When the condition of internal reversibility prevails within the system, the
temperature gradient within the system must become infinitesimal and T(x, y, z, t)
becomes the single-valued thermostatic temperature of the system, i.e.,
Z
A
ÀJ Q
T
dA
2
4
3
5 dt ¼
R
A ÀJ Q dA
Â
Ã
dt
T
¼
dQ
T
Equation (91) takes the form
dS ¼
dQ
T
InternalReversible
¼
dU þ pdV
T
ð92Þ
I shall note in Sect. 6.5 that both reversibility and internal reversibility (IR) are
subsets of the set of quasi-staticity (see also Fig. 6.3). Correspondingly, the
applicability of (92) [18] is based on.
a. reversibility as the sufficient condition,
b. internal reversibility as the necessary and sufficient condition, and,
c. quasi-staticity (see Sect. 6.5 for definition) as the necessary condition.
Equation (92) is the precise definition of the entropy, superseding the classical
formalism definition, Eq. (83) in this chapter and the Clausius definition, Eq. (62A)
in Chap. 5, as it will be summarized in Sect. 6.5.
Fig. 6.3 Venn diagram of the conditions of reversibility, internal reversibility (IR), and
quasi-staticity
6.4 Local Thermodynamic Equilibrium …
147