Show that in the limit T >> 0 the heat capacity of a solid goes towards the limit C_v → 3Nk_B, in conventional units. To obtain higher accuracy when T is only moderately larger than 0, the heat capacity can be expanded as a power series in 1/T, of the form

Determine the first non-vanishing term in the sum. Check your result by inserting T = 0 and comparing with table 4.2.

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-Σα./Τ] C, = 3Nkg X [1 -