And, the reversible useful work (maximum useful work) for process A!
restricted dead state is
U À T 0 S þ p 0 V
½
A À U À T 0 S þ p 0 V
½
B
Or,
Ex
MTL
À
Á
A
¼ U À T 0 S þ p 0 V
½
A À U À T 0 S þ p 0 V
½
0
ð117Þ
7.3.3 Discussion
Clearly, Eq. (117) is based on the first exergy definition and the physical exergy of
the system is defined in terms of the system and its environment with which the
system interacts. With the first exergy definition, the value of physical exergy is not
subjected explicitly to the notion that it is a portion of energy as the second exergy
definition declares. In the latter case, as Eq. (96) implies exergy energy (in other
words, all three quantities [energy, exergy, and anergy] are positive definite and a
negative anergy will be senseless). Yet, there are systems and their environments
for which anergys are found to be negative and, for these instances, the second
exergy definition is problematic. However, the problematic second exergy definition is necessary for the concepts of kinetic exergy and potential energy as shown in
Eqs. (115) and (116); it captures importantly that kinetic and potential exergies, as
examples of pure exergy energies, can be completely converted into other forms of
pure exergy energy, such as electrical energy. Nonetheless, while both definitions
are necessary, there is a conflict between the two definitions in that the first exergy
definition allows the possibility of exergy ! energy whereas the second exergy
definition implies that exergy, as a portion of energy, is always smaller than energy.
Pure exergy energies and physical exergy are core parts of the theory of exergy,
as treated by Bejan et al. [13]. Substitution of Eqs. (115), (116), and (117) into
(113) yields the exergy change between two states, state 1 and state 2, of a closed
system
Ex 2 À Ex 1 ¼ U 2 À U 1
ð
Þþp 0 V 2 À V 1
ð
ÞÀT 0 S 2 À S 1
ð
Þþ KE 2 À KE 1
ð
Þ þPE 2 À PE 1
ð
Þ
¼ E 2 À E 1
ð
Þþp 0 V 2 À V 1
ð
ÞÀT 0 S 2 À S 1
ð
Þ
ð118Þ
7.4 Thermodynamic Processes and Exergy Balance
Consider the application of energy balance and entropy balance to a closed system,
respectively,
174
7 Free Energy, Exergy, and Energy …
restricted dead state is
U À T 0 S þ p 0 V
½
A À U À T 0 S þ p 0 V
½
B
Or,
Ex
MTL
À
Á
A
¼ U À T 0 S þ p 0 V
½
A À U À T 0 S þ p 0 V
½
0
ð117Þ
7.3.3 Discussion
Clearly, Eq. (117) is based on the first exergy definition and the physical exergy of
the system is defined in terms of the system and its environment with which the
system interacts. With the first exergy definition, the value of physical exergy is not
subjected explicitly to the notion that it is a portion of energy as the second exergy
definition declares. In the latter case, as Eq. (96) implies exergy energy (in other
words, all three quantities [energy, exergy, and anergy] are positive definite and a
negative anergy will be senseless). Yet, there are systems and their environments
for which anergys are found to be negative and, for these instances, the second
exergy definition is problematic. However, the problematic second exergy definition is necessary for the concepts of kinetic exergy and potential energy as shown in
Eqs. (115) and (116); it captures importantly that kinetic and potential exergies, as
examples of pure exergy energies, can be completely converted into other forms of
pure exergy energy, such as electrical energy. Nonetheless, while both definitions
are necessary, there is a conflict between the two definitions in that the first exergy
definition allows the possibility of exergy ! energy whereas the second exergy
definition implies that exergy, as a portion of energy, is always smaller than energy.
Pure exergy energies and physical exergy are core parts of the theory of exergy,
as treated by Bejan et al. [13]. Substitution of Eqs. (115), (116), and (117) into
(113) yields the exergy change between two states, state 1 and state 2, of a closed
system
Ex 2 À Ex 1 ¼ U 2 À U 1
ð
Þþp 0 V 2 À V 1
ð
ÞÀT 0 S 2 À S 1
ð
Þþ KE 2 À KE 1
ð
Þ þPE 2 À PE 1
ð
Þ
¼ E 2 À E 1
ð
Þþp 0 V 2 À V 1
ð
ÞÀT 0 S 2 À S 1
ð
Þ
ð118Þ
7.4 Thermodynamic Processes and Exergy Balance
Consider the application of energy balance and entropy balance to a closed system,
respectively,
174
7 Free Energy, Exergy, and Energy …