Thermodynamics from a Few Dynamic Particles Raises Questions as to How Temperature and Entropy Should Be Perceived and Defined

In a recently developed simple particle mechanics model, in which a single particle represents the working fluid, (gas) in a heat engine, (exemplified by a piston engine) a new approach was outlined for the teaching of concepts to thermodynamic students. By mechanics reasoning, a model was developed that demonstrates the connection between the Carnot efficiency limitation of heat engines, and the Kelvin-Planck statement of Second Law, requiring only the truth of the Clausius statement. In a second paper the model was extended to introduce entropy. The particle's entropy was defined as a function of its kinetic energy, and the space that it occupies, that is analogous to that normally found in classical macroscopic analyses. In this paper, questions are raised and addressed: How should temperature and entropy be perceived and defined? Should temperature be proportional to average (molecular) translational kinetic energy and should entropy be dimensionless? INTRODUCTION In previous papers [1, 2], simple, one dimensional theoretical models of heat engines were presented that bridge the conceptual gap between the elegantly abstract Second Law approaches and physical/mechanical principles governing the limiting efficiency of heat engines. The models demonstrated clearly how a (fictitious) model heat engine could harness the kinetic energy of a particle representing a thermodynamic fluid and convert it to useful work. They showed that the engines must operate between two kinetic energy levels (the source level and the sink level) in order to produce net useful work. The maximum efficiency achievable with the engines was shown to be in agreement with the Carnot efficiency. Simple mechanical concepts allow students to grasp complex concepts in terms of readily understandable particle mechanics, without introducing the full intricacies of the kinetic theory of gases or statistical thermodynamics. The thermodynamic claims of the papers were limited to situations involving ideal gases. Discussion in [1] centered on a single particle contained in one dimensional oscillation. Traditional macroscopic thermodynamic symbols such as P, T, V, H, S and Q were not used. Yet many of the basic relationships and demonstrations of the Kinetic Theory of Gases were derived. In [2], further one dimensional models were introduced involving two or three particles in order to study the concepts of energy (heat) transfer and the tendency of systems toward equilibrium. Students and engineers have difficulty with the concept of entropy, so entropy relationships for the particles, analogous the conventional textbook definitions were explored. Total entropy was found to increase in the familiar way during ‘irreversible’ processes. Whilst some engineering thermodynamics textbooks introduce a discussion of kinetic theory of gases and statistical thermodynamics, the majority of authors e.g. [3] concentrate on developing macroscopic concepts. However, in our experience the majority of students find thermodynamic concepts difficult to grasp whether they are introduced through the classical approach, or with the aid of kinetic theory of gases and statistical thermodynamics. The significance of the approach developed in [1] is that the cause of the Carnot limitation is clearly shown in an ideal heat engine operating in a cycle, the Carnot limitation is purely due to mechanical and spatial constraints without the need for complex new (thermodynamic) concepts. In [2], the tendencies of, systems toward energy equilibrium and of entropy to maximize in the simple particle mechanical systems were demonstrated. Because of environmental and other concerns, there are intense efforts to develop fuel cells, thermoelectric and photovoltaic systems as well as many other processes for energy generation. Mechanical engineering students need to be well acquainted with such devices so that grounding in traditional heat engines may not be sufficient for an adequate understanding of the phenomena involved in these new fields which all require an understanding of the principles of the kinetic theory of gases, statistical and a modicum of quantum mechanics. We believe that many mechanical engineering students have difficulties understanding the abstract concepts involved, so that a visual, more mechanistic approach is now essential in teaching the fundamentals of thermodynamics. As an example, consider the Clausius statement of the