Crítica, Revista Hispanoamericana de Filosofía, Volume 19, number 56, agosto 1987
Formulaciones del segundo principio
de la termodinámica
[]
Julián Garrido Garrido
Facultad de Ciencias
Departamento de Filosofía
Universidad de Granada
Abstract: The second principle is usually considered as an axiom of Classical
Equilibrium Thermodynamics (CET), but there are different
versions of that law and the deductive relations between them are
not immediately evident. That is so because the formulations were
given in distinct epochs using very heterogeneous concepts, from
the “mechanist" language before the stable construction of CET
until the properly theoretical language of systems and states.
The versions of KelvinPlanck (KP), Clausius (C1) and Carnot
(Ca) preceded the concept of entropy. That emerged tied to the
formulation of the second principle given by classical entropy (SC):
ΔS ≥ Σ1 ∫ dQ1/T1 (where the 1s are the systems that interchange
heat with the system that varies its entropy, its heat surroundings).
The law of increasing entropy (AS), that of potential
entropy (PS) and the statemet of Carathéodory (Cth) are postentropic
formulations of the second principle. From another point
of view, the expressions KP, C1, Ca, SC and Cth can be classified as
belonging to the classical developments of the theory, and the law
PS as a member of the Gibbsian representations. Formulation AS
could be considered as above this second clasification, since from
this study it follows that it constitutes the most powerful version
of the second principle, which permits the deduction equally of the
Gibbsian expression (PS) as the classical ones (first SC, and on
that basis the remaining four, which are more specific).
The deductive tree of such diverse laws can only be realized after
a systematic analysis of the basic concepts of CET, which permits a
homogeneous reformulation of them all. For that task the genetic,
historical and intuitive point of view should be left aside so as
to adopt a purely axiomaticdeductive point of view. The results
of my formulation of CET, Garrido (19831986), realized following
the axiomatic focus designed by Bunge (1967) for factual theories,
have been used in this previous conceptual analysis. On the other
hand, the deductive tree of the formuIations of the second principle
constructed here has as effect a modification, small but interesting,
of the axiomatic base for my proposal for CET: in my previous
work I considered the laws SC and AS strictly equivalent and as
such interchangeable as axioms, and I had chosen precisely SC for
that purpose. Now, as l argue here in detail, I have confirmed that
AS is more general than SC and so should be the formulation of
the second principle that appears as an axiom of the theory.
Amongst the basic concepts of the domain of reference of the
laws of this theory which are used here, the strangest is that of
pseudoequilibrium (the state of those systems which are not in
equilibrium, but whose subsystems are). In the usual statements
of the theory this concept at times appears explicitly and with
varying denominations (system with internal constraints, internally
constrained system, etc.), and on many occasions appears
in an implicit way, with no proper name (the term equilibrium is
frequently used in a wide sense, covering pseudoequilibrium, but
that ambiguity is a source of confusion and obscurity). Here a general
and exact definition of this concept is presented and, aboye all,
is systematically used, greatly easing the theoretical and homogeneous
formulation of versions of the second principle, in particular
that of the law of increasing entropy:
(AS) For any isolated system, between two instants in which it is in a state of equilibrium or pseudoequilibrium: ΔS ≥ 0, yielding
identity when in all the intermediate instants the system maintains
itself in equilibrium or pseudoequilibrium.
Even if this law is the most powerful expression of the second
principle, it is not sufficient for the deduction of the remaining versions.
It is also necessary to consider other axioma of CET, such as
the first principle, the law of heat, and the postulate of isolation
and equilibrium. Nevertheless, even if they are not exclusively theorems
of AS, they can still be considered as (weak) formulations
of the second principle, That is due to the fact that what is most
peculiar about them, inequality, is deductively inherited from AS
(the only axiom of the theory that contains it).
Keywords:
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