Entropy production in a heat conduction problem

Abstract

Heat conduction along an isolated bar placed between two reservoirs at different temperatures is studied. The entropy production is considered in detail with two different approaches. In the first one, the whole system (the bar and the two reservoirs) is analysed in the steady state with the help of standard thermodynamics. In the second one, the bar is divided into n cells and a simple finite difference method is used to evaluate the time evolution of the entropy production. This approach is useful because the transient behaviour can be studied. In this way, it is shown a simple example of a non-equilibrium system where the entropy production (even its transient behaviour) can be evaluated with tools at hand of a motivated undergraduate.