The free electrons which are responsible for conduction in metals can be regarded as an exotic kind of gas. The behaviour depends on a parameter called the Fermi temperature, given by
$$
T_{\mathrm{F}}=\left(3 \pi^2 n\right)^{2 / 3} \frac{\hbar^2}{2 m k_{\mathrm{B}}}
$$
where $n=N / V$ is the number density of free electrons, $m$ is the electron mass, and $\hbar$ is the reduced Planck constant. When the actual temperature $T \ll T_{\mathrm{F}}$, the pressure becomes a function of density alone, given by
$$
p=\frac{2}{5} n k_{\mathrm{B}} T_{\mathrm{F}}
$$
Find the pressure of the electron gas in sodium at room temperature, given that the density of sodium is $970 \mathrm{~kg} / \mathrm{m}^3$, the atomic mass number is 23 , and there is one free electron per atom.