Heat and Thermodynamics

12.18 Debye's Theory of Specific Heat

According to Debye, the actual vibration of an atom in an elastic solid must be necessarily complex owing to collisions and mutual action of the neighbouring atoms. This complex vibration of an atom can be analysed into a large number of simple components. The number of such components must be finite, though large because the total number of degrees of freedom cannot exceed 3N where N is the number of atoms constituting the monatomic solid. Hence, the possible frequencies must have an upper limit. Let us call this limiting frequency v_m.

Now, a solid can transmit both longitudinal and transverse waves represented by c_L and c_T, respectively. We have already proved in Eq. 12.68 that the number of degrees of ...