## 1 Introduction  
In the design and optimization of many applications based on latent heat, be it storages or thermal regulations for instance, the need for a precise determination of the properties of the PCM has critically increased. Usually, this demand is fulfilled in two manners: either the determination of the temperature(s) connected to the phase change and the corresponding latent heat(s), or the determination of the enthalpy function. In this latter case, the influence of the pressure on this thermodynamical function is generally neglected (applications under pressure being very rare) and only the dependency on the temperature and on the relative local liquid (or solid) mass fraction--during the phase transition--are required. In summary, the goal is to determine the correct formulation of the specific enthalpy \(h\) of the involved material:  
\[h=h\left(T,P,\chi_{i}^{S},\chi_{i}^{L}\right)\approx h\left(T,\chi_{i}^{S},\chi _{i}^{L}\right) \tag{1}\]where \(i\) represent the various substances, which can be pure or in solution (solvent in majority or various solutes), and \(\chi_{i}^{\gamma}\) the corresponding mass fractions with \(\gamma=\) liquid (\(L\)) or solid (\(S\)). Keeping in mind these two types of characterization, the aim of the present paper is to challenge the usual approaches encountered when tackling such an issue:  
* In the first case, where only the global values for the characteristic data (temperature(s) and latent heat(s)) are searched for, the main methods are based on a graphical exploitation of the DSC curve. Thus, by looking specific points of the thermogram, as for instance the onset temperature, one tries to obtain a correct determination of the temperature(s) which can be representative of the phase change. Then, by defining an integration method, the corresponding latent heat(s) could be obtained. * In the second case, where the complete mathematical expression of the enthalpy is searched for, the main method often relies on the so-called equivalent heat capacity method that assumes that the thermogram can be interpreted as the derivative of the enthalpy. Thus, a direct integration of the DSC curve, favoring low heating rates, should permit to go back up to the enthalpy function. The main conclusions of the present study are that both approaches are, in the best cases, mainly approximate solutions. Moreover, in many situations, they could be misleading and can furnish a wrong characterization incompatible with thermodynamics. These conclusions principally stream from an incomplete view from the physical phenomenon involved during the phase transition when analyzing the DSC curve. Indeed, the thermal transfers are generally considered only at the boundaries of the sample, i.e., with the apparatus, however the thermal transfers inside the sample are completely neglected although a thermal gradient is known to exist in such a case [1; 2; 3]. Another common reason for this incorrect estimation often lies in the expression of the enthalpy, which does not correspond to the real behavior of the sample. Thus, in almost all cases, all materials are analyzed as if they were pure substances despite their scarce availability (even with laboratory grade materials--without speaking of technical grades). In the present paper, several models will be presented in order to reproduce the behavior of various materials. The cornerstone of this approach is to always rely on the basic laws of thermodynamics. It is then shown that every usual thermograms can thus be easily reproduced and analyzed, and that no need for artefacts or \"extra-thermodynamics\" assumptions is required. The first part of this paper will recall the usual impediment associated with the classical analysis. Then, in Section 3 the present approach is developped: by coupling numerical simulations with experimental measurements, it is proposed a painstaking analysis of the various shapes of the DSC curves.