Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 3 / 35C / b / Solution

At zero temperature, a two-dimensional free Fermi gas satisfies
$$
N=gE_F,
\qquad
E_{\rm tot}=\frac12NE_F,
\qquad
p=-\left(\frac{\partial E_{\rm tot}}{\partial A}\right)_N
=\frac{NE_F}{2A}.
$$


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 Incoming links: Degeneracy pressure of a two-dimensional Fermi gas