Figure 2.12a shows one of two possible orientations that such a molecule
may have. In this example, the “up” orientation has the same energy as
the “down” orientation. We say that this system has degeneracy of 2.
Furthermore, since N = 1, the corresponding entropy of this single particle
system is
S = k B ln W = k B ln g
N
À Á
= Nk B ln g = k B ln 2
(2.37)
If we had a larger assembly of these molecules such that they formed a
nanofilm comprising 11 molecules arranged as a monolayer (Figure
2.11a), we would expect W to be much larger. This nanofilm can be
viewed as an ordered assembly in which some defects exist where
some molecules have reversed orientations. Again, g = 2 in this system,
but N = 11. Therefore, the entropy corresponding to the nanofilm is
S = k B ln g
N
À Á
= Nk B ln g = 11k B ln 2
(2.38)
or
N = 11, g = 2
A
B
C
C
A
B
B
C
A
or
or
or
(a)
(b)
(c)
N = 1, g = 3
N = 1, g = 2
N = 1, g = 2
Nanofilm
Figure 2.12 Molecular building blocks (a), (b), and (c) that can arrange themselves
into well-defined orientations. The allowed orientations for each molecule have the
same energy and provide the number of microstates, and hence entropy, available to
the system.
THE ENTROPY STATE FUNCTION: THE SECOND AND THIRD LAWS
43