Remarks on the Second Law and Irreversible Processes

For an ideal gas, (Sf//dV) y— 0, because the energy U is only a function of T— as was demonstrated in the experiments of Joule and Gay-Lussac (section 1.3 and equation (1.3.6)). Also, by definition dU/dT)y= NCy in which Cy is the molar heat capacity at constant volume, which is found to be a constant. Hence (3.7.1) may be written as 

In this expression the extensivity of 5 as a function of V and N is not explicit. Since S is assumed to be extensive in V and N, the entropy of an ideal gas is usually written as 

The generality of the Second Law gives us a powerful means to understand the thermodynamic aspects of real systems through the usage of ideal systems. A classic example is Planck s analysis of radiation in thermodynamic equilibrium with matter (blackbody radiation) in which Planck considered idealized simple 

Mendoza, E. (ed.) Reflections on the Motive Force of Fire by Sadi Carnot and other Papers on the Second Law of Thermodynamics by E. Clapeyron and R. Clausius. 1977, Glouster, MA Peter Smith. 

Kastler, A., L Oeuvre posthume de Sadi Carnot, in Sadi Carnot et I Essor de la Thermodynamique, A.N. Editor (ed.) 1974, Paris CNRS. 

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