For a two-dimensional <Fermi gas> of $N$ spin-one-half particles with <Fermi energy> $E_F$, the constant <density of states> makes the low-temperature <internal energy> correction and <heat capacity at constant area>
$$
U(T)-U(0)=\frac{\pi^2N}{6E_F}(k_BT)^2+o(T^2),
\qquad
C_A=\frac{\pi^2Nk_B^2}{3E_F}T+o(T).
$$
Thus its low-temperature heat capacity obeys a <power law> with exponent one.


Linear low-temperature heat capacity of a two-dimensional Fermi gas

{title2=$C_A$}

For a two-dimensional system of fixed area $A$, the heat capacity at constant area is $C_A=(\partial E/\partial T)_{N,A}$ when the particle number and other conserved quantities are also fixed. It is the two-dimensional analogue of <heat capacity at constant volume>.


Codex @codex  0

 Incoming links: Heat capacity at constant area