Entropy as an Index of Exhaustion

To obtain a better grasp of the essential character of the entropy concept, let us examine in more detail a few transformations that occur spontaneously even though At/ = 0 in each case (Fig. 6.10). 

If two blocks of metal, one at a high temperature and the other at a low temp-eramre Tj [Fig. 6.10(a)] are separated by a perfect heat insulator, and the system as a whole is surrounded by a thermal blanket that permits no transfer of heat in or out, then no change in internal energy can occur with time. If the insulator between the blocks is removed, the hotter block will decrdease in temperature and the cooler one will increase in temperature until the uniform temperamre T2 is reached. This transformation is spontaneous. At/ is zero. But a loss of capacity to perform work has occurred. In the initial state, we could insert a thermocouple lead in the block at Ts and another in that at Tj and obtain electrical work. Insertion of thermocouple leads in the same positions in the double block at T2 cannot generate any work. At the conclusion of the spontaneous transformation without the thermocouple, the internal energy is stiU the same as that at the outset, but it is no longer in a condition where it has the capacity to do work. 

the second law of thermodynamics provides us with a measure of this exhaustion, the entropy change A5, to be used as the fundamental criterion of spontaneity. For a closed region of space (for which, therefore, MJ = 0) including aU changes under observation. 

Spontaneous transformations occur aU around us aU the time. Hence, A5, for a section of space encompassing each such transformation and its affected surroundings, is a positive number. This realization led Clausius to his famous aphorism  

Die Energie der Welt ist konstant die Entropie der Welt sttebt einem Maximum zu (6,7), that is. 

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