Work diagrams Clapeyron

We are permitted to assume that dp is directly proportional to dT because AH and AV are regarded as constants, although even a casual inspection of a phase diagram shows how curved the solid-gas and liquid-gas phase boundaries are. Such curvature clearly indicates that the Clapeyron equation fails to work except over extremely limited ranges of p and T. Why ... 

The Clapeyron equation, Equation (5.1), yields a quantitative description of a phase boundary on a phase diagram. Equation (5.1) works quite well for the liquid-solid phase boundary, but if the equilibrium is boiling or sublimation - both of which involve a gaseous phase - then the Clapeyron equation is a poor predictor. 

If the diagram has several loops as shown in Fig. 108, the total work is the sum of the areas of the several loops developed by the point travelling in the same direction as the hands of a clock, minus the sum of the areas developed when the point travels in a contrary direction. This graphic mode of representing work was first used by Clapeyron. The diagrams are called Clapeyron s Work Diagrams. 

Two years later his work was brought to public attention in a paper written by Emile Clapeyron (page 217), who used indicator diagrams to explain Carnot s ideas. 

Figure 3.2 The Carnot cycle. The upper part shows the four steps of the Camot cycle, during which the engine absorbs heat from the hot reservoir, produces work and returns heat to the cold reservoir. The lower part shows the representation of this process in a p-V diagram used by Clapeyron in his exposition of Carnot s work...

Example Superconductor Thermodynamics. Figure4.19 shows a phase diagram in the T-//-plane, i.e. in this system the magnetic //-field assumes the role of P. The two phases are named s and n. We easily can work out a version of the Clapeyron equation in this case. Our starting point is Eq. (4.44), i.e. 

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