The effect of hydrostatic pressure (P) on the phase transitions of polystyrene-block-poly(n-pentyl methacrylate) copolymer [PS-b-PnPMA] was investigated with FTIR spectroscopy at various temperatures. The experiments were performed by using a specially designed pressure cell optimized for low-pressure regime (< 100 bar) with a higher resolution (similar to 1 bar). The size of the closed loop consisting of both the lower disorder-to-order transition (LDOT) and the upper order-to-disorder transition (UODT) measured by FTIR spectroscopy becomes smaller with increasing P, consistent with results obtained from birefringence measurement. At lower temperatures with increasing P, the PS main chains are found to move before the PnPMA main chains. This is because the mobility of the PnPMA main chains is restricted due to the cluster formation of the alkyl side chain. At higher temperatures, the PnPMA block chains are more mobile than the PS block chains due to their larger specific volumes. The results indicate that the LDOT is mainly affected by a favorable directional interaction between PS and PnPMA blocks due to the cluster formation of the alkyl side chain, whereas the UODT depends on the combinatorial entropy.