A Novel Approach to the Teaching of Thermodynamic Cycles and the Laws of Thermodynamics

This paper outlines a simple particle mechanics model in which a single particle represents the thermodynamic fluid (gas) in a heat engine (exemplified by a piston engine). By mechanics based reasoning the model 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. INTRODUCTION Mechanical engineers place great importance on basic mechanics because it is the basis of all other engineering activities. This differs significantly from the early internal combustion engine inventors and designers who were largely practical people. It took engine builders of the Otto and Langden era (in the 1800’s) [10, 20] some decades to realise that a compression stroke would greatly improve the performance of the early gas engines. This helped engineers to recognise the importance of the concept of the thermodynamic cycle, in addition it would also have steered their thinking toward the Carnot cycle with its high temperature source and lower temperature sink. During the same era, physicists were thinking about the laws of thermodynamics, the kinetic theory of gases and statistical mechanics providing a sound, organised basis for the development of devices involving heat and work, so modern students are exposed to the logical structure of modern engineering thermodynamics with its laws as outlined in innumerable textbooks. Thus they lack the “feel” that the early engine designers had. This want is particularly evident in the treatment of The Second Law, its many statements and the Carnot efficiency that leaves life-long doubt with many mechanical engineers. The Second Law of Thermodynamics has its historical origins in Carnot’s work which imposed an upper limiting efficiency on heat engines. Traditional engineering thermodynamics textbooks for example [4, 6, 13, 15, 18] introduce both the Second Law of Thermodynamics and the Carnot efficiency in elegantly general ways based on classical thermodynamics. These presentations are not easily related to the practical and physical causes of the Carnot limitation. The introduction of statistical mechanics into thermodynamics text [eg 16] is often used as an attempt to clarify the physical basis of the concepts involved, but is not always successful. Occasionally, older texts [20] contained a chapter on the Kinetic Theory of Gases. In this paper, simple, one dimensional theoretical models of heat engines are presented that bridge the conceptual gap between these elegantly abstract Second Law approaches and physical/mechanical principles governing the limiting efficiency of heat engines. We concentrate our discussions on one dimensional, single particle models representing an ideal gas. Our models demonstrate clearly how heat engines harness the kinetic energy of the particle and convert it to useful work. They show that the engines must operate between two kinetic energy levels (the source level and the sink level) in order to produce net useful work. We demonstrate that the maximum efficiency achievable with our engines is in agreement with the Carnot efficiency. We also demonstrate that Carnot’s analogy to the water wheel of his day was an appropriate approach, even though he falsely reasoned that the caloric flowing from the source (to drive the engine) had to be rejected at the sink. Our models demonstrate that if the flow analogy is to be used then it is kinetic energy, and that it “flows” from a higher kinetic energy level into the thermodynamic fluid and part of it must be rejected at a lower kinetic energy level. Fortunately a part of this (limited by the Carnot formula) may be converted to useful work. This approach uses simple mechanical concepts allowing students to grasp complex concepts in terms of readily understood particle mechanics, without introducing the full intricacies of the kinetic theory of gases or statistical thermodynamics. Of course we must limit our thermodynamic