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Entropy 53

The thermodynamic definition of entropy is constructed in such a way as to aid
calculation of entropy changes in real systems. In addition to the thermodynamic
definition, it is also possible to define entropy in statistical terms, so providing an insight
into the real meaning of entropy and entropy changes. For any system, the entropy is
given by the Boltzmann equation:
S=k Bln(w)

where w is the number of possible configurations of the system and k B is Boltzmann’s
constant. This definition allows the entropy to be understood as a measure of the
disorder in a system. In an example of a hypothetical crystal containing six 127 126
I I
molecules, then the number of ways in which the molecules can be arranged if the crystal
is perfectly ordered is one (Fig. 3a). If two molecules are reversed, so increasing the
disorder, the number of distinguishable arrangements increases to 15. Reversing three of
the molecules further increases the number of possible configurations to 20. If all
configurations are energetically equivalent, the most probable arrangement is the one
with the highest number of possible configurations, the most ‘disordered’. This also
means that the perfectly ordered situation, having the lowest number of possible
configurations and lowest entropy, is the most improbable.
The thermodynamic and statistical descriptions offer different portrayals of entropy,
but are both equally valid descriptions of the same concept. The statistical definition has
the advantage of being conceptually more accessible, but is

Fig. 3. (a) The only possible ordered
I
arrangement of six 127 126 I molecules in
a lattice; (b) one of 15 possible
arrangements where two of the
molecules are reversed.

only practically applicable to very simple and well-defined systems. Although less easily
visualized, the thermodynamic definition allows entropy changes to be assessed in
complex systems through the use of relatively simple thermodynamic measurements.

The third law of thermodynamics

The third law of thermodynamics states that

‘the entropy of a perfectly crystalline solid at the absolute zero of temperature is zero’.
For a perfectly crystalline solid, there can be only one possible spatial configuration of
the components of the crystal, and as the material is at the absolute zero of temperature,