Modern Engineering Thermodynamics

208 CHAPTER 7: Second Law of Thermodynamics and Entropy Transport and Production Mechanisms
IS ENTROPY CONSERVED LIKE ENERGY AND MOMENTUM?
No, but it turns out that, if you “assume” the entropy production equal to zero, then the second law becomes a conservation
law. This makes entropy problems easier to solve, because it eliminates the entropy production term in the entropy
balance equation. But, since entropy is never actually conserved in any real process, processes that “assume” zero entropy
production are only approximations of real world behavior.
We have a special word that we use to tell you when you are to assume the entropy production is zero. The word is reversible.
When you see that word in a problem statement, you know that the entropy production term is assumed to be zero.
However, remember that reversible processes are only approximations of real (irreversible) processes.
At this point we must develop the auxiliary formulae for the entropy transport and production terms before
Eqs. (7.2) and (7.3) can be put to any practical use. Unfortunately, this is not an easy task. To understand the
concepts of entropy transport and production, we must go back to the original 19th century classical ideas of
Carnot, Clausius, and Thomson (Lord Kelvin), the early developers of this field. When this is completed, we
bring the subject forward to a modern formulation.
7.4 CARNOT’S HEAT ENGINE AND THE SECOND LAW
OF THERMODYNAMICS
The origins of the second law of thermodynamics lie in the work of a young 19th century French military
engineer named Nicolas Leonard Sadi Carnot 1 (1796–1832). Sadi was the son of one of Napoleon’s most
successful generals, Lazare Carnot, and was educated at the famous Ecole Polytechnique in Paris. This institution
was established in 1794 as an army engineering school and provided a rigorous program of study in chemistry,
physics, and mathematics. Between 1794 and 1830, the Ecole Polytechnique had such famous instructors as
Lagrange, Fourier, Laplace, Ampere, Cauchy, Coriolis, Poisson, Guy-Lussac, and Poiseuille.
After his formal education, Carnot chose a career as an army officer. At that time, Britain was a powerful military
force, primarily as a result of the Industrial Revolution brought about by the British development of the steam
engine. French technology was not developing as fast as Britain’s, and in the 1820s, Carnot became convinced that
France’s inadequate utilization of steam power had made it militarily inferior. He began to study the fundamentals
of steam engine technology, and in 1824, he published the results of his studies in a small book entitled Reflections
on the Motive Power of Fire (the French word for fire was then a common term for what we call heat today).
Sadi Carnot was trained in the basic principles of hydraulics, pumps, and water wheels at the Ecole Polytechnique.
It was clear to him that the power of a steam engine was released as the heat fluid (caloric) fell from the
high temperature of the boiler to the lower temperature of the condenser, in much the same way that water falls
through a water wheel to produce a mechanical shaft work output. He conjectured that
According to established principles at the present time, we can compare with sufficient accuracy the motive
power of heat to that of a waterfall. The motive power of a waterfall depends on its height and on the
quantity of liquid; the motive power of heat depends also on the quantity of caloric used, and on what may
be termed, on what in fact we will call, the height of its fall, that is to say, the difference of temperature of
the bodies between which the exchange of caloric is made.
WHAT IS HEAT ANYWAY?
The essence of the concept of heat was a very actively debated scientific topic at the time. In 1789, the great French chemist
Antoine Lavoisier (1743–1794) proposed the caloric theory of heat, in which heat was presumed to be a colorless, odorless,
weightless fluid called caloric that could be poured from one object to another. When an object became full of caloric, it was said
to be saturated with it. This was the origin of the terms saturated liquid, saturated vapor, and so on that we use in thermodynamics
today. These terms were introduced into the scientific literature in the early 19th century, when the caloric theory of heat was
popular, and they were never removed when it was later proven that heat was not a fluid. Today, they are simply misnomers.
Now, when we use the word heat in a technical sense, we normally mean an energy transport arising from a temperature difference.
1 Pronounced car-no. Many French words have a silent t ending. For example, Peugot, Tissot, Monet, ballet, chalet, Chevrolet, and Renault.
Sadi was named after the medieval Persian poet Saadi Musharif ed Din, whose poems became popular in France in the late 18th century.