3.4 The pressure of a non-relativistic degenerate gas

In the non-relativistic limit (i.e. when v << c), the total energy of the gas may be expressed as

The second term in the brackets in Equation (9) is simply the rest-mass energy per particle, and the first term is the kinetic energy per particle. Furthermore, the kinetic energy per unit volume is the kinetic energy per particle multiplied by the number of particles per unit volume. So the kinetic energy per unit volume is .

Now, the pressure provided by non-relativistic particles is 2/3 of the kinetic energy per unit volume, so

Then, using Equation (8), we have

The equation of state for non-relativistic degenerate electrons may therefore be written as follows: