June 15, 2014
June 15, 2014
June 18, 2014
Energy Conversion and Conservation
24.89.1 - 24.89.12
Practical Approach to the Carnot EfficiencyMost thermodynamic textbooks typically present the Carnot efficiency (maximum performanceof an energy system) from a theoretical standpoint using the Carnot principles and thethermodynamic temperature scale. This paper presents a practical approach to developing theCarnot cycle by starting with a real cycle and exploring what happens as the ideal cycle isapproached. This approach has been applied to first semester thermodynamic studentssuccessfully for at least five years. It begins with an understanding of the irreversibility of heattransfer through a finite temperature difference. A multi-sensory and multi-media presentation,which can be readily adapted to any mediated classroom equipped with a document camera, isuseful to the students understanding of this concept.Another fundamental tool to understanding the Carnot cycle from a practical approach is theintroducing the students to the conductance (UA) form of the heat transfer equation for heatexchangers. The students have already been exposed to Fourier's law for conduction andNewton's law of cooling for convection heat transfer. The thermal resistance network candeveloped here to explain where the overall heat transfer coefficient originates but to save time aqualitative explanation is sufficient at this point in their education. This heat transfer equationties the two sides of the heat exchanger together since the driving potential is the temperaturedifference between the two fluids. The primary purpose of this equation is to relate the size ofthe heat exchanger to the temperature difference between the two fluids. As the area of the heatexchanger increases the temperature of the working fluid approaches the temperature of thethermal reservoir. This paper presents a visual way to display this phenomena with a uniqueway to use the property plots with which the students are familiar.Once these two building blocks are in place the Carnot efficiency can be developed by applyingthe definition of efficiency to the cycle. The work is then related to heat transfer by applying theconservation of energy to the entire cycle. Now the efficiency is related to the heat transfer inthe heat exchangers of the cycle alone. The ideal cycle is reversible so as the area of the heatexchangers approaches infinity the temperature difference approaches zero where the heattransfer becomes reversible. This practical approach is applied to heat engines, refrigeration andheat pump cycles in this paper and can readily be used in any first semester thermodynamiccourse.
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