Gas Parameters
T/T_F = 0.050
N = 20
Fermi Gas Properties
Fermi energy E_F—
Chemical potential μ—
Temperature T—
Thermal smearing 4k_BT—
Average energy ⟨E⟩/E_F—
Zero-pt pressure P₀—
The Pauli exclusion principle forbids two fermions from occupying the same quantum state. At T=0, electrons fill all states up to the Fermi energy E_F — a sharp step function. As temperature increases, states are thermally excited above E_F while states below E_F are vacated, smearing the distribution over a range ~4k_BT. Even at T=0, the Fermi gas has non-zero kinetic energy (zero-point pressure), which stabilizes white dwarf stars against gravitational collapse.