In fact we can scale up the number of molecules to 1 mole (N = N A ) to
arrive at the molar entropy of this assembly (Equation 2.39):
S = k B ln g
N A
À Á
= N A k B ln g = R ln 2
(2.39)
In the above equation we have recognized that the product N A k B is equal
to the molar gas constant R (8.314 Jmol
−1 K
−1 ).
The example described in Figure 2.11a provides the inherent entropy of a
material in which two states of equal energy are possible. This twofold
degenerate system yields the orientational contribution to the overall
entropy of the material. Another example of orientational entropy is that
shown in Figure 2.11b in which a molecule can have one of three possible
orientations. Figure 2.11c illustrates conformational entropy in which a
molecule can adopt one of two possible conformations of the same energy.
To conclude this section we consider the situation where we have a
perfectly ordered system such that W = 1. According to Equation 2.35,
such a system will have zero entropy. We can imagine a perfect crystal at a
very low temperature to approximate such a system. This is the basis of
the third law of thermodynamics, which states that the entropy of a
perfect crystal is zero at zero kelvin.
2.5 THE GIBBS ENERGY STATE FUNCTION
2.5.1 The direction of spontaneous change
Consider the first law of thermodynamics in which heat and work are the
only forms of energy transfer (Equation 2.40):
ΔE = q + w
(2.40)
The second law of thermodynamics gives the entropy change for an
irreversible (spontaneous) process (Equation 2.41):
ΔS >
q
T
(2.41)
Rearranging the above expression for q gives;
q < TΔS
(2.42)
CHAPTER 2: Thermodynamics and Nanoscience
44