4.5.4 Caloric or Heat: Interpreted as Both Heat Flow
and “Entropy” Flow
The heat exchange of a system is always balanced with the work exchange
regardless of whether the cyclic process is reversible or irreversible. The simple
balance of “entropy”-inflow with “entropy”-outflow, i.e., “entropy” conservation, is
an entirely different matter; “entropy”-flow is balanced in this simple manner only
in this special case of reversible cyclic process. In fact, perfect reversibility, which
is a theoretical construct, does not exist in the real physical world. All real processes, natural spontaneous ones as well as artificial ones, are irreversible and, thus,
involve entropy production (see Chap. 6). The entropy balance of all real cases must
take into consideration this inevitable entropy production in addition to the balance
of entropy flow
5 (see Sect. 6.4.1).
The earlier conceptual differentiation of “caloric” into heat flow and heat energy
(the MEH differentiation, Sect. 3.3), and the conceptual differentiation here of the
“flow of caloric” into heat flow and “entropy” flow (Fig. 4.5a, b) are connected but
distinctive moves: That is to say, the two moves together suggest that the single
concept of caloric, as used differently by Joule (Q), Clausius (Q and U), and Carnot
(Q*), should be conceptually differentiated into the concepts of heat flow, thermal
internal energy, and “entropy” flow as shown in Fig. 4.6. With the conceptual
differentiation, both Carnot’s “falling of caloric” understanding of work production
as a result of the transfer of caloric (“entropy”) shown in Fig. 4.5b and Joule’s
understanding of work production as a result of the consumption of heat shown in
Fig. 4.5a are consistent with each other. An unsettled question is the meaning of
“consumption” used in the MEH.
The aforementioned concept of caloric in Fig. 4.6 is used interpretatively, rather
than as a definition. It has the same meaning of the term that I call heat; no attempt
of giving either term a definition is made here, rather, the use of either term implies
their understanding requires both energetic and entropic points of view
6
: The MEH
differentiation stresses the quantitatively energetic equivalence of the effects of heat
flow and work (flow) on change in system internal energy. The new differentiation
here, instead, highlights the qualitatively entropic difference between heat flow and
5
In the case of a steady-state general system, it may be noted that the entropy flowing out of the
system is always larger than the entropy flowing into the system as a result of entropy production.
See Chap. 6 for more details.
6
The treatment of the second law advocated here is closest to that of Planck, which stresses the
centrality of the second law and the energetic/entropic understanding of heat. A distinction is made
between MEH (in its pure sense, not how Joule and Kelvin interpreted it as discussed in Sect. 4.7)
and the “reductive” mechanical theory of heat. In the specific treatment of Q (heat exchange, not
heat in the general inclusive sense) in Sects. 3.2 and 3.3 in the above, however, I followed
Helmholtz and Born by adopting the “mechanical” definition of Q—which is different from
Planck, who considers heat to be a primitive concept and elects to stay away from the reductive
mechanical theory of heat approach. For clarity, it is noted again that the use of the “mechanical”
definition of Q in Sect. 3.3 does not require the full acceptance of the reductive mechanical theory
of heat.
80
4 Carnot’s Theory of Heat, and Kelvin’s Adoption …
and “Entropy” Flow
The heat exchange of a system is always balanced with the work exchange
regardless of whether the cyclic process is reversible or irreversible. The simple
balance of “entropy”-inflow with “entropy”-outflow, i.e., “entropy” conservation, is
an entirely different matter; “entropy”-flow is balanced in this simple manner only
in this special case of reversible cyclic process. In fact, perfect reversibility, which
is a theoretical construct, does not exist in the real physical world. All real processes, natural spontaneous ones as well as artificial ones, are irreversible and, thus,
involve entropy production (see Chap. 6). The entropy balance of all real cases must
take into consideration this inevitable entropy production in addition to the balance
of entropy flow
5 (see Sect. 6.4.1).
The earlier conceptual differentiation of “caloric” into heat flow and heat energy
(the MEH differentiation, Sect. 3.3), and the conceptual differentiation here of the
“flow of caloric” into heat flow and “entropy” flow (Fig. 4.5a, b) are connected but
distinctive moves: That is to say, the two moves together suggest that the single
concept of caloric, as used differently by Joule (Q), Clausius (Q and U), and Carnot
(Q*), should be conceptually differentiated into the concepts of heat flow, thermal
internal energy, and “entropy” flow as shown in Fig. 4.6. With the conceptual
differentiation, both Carnot’s “falling of caloric” understanding of work production
as a result of the transfer of caloric (“entropy”) shown in Fig. 4.5b and Joule’s
understanding of work production as a result of the consumption of heat shown in
Fig. 4.5a are consistent with each other. An unsettled question is the meaning of
“consumption” used in the MEH.
The aforementioned concept of caloric in Fig. 4.6 is used interpretatively, rather
than as a definition. It has the same meaning of the term that I call heat; no attempt
of giving either term a definition is made here, rather, the use of either term implies
their understanding requires both energetic and entropic points of view
6
: The MEH
differentiation stresses the quantitatively energetic equivalence of the effects of heat
flow and work (flow) on change in system internal energy. The new differentiation
here, instead, highlights the qualitatively entropic difference between heat flow and
5
In the case of a steady-state general system, it may be noted that the entropy flowing out of the
system is always larger than the entropy flowing into the system as a result of entropy production.
See Chap. 6 for more details.
6
The treatment of the second law advocated here is closest to that of Planck, which stresses the
centrality of the second law and the energetic/entropic understanding of heat. A distinction is made
between MEH (in its pure sense, not how Joule and Kelvin interpreted it as discussed in Sect. 4.7)
and the “reductive” mechanical theory of heat. In the specific treatment of Q (heat exchange, not
heat in the general inclusive sense) in Sects. 3.2 and 3.3 in the above, however, I followed
Helmholtz and Born by adopting the “mechanical” definition of Q—which is different from
Planck, who considers heat to be a primitive concept and elects to stay away from the reductive
mechanical theory of heat approach. For clarity, it is noted again that the use of the “mechanical”
definition of Q in Sect. 3.3 does not require the full acceptance of the reductive mechanical theory
of heat.
80
4 Carnot’s Theory of Heat, and Kelvin’s Adoption …