The velocity of sound in a fluid is given by the formula

\[
w=\sqrt{ }(\partial P / \partial ho)_{s}
\]

where \(ho\) is the mass density of the fluid. Show that for an ideal Bose gas

\[
w^{2}=\frac{5 k T}{3 m} \frac{g_{5 / 2}(z)}{g_{3 / 2}(z)}=\frac{5}{9}\left\langle u^{2}ightangle
\]

where \(\left\langle u^{2}ightangle\) is the mean square speed of the particles in the gas.

7.9. Show that for an ideal Bose gas