Let the Fermi distribution at low temperatures be represented by a broken line, as shown in Figure 8.13, the line being tangential to the actual curve at \(\varepsilon=\mu\). Show that this approximate representation yields a "correct" result for the low-temperature specific heat of the Fermi gas, except that the numerical factor turns out to be smaller by a factor of \(4 / \pi^{2}\). Discuss, in a qualitative manner, the origin of this numerical discrepancy.