Statistical Mechanics: Can't Find Source of Equation

[latentcorpse]

http://www.ph.ed.ac.uk/~pmonthou/Statistical-Mechanics/documents/SM15.pdf

At the top of page 59 in the above link, I can't see where the first three bullet points that follow

$E(T=0)=\int_0^{\epsilon_f} g(\epsilon) d \epsilon$

come from?

can anyone help?

 

[phz]

The first and second bullet point follow from the bottom of page 58. Study the expression for $\epsilon_f$ and see how it depends on $m$ and $N / V$.

The third bullet point follow from the definition of $k_B$ in a way. $k_B$ relates energy to temperature, so the Fermi temperature associated with the energy of the electrons at the Fermi level is just $T_f = \epsilon_f / k_B$.

See
http://en.wikipedia.org/wiki/Fermi_temperature#Fermi_level
http://en.wikipedia.org/wiki/Boltzmann_constant