A New Application of the Bar Method for the Measurement of Thermal Conductivity.

Thermal conductivity.—(1) Electrically heated bar method of measurement. Equations are derived for the case of a long thermally insulated bar, with ends kept at the same constant temperature, and carrying an alternating current such as to make the temperature distribution parabolic. This is possible only with conductors for which $(\alpha -3\mathrm{}\beta )>\mathrm{}0\mathrm{}$, where $\alpha$ and $\beta$ are the temperature coefficients of electrical and thermal conductivity, respectively. It is shown that the conductivity at each end $K_{\theta }=\frac{j{I}^2{R}_0{L}^2}{2A{\theta }_m}=\frac{j{I}^2{R}_{0}L}{A{p}_0}$, where $j{I}^2{R}_0$ is the heat generated per unit length at the ends, $2L$ is the length, $A$ is the cross section, ${\theta }_m$ is the mean temperature above that at the ends, and $p_0$ is the temperature gradient at the ends. (2) Conductivity of lead and tin. A long test bar was used, with ends fastened into heavy copper blocks, insulated from each other but both in the same thermostatic oil bath. The temperature distribution was determined by thermo-junctions and the critical current found by interpolation. For lead, $K_0=.\mathrm{}0877\mathrm{}$, $\beta =.\mathrm{}000138\mathrm{}$; for tin $K_0=.\mathrm{}1575\mathrm{}$, $\beta =.\mathrm{}00067\mathrm{}$.