A Novel Approach to the Teaching of Etropy Based on a Recent Single Particle Heat Engine Model

Abstract

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 this paper the model is extended to introduce entropy. Here the particle's entropy is 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.

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

“…Further to [1] and [2], we now note as part of this paper, that the Carnot Cycle is bounded by stationary lines of the properties in question in this paper: temperature and entropy. The upper isothermal involves 100% conversion of heat to work, whilst a part of this is lost in proportion to the temperature ratio in the lower isothermal.…”

“…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.…”

“…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.…”

“…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.…”

“…As an example, consider the Clausius statement of the Second Law of Thermodynamics which proposes that heat can only be transferred, unaided, from a higher to a lower temperature. In [1] it was assumed that this statement was a 'law of thermodynamics', however, in [2], the one-dimensional models demonstrated that the Clausius' statement of the second law of thermodynamics is a consequence of simple principles of mechanics.…”