Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

states of that system, called thermodynamic probability p, by the Boltz-
mann relation,expressed as

(7–20)

where k1.3806 10 ^23 J/K is the Boltzmann constant.Therefore, from
a microscopic point of view, the entropy of a system increases whenever the
molecular randomness or uncertainty (i.e., molecular probability) of a sys-
tem increases. Thus, entropy is a measure of molecular disorder, and the
molecular disorder of an isolated system increases anytime it undergoes a
process.
As mentioned earlier, the molecules of a substance in solid phase continu-
ally oscillate, creating an uncertainty about their position. These oscilla-
tions, however, fade as the temperature is decreased, and the molecules
supposedly become motionless at absolute zero. This represents a state of
ultimate molecular order (and minimum energy). Therefore,the entropy of a
pure crystalline substance at absolute zero temperature is zerosince there is
no uncertainty about the state of the molecules at that instant (Fig. 7–21).
This statement is known as the third law of thermodynamics.The third
law of thermodynamics provides an absolute reference point for the deter-
mination of entropy. The entropy determined relative to this point is called
absolute entropy,and it is extremely useful in the thermodynamic analysis
of chemical reactions. Notice that the entropy of a substance that is not pure
crystalline (such as a solid solution) is not zero at absolute zero tempera-
ture. This is because more than one molecular configuration exists for such
substances, which introduces some uncertainty about the microscopic state
of the substance.
Molecules in the gas phase possess a considerable amount of kinetic
energy. However, we know that no matter how large their kinetic energies
are, the gas molecules do not rotate a paddle wheel inserted into the con-
tainer and produce work. This is because the gas molecules, and the energy
they possess, are disorganized. Probably the number of molecules trying to
rotate the wheel in one direction at any instant is equal to the number of
molecules that are trying to rotate it in the opposite direction, causing the
wheel to remain motionless. Therefore, we cannot extract any useful work
directly from disorganized energy (Fig. 7–22).
Now consider a rotating shaft shown in Fig. 7–23. This time the energy of
the molecules is completely organized since the molecules of the shaft are
rotating in the same direction together. This organized energy can readily be
used to perform useful tasks such as raising a weight or generating electric-
ity. Being an organized form of energy, work is free of disorder or random-
ness and thus free of entropy. There is no entropy transfer associated with
energy transfer as work. Therefore, in the absence of any friction, the
process of raising a weight by a rotating shaft (or a flywheel) does not pro-
duce any entropy. Any process that does not produce a net entropy is
reversible, and thus the process just described can be reversed by lowering
the weight. Therefore, energy is not degraded during this process, and no
potential to do work is lost.
Instead of raising a weight, let us operate the paddle wheel in a container
filled with a gas, as shown in Fig. 7–24. The paddle-wheel work in this case

Sk ln p

Chapter 7 | 347

LOAD

FIGURE 7–22

Disorganized energy does not create

much useful effect, no matter how

large it is.

Wsh

WEIGHT

FIGURE 7–23

In the absence of friction, raising a

weight by a rotating shaft does not

create any disorder (entropy), and thus

energy is not degraded during this

process.

Pure crystal

T = 0 K

Entropy = 0

FIGURE 7–21

A pure crystalline substance at

absolute zero temperature is in

perfect order, and its entropy is zero

(the third law of thermodynamics).