## 7 Conclusions  
In this paper we have considered that, obviously, the physical (thermodynamical) laws are the same whatever the volume of the sample may be. So, even when the samples studied by calorimetry are relatively small (a few mm\({}^{3}\)), the thermodynamic laws of melting (solid-liquid equilibrium) and the physical laws of the conductive heat transfers are both taken into account. The detailed study of the melting of a pure substance indicates that the heat flow rate which constitutes the thermogram is representative of the phase change considering the temporal evolution  
Figure 39: DSC curves for a PCM at the cooling at \(\beta=-5\) K/min (red curve) and at the heatings at \(\beta=5\) K/min (blue curve), \(\beta=2\) K/min (green curve) and \(\beta=1\) K/min (orange curve) with drawing to determine \(T_{\rm liquidus}\) and \(T_{\rm C}\) [see text]. Figure 38: DSC curves for a PCM at the cooling at \(\beta=-5\) K/min (red curve) and at the heating at \(\beta=5\) K/min (blue curve) with drawing to determine \(T_{\rm onset}\) and \(T_{\rm C}\) [see text]. and not the linear evolution of the temperature of the plate of the calorimeter. Indeed, inside the cell, the phase change at constant temperature occurs on an interface which evolves with time from the walls of the cell to its center. At no moment there exists a particle melting at a temperature different from \(T_{F}\), contrary what is asserted by previous studies stating that the sample would have a homogeneous temperature almost equal to the one of the plate. Through this study on pure substances, whose the local melting is at a fixed temperature, several observations and conclusions have been drawn. _Firstly_, there are always temperature gradients inside the sample during phase change, whatever the heating rate and the mass. _Secondly_, this thermal gradient leads to a differentiated temperature field between the interface temperature and the plate's one. Consequently, the DSC curve is spread over time and \"appears\" to be spread also with the temperature (of the plate). However, this spreading is not representative of the phase transition and seems to depend on the heating rate and mass sample. _Thirdly_, and because of the previous remark, it is not relevant to directly integrate the thermogram, even non-dimensionnalized, to try to build the enthalpy function. _Fourthly_, the attempt to reduce the thermal gradient by lowering the heating rate can anyway give an enlarged enthalpy function, especially if larger masses are used for the samples. Meanwhile, the limit of the noise to ratio signal raises the uncertainties. _Fifthly_, the so-called hysteresis phenomenon is only due to an incorrect interpretation of the thermogram and does not exist in reality. Nevertheless, it does not mean none information can be taken from such a model on pure substances: we have demonstrated that as it is always possible to determine \(T_{F}\) the melting temperature, possibly with a modified procedure of calibration, and the associated latent heat \(\ell_{F}\) with a good approximation. For the saline solutions, we can also explain why the thermograms are more enlarged than the thermodynamic temperature range and over the liquidus temperature. This enlargement depends on the heating rates and the classical onset temperature has no meaning. A procedure to determine the temperature of the liquidus is detailed. The results are applied for the particular case of the small concentrations. We found that to use the thermograms as if a pure substance were concerned corresponds to very small concentrations (\(\leq\)0.01% in moles). For higher concentrations, the thermograms are not compatible with a validation of the onset temperature. Although the errors are very small, a significant bad evaluation of the melted quantities is predictable. Our model can be extended to the binaries with solid solutions. The case of ideal solutions is detailed.