Ohm’s law for a wire in contact with a thermal reservoir

Ohm's law is one of the key empirical relations taught in introductory courses on electricity. Students often do a straightforward experiment to measure the current through a resistor as a function of voltage. These experiments typically yield a linear relation between the current and the voltage using carbon film resistors. However, the same measurements on long lengths of conducting wire (such as common wire resistivity kits) typically have a clear nonlinear component. The nonlinear behavior can be modeled using simple principles of heat transfer with a thermal reservoir. Experimental results are shown to agree well with this simple model.