We report calorimetric and X-ray measurements in the R1, R2, and R5 rotator phases of a long chain alkane (n-tetracosane) in bulk and confined to porous matrices (PTFE and Anopore) of two different length scales. Probing the order within and normal to the layers, in the Anopore case having a mesoscopic length scale (200 nm), drastic weakening of the R2-R1 and R1-R5 transitions is seen. The effect on the latter is to such an extent that it results in the first observation of a confinement-driven second order transition in these systems. A significant reduction of the temperature range of the R1 phase is also seen in the Anopore case, a feature argued to cause the change in the order of the transition. Comparisons are also made on the recent prediction of such a point in a Landau model. These findings, while paving a new means of realizing a tricritical point, will lead to better understanding of finite size effects in alkanes.