Modern Engineering Thermodynamics

206 CHAPTER 7: Second Law of Thermodynamics and Entropy Transport and Production Mechanisms
systems, as in Chapter 6. Then appropriate applications are presented, dealing with a variety of common
open systems of engineering interest, such as nozzles, diffusers, throttling devices, heat exchangers, and mixing.
Chapter 9 ends with a brief discussion of shaft work machines and unsteady state processes.
7.2 WHAT IS ENTROPY?
When we discussed the first law of thermodynamics in Chapter 4, it was fairly easy to apply the general balance
equations to the energy concept and to invoke the conservation of energy principle to obtain a workable energy
balance equation. Energy is a common English word, and it is also a well-accepted technical term. Everyone has
a basic understanding of what the word means, though we would all have a difficult time defining it precisely.
Thesamecanbesaidforthewordsforce and momentum. They are such familiar words that we easily accept
mathematical formulae and logical arguments structured around them.
Most people are intrigued by seeing a movie run backward because it produces images of things never observed
in the real world. What they do not realize is that they are seeing the effects of the second law of thermodynamics
in action. The second law dictates the direction of the arrow of time. That is, things occur only in a
certain way in the real world; and by applying the second law to an observation (like the screening of a movie),
we can determine whether the event is running forwardorbackwardintime.Thesecondlawofthermodynamics
is what prohibits us from actually traveling backward in time. Curiously, it is the only law of nature
that has such a restriction. All the other laws of mechanics and thermodynamics are valid regardless of whether
time is moving forward or backward. Only the second law of thermodynamics is violated when time is reversed.
At this point we need to introduce a new thermodynamic property that is simply a measure of the amount of
molecular disorder within a system. The name of this new property is entropy. The meaning of this particular
name is explained later, but note that a system that has a high degree of molecular disorder (such as a hightemperature
gas) has a very high entropy value and, conversely, a system that has a very low degree of molecular
disorder (such as a crystalline solid) has a very low entropy value. This new property is very important because
entropy is at the core of the second law of thermodynamics.
A system that has all its atoms arranged in some perfectly ordered manner has an entropy value of zero. This is the
substance of the third law of thermodynamics. This law, introduced in 1906 by Walter H. Nernst (1864–1941),
states that the entropy of a pure substance is a constant at absolute zero temperature. In 1911, Max Planck modified
this law by setting the entropies of all pure substances equal to zero at absolute zero temperature. This had
the effect of normalizing entropy values and thus creating a uniform absolute entropy scale for all substances.
Therefore, we can write the following simple mathematical statement of the third law of thermodynamics:
The third law of thermodynamics: The entropy of a pure substance is zero at absolute zero temperature, or
lim ð Entropy of a pure substance Þ = 0 (7.1)
T!0
With this simple entropy-disorder concept in mind, we would expect that the entropy of solid water (ice), with
its highly ordered molecular structure, would be less than that of liquid water with its amorphous molecular
structure, which in turn would be less than that of water vapor with its highly random molecular order. This is
in fact true, for at the triple point of water (the only point where the solid, liquid, and vapor phases coexist in
equilibrium), the values of the specific entropies of these phases are
Specific entropy of ice at the triple point = −1:221 kJ/ ðkg.KÞ = −0:292 Btu/ ðlbm.RÞ
Specific entropy of liquid water at the triple point = 0:0 kJ/ ðkg.KÞ = 0:0 Btu/ ðlbm.RÞ
Specific entropy of water vapor at the triple point = 9:157 kJ/ ðkg.KÞ = 2:187 Btu/ ðlbm.RÞ
So clearly the entropy of a solid < the entropy of a liquid < the entropy of a vapor or gas.
IS ENTROPY LIMITED TO MOLECULES?
Even though the physical concept of entropy is based on the behavior of molecular systems, order and disorder phenomena
exist at all levels. For example, if entropy is a measure of disorder, then what is the entropy of your bedroom? If you
have a messy room it is very disordered, so its entropy is high, but if you are a neat person and keep things picked up and
put away, then it has a low entropy. Things seem to get messy easily, and to maintain cleanliness and order requires constant
effort. This is a fundamental characteristic of the second law of thermodynamics. The natural progression of things is
from ordered to disorganized and to keep it organized requires the input of energy. If entropy had been named disorder,
perhaps it would not be so difficult to understand.