Finding COP: A Project to Unify Topics in Fundamentals of Thermodynamics Course

In a typical introduction to thermodynamics course, concepts such as the first law, property relations, second law, etc. are usually taught in succession. To aid in further understanding these concepts, and to help solidifying the “point” of studying thermodynamics, a high-stake project that unifies some of the major topics is necessary. Such a project should be readily relatable to everyday life, and yet should require a higher-level exploration of meanings. An example of such project has been successfully implemented in a basic thermodynamics course for a number of years. The goal is simply to find the coefficient of performance (COP) of students' refrigerators at home, without having to analyze the refrigeration system (which generally is studied in intermediate thermodynamics). Instead, students are expected to approach this problem from the angle of the refrigerator compartments, by estimating the amount of heat to be removed from inside the refrigerator. The electrical work may be determined experimentally, either via an instrument or by observing the frequency and duration of the refrigerator's operation. This project may be assigned as soon as the first law for cycles has been introduced, and may be split into two phases: Methodology followed by Experimentation and Solution. For the Methodology phase, students may be teamed up to brainstorm the meaning of the problem statement, research how a refrigerator works, identify the physics involved, and develop a strategy for collecting data necessary for the calculations. In the Experimentation and Solution phase, to be assigned as an individual project once the second law is introduced, students proceed to conduct experiments, solicit data that may be unavailable in the textbook, and assemble results into a report. The expected outcome of the project is an appreciation of the first law applied to incompressible substances (e.g., foodstuffs), ideal gas (air inside the compartment and its relation to door opening), electrical power and work, as well as the ability to construct and solve equations in a real-world setting. Assessment of effectiveness includes comparison of average test and course grades between control groups and other terms with this project implemented. End-of-semester course evaluation data and comments are also compiled and analyzed. Both quantitative and qualitative data indicate a positive and compelling effect of the project. Introduction Thermodynamics is a challenging class,1 and is an important subject relevant to multiple engineering disciplines. An introduction to thermodynamics course, therefore, is typically required across majors. The diversity of student body in such a class presents unique challenges for teaching and learning. The topics covered are mostly conceptual, such as property relations, heat, work, first and second laws, etc.2 and topics are usually presented piecemeal. While some materials are inherently interrelated, e.g., heat, work and first law, others are inevitably decoupled from the rest, making it a challenge for students to progress through the Bloom's taxonomy.3 Recent evidence shows that engineering students enrolled in intermediate-level thermodynamics course often do not retain basic understanding of thermodynamics and struggle to advance to the next stages of learning. To enable higher-level cognition and knowledge retention, a means to unify topics in introductory thermodynamics may be necessary. One such means is the use of projects. Projectbased learning, or PBL, has been studied by many researchers and its positive impact has been well documented. In engineering, PBL is a particularly useful tool to enhance student learning and performance. An important element in overcoming conceptual challenges, as often encountered in thermodynamics, is the self-guided process where students rely, and eventually trust, their cognitive resources to form a knowledge base.4 PBL, if implemented with care, can serve as a powerful way to enable self-reliance. Savage et al.5 investigated, and ascertained, the effectiveness of PBL throughout the engineering curriculum, while cautioning that its success requires that the project be relevant, not overly complex or resource intensive, and easy to implement by the instructor. Many educators have integrated PBL, of varying capacity, in introductory thermodynamics,6-13 including some projects that have been creatively implemented.14-15 While the consensus is overwhelmingly encouraging, the methods of assessment used in these studies vary significantly, from anecdotal evidence to quantitative analysis. As Savage et al.5 concluded, quantitatively evaluating the effect of PBL in the individual level is a difficult task, and alluded to the grander challenge of defining the measure of student success. In this paper, a project that attempts to unify key concepts in introductory thermodynamics is presented and detailed. It is immediately relatable to students, is easy to adopt, and does not require specialized tools or instruments. The implementation requires little faculty time or resources other than a simple update of grading policy and mentoring of students (or teams) throughout the course of the project. The mentoring, and guiding, effort is crucial in achieving the learning objectives,16 and may be fulfilled by the already-existing office hours, supplemental instructions, recitation sessions, or planned in-class activities. The project's flexibility means it is suitable for both conventional or flipped model of instruction. The impact of this project is measured by the following methods: 1). Quantitative analysis of final exam data, including comparison with a control group consisting of multiple terms where no such project was incorporated. 2). End-of-course student comments. 3.) Anecdotal evidence. The topics to be unified are: • Property relations for ideal gas • Property relations for incompressible substance • Heat and adiabatic process • Work and power • Energy as a property (particularly internal energy) • First law of thermodynamics • Closed system vs. open system • Cycles and performance • Second law of thermodynamics While the list above may seem vast, the project naturally ties one concept to another in a subtle and unintimidating way that invites meaning exploration, from comprehension to evaluation stage of learning. This project has been integrated into three instances of introductory thermodynamics since 2013. A control group that consists of seven prior terms without the project is compared, and the results are discussed and conclusion drawn in later sections. The Project The project description and expected outcomes are detailed in this section, complete with a sample calculation. Problem Statement Simply put, students are tasked with calculating both the actual and ideal coefficients of performance (COPs) of their refrigerators at home. The problem statement may seem simplistic at first, but would soon yield layers of complexity once the definition of COP is revealed: COPactual= Qc W , COP ideal= T c T h−T c where Qc is the total amount of heat removed from the cold reservoir, W the total work supplied to the refrigerator, and T c & T h the temperatures of the cold and hot reservoirs, respectively. The complexity built into these equations requires exploration of meaning, and the sample calculation presented below illustrates the multilayered process. Nevertheless, the concepts spanning this project are rather straightforward, and the process involved in solving the problem is logical and challenging without being excessive. Objectives & Outcomes The project is designed with the following objectives: • Enhance understanding of thermodynamics through experiential learning through an everyday object • Incentivize self-guided research, planning, and project management • Obtain data with relative ease, without the need to examine refrigerant properties and flow, and without having to fuss over accuracy • Compare actual and ideal efficiencies Upon successful completion of the project, students are expected to exhibit the following learning outcomes: • Be able to model an otherwise complex phenomenon, make reasonable assumptions, and formulate the physics involved • Draw a meaningful connection between textbook and the real world • Appreciate the interrelationship of the various elements in the first law of thermodynamics, property relations of incompressible substances (e.g., foodstuffs), property relations of ideal gas (air inside the refrigerator compartment, electrical power and work • Demonstrate knowledge gained through performance in final exam • Demonstrate knowledge retained through performance in a subsequent course (e.g., intermediate thermodynamics or heat transfer). Constraints As an important and fundamental restriction to this project, students are prohibited from approaching the problem by analyzing the refrigeration system, i.e., the refrigerant flow. Instead, students must explore the meaning of the quantities involved, particularly heat and work, by examining the refrigerator compartments. In other words, instead of investigating where the energy is going to, students should question where it is coming from. It should be noted that the actual COP may also be defined in terms of the rate of energy transfer: COPactual= Q̇ c Ẇ Students are encouraged to consider both definitions (i.e., Joule vs Watt), and select one that is more convenient to use. Why Refrigerator? Since the industrial revolution, refrigeration has helped shape cultures and lifestyles, and is an essential element in today's societal functions. As commonplace as they are, refrigerators are however often taken for granted. Questions such as "how does it work?" and "what does Energy Star, or kWh, really mean?" may not be in a student's mind every time he or she uses the refrigerator. Meanwhile, for students studying thermodynamics, the theories are in fact hard at work before their eyes