Temperature/Resitance Relation?

[Berdi]

In a few of my undergraduate lab sessions, we have been given a formula in the lab script;

$$\[R=R_{20}(1+\alpha T+\beta T^{2})\]$$

Where Alpha and Beta have varied depending on the experiment.For example, to calculate the temperature of a cathode, at resitance R, $$\[\alpha \]$$ was 5.24x10^-3 and $$\[\beta\]$$ was 7x10^-7 (this was in degrees).

What actually is this equation? I'm curious to see where it's come from.

 

[torquil]

First of all, it looks like a phenomenological equation, i.e. a simple truncated Taylor expansion in the temperature, where the coefficients would be determined by fit with experiment.

Anyway, it is explained also by theory. Check this out (the section "Temperature dependence"):

http://en.wikipedia.org/wiki/Resistivity

A quote: "electron–phonon interactions can play a key role"

Torquil