2025 ASEE Annual Conference & Exposition

According to the Clausius statement of the second law of Thermodynamics, “It is impossible to construct a device that will operate in a cycle and produce no effect other than the transfer of heat from a cooler body to a hotter body.” Although this negative statement cannot be "proved", it is however accepted because no experiment has ever contradicted it. Thus, this statement is accepted as an axiom which is then used to prove different theorems related to the efficiency of reversible heat engine and refrigerator cycles operating between two thermal reservoirs. A well-known example of such a theorem is the following important proposition regarding the efficiency of a reversible cycle: “It is impossible to construct a refrigerator or heat pump that operates between two given reservoirs and is more efficient than a reversible refrigerator/heat pump operating between the same two reservoirs.”
Many engineering/engineering technology students of Thermodynamics for the first time find it very difficult to appreciate the true meaning and profundity of this apparently simple statement. This is largely due to the fact that the student needs to “accept” as true this negative statement right at the outset of his/her study of the second law, without being offered any “positive” explanations or supporting reasons. This might explain why many students end up considering the fascinating course of Thermodynamics, which is deeply philosophical as well as intensely pragmatic at once, as a “difficult” subject.
To alleviate this difficulty, we have taken a novel approach to enable the student to properly understand the negative statement related to heat pumps/refrigerators in a more “positive” manner. We commence the analysis by constructing several thermodynamic cycles using an ideal gas as the working substance and consisting of both reversible and irreversible processes. The working substance in all these cycles interacts with only two thermal reservoirs at two different temperatures, as required by the Clausius statement. It is then shown conclusively that not a single such cycle can be designed or constructed which will have the sole effect of transferring heat from the low temperature to the high temperature reservoir.
We wish to emphasize that this is by no means a “proof” of the negative Clausius statement of the second law. However, we believe and hope that the analysis presented in this article will offer an expedient tool for enabling the struggling student to properly understand the negative statement and comfortably transition to studying the subsequent theorems, corollaries, and practical applications of the second law of Thermodynamics.