The computation of isobaric DSC curves of binary mixtures from a known phase diagram is discussed. Based on the first law of thermodynamics, universal formulas are derived that allow us to calculate the course of the specific heat capacity as a function of temperature during a transition and, additionally; the respective base line. Despite being applied to the transition of fusion in our case, all relations are equally well applicable to any other transition such as sublimation and evaporation and also to mixing-demixing phenomena. They only require the knowledge of the equilibrium curves of the phase diagram (i.e. liquidus, solidus, and solvus curves) indicating the compositions of the coexisting phases at the prevailing temperatures. As invariant transitions quite often appear in many phase diagrams, the eutectic transition and the peritectic transition of fusion are treated quantitatively, leading to the so-called "Tammann’s triangle" that characterizes the concentration-dependence of the enthalpy of transition. The calculated DSC curves prove to be coincident for the most part with the experimental data of the binary model system used, consisting of n-hexane (n-C6H14) and n-dodecane (n-C12H26). These results are likely to be improved by taking account of-the so-called "smearing effect" of the DSC caused by processes of heat transfer during a DSC scan, which will be looked at in parts 2 and 3 of this series.