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ASEE 2009 Annual Conference AC 2009-1608

Teaching control volume selection to avoid entropy accounting ‘bottlenecks’ in second law analyses. Abstract

Application of the first law is invariably reduced to identifying energy departures from, and arrivals to, assorted discrete control volumes. Because, by the nature of the first law, energy is conserved, problems reduce to simple accounting exercises, only occasionally upset by the presence of energy generation terms (e.g. nuclear or possibly chemical reactions.) When such terms do arise they are usually well defined and located in discrete control volumes so that including them in the overall energy balance is generally straightforward. When one wishes to instruct in the application of the second law, the accounting exercise and the definition of the control volume has to be undertaken with great care, as unlike energy, entropy is actually generated during transportation and transition processes, within the control volumes. It is not unusual therefore, for entropy generation terms to be allocated to the surrounding ‘environmental control volume’, as mixing, conduction, convection and radiation etc. These can of course occur well outside of the original problem focused control volume which has invariably been defined by simple consideration of the ensuing first law energy analysis and obvious geometry features. The ‘bottleneck’ referred to in the title of the paper is descriptive of what happens to the vast majority of Thermodynamics courses at this point. Students having obtained a solid understanding of the first law and its applications do not progress through to the same level of understanding with the second law. The vast majority learning to use the second law almost on autopilot without a real feel as to what the property is telling us. The paper presents an analysis therefore of a simple hot water pipe to show specific issues and areas of confusion with second law control volume selection. It concludes emphasizing the importance of consistently listing assumptions both for the student solving, and the instructor setting an assignment. In summary, this paper highlights and gives an example of novel teaching methods that have been successfully used by the authors to overcome this ‘bottleneck’ in thermodynamic instruction.

Introduction

Foley [1] derived the property entropy from consideration of a simple orifice plate in a pipe. This derivation was unique in that the entropy term derived did not arise from any heat transfer. Instead, an uncontrolled expansion was used, and as such the concept of ‘bad energy’ as the numerator in the expression for entropy was introduced. While teaching a class an interesting discussion was raised as to where exactly entropy is generated in a heat transfer process, a brief discussion in Cengel & Boles [2] while touching on the topic did not answer the legitimate concerns raised by students. This was the motivation for this paper in which the focus has changed back to a heat transfer numerator in the entropy expression as the source of the ‘bad energy’. (Unrecoverable energy transfer is another way of considering this term.) There is no subtle reason for this other than this turns out to be the easiest energy transfer to be considered in the example used, and is consistent

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Foley, A., & Plumley, M. (2009, June), Teaching Control Volume Selection To Avoid Entropy Accounting “Bottlenecks” In Second Law Analyses Paper presented at 2009 Annual Conference & Exposition, Austin, Texas. 10.18260/1-2--5442