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