Reasons for the Paradox

On the other hand, it has been pointed out that Gibbs paradox is not really a paradox [7, 8]. The paradox seems to arise because the conditions of the process of mixing are not fixed properly. Coarsely spoken we can disparage what is happening as follows two different gases are mixed and the correct entropy of mixing is obtained. 

However, after mixing, the scientist states that he was in error, the gases were not different in fact. And he is wondering that the entropy of mixing does not turn out to be zero. However, there was one further process introduced, namely, changing the identity of a component during the process. But in fact, this change of the identity is a further process, which is not included in the consideration. 

The conclusion is that we are not allowed to start the process with a certain initial assumption and after doing the process we change the initial assumption. 

To illustrate the problem of Gibbs paradox more clearly, we introduce now a thermodynamic cycle that involves a chemical reaction. di-2-Butene has a boiling point of 4 °C and frans-2-butene has a boiling point of 1 °C. 

So both substances are gases at room temperature, even when we must concede that they are not ideal gases. We assume further that we have an apparatus in that we can transform ds-2-butene into trans-2-butene in a gas mixmre of both components, for example, a UV source. Consider the process schematically shown in Fig. 10.1. 

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