Looking at the model for a degenerate electron gas in metals at very low te
mperature, we studied the macroscopic balance equations for current density
and heat flux and we analyzed the effects produced on some transport coeff
icients if the quantum aspects are taken into account. The corrections for
diffusion coefficients, electrical conductivity, etc., are explicitly carri
ed out for a quite general collision model and the relations between these
transport coefficients are pointed out.