Show that for an ideal Bose gas the temperature derivative of the specific heat \(C_{V}\) is given by
\[
\frac{1}{N k}\left(\frac{\partial C_{V}}{\partial T}ight)_{V}= \begin{cases}\frac{1}{T}\left[\frac{45}{8} \frac{g_{5 / 2}(z)}{g_{3 / 2}(z)}-\frac{9}{4} \frac{g_{3 / 2}(z)}{g_{1 / 2}(z)}-\frac{27}{8} \frac{\left\{g_{3 / 2}(z)ight\}^{2} g_{-1 / 2}(z)}{\left\{g_{1 / 2}(z)ight\}^{3}}ight] & \text { for } T>T_{c} \\ \frac{45}{8} \frac{v}{T \lambda^{3}} \zeta\left(\frac{5}{2}ight) & \text { for } T\]
Using these results and the main term of formula (D.9), verify equation (7.1.38).

Transcribed Image Text:

27Nk 3 aCy aCv 3.665- AT T=TC-0 AT T=TC+0 16 Tc Nk 665 Te