Page 61 - Entrophy Analysis in Thermal Engineering Systems

The common source of entropy increase 53

(specific entropy multiplied by mass) terms where the entropy of a substance
is determined using Eq. (1.11). Thus, there should not be a surprise that the
only phenomenon responsible for entropy generation is heat transfer. A
claim that entropy generation can take place in the absence of heat would
be in contradiction of the original definition of entropy, Eq. (1.9). A change
in the entropy of a body strictly depends on the amount of heat and its tem-
perature at which the heat transfer takes place. Entropy production is an
indication of the extent of heat transfer.
Several interpretations have been presented for entropy, which have no
or very limited connection to its original definition as introduced by
Clausius. For instance, entropy has been viewed as a measure of disorder.
This notion is originated from Boltzmannian definition of entropy that relies
on the molecular motion or the theory of probabilities where entropy is

described as a product of k B , Boltzmann constant, and ln W where W
denotes the number of microstates. The relation for the Boltzmannian
entropy S¼k B ln W rests on a critical assumption that the entropy of a state
depends on the probability of that state [8]. The notion of entropy as a mea-
sure of disorder has been discredited by recent scholars [9,10].
Entropy has also been interpreted as a measure of energy dispersal. In
1910, Kline wrote: “Growth of entropy is a passage from a concentrated
to a distributed condition of energy. Energy originally concentrated vari-
ously in the system is finally scattered uniformly in said system” [8]. This
view of entropy was further elucidated in 1996 by Leff [11] and a few years
later by Lambert [10,12]. The energy dispersal view of entropy, undo-
ubtfully better than disorder, is also based upon the statistical definition of
entropy, i.e., k B ln W, without regard to its original definition. For instance,
the entropy increase associated with the expansion of a gas is explained to be
due to microstates being more accessible in the final state than the initial
because the volume increases. The reasoning given for the case of mixing
of two ideal gases in a box, which are initially separated by a partition, is
similar, but the thermal effect is overlooked.
It must be noted that the reason why entropy generation is usually related
to mere irreversibility of expansion and mixing processes is the confusion
that appears to exist with respect to the combined first and second laws
equation, Eq. (1.19), and that the Clausius definition of entropy is replaced
with statistical arguments, which rely on S¼k B ln W. The common
misperception with respect to Eq. (1.19) is that it is usually treated as a
self-standing thermodynamic equation without recognizing where it is orig-
inated from. Eq. (1.19) is an alternative expression of the first law equation