Although the main purpose of studying reversible processes involving compressing gases is to establish a definition of temperature, most treatments of the subject either implicitly or explicitly assume the existence of a temperature function of the pressure and volume. Moreover, the discussion is usually in terms of quasi-static processes. Thus, in an isothermal process, the student is asked to comprehend how, despite the fact that the interior and exterior temperatures stay the same, a finite amount of heat flows from one system to the other. In this treatment, the temporal behaviour of a cylinder of ideal gas enclosed by a movable piston is studied in terms of differential equations describing the flow of heat and the mechanics of the piston. Firstly, it is shown that not all eligible empirical temperature functions lead to stable equilibrium. Secondly, for a system in which the working substance is an ideal gas, it is shown that in an isothermal process, the approach to the stable equilibrium is through damped oscillations. For an adiabatic process, the resulting dynamical system is non-simple with a line of fixed points which are neutrally stable. A first integral exists for this system which shows that the piston will exhibit persistent oscillations about the unique fixed point. Finally, the effect of various control strategies on the stability of the fixed points is presented.

The lecture is presented as a Mathematica notebook, reporting some experiments on how electronic learning material can be enhanced by integrating text, equations, graphics, symbolic computing, colour and sound.
 

Convenors:Simon Clarke.