Page 26 - Entrophy Analysis in Thermal Engineering Systems

Birth and evolution of thermodynamics 17

Upon concluding a series of experiments with several gases such as air,
oxygen, hydrogen, nitrogen, Gay-Lussac summarized his findings as follows:
“All gases, whatever their density or quantity of water which they hold in solution,
and all vapors expand to the same extent for the same degree of heat. In the case of the
permanent gases, the increase of volume which each of them suffers between the degree
of melting ice and that of boiling water amounts to 80/213.33 of the original volume,
for a thermometer divided in 80 parts, or 100/266.66 of the same volume, for a
centigrade thermometer.” The coefficient of expansion calculated from the
Gay-Lussac work is 0.00375, which was later corrected to 0.003665 based
on more accurate experiments of Magnus and Regnault.

2.3.1 Carnot’s contribution

It was over a century that steam engines had already been in use in mines,
ships, and many other applications, but little was known about the theory of
heat engines. To the best knowledge of the author, the earliest commercial
steam engine was patented by Thomas Savery in 1698, which was employed
for pumping water [11]. Further improvements in the design of steam
engines were introduced by Thomas Newcomen and James Watt.
It was Sadi Carnot who initiated investigating the theory of heat engines
in the early 19th century, which led to a 118-page manuscript published in
1824 [12]. In the introductory portion of his book, when acknowledging the

earlier inventors, he wrote: “If the honor of a discovery belongs to the nation in
which it has acquired its growth and all its developments, this honor cannot be here
refused to England” (see p. 6 in Ref. [12]. The English translation is taken from
Ref. [13], p. 41). The fundamental question, which laid down Carnot’s
investigation, was whether there is a limit for the power generated in a heat
engine. Carnot developed his arguments based on the caloric theory,
although it was already invalidated by Rumford and Davy as discussed in
Section 2.2.3. He then established the following supposition:
The production of motive power is then due in steam-engines not to an actual
consumption of caloric, but to its transportation from a warm body to a cold body,
that is, to its re-establishment of equilibrium … the production of heat alone is not
sufficient to give birth to the impelling power: it is necessary that there should also
be cold; without it, the heat would be useless; [13], p. 46.

It can be inferred from these statements that Carnot was somewhat aware of
the second law. The first axiom that he used in demonstration of the design
of perfect engine is that the production of power would be possible