= Conduction-electron count in the molar electronic heat capacity
{title2=$C_{V,m}\simeq(\pi^2/2)zRT/T_F$}
The low-temperature <heat capacity> of a three-dimensional <free electron gas> is $(\pi^2/2)N_ekT/T_F$. Expressed per mole of metal atoms with $z$ model conduction electrons each, this becomes the displayed result. Expressed per mole of conduction electrons, set $z=1$. A thermal-window counting argument predicts the $T/T_F$ scaling but gives only an order-one coefficient; it must still retain the number of electrons when changing the molar basis.
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