nonrepresentable nonequilibrium states during each expansion; the irreversibility of the
microexpansions is essential and irreducible. The fact that dS > 0 whereas dQ = 0 is
inconsistent with presumptive applicability of the relation dQ = TdS to all quasi-static
processes. We define (by somewhat circular logic!) the continuous free expansion process
as being “essentially irreversible” and non-quasi-static [5:99].
That micro-free-expansion is irreversible is a fact; that it can be idealized by
quasi-static process is a matter of definition (by Callen’s own definition). We have a
syllogism of a major premise (the applicability of Eq. (81)) and a subsidiary premise
(the definition) linked to a conclusion, and the conclusion is not supported by the
fact. Either the major premise or the subsidiary premise must be rejected. Callen, in
rejecting the subsidiary premise definition “micro-free-expansion = quasi-static”,
did not, in fact, commit logical error but made the wrong choice. He reached the
wrong conclusion by not questioning the validity of Eqs. (81) and (83) and, instead,
made an unusual move by abandoning the definition.
The universal premise quasi-static reversible in the context of Eq. (83) has
been questioned by a number of physicists (the latest example is in a paper by
Samiullah, who wrote, “although not all quasi-static processes are reversible, the
converse statement that all reversible processes are quasi-static is true” [8:24]).
In contrast, the equally mistaken presumptive applicability of Eq. (81) for processes of infinitely dense equilibrium states has never been critiqued! It must be
noted that since “if Eq. (81), then Eq. (83),” the rejection of Eq. (83) must be
followed by the rejection of Eq. (81) according to modus tollens. For engineering
problems of heat and work, we need a more precise condition for the applicability
of Eqs. (81) and (83) as it’ll be given in Sect. 6.5.
The classical formalism and Gibbsian thermodynamics represented the mechanistic capture of the mechanical theory of heat, which views thermodynamics as the
naturalistic science of energy rather than the engineering science of heat and
energy. Though the move had been initiated by Kelvin, Kelvin himself retained
viewing energy’s role to be its engineering capacity for doing work grounded in the
Carnot–Kelvin tradition of heat, power, and reversible processes. That tradition
underwent transformation post-Kelvin to become the Gibbs, Carathéodory, and
Callen problem of energy, entropy, and quasi-static processes of today. In that
modern view, thermodynamic events are captured completely by “differentials of
the state functions” [5(1960):viii]. This mechanistic interpretation of the mechanical
theory of heat was probably the inevitable result of the growing popularity of
atomism in the late 19th century. The classical formalism finds its great success in
application to physical and chemical problems as it’ll be treated in Chap. 9.
140
6 Reversible Processes Versus Quasi-static Processes …
microexpansions is essential and irreducible. The fact that dS > 0 whereas dQ = 0 is
inconsistent with presumptive applicability of the relation dQ = TdS to all quasi-static
processes. We define (by somewhat circular logic!) the continuous free expansion process
as being “essentially irreversible” and non-quasi-static [5:99].
That micro-free-expansion is irreversible is a fact; that it can be idealized by
quasi-static process is a matter of definition (by Callen’s own definition). We have a
syllogism of a major premise (the applicability of Eq. (81)) and a subsidiary premise
(the definition) linked to a conclusion, and the conclusion is not supported by the
fact. Either the major premise or the subsidiary premise must be rejected. Callen, in
rejecting the subsidiary premise definition “micro-free-expansion = quasi-static”,
did not, in fact, commit logical error but made the wrong choice. He reached the
wrong conclusion by not questioning the validity of Eqs. (81) and (83) and, instead,
made an unusual move by abandoning the definition.
The universal premise quasi-static reversible in the context of Eq. (83) has
been questioned by a number of physicists (the latest example is in a paper by
Samiullah, who wrote, “although not all quasi-static processes are reversible, the
converse statement that all reversible processes are quasi-static is true” [8:24]).
In contrast, the equally mistaken presumptive applicability of Eq. (81) for processes of infinitely dense equilibrium states has never been critiqued! It must be
noted that since “if Eq. (81), then Eq. (83),” the rejection of Eq. (83) must be
followed by the rejection of Eq. (81) according to modus tollens. For engineering
problems of heat and work, we need a more precise condition for the applicability
of Eqs. (81) and (83) as it’ll be given in Sect. 6.5.
The classical formalism and Gibbsian thermodynamics represented the mechanistic capture of the mechanical theory of heat, which views thermodynamics as the
naturalistic science of energy rather than the engineering science of heat and
energy. Though the move had been initiated by Kelvin, Kelvin himself retained
viewing energy’s role to be its engineering capacity for doing work grounded in the
Carnot–Kelvin tradition of heat, power, and reversible processes. That tradition
underwent transformation post-Kelvin to become the Gibbs, Carathéodory, and
Callen problem of energy, entropy, and quasi-static processes of today. In that
modern view, thermodynamic events are captured completely by “differentials of
the state functions” [5(1960):viii]. This mechanistic interpretation of the mechanical
theory of heat was probably the inevitable result of the growing popularity of
atomism in the late 19th century. The classical formalism finds its great success in
application to physical and chemical problems as it’ll be treated in Chap. 9.
140
6 Reversible Processes Versus Quasi-static Processes …