Page 34 - Entrophy Analysis in Thermal Engineering Systems

Birth and evolution of thermodynamics 25

Thomson’s paper [21] was published in May 1854. In December of that
year, Clausius published his fourth memoir [26] in Poggendoff’s Annalen in
that the first law is expressed as

(2.18)
Q ¼ U + A W
where, in accordance with the Clausius’ notations, Q denotes the heat
imparted to the system, U is the sum of the thermal energy and interior work,
and W designates the exterior work. Clausius explains that the interior work is
due to the forces “which the atoms of a body exert upon each other, and
which depend, of course, upon the nature of the body.” The exterior work
refers to the work done by the system in overcoming the external forces.

In the same paper, Clausius enunciated the Theorem of the Equivalence of
Transformations and derived the following relation for a system undergoing a
cyclical process.
Z
dQ
N ¼ 0 (2.19)
T
where N, the uncompensated transformation as denoted by Clausius, is positive
for all real processes, and zero if the process is reversible. Clausius obtained
inequality (2.19) taking the heat given off by the system as positive and the
heat imparted to the system as negative. However, in his ninth memoir [29],
Clausius adopted an opposite sign convention and therefore expressed the
inequality (2.19) as

Z
0 (2.20)
dQ
T
Later in the same memoir, he assigned a new parameter for the term under
the integration sign.

dQ
dS ¼ (2.21)
T
He wrote: “We might call S the transformational content of the body, just as we
termed the magnitude U its thermal and ergonal content. But as I hold it to be better
to borrow terms for important magnitudes from the ancient languages, so that they may
be adopted unchanged in all modern languages, I propose to call the magnitude S the
entropy of the body.”
Integrating Eq. (2.21) over a reversible path from a reference state to an
arbitrary state yields

Z
S ¼ S 0 + dQ (2.22)
T