Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 173

and therefore

To calculate thetotalenergy of thegas, we canwrite

and therefore

and we can checkthat

b) The condition forstrong degeneracy is that thetemperature should

be much smaller than the Fermi energy:

For typical metals, if weassume that there is one freeelectron peratom

and a typical interatomic distance we obtain anelectrondensity

So, most of the metals are strongly degenerate, even at

roomtemperature.

4.67 Ultrarelativistic Electron Gas (Stony Brook)

The fact that the gas is ultrarelativisticimplies that the energy of the
electron is large compared to its rest energy In thiscase, thedispersion

where again

N/V which indicates a Fermi energyof the order of