Uncompensated heat, Clausius

In contrast to Clausius, Gibbs did not discuss uncompensated heat, as he started directly with the total differential of entropy. Gibbs presentation appealed very much to De Donder, However, he wanted to find the meaning of this mysterious uncompensated heat. He considered a system whose physical conditions, such as pressure and temperature, were uniform and which was closed to the flow of matter. Chemical reactions, however, could go on inside the system. De Donder first introduced what he called the degree of advancement, , of the chemical reaction so that the reaction rate v is the time derivative of . 

Irreversible processes correspond to the time evolution in which the past and the future play different roles. In processes such as heat conduction, diffusion, and chemical reaction there is an arrow of time. As we have seen, the second law postulates the existence of entropy 5, whose time change can be written as a sum of two parts One is the flow of entropy deS and the other is the entropy production dtS, what Clausius called uncompensated heat, ... 

The term (Pgas - Pvlston)dV is the uncompensated heat as named by Clausius. 

Clausius called dQ the uncompensated heat, which is always positive or zero in classical thermodynamics it played a purely qualitative part. It was used to delimit reversible changes for which dQ = 0, and when dealing with non-equilibrium states it was sufficient to write dQ X) without attempting an explicit calculation of its value. 

The entropy created in the system is thus equal to the Clausius uncompensated heat divided by the absolute temperature this gives the uncompensated heat a physical significance. 

In his pioneering work on the thermodynamics of chemical processes, Theophile De Bonder (1872-1957) [14-16] incorporated the uncompensated transformation or uncompensated heat of Clausius into the formalism of the Second Law through the concept of affinity, which is presented in the next chapter. This modem approach incorporates irreversibility into the formalism of the Second Law by providing explicit expressions for the computation of entropy produced by irreversible processes [17-19]. We shall follow this more general approach in which, along with thermodynamic states, irreversible processes appear explicitly in the formalism. 

Though Gibbs did not consider irreversible chemical reactions, equation (4.1.1) that he introduced included all that was needed for the consideration of irreversibility and entropy production in chemical processes. By making the important distinction between the entropy change S due to exchange of matter and energy with the exterior, and the irreversible increase of entropy djS due to chemical reactions [2, 3], De Bonder formulated the thermodynamics of irreversible chemical transformations. And we can now show he took the uncompensated heat of Clausius and gave it a clear expression for chemical reactions. 

This is the uncompensated heat of Clausius for chemical reactions. The validity of this equation lies in the fact that chemical reactions occur in such a way that d S is always positive in accordance with the Second Law. For the total change in entropy dS we have ... 

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