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

TL;DR

This study models the temperature evolution of copper wire under Joule heating from 4 K to its melting point, accounting for resistivity and heat capacity variations, and highlights the impact of purity at low temperatures.

Contribution

It provides analytical and numerical solutions for copper heating dynamics considering temperature-dependent properties, a novel approach in this temperature range.

Findings

Temperature evolution follows a Lambertian function.

Heating rate at low temperatures depends on copper purity.

Solutions are valid between 293 K and 1356 K.

Abstract

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.