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

[itex]E(T=0)=\int_0^{\epsilon_f} g(\epsilon) d \epsilon[/itex]

come from?

can anyone help?

 

[phz]

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

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

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