Stability and Fluctuations in Mole Number

As before, if one part is much larger than another, V, this expression can be simplified and the condition for stability can be written as  

Fluctuations in the mole numbers of the various components of a system occur due to chemical reactions and due to transport, such as diffusion. We shall consider each case separately. 

These fluctuations can be identified as the fluctuations in the extent of reaction about its equilibrium value. Considering a fluctuation 6, the change in entropy is 

When many chemical reactions take place simultaneously, condition (12.4.3) can be generalized to the following statement [1, 2]  

The fluctuations in mole numbers considered so far were only due to chemical reactions. The fluctuation in mole number can also occur due to exchange of matter between a part of a system and the rest (Fig. 12.3). As in the case of exchange of energy, we consider the total change in entropy of the two parts of the system  

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