Thermodynamics of Mineral Resources - Thanatia: The Destiny of the Earth's Mineral Resources - page 261

n

I

n = 3

n = 2

x i

Fig.9.2Irreversibilityasafunctionofconcentrationinamixtureof n substances (Eq. (9.8))

9.3.2 Entropy, probability and information

The relationship between entropy and probability is now worth analysing, since it
allows for the understanding of many natural facts including those occurring with
mineral resources as will be seen in Sec. 9.4. At the outset this relationship might
not be evident, at least when performing empirical quantifications of formation
and reaction entropies. Such values are calculated from calorimetric data and are
essentially obtained by experimentally determining the heat capacities as a function
of temperatures and then integrating expressions like:

Z T

C p (T)
T

S = S 0 +

dT (9.9)

0

The calculated values enlighten little as to the meaning of entropy as a form
of disorder. However, there are cases where it is easy to relate the increase of
probability with entropy generation. This is the case for the replacement of some
ions, atoms or molecules with others in a crystalline structure. In such a case,
there is a solid phase mixing where entropy is created whilst at the same time,
disorder appears to be evident. The statistical analysis of this phenomenon permits
interpretation of the relationship between entropy and probability and subsequently
information.
Suppose that there are N 1 and N 2 molecules of two types that are fully ex-
changeable without affecting the internal energy of the system (see Pitzer (1995)).