ 0 ,
(2.6.5c)
for irreversible processes that take place under isothermal–isobaric conditions.
System stability is thus strongly correlated with entropy creation (or production).
The major mechanical means for entropy production is via viscous flow within
a system (microscopically associated, for example, with momentum transfer via
collisions): no viscous flow occurs when a system is in mechanical equilibrium.
Similarly, the major thermal means of entropy production is via energy (heat)
transport between two regions of a system that are at different temperatures: no
heat transport occurs within a system when it is in thermal equilibrium. For an open
system, concentration (number density) differences may create entropy by diffusion
within each phase: no diffusion (mass transport) occurs within homogeneous phases
of a system.
Consider now a thermodynamic system for which mechanical and thermal
equilibrium have already been established. We shall refer to a system that is
in mechanical and thermal equilibrium, but which has not yet fully established
chemical or phase equilibrium, as being in partial equilibrium. The only form of
entropy production that can occur is then associated with chemical reactions or with
the transport of matter from one phase to another. Moreover, we shall consider here
only systems for which T , P , and composition within each phase are uniform.
For a chemically reacting system, we may think of the degree of advancement
ξ as the relevant variable to consider, in which case, we may write in analogy with
Eq. (2.6.5b)
δQ
= A dξ ≥ 0 ,
(2.6.6)
with the inequality corresponding to spontaneous reaction and the equality corresponding to equilibrium. The symbol A ≡ A(x, y, ξ), with x, y representing a
pair of thermodynamic variables such as T , P or T , V , is called the affinity, a
thermodynamic function introduced in 1922 by the Belgian chemist de Donder,
after whom the inequality (2.6.6) is named. As chemical reactions are most often
87
provides the relevant condition for irreversible processes occurring under
isothermal–isochoric conditions.
A similar line of reasoning for irreversible processes occurring at constant T and
P , brings the Gibbs energy, G, into play as the relevant thermodynamic potential.
Thus, with dG given by
dG = −SdT + V dP − δQ
,
(2.6.5a)
we obtain the condition
δQ
= −dG > 0 ,
(2.6.5b)
or, equivalently,
dG ≤ 0 ,
(2.6.5c)
for irreversible processes that take place under isothermal–isobaric conditions.
System stability is thus strongly correlated with entropy creation (or production).
The major mechanical means for entropy production is via viscous flow within
a system (microscopically associated, for example, with momentum transfer via
collisions): no viscous flow occurs when a system is in mechanical equilibrium.
Similarly, the major thermal means of entropy production is via energy (heat)
transport between two regions of a system that are at different temperatures: no
heat transport occurs within a system when it is in thermal equilibrium. For an open
system, concentration (number density) differences may create entropy by diffusion
within each phase: no diffusion (mass transport) occurs within homogeneous phases
of a system.
Consider now a thermodynamic system for which mechanical and thermal
equilibrium have already been established. We shall refer to a system that is
in mechanical and thermal equilibrium, but which has not yet fully established
chemical or phase equilibrium, as being in partial equilibrium. The only form of
entropy production that can occur is then associated with chemical reactions or with
the transport of matter from one phase to another. Moreover, we shall consider here
only systems for which T , P , and composition within each phase are uniform.
For a chemically reacting system, we may think of the degree of advancement
ξ as the relevant variable to consider, in which case, we may write in analogy with
Eq. (2.6.5b)
δQ
= A dξ ≥ 0 ,
(2.6.6)
with the inequality corresponding to spontaneous reaction and the equality corresponding to equilibrium. The symbol A ≡ A(x, y, ξ), with x, y representing a
pair of thermodynamic variables such as T , P or T , V , is called the affinity, a
thermodynamic function introduced in 1922 by the Belgian chemist de Donder,
after whom the inequality (2.6.6) is named. As chemical reactions are most often