# Black holes, white dwarfs and neutron stars-Shapiro, Teukolsky

1. Nov 18, 2014

### Vrbic

1. The problem statement, all variables and given/known data
Hello, I try to recompute all exercises in this book and sometime I hit the snag :) One of the first is:
Exercise 2.6 (page 28)
Show that mean kinetic energy of an electron in a degenerate gas is $\frac{3}{5}E'_f$ in the nonrelativistic limit and $\frac{4}{5}E_f$ in relativistic limit. Here $E'_f=E_f-m_ec^2=p_f^2/2m_e$.

2. Relevant equations

3. The attempt at a solution
I know that for nonrelativistic limit $\epsilon=\frac{m_ec^2}{\lambda_e^3 \pi^2}\chi(x)$ and $\chi(x)->\frac{x^3}{3\pi^2}$. So my idea was to integrate this energy density from 0 to x-fermi, where $x=p/mc$. But result $\frac{2\pi}{3h^3}cp_f^4$ doesnt recover their.
Do have anybody some suggestions?

2. Nov 23, 2014