With the help of the Euler-Maclaurin formula (6.5.19), derive high-temperature expansions for \(r_{\text {even }}\) and \(r_{\text {odd }}\), as defined by equations (6.5.29) and (6.5.30), and obtain corresponding expansions for \(C_{\text {even }}\) and \(C_{\text {odd }}\), as defined by equation (6.5.39). Compare the mathematical trend of these results with the nature of the corresponding curves in Figure 6.7. Also study the low-temperature behavior of the two specific heats and once again compare your results with the relevant parts of the aforementioned curves.

Figure 6.7 

Data From Equation (6.5.29)

Data From Equation (6.5.30)

Data From Equation (6.5.39)

Transcribed Image Text:

Cv Nk 2.0 1.5 1.0 1 0.5 2 0 1 2 3 4 5 (Tier)