Fig. 6.1) to be closely positioned in the thermodynamic space. But, unless an
additional condition that the net force acting on the piston is infinitesimal also
prevails through a design arrangement of balancing all forces (Fig. 6.2 and
Problem 6.3), the changes at the relaxation of each constraint will be sudden, not
slow. This force-balance design arrangement is present either explicitly or tacitly
when one applies Eq. (81). In absence of such arrangement, during each transition
between neighboring equilibrium states “the system necessarily passes through
non-equilibrium states” [5:99] as noted Callen, no matter how dense the set of the
equilibrium states is; for such cases Eq. (81) is not applicable.
The idea of design (force-balance design) is always present, tacitly or explicitly,
in the classical formalism of thermodynamics of Gibbs, Carathéodory, and Callen.
What is absent is useful work (definition in Sect. 6.5), not the idea of design or
machines.
Internal reversibility (see Sects. 6.4 and 6.5), not quasi-static processes, should
be the central concept in classical formalism as we shall see in the following.
Max Planck
6.4 Local Thermodynamic Equilibrium and the Modern
(Brussels School) Formalism
The synthesis of Carnot–Kelvin–Clausius was presented by Planck in an authoritative exposition [9]. Planck puts the second law, the concept of entropy, and
irreversibility in nonequilibrium systems at the very center of thermodynamics. As
a working knowledge, however, thermodynamics was restricted to handle problems
of equilibrium systems. How to incorporate the handling of irreversibility
142
6 Reversible Processes Versus Quasi-static Processes …
additional condition that the net force acting on the piston is infinitesimal also
prevails through a design arrangement of balancing all forces (Fig. 6.2 and
Problem 6.3), the changes at the relaxation of each constraint will be sudden, not
slow. This force-balance design arrangement is present either explicitly or tacitly
when one applies Eq. (81). In absence of such arrangement, during each transition
between neighboring equilibrium states “the system necessarily passes through
non-equilibrium states” [5:99] as noted Callen, no matter how dense the set of the
equilibrium states is; for such cases Eq. (81) is not applicable.
The idea of design (force-balance design) is always present, tacitly or explicitly,
in the classical formalism of thermodynamics of Gibbs, Carathéodory, and Callen.
What is absent is useful work (definition in Sect. 6.5), not the idea of design or
machines.
Internal reversibility (see Sects. 6.4 and 6.5), not quasi-static processes, should
be the central concept in classical formalism as we shall see in the following.
Max Planck
6.4 Local Thermodynamic Equilibrium and the Modern
(Brussels School) Formalism
The synthesis of Carnot–Kelvin–Clausius was presented by Planck in an authoritative exposition [9]. Planck puts the second law, the concept of entropy, and
irreversibility in nonequilibrium systems at the very center of thermodynamics. As
a working knowledge, however, thermodynamics was restricted to handle problems
of equilibrium systems. How to incorporate the handling of irreversibility
142
6 Reversible Processes Versus Quasi-static Processes …