A Simple Relation Between Thermal Conductivity, Specific Heat and Absolute Temperature

A relation of the form $\frac{k}{\mathrm{aC}}=\frac{K_1}{T}+K_2$, between thermal conductivity $k$, atomic heat ($\mathrm{aC}$), and absolute temperature $T$, is shown to hold for zinc, sodium, lithium, copper, lead, aluminum and mercury. The possibility is indicated of an equation of this sort based on the assumption of a double mechanism of heat conduction—an atomic lattice along which energy is transmitted as elastic waves (Debye) and a structure of atoms (crystalline or amorphous), through which energy is transferred by impacts. The lattice and atomic contributions to the thermal conductivity may be obtained from the slopes and intercepts of the lines. The values at 0°C are as follows (lattice part being given first): lithium 0.150, 0.006; sodium 0.092, 0.169; zinc 0.084, 0.192; copper 0.920, 0.171; lead 0.018, 0.068; aluminum 0.127, 0.358; mercury 0.031, 0.033. The line for mercury suggests that the atomic part is at least approximately the conductivity in the liquid state. The single and poly-crystal zinc lines have the same intercept but different slopes indicating that the increased thermal conductivity of the single crystal specimen is in the elastic wave contribution.