…Clearly, human techno-economic systems have the capacity to emerge in harmful forms.
But if we are to find viable pathways beyond our present global ecological,
techno-economic, social and cultural problems, our efforts to create these better futures will
benefit from the most comprehensive and thorough understandings of current realities and
future possibilities that we can construct. Better knowledge of how our basic physical
foundations operate is an essential part of this. [38:1042)]
The predicative entropic theory can be an essential part of the knowledge by clearly
envisioning possibilities in the Poincare range and in the role of natural EGP.
Problems
8:1 An ideal gas of 0.1 kmol at the initial state of 298.15 K and 303.9 kPa
occupies one chamber of a composite system. The other chamber (of double
volume of the first) contains a vacuum. The two chambers are separated by
a frictionless piston. The piston is now connected to a mechanism that
balances the force exerted by the gas on the piston and is equipped with
work storage capacity––and the whole composite system is submerged in a
heat reservoir/bath at 298.15 K. The ideal gas undergoes an isothermal
expansion from its initial volume V 1 to its final volume 3 V 1 . Determine V 1 ,
the final pressure, and the EGP of the composite system. Also, determine
the entropy change of the ideal gas expansion process, heat absorbed by the
ideal gas during isothermal expansion, and work produced by the ideal gas
during isothermal expansion. What is the total entropy change of the
composite system and the bath?
0:816 m
3
; 101:3kPa; EGP ¼ 0:9134 kJ/K
0:9134 kJ/K
Q ¼ T 0 DS ¼ 272:3 kJ
W ¼ T 0 DS ¼ 298:15 Á 0:913 ¼ 272:3 kJ
DS
ð Þ univ ¼ 0:9134 þ
ÀQ
298:15
¼ 0
8:2 Consider the case of a cold body initially at T, which is lower than T 0 of the
surrounding reservoir. Heat flows in this case out of the reservoir into the
body. Show that the total entropy production corresponding to the spontaneous process of the cold body approaching thermal equilibrium with the
reservoir is
ðD P SÞ spon tan eous ¼ À
C p ðT 0 À TÞ
T 0
þ C p ln
T 0
T
! 0
(The above expression may be written as—by introducing
TÀT 0
T 0
x À ln
1
1 þ x À x
h
i
. It can be readily shown that ln
1
1 þ x À x
h
i
! 0
when À1 x 0.)
8.8 Entropy Growth Potential and Reversibility’s Triadic Framework
227
But if we are to find viable pathways beyond our present global ecological,
techno-economic, social and cultural problems, our efforts to create these better futures will
benefit from the most comprehensive and thorough understandings of current realities and
future possibilities that we can construct. Better knowledge of how our basic physical
foundations operate is an essential part of this. [38:1042)]
The predicative entropic theory can be an essential part of the knowledge by clearly
envisioning possibilities in the Poincare range and in the role of natural EGP.
Problems
8:1 An ideal gas of 0.1 kmol at the initial state of 298.15 K and 303.9 kPa
occupies one chamber of a composite system. The other chamber (of double
volume of the first) contains a vacuum. The two chambers are separated by
a frictionless piston. The piston is now connected to a mechanism that
balances the force exerted by the gas on the piston and is equipped with
work storage capacity––and the whole composite system is submerged in a
heat reservoir/bath at 298.15 K. The ideal gas undergoes an isothermal
expansion from its initial volume V 1 to its final volume 3 V 1 . Determine V 1 ,
the final pressure, and the EGP of the composite system. Also, determine
the entropy change of the ideal gas expansion process, heat absorbed by the
ideal gas during isothermal expansion, and work produced by the ideal gas
during isothermal expansion. What is the total entropy change of the
composite system and the bath?
0:816 m
3
; 101:3kPa; EGP ¼ 0:9134 kJ/K
0:9134 kJ/K
Q ¼ T 0 DS ¼ 272:3 kJ
W ¼ T 0 DS ¼ 298:15 Á 0:913 ¼ 272:3 kJ
DS
ð Þ univ ¼ 0:9134 þ
ÀQ
298:15
¼ 0
8:2 Consider the case of a cold body initially at T, which is lower than T 0 of the
surrounding reservoir. Heat flows in this case out of the reservoir into the
body. Show that the total entropy production corresponding to the spontaneous process of the cold body approaching thermal equilibrium with the
reservoir is
ðD P SÞ spon tan eous ¼ À
C p ðT 0 À TÞ
T 0
þ C p ln
T 0
T
! 0
(The above expression may be written as—by introducing
TÀT 0
T 0
x À ln
1
1 þ x À x
h
i
. It can be readily shown that ln
1
1 þ x À x
h
i
! 0
when À1 x 0.)
8.8 Entropy Growth Potential and Reversibility’s Triadic Framework
227