IGNOU PHE 15 2018 - Show that the pressure of a degenerate gas is independent of its tempe

Question

Show that the pressure of a degenerate gas is independent of its temperature.

01 Feb 2018

Answer :

Word Count : 400

In a degenerate gas of fermions, the fermions fully occupy momentum states from zero up to a momentum corresponding to the Fermi energy. It is the momentum of the fermions that leads to degeneracy pressure.

As long as the kinetic energy of particles at the Fermi energy is much less than kT

, then the fermions can be considered completely degenerate, so that the situation above applies and there are no fermions that occupy energy states higher than the Fermi energy. The Fermi energy only depends on the density of fermions.

The pressure is given by

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