Heat generated by electrical discharge and induction

Helmholtz (1847) treated the heat developed by a current as something that could be calculated for a whole circuit. He took as the unit of resistance the length of wire in which a unit current develops one heat unit in one unit of time. For wires with several branches, he gave the total resistance in terms of the branch resistances and then summed the heat developed in the branches. His result for the whole branched chain holds if Lenz's law also applies to liquid conductors, as Joule had found¹.

Helmholtz also discussed how heat relates to work. Holtzmann argued that heat entering a gas can raise its temperature or make it expand. He used the work done in expansion as the mechanical equivalent of heat. Helmholtz said this reasoning is valid only if the free and latent heat in the expanded gas equals that in the denser gas at the same temperature. On that view a gas expanding without doing work should not change temperature, which Joule's experiment appeared to show².

In electrotaxis research, Joule heating is treated as an unwanted side effect. Sun (2017) described microfluidic devices for studying collective cell migration under applied electric fields. These devices have closed, well-defined dimensions, which give controlled and precise fields. Their small size could raise experimental throughput and also reduce Joule heating³. Palacios and colleagues (2020) mention heat production by warm-blooded animals as an interaction that crosses a physical boundary, alongside ion flow through membrane channels⁴.