Students' reasoning in thermodynamics

Thermodynamics is a subject which involves multivariable problems. The behaviour of a huge number of particles is described using a small number of variables, which are mean values or macroscopic quantities. These variables can be linked, at thermodynamic equilibrium, by certain relationships, for example PV=NRT for perfect gases. In any transformation, such relation­ ships hold for initial and final equilibrium states. In transformations considered as "quasistatic", these relationships hold as well for any intermediate state, then also considered as equilibrium states. That is to say that we have to consider several variables, most of the time more than two, changing simultaneously under the constraint of one or several relationships. Such a mental activity a priori raises obvious difficulties. Piaget and Inhelder (1941) have shown that children, dealing with three kinematic variables (s,v,t), in fact consider one of these quantities as linked to a single other one: "the faster, the further". Other studies (Viennot, 1982; Maurines, 1986) show similar difficulties. In this paper, we will illustrate, in the domain of thermo­ dynamics, how students, and others, commonly reduce the intrinsic complexity of such problems. These tendencies towards "functional reduction" in common reasoning, will be shown to range from a simple reduction in the number of variables con­ sidered to a more elaborate procedure where all the variables are taken into account, but in a simplified way: the "linear causal reasoning".