Answer Happy

A mechanical system consisting of n identical masses (each of mass m) connected in a straight line by identical springs (of stiffness K) has natural vibrational frequencies given by wr 2, = 2√/ (+1) sin(- -);r=1,2,... (n − 1). Correspondingly, a linear molecule composed of n identical atoms may be regarded as having a vibrational spectrum given by vr = vc sin(); r = 1,2,... (n − 1), where v is a characteristic vibrational frequency of the molecule. Show that this model leads to a vibrational specific heat per molecule that varies as T¹ at low temperatures and tends to the limiting value (n-1)k at high temperatures.