statistical mechanical foundation of the second law nor the axiomatic foundations
of the law, but it does consider the engineering application of the second law to be
its central goal.
With that in mind, it is important to warn against a dangerous view in engineering that entropy and the second law should be avoided in favor of an
energy-centric treatment of engineering thermodynamics [3]. This would have been
a grave mistake, the consequence of which would be condemning practitioners of
engineering thermodynamics to be the second-class scientists/engineers instead of
the true descendants of Carnot.
The purpose of this section is to show that, through the introduction of Helmholtz free energy and Gibbs free energy, the direct application of the entropy
principle leads to the idea of useful energy and exergy, the idea that gave meaning
to energy as we understand it. The idea, without which modern engineering practice
cannot exist.
An isothermal composite system of constant system volume in interaction with
an isothermal heat reservoir at T
r , initially at V
1
ð Þ
1 and V
2
ð Þ
1 , corresponding to A H 1 ,
will approach equilibrium when,
V
1
ð Þ
! V
1
ð Þ
equili and V
2
ð Þ
! V
1
ð Þ
1 þ V
2
ð Þ
1
h
i
À V
1
ð Þ
equili
corresponding to the minimization of the system Helmholtz function, A H ! A H min .
The difference in system Helmholtz function, A H 1 À A H min , is subject to the following interpretation: Note first the relation
A H 1 À A H min ¼ U À T
r S
ð
Þ 1 À U À T
r S
ð
Þ equili ¼ U 1 À U equili
À
Á À T
r S 1 À S equili
À
Á
Consider the process to be reversible and we have Q 1!equili ¼ T
r S equili À S 1
À
Á
.
Correspondingly,
A H 1 À A H min ¼ U 1 À U equili
À
Á þ Q 1!equili
By the first law, DU ¼ Q 1!equili À W 1!equili , it follows
A H 1 À A H min ¼ U 1 À U equili
À
Á þ Q 1!equili ¼ W 1!equili
À
Á
rev
That is,
Helmholtz free energy ¼ A H 1 À A H min ¼ Reversible Useful Work
ð106Þ
teaching the second law. One thing I noticed is that there is little in common in their presentations,
which means we have a long way from finding a unified approach in teaching the second law.
I was particularly pleased to hear that MIT is team teaching a combined energy-philosophy course,
which, I think, is very interesting. I wish Professor Trout the best of luck in this undertaking…”
164
7 Free Energy, Exergy, and Energy …
of the law, but it does consider the engineering application of the second law to be
its central goal.
With that in mind, it is important to warn against a dangerous view in engineering that entropy and the second law should be avoided in favor of an
energy-centric treatment of engineering thermodynamics [3]. This would have been
a grave mistake, the consequence of which would be condemning practitioners of
engineering thermodynamics to be the second-class scientists/engineers instead of
the true descendants of Carnot.
The purpose of this section is to show that, through the introduction of Helmholtz free energy and Gibbs free energy, the direct application of the entropy
principle leads to the idea of useful energy and exergy, the idea that gave meaning
to energy as we understand it. The idea, without which modern engineering practice
cannot exist.
An isothermal composite system of constant system volume in interaction with
an isothermal heat reservoir at T
r , initially at V
1
ð Þ
1 and V
2
ð Þ
1 , corresponding to A H 1 ,
will approach equilibrium when,
V
1
ð Þ
! V
1
ð Þ
equili and V
2
ð Þ
! V
1
ð Þ
1 þ V
2
ð Þ
1
h
i
À V
1
ð Þ
equili
corresponding to the minimization of the system Helmholtz function, A H ! A H min .
The difference in system Helmholtz function, A H 1 À A H min , is subject to the following interpretation: Note first the relation
A H 1 À A H min ¼ U À T
r S
ð
Þ 1 À U À T
r S
ð
Þ equili ¼ U 1 À U equili
À
Á À T
r S 1 À S equili
À
Á
Consider the process to be reversible and we have Q 1!equili ¼ T
r S equili À S 1
À
Á
.
Correspondingly,
A H 1 À A H min ¼ U 1 À U equili
À
Á þ Q 1!equili
By the first law, DU ¼ Q 1!equili À W 1!equili , it follows
A H 1 À A H min ¼ U 1 À U equili
À
Á þ Q 1!equili ¼ W 1!equili
À
Á
rev
That is,
Helmholtz free energy ¼ A H 1 À A H min ¼ Reversible Useful Work
ð106Þ
teaching the second law. One thing I noticed is that there is little in common in their presentations,
which means we have a long way from finding a unified approach in teaching the second law.
I was particularly pleased to hear that MIT is team teaching a combined energy-philosophy course,
which, I think, is very interesting. I wish Professor Trout the best of luck in this undertaking…”
164
7 Free Energy, Exergy, and Energy …