Some notes on entropy

The concept of entropy as a general measure of the disorder of a system is, of course, highly relevant in solid-liquid separation because the degree of restoration of the order (the reduction in entropy) describes the success of the separation process. Fundamentally, entropy is a measure of the way in which the total energy of the system is distributed amongst its constituent atoms. 

In order to be able to evaluate the relative reduction in entropy during or after the separation process, we have to be able to calculate the entropy of the suspension as a function of the sohds concentration. The necessary relationship may be derived in analogy with a molecular model for an ideal solution as used in chemical thermodynamics, summarized in the following. A very small sohd particle is treated simply as if it were a large molecule. 

Assuming, in the first instance, mono-sized particles, completely interchangeable with pockets of fluid of the same size without affecting the 

From molecular thermodynamics, the entropy, S, is proportional to the natural logarithm of the multiplicity W, i.e. 

Stirling s approximation for equation 18.29, used with equation 18.30, gives the entropy of a suspension 

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