Pedagogical Visualization of a Nonideal Carnot Engine

We have implemented a visualization tool for the demonstration of a nonideal Carnot engine, operating at finite time. The cycle time can be varied using a slide bar and the pressure-volume, temperature-entropy, power-time, and efficiency-time diagrams change interactively and are shown on one screen. We have evaluated the visualization tool among engineering students at university level during an introductory course on thermodynamics and we review and discuss the outcome of the evaluation. 1. Introduction In 1975, Curzon and Ahlborn made the observation that most undergraduate textbooks on thermodynamics do not treat the time aspects of thermodynamic cycles; thus lacking the explanation of how power is generated from, for example, heat engines. In their investigation, Curzon and Ahlborn considered a Carnot cycle operating at finite time by modeling the time-dependent energy losses in the isotherms [1]. This approach enabled them to derive a general expression for the efficiency at maximum power, depending only on the temperatures of the reservoirs, just as the Carnot efficiency. Curzon and Ahlborn’s motivation was purely pedagogical and at the time they were probably not aware that the same expression had been published already in 1957 by Novikov [2] (the original paper in Russian was published in 1957) and by Chambadal [3]. Nevertheless, this efficiency is most commonly referred to as the Curzon-Ahlborn efficiency and their work paved the way for finite time thermodynamics [4]. The purpose of this investigation is to construct an interactive visualization tool in the form of a computer program illustrating the time dependence of a nonideal Carnot engine and to evaluate this demonstration tool among university students during an introductory thermodynamics course. The reason for doing this is the lack of time and power aspects of thermodynamic cycles in undergraduate textbooks. The visualization tool may thus fill a gap in thermodynamics courses since it increases the awareness of these important engineering aspects. Illustrating the concepts by an interactive visualization may enable a more holistic understanding, which, in turn, will allow for deep learning. 2. Theoretical Model We base our nonideal Carnot engine on Curzon-Ahlborn’s model [1]; that is, the engine spends finite times in the isotherms so that the high temperature of the working medium (which we will implicitly consider to be an ideal gas), , will not reach the temperature of the hot reservoir, . Correspondingly, the low temperature of the working medium, , will not reach the temperature