Chapter 7.3, Problem 32P

(a)

To determine

The value of the integral of the total number of electrons in the density of states for Fermi energy equal to $kT$ and zero chemical potential.

(b)

To determine

The value of the integral of the total number of electrons in the density of states for $\frac{kT}{{\epsilon }_{\text{F}}}$ range between $0.1$ to $2$ and sketch the results on the graph.

(c)

To determine

The values and the plot of the integral for the energy as a function of temperature and $kT$ upto $2{\epsilon }_{\text{F}}$ and the value of heat capacity.