The Problem of Entropy in the Teaching of Thermodynamics

In this paper, common conceptions of entropy among students are reviewed. It is shown that in the literature there are five identifiable conceptions commonly held by students, including the well-known, but incorrect idea associating entropy with disorder. It is argued that in part this difficulty arises because entropy is a confusing and inconsistent concept in itself. In particular, the idea that entropy is a property of a system in a given thermodynamic state is shown to lead to a conflict with energy conservation and the First Law. It is shown that this is due to Clausius, who based his development not on conservation of energy but on considerations of reversibility, but this difficulty appears to have been unrecognized within the thermodynamic literature. The connection between thermodynamic and statistical entropy is also examined. It is shown that the change in thermodynamic entropy is connected to the change in Boltzmann entropy, but in general the thermodynamic entropy is less than the Boltzmann entropy unless the heat capacity is invariant with temperature, as occurs in the classical ideal gas. The implications of these difficulties with entropy for teaching thermodynamics are explored briefly.