6.3 Infinitely Dense State Function Does Not Always Equal
to Infinitely Slow Process
In the application to engineering problems of heat and work, however, the fundamental mistake of the classical formalism is the presumption that a series of infinitely dense equilibrium states (see Fig. 6.1 and Problem 6.2) is synonymous with
an infinitely slow process (see Fig. 6.2 and Problem 6.3). Making a process to be a
series of infinitely dense equilibrium states does not ensure that the process also
proceeds infinitely slow. A set of very closely spaced constraints for the piston
placement of a gas-filled piston cylinder will ensure the system equilibrium states
(resulting from relaxation of constraints [see Ref. [5] for definition] as shown in
Fig. 6.1 Quasi-static process resulting from relaxation of constraints, which is a set of infinitely
dense equilibrium states (this figure represents the same process in Fig. 1.6)
Fig. 6.2 Reversible process resulting from the infinitesimally small net force, which is a set of
equilibrium states moving infinitely slow from one equilibrium state to the next equilibrium state
(this figure represents the same process in Fig. 1.5)
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