The character of the R-II-R-I and the R-I-R-V transitions was studied in alkane samples by analyzing the hysteresis the specific heat shows between heating and cooling measurements, using photopyroelectric calorimetry. The hysteresis systematically shows up in all the investigated samples over the R-II-R-I transition, similarly to what also observed over the liquid-R-II and the R-V-crystal phase transitions, thus confirming the first order character of all such phase transitions. Over the R-I-R-V transition a hysteresis is also present but with varying characteristics depending on the width of the temperature range of the R-I phase, the first order character being smaller for decreasing R-I range. The observed results were explained in terms of possible varying strength of the coupling term in the free energy between the distortion and tilt angle order parameters in the different samples, a variation which can induce a change in the order character of the transition. The results are compared to those obtained in an alkane sample under increasing ambient pressure, which turned the transition from first to second order. In both cases it was suggested that the variations of the coupling strength between the two order parameters could be associated with changes in the effectiveness of the molecular interaction between the layers relative to that occurring within each layer.