Adiabatic bulk modulus of a free electron gas at T=0

[rayman123]

Homework Statement

Show that the adiabatic bulk modulus of a free electron gas can be given by
$$B= \frac{2nE_{F}}{3}$$

where
n-number density
$$E_{F}$$ -Fermi energy

Homework Equations

I started with the adiabatic bulk for an ideal gas
$$K=\gamma P$$
where $$\gamma=\frac{C_{p}}{C_{v}}$$

but i do not have idea how to continue with the problem to obtain solution.
I appreciate any help.

The Attempt at a Solution

 

[NateD]

I started with the adiabatic bulk for an ideal gas K=\gamma P where \gamma=\frac{C_{p}}{C_{v}}but i do not have idea how to continue with the problem to obtain solution.I appreciate any help.