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Is there any expression for the direct change in conductivity of metals with temperature ?

I am aware of change in resistivity with temperature.

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    \$\begingroup\$ Conductivity is the inverse of resistivity. \$\endgroup\$ – Chu Nov 19 '18 at 7:02
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    \$\begingroup\$ If with 'expression for the direct change' you mean an exact mathematical model, there are a few of various accuracy (starting with simple electron-cloud concepts to full-on quantum-mechanics). \$\endgroup\$ – Joren Vaes Nov 19 '18 at 7:34
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Since

$$\sigma = \frac1\rho $$

and, for a good approximation on typical temperatures where the metal is solid and and warmer than 180 K (==-90 °C):

$$\rho = \rho_0 + \alpha T$$

(with $\alpha$ being the temperature coefficient) it follows that

$$\sigma = \frac1{\rho_0 + \alpha T} $$

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