The study of defects or vacancies helps to understand the transport mechanism that occurs electrically and thermally in materials. It also deals with the mechanical properties of materials. In the present study, the extension of qualitative size-dependent model proposed by Jiang for cohesive energy of nanomaterials is done and size dependence of vacancy formation energy, vibrational frequency and vacancy concentration in nanomaterials is studied. The variation in vacancy concentration in nanomaterials is studied using the extended Jiang model for different dimensional nanomaterials with size and temperature. The model calculations depict the increase in vacancy concentration in free-standing nanomaterials as size of the nanomaterial is reduced and temperature is increased. The behaviour of concentration variation is found just opposite in embedded nanomaterials. The present predicted results of variation in concentration of vacancies follow the same trend as explained in previous studies. The study validates that defects help in the displacement of atoms. The variation in melting temperature and vibrational frequency of nanomaterials with size-dependent vacancy concentration is also discussed.