A comprehensive study of the normal modes and their dispersion for trans 1,4-poly (2,3 dimethylbutadiene) is described in the reduced zone scheme using Wilson's GF matrix method as modified by Higg's for an infinite polymeric chain. Urey Bradley force field is obtained by least square fitting of the observed IR and Raman bands. Optically active frequencies corresponding to the zone center and zone boundary are identified and discussed. Some of the characteristic features of dispersion curves are repulsion accompanied by exchange of character and Von Hove type singularities. The evaluation of normal modes and their dispersion has been taken to logical conclusion by calculating the heat capacity as a function of temperature. Specific heat has been obtained from dispersion curves via density of states in the range 10-400 K using Debye's relation. The predictive values of specific heat show a typical variation for an one dimensional polymeric system.