Conductivity of a copper wire at 4K

Hi everyone,

I am trying to find the mean free time between collisions for free electrons in a copper wire given the dimensions of the wire and the resistance, electron density and temperature.

I figured I needed to find the conductivity, plug that into an expression for mean free path then use the energy of the electron at 4K to determine its speed, and find the time between collisions from that, although it's quite possible there is a more straightforward way than this.

Anyway with that being the method I first tried using the resistivity eqn

ρ=RA/L

where my resistance is 2x10-5
my wire is 1m long with cross section 1mm2

this gave me a resistivity of 2x10-11

resistivity being the reciprocal of conductivity gave me a conductivity of
σ=5x1010

However it seems strange that temperature does not feature in this eqn as that must have an effect on resistivity and therefore conduction.
I can't find any eqn involving temperature. Could anyone suggest an eqn which may be suitable? Or indeed tell me if I am on the complete wrong track.

Thanks a bunch
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