93. Dependence of resistance on temperature

The specific resistance of a conductor, and therefore its resistance \(R\), depends on the temperature. For metals and electrolytes, as experience shows, this dependence at high enough temperature approximation can be considered linear.

Let \(\rho{_0}\) - specific resistance of conductor at temperature \(0^0\,С\). Then specific resistance at temperature \(t\) is equal:

\(\rho \,= \,\rho{_0}(1 \,+ \,\alpha \,t)\)

Here \(\alpha\) - temperature coefficient of resistance. For all metals \(\alpha \,> \,0\), i.e. the resistance of metals increases with temperature. On the contrary, for electrolytes \(\alpha \,< \,0\): their resistance decreases with increasing temperature. Later we will find out why.

For both metals and electrolytes, the coefficient a is small. For pure metals \(\,\alpha \,= \,\frac{1}{273} deg^{-1}\), i.e. the same as the temperature coefficient of expansion of gases. For 10 percent aqueous solution of table salt \(\,\alpha \,= \,\frac{1}{-0.02} deg^{-1}.\)

The dependence of metal resistance on temperature is used in resistance thermometers. Typically, as the main working element of such a thermometer platinum wire is used, the dependence of resistance which is well known from the temperature. On all changes in temperature is judged by the change in resistance of the wire, which can be measured. Such thermometers can measure very low and very high temperatures when conventional liquid thermometers are not suitable.