Question

Why resistivity decreases with temperature in metal case?

Answer 1

Resistivity do not depend on temp. It is a material property

Answer 2

Resistivity increases with the temperature in case of metals while it decreases in electrolytic conductors. The conductance of a metallic conductor decreases with rise in temperature as the residual positive charges(kernels) gain energy and vibrate with increasing temperature. These collide with the free electrons, therefore increasing resistance i.e increasing resistivity and decreasing conductance.