W useful
À
Á
rev
¼ Q rev À Q spon
ð124AÞ
This value, Q rev À Q spon , can be shown to be related to the “entropy generation”
of a spontaneous natural event. First, consider the spontaneous event shown
schematically in Fig. 8.1, where the system entropy change is DS ¼ S B ÀS A
ð
Þ, the
entropy change of the surrounding reservoir is DS 0 ¼ ÀQ spon =T 0 : Since the entropy
exchange of the universe D E S
ð
Þ universe is by definition zero, the entropy “generation” (we are not sure of it being positive yet) of the universe equals the total
entropy change of the universe according to Eq. (84C)
entropy generation in the universe ¼ entropy change of the universe
That is,
DS
ð Þ universe ¼ DS þ ÀQ spon =T 0
À
Á
the sum of the system entropy change DS and the entropy change of the reservoir
DS 0 ¼ ÀQ spon =T 0 : Note that even though the large dissipative process of entropy
production is taking place within the transmission medium in Fig. 8.1, the entropy
change of the medium is zero in the above expression due to the assumption of the
infinitesimal medium mass.
A spontaneous natural event must be associated with positive entropy generation. Whether transformation direction A ! B or B ! A will take place spontaneously is dependent on which transformation results in entropy increase.
Assuming A ! B to be the case
Fig. 8.1 The “universe” of a spontaneous event
8.3 The Entropic Drive Corollary
199
À
Á
rev
¼ Q rev À Q spon
ð124AÞ
This value, Q rev À Q spon , can be shown to be related to the “entropy generation”
of a spontaneous natural event. First, consider the spontaneous event shown
schematically in Fig. 8.1, where the system entropy change is DS ¼ S B ÀS A
ð
Þ, the
entropy change of the surrounding reservoir is DS 0 ¼ ÀQ spon =T 0 : Since the entropy
exchange of the universe D E S
ð
Þ universe is by definition zero, the entropy “generation” (we are not sure of it being positive yet) of the universe equals the total
entropy change of the universe according to Eq. (84C)
entropy generation in the universe ¼ entropy change of the universe
That is,
DS
ð Þ universe ¼ DS þ ÀQ spon =T 0
À
Á
the sum of the system entropy change DS and the entropy change of the reservoir
DS 0 ¼ ÀQ spon =T 0 : Note that even though the large dissipative process of entropy
production is taking place within the transmission medium in Fig. 8.1, the entropy
change of the medium is zero in the above expression due to the assumption of the
infinitesimal medium mass.
A spontaneous natural event must be associated with positive entropy generation. Whether transformation direction A ! B or B ! A will take place spontaneously is dependent on which transformation results in entropy increase.
Assuming A ! B to be the case
Fig. 8.1 The “universe” of a spontaneous event
8.3 The Entropic Drive Corollary
199