Adiabatic Joule Heating of Copper from 4 K to the Melting Temperature

Considering a copper wire heated by Joule effect and the variation of its resistivity and specific heat with temperature, we established numerical and analytical solutions (between 293 and 1356 K for the latter) for the evolution of its temperature over time. The Temperature vs. Time evolution follows a Lambertian function. The calculations are based on the assumption of adiabatic heating and uniform current distribution within the wire. We demonstrate that at very low temperature the heating rate is strongly dependent on copper purity.