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4 The Thermodynamics of Real Systems
Once a system has reached equilibrium, its state is independent of how that state
was reached. The Gibbs energy is at a minimum if processes at constant T and P are
considered. The Helmholtz energy is at a minimum if processes at constant T and V are
considered. If a simple closed system is at constant T and P but not yet at equilibrium,
a spontaneous process could possibly increase the value of A, but must decrease the
value of G. If a simple closed system is at constant T and V but is not yet at equilibrium,
a spontaneous process could possibly increase the value of G, but must decrease the
value of A.
Maximum Work
We now seek criteria for the maximum work that can be done on the surroundings by
a closed system. For a system at constant temperature, Eq. (4.1-5) is
dU − TdS − dw dA − dw ≤ 0 (T constant)
(4.1-24)
This is the same as
dA ≤ dw (T constant)
(4.1-25)
For a finite process at constant temperature
∆A ≤ w (T constant)
(4.1-26)
At constant temperature, the Helmholtz energy of a system can be increased by doing
work on the system, but ∆A cannot exceed w. Alternatively, the system can do work
on the surroundings by lowering its Helmholtz energy, but the work done on the surroundings is limited by
dw surr ≤ −dA (T constant)
(4.1-27)
For a finite process at constant temperature
w surr ≤ −∆A (T constant)
(4.1-28)
A system that is not a simple system can exchange work with the surroundings in
different ways. We write
dw −P(transmitted) dV + dw net
(4.1-29)
The term −P(transmitted) dV represents the work that can be done on the system by
changing its volume. We now call this term compression work or P–V work. The term
dw net represents any work in addition to compression work that can be done on a nonsimple system. We call it the net work. Two examples of net work are electrical work
and stress-strain work (stretching a spring or a rubber band). If the volume of a system
is constant, dw dw net and we can write
w net,surr ≤ −∆A (T and V constant)
(4.1-30)
4 The Thermodynamics of Real Systems
Once a system has reached equilibrium, its state is independent of how that state
was reached. The Gibbs energy is at a minimum if processes at constant T and P are
considered. The Helmholtz energy is at a minimum if processes at constant T and V are
considered. If a simple closed system is at constant T and P but not yet at equilibrium,
a spontaneous process could possibly increase the value of A, but must decrease the
value of G. If a simple closed system is at constant T and V but is not yet at equilibrium,
a spontaneous process could possibly increase the value of G, but must decrease the
value of A.
Maximum Work
We now seek criteria for the maximum work that can be done on the surroundings by
a closed system. For a system at constant temperature, Eq. (4.1-5) is
dU − TdS − dw dA − dw ≤ 0 (T constant)
(4.1-24)
This is the same as
dA ≤ dw (T constant)
(4.1-25)
For a finite process at constant temperature
∆A ≤ w (T constant)
(4.1-26)
At constant temperature, the Helmholtz energy of a system can be increased by doing
work on the system, but ∆A cannot exceed w. Alternatively, the system can do work
on the surroundings by lowering its Helmholtz energy, but the work done on the surroundings is limited by
dw surr ≤ −dA (T constant)
(4.1-27)
For a finite process at constant temperature
w surr ≤ −∆A (T constant)
(4.1-28)
A system that is not a simple system can exchange work with the surroundings in
different ways. We write
dw −P(transmitted) dV + dw net
(4.1-29)
The term −P(transmitted) dV represents the work that can be done on the system by
changing its volume. We now call this term compression work or P–V work. The term
dw net represents any work in addition to compression work that can be done on a nonsimple system. We call it the net work. Two examples of net work are electrical work
and stress-strain work (stretching a spring or a rubber band). If the volume of a system
is constant, dw dw net and we can write
w net,surr ≤ −∆A (T and V constant)
(4.1-30)