.GNU_ScientificLibrary.Examples.specfunc.ElectronDegPres

Note the use of the 'FermiDirac_InvertFhalf' block for numerically determining x from F_1/2(x)-y=0, essentially obtaining the chemical potential, mu=x*k*T, from the number density (~ F_1/2(x)*T^3/2) and temperature (T). x is then used to find the pressure from F_3/2(x) and T (p ~ F_3/2(x)*T^5/2).

A parametric plot of 'log10_pres.y' (in log10 Pa) vs 'log10_ndens.y' (in log10 m^-3) should impress upon one the phenomenal pressures exerted by fermions' inability to occupy the same quantum states, and the tremendous forces (internal or external) at play for these to be counteracted in materials (EM in solids, gravity in stars). At lower densities, this plot reveals a slope of about 1 (or P ~ n; Maxwell-Boltzmann gas), while at higher densities, the slope tends toward 5/3 (P ~ n^5/3; degenerate gas; EoS becomes stiffer). If one considers Cu, with 8.43*10²⁸ conduction-e/m³, at T=300K, this is well in the degenerate region (x=270), with P = 38 GPa ! (It is not encoded herein, but at extremely high densities, mu > m_e*c², relativistic effects become important and the EoS should turn over to P ~ n^4/3.)